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/*====================================================================*
- Copyright (C) 2001 Leptonica. All rights reserved.
-
- Redistribution and use in source and binary forms, with or without
- modification, are permitted provided that the following conditions
- are met:
- 1. Redistributions of source code must retain the above copyright
- notice, this list of conditions and the following disclaimer.
- 2. Redistributions in binary form must reproduce the above
- copyright notice, this list of conditions and the following
- disclaimer in the documentation and/or other materials
- provided with the distribution.
-
- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
- ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
- LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
- A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL ANY
- CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
- EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
- PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
- PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
- OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
- NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*====================================================================*/
/*!
* \file numafunc2.c
* <pre>
*
* --------------------------------------
* This file has these Numa utilities:
* - morphological operations
* - arithmetic transforms
* - windowed statistical operations
* - histogram extraction
* - histogram comparison
* - extrema finding
* - frequency and crossing analysis
* --------------------------------------
* Morphological (min/max) operations
* NUMA *numaErode()
* NUMA *numaDilate()
* NUMA *numaOpen()
* NUMA *numaClose()
*
* Other transforms
* NUMA *numaTransform()
* l_int32 numaSimpleStats()
* l_int32 numaWindowedStats()
* NUMA *numaWindowedMean()
* NUMA *numaWindowedMeanSquare()
* l_int32 numaWindowedVariance()
* NUMA *numaWindowedMedian()
* NUMA *numaConvertToInt()
*
* Histogram generation and statistics
* NUMA *numaMakeHistogram()
* NUMA *numaMakeHistogramAuto()
* NUMA *numaMakeHistogramClipped()
* NUMA *numaRebinHistogram()
* NUMA *numaNormalizeHistogram()
* l_int32 numaGetStatsUsingHistogram()
* l_int32 numaGetHistogramStats()
* l_int32 numaGetHistogramStatsOnInterval()
* l_int32 numaMakeRankFromHistogram()
* l_int32 numaHistogramGetRankFromVal()
* l_int32 numaHistogramGetValFromRank()
* l_int32 numaDiscretizeRankAndIntensity()
* l_int32 numaGetRankBinValues()
*
* Splitting a distribution
* l_int32 numaSplitDistribution()
*
* Comparing histograms
* l_int32 grayHistogramsToEMD()
* l_int32 numaEarthMoverDistance()
* l_int32 grayInterHistogramStats()
*
* Extrema finding
* NUMA *numaFindPeaks()
* NUMA *numaFindExtrema()
* l_int32 *numaCountReversals()
*
* Threshold crossings and frequency analysis
* l_int32 numaSelectCrossingThreshold()
* NUMA *numaCrossingsByThreshold()
* NUMA *numaCrossingsByPeaks()
* NUMA *numaEvalBestHaarParameters()
* l_int32 numaEvalHaarSum()
*
* Generating numbers in a range under constraints
* NUMA *genConstrainedNumaInRange()
*
* Things to remember when using the Numa:
*
* (1) The numa is a struct, not an array. Always use accessors
* (see numabasic.c), never the fields directly.
*
* (2) The number array holds l_float32 values. It can also
* be used to store l_int32 values. See numabasic.c for
* details on using the accessors. Integers larger than
* about 10M will lose accuracy due on retrieval due to round-off.
* For large integers, use the dna (array of l_float64) instead.
*
* (3) Occasionally, in the comments we denote the i-th element of a
* numa by na[i]. This is conceptual only -- the numa is not an array!
*
* Some general comments on histograms:
*
* (1) Histograms are the generic statistical representation of
* the data about some attribute. Typically they're not
* normalized -- they simply give the number of occurrences
* within each range of values of the attribute. This range
* of values is referred to as a 'bucket'. For example,
* the histogram could specify how many connected components
* are found for each value of their width; in that case,
* the bucket size is 1.
*
* (2) In leptonica, all buckets have the same size. Histograms
* are therefore specified by a numa of occurrences, along
* with two other numbers: the 'value' associated with the
* occupants of the first bucket and the size (i.e., 'width')
* of each bucket. These two numbers then allow us to calculate
* the value associated with the occupants of each bucket.
* These numbers are fields in the numa, initialized to
* a startx value of 0.0 and a binsize of 1.0. Accessors for
* these fields are functions numa*Parameters(). All histograms
* must have these two numbers properly set.
* </pre>
*/
#include <math.h>
#include "allheaders.h"
/* bin sizes in numaMakeHistogram() */
static const l_int32 BinSizeArray[] = {2, 5, 10, 20, 50, 100, 200, 500, 1000,\
2000, 5000, 10000, 20000, 50000, 100000, 200000,\
500000, 1000000, 2000000, 5000000, 10000000,\
200000000, 50000000, 100000000};
static const l_int32 NBinSizes = 24;
#ifndef NO_CONSOLE_IO
#define DEBUG_HISTO 0
#define DEBUG_CROSSINGS 0
#define DEBUG_FREQUENCY 0
#endif /* ~NO_CONSOLE_IO */
/*----------------------------------------------------------------------*
* Morphological operations *
*----------------------------------------------------------------------*/
/*!
* \brief numaErode()
*
* \param[in] nas
* \param[in] size of sel; greater than 0, odd. The origin
* is implicitly in the center.
* \return nad eroded, or NULL on error
*
* <pre>
* Notes:
* (1) The structuring element (sel) is linear, all "hits"
* (2) If size == 1, this returns a copy
* (3) General comment. The morphological operations are equivalent
* to those that would be performed on a 1-dimensional fpix.
* However, because we have not implemented morphological
* operations on fpix, we do this here. Because it is only
* 1 dimensional, there is no reason to use the more
* complicated van Herk/Gil-Werman algorithm, and we do it
* by brute force.
* </pre>
*/
NUMA *
numaErode(NUMA *nas,
l_int32 size)
{
l_int32 i, j, n, hsize, len;
l_float32 minval;
l_float32 *fa, *fas, *fad;
NUMA *nad;
PROCNAME("numaErode");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
if (size <= 0)
return (NUMA *)ERROR_PTR("size must be > 0", procName, NULL);
if ((size & 1) == 0 ) {
L_WARNING("sel size must be odd; increasing by 1\n", procName);
size++;
}
if (size == 1)
return numaCopy(nas);
/* Make a source fa (fas) that has an added (size / 2) boundary
* on left and right, contains a copy of nas in the interior region
* (between 'size' and 'size + n', and has large values
* inserted in the boundary (because it is an erosion). */
n = numaGetCount(nas);
hsize = size / 2;
len = n + 2 * hsize;
if ((fas = (l_float32 *)LEPT_CALLOC(len, sizeof(l_float32))) == NULL)
return (NUMA *)ERROR_PTR("fas not made", procName, NULL);
for (i = 0; i < hsize; i++)
fas[i] = 1.0e37;
for (i = hsize + n; i < len; i++)
fas[i] = 1.0e37;
fa = numaGetFArray(nas, L_NOCOPY);
for (i = 0; i < n; i++)
fas[hsize + i] = fa[i];
nad = numaMakeConstant(0, n);
numaCopyParameters(nad, nas);
fad = numaGetFArray(nad, L_NOCOPY);
for (i = 0; i < n; i++) {
minval = 1.0e37; /* start big */
for (j = 0; j < size; j++)
minval = L_MIN(minval, fas[i + j]);
fad[i] = minval;
}
LEPT_FREE(fas);
return nad;
}
/*!
* \brief numaDilate()
*
* \param[in] nas
* \param[in] size of sel; greater than 0, odd. The origin
* is implicitly in the center.
* \return nad dilated, or NULL on error
*
* <pre>
* Notes:
* (1) The structuring element (sel) is linear, all "hits"
* (2) If size == 1, this returns a copy
* </pre>
*/
NUMA *
numaDilate(NUMA *nas,
l_int32 size)
{
l_int32 i, j, n, hsize, len;
l_float32 maxval;
l_float32 *fa, *fas, *fad;
NUMA *nad;
PROCNAME("numaDilate");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
if (size <= 0)
return (NUMA *)ERROR_PTR("size must be > 0", procName, NULL);
if ((size & 1) == 0 ) {
L_WARNING("sel size must be odd; increasing by 1\n", procName);
size++;
}
if (size == 1)
return numaCopy(nas);
/* Make a source fa (fas) that has an added (size / 2) boundary
* on left and right, contains a copy of nas in the interior region
* (between 'size' and 'size + n', and has small values
* inserted in the boundary (because it is a dilation). */
n = numaGetCount(nas);
hsize = size / 2;
len = n + 2 * hsize;
if ((fas = (l_float32 *)LEPT_CALLOC(len, sizeof(l_float32))) == NULL)
return (NUMA *)ERROR_PTR("fas not made", procName, NULL);
for (i = 0; i < hsize; i++)
fas[i] = -1.0e37;
for (i = hsize + n; i < len; i++)
fas[i] = -1.0e37;
fa = numaGetFArray(nas, L_NOCOPY);
for (i = 0; i < n; i++)
fas[hsize + i] = fa[i];
nad = numaMakeConstant(0, n);
numaCopyParameters(nad, nas);
fad = numaGetFArray(nad, L_NOCOPY);
for (i = 0; i < n; i++) {
maxval = -1.0e37; /* start small */
for (j = 0; j < size; j++)
maxval = L_MAX(maxval, fas[i + j]);
fad[i] = maxval;
}
LEPT_FREE(fas);
return nad;
}
/*!
* \brief numaOpen()
*
* \param[in] nas
* \param[in] size of sel; greater than 0, odd. The origin
* is implicitly in the center.
* \return nad opened, or NULL on error
*
* <pre>
* Notes:
* (1) The structuring element (sel) is linear, all "hits"
* (2) If size == 1, this returns a copy
* </pre>
*/
NUMA *
numaOpen(NUMA *nas,
l_int32 size)
{
NUMA *nat, *nad;
PROCNAME("numaOpen");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
if (size <= 0)
return (NUMA *)ERROR_PTR("size must be > 0", procName, NULL);
if ((size & 1) == 0 ) {
L_WARNING("sel size must be odd; increasing by 1\n", procName);
size++;
}
if (size == 1)
return numaCopy(nas);
nat = numaErode(nas, size);
nad = numaDilate(nat, size);
numaDestroy(&nat);
return nad;
}
/*!
* \brief numaClose()
*
* \param[in] nas
* \param[in] size of sel; greater than 0, odd. The origin
* is implicitly in the center.
* \return nad closed, or NULL on error
*
* <pre>
* Notes:
* (1) The structuring element (sel) is linear, all "hits"
* (2) If size == 1, this returns a copy
* (3) We add a border before doing this operation, for the same
* reason that we add a border to a pix before doing a safe closing.
* Without the border, a small component near the border gets
* clipped at the border on dilation, and can be entirely removed
* by the following erosion, violating the basic extensivity
* property of closing.
* </pre>
*/
NUMA *
numaClose(NUMA *nas,
l_int32 size)
{
NUMA *nab, *nat1, *nat2, *nad;
PROCNAME("numaClose");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
if (size <= 0)
return (NUMA *)ERROR_PTR("size must be > 0", procName, NULL);
if ((size & 1) == 0 ) {
L_WARNING("sel size must be odd; increasing by 1\n", procName);
size++;
}
if (size == 1)
return numaCopy(nas);
nab = numaAddBorder(nas, size, size, 0); /* to preserve extensivity */
nat1 = numaDilate(nab, size);
nat2 = numaErode(nat1, size);
nad = numaRemoveBorder(nat2, size, size);
numaDestroy(&nab);
numaDestroy(&nat1);
numaDestroy(&nat2);
return nad;
}
/*----------------------------------------------------------------------*
* Other transforms *
*----------------------------------------------------------------------*/
/*!
* \brief numaTransform()
*
* \param[in] nas
* \param[in] shift add this to each number
* \param[in] scale multiply each number by this
* \return nad with all values shifted and scaled, or NULL on error
*
* <pre>
* Notes:
* (1) Each number is shifted before scaling.
* </pre>
*/
NUMA *
numaTransform(NUMA *nas,
l_float32 shift,
l_float32 scale)
{
l_int32 i, n;
l_float32 val;
NUMA *nad;
PROCNAME("numaTransform");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
n = numaGetCount(nas);
if ((nad = numaCreate(n)) == NULL)
return (NUMA *)ERROR_PTR("nad not made", procName, NULL);
numaCopyParameters(nad, nas);
for (i = 0; i < n; i++) {
numaGetFValue(nas, i, &val);
val = scale * (val + shift);
numaAddNumber(nad, val);
}
return nad;
}
/*!
* \brief numaSimpleStats()
*
* \param[in] na input numa
* \param[in] first first element to use
* \param[in] last last element to use; -1 to go to the end
* \param[out] pmean [optional] mean value
* \param[out] pvar [optional] variance
* \param[out] prvar [optional] rms deviation from the mean
* \return 0 if OK, 1 on error
*/
l_ok
numaSimpleStats(NUMA *na,
l_int32 first,
l_int32 last,
l_float32 *pmean,
l_float32 *pvar,
l_float32 *prvar)
{
l_int32 i, n, ni;
l_float32 sum, sumsq, val, mean, var;
PROCNAME("numaSimpleStats");
if (pmean) *pmean = 0.0;
if (pvar) *pvar = 0.0;
if (prvar) *prvar = 0.0;
if (!pmean && !pvar && !prvar)
return ERROR_INT("nothing requested", procName, 1);
if (!na)
return ERROR_INT("na not defined", procName, 1);
if ((n = numaGetCount(na)) == 0)
return ERROR_INT("na is empty", procName, 1);
first = L_MAX(0, first);
if (last < 0) last = n - 1;
if (first >= n)
return ERROR_INT("invalid first", procName, 1);
if (last >= n) {
L_WARNING("last = %d is beyond max index = %d; adjusting\n",
procName, last, n - 1);
last = n - 1;
}
if (first > last)
return ERROR_INT("first > last\n", procName, 1);
ni = last - first + 1;
sum = sumsq = 0.0;
for (i = first; i <= last; i++) {
numaGetFValue(na, i, &val);
sum += val;
sumsq += val * val;
}
mean = sum / ni;
if (pmean)
*pmean = mean;
if (pvar || prvar) {
var = sumsq / ni - mean * mean;
if (pvar) *pvar = var;
if (prvar) *prvar = sqrtf(var);
}
return 0;
}
/*!
* \brief numaWindowedStats()
*
* \param[in] nas input numa
* \param[in] wc half width of the window
* \param[out] pnam [optional] mean value in window
* \param[out] pnams [optional] mean square value in window
* \param[out] pnav [optional] variance in window
* \param[out] pnarv [optional] rms deviation from the mean
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) This is a high-level convenience function for calculating
* any or all of these derived arrays.
* (2) These statistical measures over the values in the
* rectangular window are:
* ~ average value: [x] (nam)
* ~ average squared value: [x*x] (nams)
* ~ variance: [(x - [x])*(x - [x])] = [x*x] - [x]*[x] (nav)
* ~ square-root of variance: (narv)
* where the brackets [ .. ] indicate that the average value is
* to be taken over the window.
* (3) Note that the variance is just the mean square difference from
* the mean value; and the square root of the variance is the
* root mean square difference from the mean, sometimes also
* called the 'standard deviation'.
* (4) Internally, use mirrored borders to handle values near the
* end of each array.
* </pre>
*/
l_ok
numaWindowedStats(NUMA *nas,
l_int32 wc,
NUMA **pnam,
NUMA **pnams,
NUMA **pnav,
NUMA **pnarv)
{
NUMA *nam, *nams;
PROCNAME("numaWindowedStats");
if (!nas)
return ERROR_INT("nas not defined", procName, 1);
if (2 * wc + 1 > numaGetCount(nas))
L_WARNING("filter wider than input array!\n", procName);
if (!pnav && !pnarv) {
if (pnam) *pnam = numaWindowedMean(nas, wc);
if (pnams) *pnams = numaWindowedMeanSquare(nas, wc);
return 0;
}
nam = numaWindowedMean(nas, wc);
nams = numaWindowedMeanSquare(nas, wc);
numaWindowedVariance(nam, nams, pnav, pnarv);
if (pnam)
*pnam = nam;
else
numaDestroy(&nam);
if (pnams)
*pnams = nams;
else
numaDestroy(&nams);
return 0;
}
/*!
* \brief numaWindowedMean()
*
* \param[in] nas
* \param[in] wc half width of the convolution window
* \return nad after low-pass filtering, or NULL on error
*
* <pre>
* Notes:
* (1) This is a convolution. The window has width = 2 * %wc + 1.
* (2) We add a mirrored border of size %wc to each end of the array.
* </pre>
*/
NUMA *
numaWindowedMean(NUMA *nas,
l_int32 wc)
{
l_int32 i, n, n1, width;
l_float32 sum, norm;
l_float32 *fa1, *fad, *suma;
NUMA *na1, *nad;
PROCNAME("numaWindowedMean");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
n = numaGetCount(nas);
width = 2 * wc + 1; /* filter width */
if (width > n)
L_WARNING("filter wider than input array!\n", procName);
na1 = numaAddSpecifiedBorder(nas, wc, wc, L_MIRRORED_BORDER);
n1 = n + 2 * wc;
fa1 = numaGetFArray(na1, L_NOCOPY);
nad = numaMakeConstant(0, n);
fad = numaGetFArray(nad, L_NOCOPY);
/* Make sum array; note the indexing */
if ((suma = (l_float32 *)LEPT_CALLOC(n1 + 1, sizeof(l_float32))) == NULL) {
numaDestroy(&na1);
numaDestroy(&nad);
return (NUMA *)ERROR_PTR("suma not made", procName, NULL);
}
sum = 0.0;
suma[0] = 0.0;
for (i = 0; i < n1; i++) {
sum += fa1[i];
suma[i + 1] = sum;
}
norm = 1. / (2 * wc + 1);
for (i = 0; i < n; i++)
fad[i] = norm * (suma[width + i] - suma[i]);
LEPT_FREE(suma);
numaDestroy(&na1);
return nad;
}
/*!
* \brief numaWindowedMeanSquare()
*
* \param[in] nas
* \param[in] wc half width of the window
* \return nad containing windowed mean square values, or NULL on error
*
* <pre>
* Notes:
* (1) The window has width = 2 * %wc + 1.
* (2) We add a mirrored border of size %wc to each end of the array.
* </pre>
*/
NUMA *
numaWindowedMeanSquare(NUMA *nas,
l_int32 wc)
{
l_int32 i, n, n1, width;
l_float32 sum, norm;
l_float32 *fa1, *fad, *suma;
NUMA *na1, *nad;
PROCNAME("numaWindowedMeanSquare");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
n = numaGetCount(nas);
width = 2 * wc + 1; /* filter width */
if (width > n)
L_WARNING("filter wider than input array!\n", procName);
na1 = numaAddSpecifiedBorder(nas, wc, wc, L_MIRRORED_BORDER);
n1 = n + 2 * wc;
fa1 = numaGetFArray(na1, L_NOCOPY);
nad = numaMakeConstant(0, n);
fad = numaGetFArray(nad, L_NOCOPY);
/* Make sum array; note the indexing */
if ((suma = (l_float32 *)LEPT_CALLOC(n1 + 1, sizeof(l_float32))) == NULL) {
numaDestroy(&na1);
numaDestroy(&nad);
return (NUMA *)ERROR_PTR("suma not made", procName, NULL);
}
sum = 0.0;
suma[0] = 0.0;
for (i = 0; i < n1; i++) {
sum += fa1[i] * fa1[i];
suma[i + 1] = sum;
}
norm = 1. / (2 * wc + 1);
for (i = 0; i < n; i++)
fad[i] = norm * (suma[width + i] - suma[i]);
LEPT_FREE(suma);
numaDestroy(&na1);
return nad;
}
/*!
* \brief numaWindowedVariance()
*
* \param[in] nam windowed mean values
* \param[in] nams windowed mean square values
* \param[out] pnav [optional] numa of variance -- the ms deviation
* from the mean
* \param[out] pnarv [optional] numa of rms deviation from the mean
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) The numas of windowed mean and mean square are precomputed,
* using numaWindowedMean() and numaWindowedMeanSquare().
* (2) Either or both of the variance and square-root of variance
* are returned, where the variance is the average over the
* window of the mean square difference of the pixel value
* from the mean:
* [(x - [x])*(x - [x])] = [x*x] - [x]*[x]
* </pre>
*/
l_ok
numaWindowedVariance(NUMA *nam,
NUMA *nams,
NUMA **pnav,
NUMA **pnarv)
{
l_int32 i, nm, nms;
l_float32 var;
l_float32 *fam, *fams, *fav, *farv;
NUMA *nav, *narv; /* variance and square root of variance */
PROCNAME("numaWindowedVariance");
if (pnav) *pnav = NULL;
if (pnarv) *pnarv = NULL;
if (!pnav && !pnarv)
return ERROR_INT("neither &nav nor &narv are defined", procName, 1);
if (!nam)
return ERROR_INT("nam not defined", procName, 1);
if (!nams)
return ERROR_INT("nams not defined", procName, 1);
nm = numaGetCount(nam);
nms = numaGetCount(nams);
if (nm != nms)
return ERROR_INT("sizes of nam and nams differ", procName, 1);
if (pnav) {
nav = numaMakeConstant(0, nm);
*pnav = nav;
fav = numaGetFArray(nav, L_NOCOPY);
}
if (pnarv) {
narv = numaMakeConstant(0, nm);
*pnarv = narv;
farv = numaGetFArray(narv, L_NOCOPY);
}
fam = numaGetFArray(nam, L_NOCOPY);
fams = numaGetFArray(nams, L_NOCOPY);
for (i = 0; i < nm; i++) {
var = fams[i] - fam[i] * fam[i];
if (pnav)
fav[i] = var;
if (pnarv)
farv[i] = sqrtf(var);
}
return 0;
}
/*!
* \brief numaWindowedMedian()
*
* \param[in] nas
* \param[in] halfwin half width of window over which the median is found
* \return nad after windowed median filtering, or NULL on error
*
* <pre>
* Notes:
* (1) The requested window has width = 2 * %halfwin + 1.
* (2) If the input nas has less then 3 elements, return a copy.
* (3) If the filter is too small (%halfwin <= 0), return a copy.
* (4) If the filter is too large, it is reduced in size.
* (5) We add a mirrored border of size %halfwin to each end of
* the array to simplify the calculation by avoiding end-effects.
* </pre>
*/
NUMA *
numaWindowedMedian(NUMA *nas,
l_int32 halfwin)
{
l_int32 i, n;
l_float32 medval;
NUMA *na1, *na2, *nad;
PROCNAME("numaWindowedMedian");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
if ((n = numaGetCount(nas)) < 3)
return numaCopy(nas);
if (halfwin <= 0) {
L_ERROR("filter too small; returning a copy\n", procName);
return numaCopy(nas);
}
if (halfwin > (n - 1) / 2) {
halfwin = (n - 1) / 2;
L_INFO("reducing filter to halfwin = %d\n", procName, halfwin);
}
/* Add a border to both ends */
na1 = numaAddSpecifiedBorder(nas, halfwin, halfwin, L_MIRRORED_BORDER);
/* Get the median value at the center of each window, corresponding
* to locations in the input nas. */
nad = numaCreate(n);
for (i = 0; i < n; i++) {
na2 = numaClipToInterval(na1, i, i + 2 * halfwin);
numaGetMedian(na2, &medval);
numaAddNumber(nad, medval);
numaDestroy(&na2);
}
numaDestroy(&na1);
return nad;
}
/*!
* \brief numaConvertToInt()
*
* \param[in] nas source numa
* \return na with all values rounded to nearest integer, or
* NULL on error
*/
NUMA *
numaConvertToInt(NUMA *nas)
{
l_int32 i, n, ival;
NUMA *nad;
PROCNAME("numaConvertToInt");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
n = numaGetCount(nas);
if ((nad = numaCreate(n)) == NULL)
return (NUMA *)ERROR_PTR("nad not made", procName, NULL);
numaCopyParameters(nad, nas);
for (i = 0; i < n; i++) {
numaGetIValue(nas, i, &ival);
numaAddNumber(nad, ival);
}
return nad;
}
/*----------------------------------------------------------------------*
* Histogram generation and statistics *
*----------------------------------------------------------------------*/
/*!
* \brief numaMakeHistogram()
*
* \param[in] na
* \param[in] maxbins max number of histogram bins
* \param[out] pbinsize size of histogram bins
* \param[out] pbinstart [optional] start val of minimum bin;
* input NULL to force start at 0
* \return na consisiting of histogram of integerized values,
* or NULL on error.
*
* <pre>
* Notes:
* (1) This simple interface is designed for integer data.
* The bins are of integer width and start on integer boundaries,
* so the results on float data will not have high precision.
* (2) Specify the max number of input bins. Then %binsize,
* the size of bins necessary to accommodate the input data,
* is returned. It is one of the sequence:
* {1, 2, 5, 10, 20, 50, ...}.
* (3) If &binstart is given, all values are accommodated,
* and the min value of the starting bin is returned.
* Otherwise, all negative values are discarded and
* the histogram bins start at 0.
* </pre>
*/
NUMA *
numaMakeHistogram(NUMA *na,
l_int32 maxbins,
l_int32 *pbinsize,
l_int32 *pbinstart)
{
l_int32 i, n, ival, hval;
l_int32 iminval, imaxval, range, binsize, nbins, ibin;
l_float32 val, ratio;
NUMA *nai, *nahist;
PROCNAME("numaMakeHistogram");
if (!na)
return (NUMA *)ERROR_PTR("na not defined", procName, NULL);
if (!pbinsize)
return (NUMA *)ERROR_PTR("&binsize not defined", procName, NULL);
/* Determine input range */
numaGetMin(na, &val, NULL);
iminval = (l_int32)(val + 0.5);
numaGetMax(na, &val, NULL);
imaxval = (l_int32)(val + 0.5);
if (pbinstart == NULL) { /* clip negative vals; start from 0 */
iminval = 0;
if (imaxval < 0)
return (NUMA *)ERROR_PTR("all values < 0", procName, NULL);
}
/* Determine binsize */
range = imaxval - iminval + 1;
if (range > maxbins - 1) {
ratio = (l_float64)range / (l_float64)maxbins;
binsize = 0;
for (i = 0; i < NBinSizes; i++) {
if (ratio < BinSizeArray[i]) {
binsize = BinSizeArray[i];
break;
}
}
if (binsize == 0)
return (NUMA *)ERROR_PTR("numbers too large", procName, NULL);
} else {
binsize = 1;
}
*pbinsize = binsize;
nbins = 1 + range / binsize; /* +1 seems to be sufficient */
/* Redetermine iminval */
if (pbinstart && binsize > 1) {
if (iminval >= 0)
iminval = binsize * (iminval / binsize);
else
iminval = binsize * ((iminval - binsize + 1) / binsize);
}
if (pbinstart)
*pbinstart = iminval;
#if DEBUG_HISTO
fprintf(stderr, " imaxval = %d, range = %d, nbins = %d\n",
imaxval, range, nbins);
#endif /* DEBUG_HISTO */
/* Use integerized data for input */
if ((nai = numaConvertToInt(na)) == NULL)
return (NUMA *)ERROR_PTR("nai not made", procName, NULL);
n = numaGetCount(nai);
/* Make histogram, converting value in input array
* into a bin number for this histogram array. */
if ((nahist = numaCreate(nbins)) == NULL) {
numaDestroy(&nai);
return (NUMA *)ERROR_PTR("nahist not made", procName, NULL);
}
numaSetCount(nahist, nbins);
numaSetParameters(nahist, iminval, binsize);
for (i = 0; i < n; i++) {
numaGetIValue(nai, i, &ival);
ibin = (ival - iminval) / binsize;
if (ibin >= 0 && ibin < nbins) {
numaGetIValue(nahist, ibin, &hval);
numaSetValue(nahist, ibin, hval + 1.0);
}
}
numaDestroy(&nai);
return nahist;
}
/*!
* \brief numaMakeHistogramAuto()
*
* \param[in] na numa of floats; these may be integers
* \param[in] maxbins max number of histogram bins; >= 1
* \return na consisiting of histogram of quantized float values,
* or NULL on error.
*
* <pre>
* Notes:
* (1) This simple interface is designed for accurate binning
* of both integer and float data.
* (2) If the array data is integers, and the range of integers
* is smaller than %maxbins, they are binned as they fall,
* with binsize = 1.
* (3) If the range of data, (maxval - minval), is larger than
* %maxbins, or if the data is floats, they are binned into
* exactly %maxbins bins.
* (4) Unlike numaMakeHistogram(), these bins in general have
* non-integer location and width, even for integer data.
* </pre>
*/
NUMA *
numaMakeHistogramAuto(NUMA *na,
l_int32 maxbins)
{
l_int32 i, n, imin, imax, irange, ibin, ival, allints;
l_float32 minval, maxval, range, binsize, fval;
NUMA *nah;
PROCNAME("numaMakeHistogramAuto");
if (!na)
return (NUMA *)ERROR_PTR("na not defined", procName, NULL);
maxbins = L_MAX(1, maxbins);
/* Determine input range */
numaGetMin(na, &minval, NULL);
numaGetMax(na, &maxval, NULL);
/* Determine if values are all integers */
n = numaGetCount(na);
numaHasOnlyIntegers(na, maxbins, &allints);
/* Do simple integer binning if possible */
if (allints && (maxval - minval < maxbins)) {
imin = (l_int32)minval;
imax = (l_int32)maxval;
irange = imax - imin + 1;
nah = numaCreate(irange);
numaSetCount(nah, irange); /* init */
numaSetParameters(nah, minval, 1.0);
for (i = 0; i < n; i++) {
numaGetIValue(na, i, &ival);
ibin = ival - imin;
numaGetIValue(nah, ibin, &ival);
numaSetValue(nah, ibin, ival + 1.0);
}
return nah;
}
/* Do float binning, even if the data is integers. */
range = maxval - minval;
binsize = range / (l_float32)maxbins;
if (range == 0.0) {
nah = numaCreate(1);
numaSetParameters(nah, minval, binsize);
numaAddNumber(nah, n);
return nah;
}
nah = numaCreate(maxbins);
numaSetCount(nah, maxbins);
numaSetParameters(nah, minval, binsize);
for (i = 0; i < n; i++) {
numaGetFValue(na, i, &fval);
ibin = (l_int32)((fval - minval) / binsize);
ibin = L_MIN(ibin, maxbins - 1); /* "edge" case; stay in bounds */
numaGetIValue(nah, ibin, &ival);
numaSetValue(nah, ibin, ival + 1.0);
}
return nah;
}
/*!
* \brief numaMakeHistogramClipped()
*
* \param[in] na
* \param[in] binsize typically 1.0
* \param[in] maxsize of histogram ordinate
* \return na histogram of bins of size %binsize, starting with
* the na[0] (x = 0.0 and going up to a maximum of
* x = %maxsize, by increments of %binsize), or NULL on error
*
* <pre>
* Notes:
* (1) This simple function generates a histogram of values
* from na, discarding all values < 0.0 or greater than
* min(%maxsize, maxval), where maxval is the maximum value in na.
* The histogram data is put in bins of size delx = %binsize,
* starting at x = 0.0. We use as many bins as are
* needed to hold the data.
* </pre>
*/
NUMA *
numaMakeHistogramClipped(NUMA *na,
l_float32 binsize,
l_float32 maxsize)
{
l_int32 i, n, nbins, ival, ibin;
l_float32 val, maxval;
NUMA *nad;
PROCNAME("numaMakeHistogramClipped");
if (!na)
return (NUMA *)ERROR_PTR("na not defined", procName, NULL);
if (binsize <= 0.0)
return (NUMA *)ERROR_PTR("binsize must be > 0.0", procName, NULL);
if (binsize > maxsize)
binsize = maxsize; /* just one bin */
numaGetMax(na, &maxval, NULL);
n = numaGetCount(na);
maxsize = L_MIN(maxsize, maxval);
nbins = (l_int32)(maxsize / binsize) + 1;
/* fprintf(stderr, "maxsize = %7.3f, nbins = %d\n", maxsize, nbins); */
if ((nad = numaCreate(nbins)) == NULL)
return (NUMA *)ERROR_PTR("nad not made", procName, NULL);
numaSetParameters(nad, 0.0, binsize);
numaSetCount(nad, nbins); /* interpret zeroes in bins as data */
for (i = 0; i < n; i++) {
numaGetFValue(na, i, &val);
ibin = (l_int32)(val / binsize);
if (ibin >= 0 && ibin < nbins) {
numaGetIValue(nad, ibin, &ival);
numaSetValue(nad, ibin, ival + 1.0);
}
}
return nad;
}
/*!
* \brief numaRebinHistogram()
*
* \param[in] nas input histogram
* \param[in] newsize number of old bins contained in each new bin
* \return nad more coarsely re-binned histogram, or NULL on error
*/
NUMA *
numaRebinHistogram(NUMA *nas,
l_int32 newsize)
{
l_int32 i, j, ns, nd, index, count, val;
l_float32 start, oldsize;
NUMA *nad;
PROCNAME("numaRebinHistogram");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
if (newsize <= 1)
return (NUMA *)ERROR_PTR("newsize must be > 1", procName, NULL);
if ((ns = numaGetCount(nas)) == 0)
return (NUMA *)ERROR_PTR("no bins in nas", procName, NULL);
nd = (ns + newsize - 1) / newsize;
if ((nad = numaCreate(nd)) == NULL)
return (NUMA *)ERROR_PTR("nad not made", procName, NULL);
numaGetParameters(nad, &start, &oldsize);
numaSetParameters(nad, start, oldsize * newsize);
for (i = 0; i < nd; i++) { /* new bins */
count = 0;
index = i * newsize;
for (j = 0; j < newsize; j++) {
if (index < ns) {
numaGetIValue(nas, index, &val);
count += val;
index++;
}
}
numaAddNumber(nad, count);
}
return nad;
}
/*!
* \brief numaNormalizeHistogram()
*
* \param[in] nas input histogram
* \param[in] tsum target sum of all numbers in dest histogram; e.g., use
* %tsum= 1.0 if this represents a probability distribution
* \return nad normalized histogram, or NULL on error
*/
NUMA *
numaNormalizeHistogram(NUMA *nas,
l_float32 tsum)
{
l_int32 i, ns;
l_float32 sum, factor, fval;
NUMA *nad;
PROCNAME("numaNormalizeHistogram");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
if (tsum <= 0.0)
return (NUMA *)ERROR_PTR("tsum must be > 0.0", procName, NULL);
if ((ns = numaGetCount(nas)) == 0)
return (NUMA *)ERROR_PTR("no bins in nas", procName, NULL);
numaGetSum(nas, &sum);
factor = tsum / sum;
if ((nad = numaCreate(ns)) == NULL)
return (NUMA *)ERROR_PTR("nad not made", procName, NULL);
numaCopyParameters(nad, nas);
for (i = 0; i < ns; i++) {
numaGetFValue(nas, i, &fval);
fval *= factor;
numaAddNumber(nad, fval);
}
return nad;
}
/*!
* \brief numaGetStatsUsingHistogram()
*
* \param[in] na an arbitrary set of numbers; not ordered and not
* a histogram
* \param[in] maxbins the maximum number of bins to be allowed in
* the histogram; use an integer larger than the
* largest number in %na for consecutive integer bins
* \param[out] pmin [optional] min value of set
* \param[out] pmax [optional] max value of set
* \param[out] pmean [optional] mean value of set
* \param[out] pvariance [optional] variance
* \param[out] pmedian [optional] median value of set
* \param[in] rank in [0.0 ... 1.0]; median has a rank 0.5;
* ignored if &rval == NULL
* \param[out] prval [optional] value in na corresponding to %rank
* \param[out] phisto [optional] Numa histogram; use NULL to prevent
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) This is a simple interface for gathering statistics
* from a numa, where a histogram is used 'under the covers'
* to avoid sorting if a rank value is requested. In that case,
* by using a histogram we are trading speed for accuracy, because
* the values in %na are quantized to the center of a set of bins.
* (2) If the median, other rank value, or histogram are not requested,
* the calculation is all performed on the input Numa.
* (3) The variance is the average of the square of the
* difference from the mean. The median is the value in na
* with rank 0.5.
* (4) There are two situations where this gives rank results with
* accuracy comparable to computing stastics directly on the input
* data, without binning into a histogram:
* (a) the data is integers and the range of data is less than
* %maxbins, and
* (b) the data is floats and the range is small compared to
* %maxbins, so that the binsize is much less than 1.
* (5) If a histogram is used and the numbers in the Numa extend
* over a large range, you can limit the required storage by
* specifying the maximum number of bins in the histogram.
* Use %maxbins == 0 to force the bin size to be 1.
* (6) This optionally returns the median and one arbitrary rank value.
* If you need several rank values, return the histogram and use
* numaHistogramGetValFromRank(nah, rank, &rval)
* multiple times.
* </pre>
*/
l_ok
numaGetStatsUsingHistogram(NUMA *na,
l_int32 maxbins,
l_float32 *pmin,
l_float32 *pmax,
l_float32 *pmean,
l_float32 *pvariance,
l_float32 *pmedian,
l_float32 rank,
l_float32 *prval,
NUMA **phisto)
{
l_int32 i, n;
l_float32 minval, maxval, fval, mean, sum;
NUMA *nah;
PROCNAME("numaGetStatsUsingHistogram");
if (pmin) *pmin = 0.0;
if (pmax) *pmax = 0.0;
if (pmean) *pmean = 0.0;
if (pvariance) *pvariance = 0.0;
if (pmedian) *pmedian = 0.0;
if (prval) *prval = 0.0;
if (phisto) *phisto = NULL;
if (!na)
return ERROR_INT("na not defined", procName, 1);
if ((n = numaGetCount(na)) == 0)
return ERROR_INT("numa is empty", procName, 1);
numaGetMin(na, &minval, NULL);
numaGetMax(na, &maxval, NULL);
if (pmin) *pmin = minval;
if (pmax) *pmax = maxval;
if (pmean || pvariance) {
sum = 0.0;
for (i = 0; i < n; i++) {
numaGetFValue(na, i, &fval);
sum += fval;
}
mean = sum / (l_float32)n;
if (pmean) *pmean = mean;
}
if (pvariance) {
sum = 0.0;
for (i = 0; i < n; i++) {
numaGetFValue(na, i, &fval);
sum += fval * fval;
}
*pvariance = sum / (l_float32)n - mean * mean;
}
if (!pmedian && !prval && !phisto)
return 0;
nah = numaMakeHistogramAuto(na, maxbins);
if (pmedian)
numaHistogramGetValFromRank(nah, 0.5, pmedian);
if (prval)
numaHistogramGetValFromRank(nah, rank, prval);
if (phisto)
*phisto = nah;
else
numaDestroy(&nah);
return 0;
}
/*!
* \brief numaGetHistogramStats()
*
* \param[in] nahisto histogram: y(x(i)), i = 0 ... nbins - 1
* \param[in] startx x value of first bin: x(0)
* \param[in] deltax x increment between bins; the bin size; x(1) - x(0)
* \param[out] pxmean [optional] mean value of histogram
* \param[out] pxmedian [optional] median value of histogram
* \param[out] pxmode [optional] mode value of histogram:
* xmode = x(imode), where y(xmode) >= y(x(i)) for
* all i != imode
* \param[out] pxvariance [optional] variance of x
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) If the histogram represents the relation y(x), the
* computed values that are returned are the x values.
* These are NOT the bucket indices i; they are related to the
* bucket indices by
* x(i) = startx + i * deltax
* </pre>
*/
l_ok
numaGetHistogramStats(NUMA *nahisto,
l_float32 startx,
l_float32 deltax,
l_float32 *pxmean,
l_float32 *pxmedian,
l_float32 *pxmode,
l_float32 *pxvariance)
{
PROCNAME("numaGetHistogramStats");
if (pxmean) *pxmean = 0.0;
if (pxmedian) *pxmedian = 0.0;
if (pxmode) *pxmode = 0.0;
if (pxvariance) *pxvariance = 0.0;
if (!nahisto)
return ERROR_INT("nahisto not defined", procName, 1);
return numaGetHistogramStatsOnInterval(nahisto, startx, deltax, 0, -1,
pxmean, pxmedian, pxmode,
pxvariance);
}
/*!
* \brief numaGetHistogramStatsOnInterval()
*
* \param[in] nahisto histogram: y(x(i)), i = 0 ... nbins - 1
* \param[in] startx x value of first bin: x(0)
* \param[in] deltax x increment between bins; the bin size; x(1) - x(0)
* \param[in] ifirst first bin to use for collecting stats
* \param[in] ilast last bin for collecting stats; -1 to go to the end
* \param[out] pxmean [optional] mean value of histogram
* \param[out] pxmedian [optional] median value of histogram
* \param[out] pxmode [optional] mode value of histogram:
* xmode = x(imode), where y(xmode) >= y(x(i)) for
* all i != imode
* \param[out] pxvariance [optional] variance of x
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) If the histogram represents the relation y(x), the
* computed values that are returned are the x values.
* These are NOT the bucket indices i; they are related to the
* bucket indices by
* x(i) = startx + i * deltax
* </pre>
*/
l_ok
numaGetHistogramStatsOnInterval(NUMA *nahisto,
l_float32 startx,
l_float32 deltax,
l_int32 ifirst,
l_int32 ilast,
l_float32 *pxmean,
l_float32 *pxmedian,
l_float32 *pxmode,
l_float32 *pxvariance)
{
l_int32 i, n, imax;
l_float32 sum, sumval, halfsum, moment, var, x, y, ymax;
PROCNAME("numaGetHistogramStatsOnInterval");
if (pxmean) *pxmean = 0.0;
if (pxmedian) *pxmedian = 0.0;
if (pxmode) *pxmode = 0.0;
if (pxvariance) *pxvariance = 0.0;
if (!nahisto)
return ERROR_INT("nahisto not defined", procName, 1);
if (!pxmean && !pxmedian && !pxmode && !pxvariance)
return ERROR_INT("nothing to compute", procName, 1);
n = numaGetCount(nahisto);
ifirst = L_MAX(0, ifirst);
if (ilast < 0) ilast = n - 1;
if (ifirst >= n)
return ERROR_INT("invalid ifirst", procName, 1);
if (ilast >= n) {
L_WARNING("ilast = %d is beyond max index = %d; adjusting\n",
procName, ilast, n - 1);
ilast = n - 1;
}
if (ifirst > ilast)
return ERROR_INT("ifirst > ilast", procName, 1);
for (sum = 0.0, moment = 0.0, var = 0.0, i = ifirst; i <= ilast ; i++) {
x = startx + i * deltax;
numaGetFValue(nahisto, i, &y);
sum += y;
moment += x * y;
var += x * x * y;
}
if (sum == 0.0) {
L_INFO("sum is 0\n", procName);
return 0;
}
if (pxmean)
*pxmean = moment / sum;
if (pxvariance)
*pxvariance = var / sum - moment * moment / (sum * sum);
if (pxmedian) {
halfsum = sum / 2.0;
for (sumval = 0.0, i = ifirst; i <= ilast; i++) {
numaGetFValue(nahisto, i, &y);
sumval += y;
if (sumval >= halfsum) {
*pxmedian = startx + i * deltax;
break;
}
}
}
if (pxmode) {
imax = -1;
ymax = -1.0e10;
for (i = ifirst; i <= ilast; i++) {
numaGetFValue(nahisto, i, &y);
if (y > ymax) {
ymax = y;
imax = i;
}
}
*pxmode = startx + imax * deltax;
}
return 0;
}
/*!
* \brief numaMakeRankFromHistogram()
*
* \param[in] startx xval corresponding to first element in nay
* \param[in] deltax x increment between array elements in nay
* \param[in] nasy input histogram, assumed equally spaced
* \param[in] npts number of points to evaluate rank function
* \param[out] pnax [optional] array of x values in range
* \param[out] pnay rank array of specified npts
* \return 0 if OK, 1 on error
*/
l_ok
numaMakeRankFromHistogram(l_float32 startx,
l_float32 deltax,
NUMA *nasy,
l_int32 npts,
NUMA **pnax,
NUMA **pnay)
{
l_int32 i, n;
l_float32 sum, fval;
NUMA *nan, *nar;
PROCNAME("numaMakeRankFromHistogram");
if (pnax) *pnax = NULL;
if (!pnay)
return ERROR_INT("&nay not defined", procName, 1);
*pnay = NULL;
if (!nasy)
return ERROR_INT("nasy not defined", procName, 1);
if ((n = numaGetCount(nasy)) == 0)
return ERROR_INT("no bins in nas", procName, 1);
/* Normalize and generate the rank array corresponding to
* the binned histogram. */
nan = numaNormalizeHistogram(nasy, 1.0);
nar = numaCreate(n + 1); /* rank numa corresponding to nan */
sum = 0.0;
numaAddNumber(nar, sum); /* first element is 0.0 */
for (i = 0; i < n; i++) {
numaGetFValue(nan, i, &fval);
sum += fval;
numaAddNumber(nar, sum);
}
/* Compute rank array on full range with specified
* number of points and correspondence to x-values. */
numaInterpolateEqxInterval(startx, deltax, nar, L_LINEAR_INTERP,
startx, startx + n * deltax, npts,
pnax, pnay);
numaDestroy(&nan);
numaDestroy(&nar);
return 0;
}
/*!
* \brief numaHistogramGetRankFromVal()
*
* \param[in] na histogram
* \param[in] rval value of input sample for which we want the rank
* \param[out] prank fraction of total samples below rval
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) If we think of the histogram as a function y(x), normalized
* to 1, for a given input value of x, this computes the
* rank of x, which is the integral of y(x) from the start
* value of x to the input value.
* (2) This function only makes sense when applied to a Numa that
* is a histogram. The values in the histogram can be ints and
* floats, and are computed as floats. The rank is returned
* as a float between 0.0 and 1.0.
* (3) The numa parameters startx and binsize are used to
* compute x from the Numa index i.
* </pre>
*/
l_ok
numaHistogramGetRankFromVal(NUMA *na,
l_float32 rval,
l_float32 *prank)
{
l_int32 i, ibinval, n;
l_float32 startval, binsize, binval, maxval, fractval, total, sum, val;
PROCNAME("numaHistogramGetRankFromVal");
if (!prank)
return ERROR_INT("prank not defined", procName, 1);
*prank = 0.0;
if (!na)
return ERROR_INT("na not defined", procName, 1);
numaGetParameters(na, &startval, &binsize);
n = numaGetCount(na);
if (rval < startval)
return 0;
maxval = startval + n * binsize;
if (rval > maxval) {
*prank = 1.0;
return 0;
}
binval = (rval - startval) / binsize;
ibinval = (l_int32)binval;
if (ibinval >= n) {
*prank = 1.0;
return 0;
}
fractval = binval - (l_float32)ibinval;
sum = 0.0;
for (i = 0; i < ibinval; i++) {
numaGetFValue(na, i, &val);
sum += val;
}
numaGetFValue(na, ibinval, &val);
sum += fractval * val;
numaGetSum(na, &total);
*prank = sum / total;
/* fprintf(stderr, "binval = %7.3f, rank = %7.3f\n", binval, *prank); */
return 0;
}
/*!
* \brief numaHistogramGetValFromRank()
*
* \param[in] na histogram
* \param[in] rank fraction of total samples
* \param[out] prval approx. to the bin value
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) If we think of the histogram as a function y(x), this returns
* the value x such that the integral of y(x) from the start
* value to x gives the fraction 'rank' of the integral
* of y(x) over all bins.
* (2) This function only makes sense when applied to a Numa that
* is a histogram. The values in the histogram can be ints and
* floats, and are computed as floats. The val is returned
* as a float, even though the buckets are of integer width.
* (3) The numa parameters startx and binsize are used to
* compute x from the Numa index i.
* </pre>
*/
l_ok
numaHistogramGetValFromRank(NUMA *na,
l_float32 rank,
l_float32 *prval)
{
l_int32 i, n;
l_float32 startval, binsize, rankcount, total, sum, fract, val;
PROCNAME("numaHistogramGetValFromRank");
if (!prval)
return ERROR_INT("prval not defined", procName, 1);
*prval = 0.0;
if (!na)
return ERROR_INT("na not defined", procName, 1);
if (rank < 0.0) {
L_WARNING("rank < 0; setting to 0.0\n", procName);
rank = 0.0;
}
if (rank > 1.0) {
L_WARNING("rank > 1.0; setting to 1.0\n", procName);
rank = 1.0;
}
n = numaGetCount(na);
numaGetParameters(na, &startval, &binsize);
numaGetSum(na, &total);
rankcount = rank * total; /* count that corresponds to rank */
sum = 0.0;
for (i = 0; i < n; i++) {
numaGetFValue(na, i, &val);
if (sum + val >= rankcount)
break;
sum += val;
}
if (val <= 0.0) /* can == 0 if rank == 0.0 */
fract = 0.0;
else /* sum + fract * val = rankcount */
fract = (rankcount - sum) / val;
/* The use of the fraction of a bin allows a simple calculation
* for the histogram value at the given rank. */
*prval = startval + binsize * ((l_float32)i + fract);
/* fprintf(stderr, "rank = %7.3f, val = %7.3f\n", rank, *prval); */
return 0;
}
/*!
* \brief numaDiscretizeRankAndIntensity()
*
* \param[in] na normalized histo of probability density vs intensity
* \param[in] nbins number of bins at which the rank is divided
* \param[out] pnarbin [optional] rank bin value vs intensity
* \param[out] pnam [optional] median intensity in a bin vs rank bin
* value, with %nbins of discretized rank values
* \param[out] pnar [optional] rank vs intensity; this is
* a cumulative norm histogram
* \param[out] pnabb [optional] intensity at the right bin boundary
* vs rank bin
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) We are inverting the rank(intensity) function to get
* the intensity(rank) function at %nbins equally spaced
* values of rank between 0.0 and 1.0. We save integer values
* for the intensity.
* (2) We are using the word "intensity" to describe the type of
* array values, but any array of non-negative numbers will work.
* (3) The output arrays give the following mappings, where the
* input is a normalized histogram of array values:
* array values --> rank bin number (narbin)
* rank bin number --> median array value in bin (nam)
* array values --> cumulative norm = rank (nar)
* rank bin number --> array value at right bin edge (nabb)
* </pre>
*/
l_ok
numaDiscretizeRankAndIntensity(NUMA *na,
l_int32 nbins,
NUMA **pnarbin,
NUMA **pnam,
NUMA **pnar,
NUMA **pnabb)
{
NUMA *nar; /* rank value as function of intensity */
NUMA *nam; /* median intensity in the rank bins */
NUMA *nabb; /* rank bin right boundaries (in intensity) */
NUMA *narbin; /* binned rank value as a function of intensity */
l_int32 i, j, npts, start, midfound, mcount, rightedge;
l_float32 sum, midrank, endrank, val;
PROCNAME("numaDiscretizeRankAndIntensity");
if (pnarbin) *pnarbin = NULL;
if (pnam) *pnam = NULL;
if (pnar) *pnar = NULL;
if (pnabb) *pnabb = NULL;
if (!pnarbin && !pnam && !pnar && !pnabb)
return ERROR_INT("no output requested", procName, 1);
if (!na)
return ERROR_INT("na not defined", procName, 1);
if (nbins < 2)
return ERROR_INT("nbins must be > 1", procName, 1);
/* Get cumulative normalized histogram (rank vs intensity value).
* For a normalized histogram from an 8 bpp grayscale image
* as input, we have 256 bins and 257 points in the
* cumulative (rank) histogram. */
npts = numaGetCount(na);
if ((nar = numaCreate(npts + 1)) == NULL)
return ERROR_INT("nar not made", procName, 1);
sum = 0.0;
numaAddNumber(nar, sum); /* left side of first bin */
for (i = 0; i < npts; i++) {
numaGetFValue(na, i, &val);
sum += val;
numaAddNumber(nar, sum);
}
nam = numaCreate(nbins);
narbin = numaCreate(npts);
nabb = numaCreate(nbins);
if (!nam || !narbin || !nabb) {
numaDestroy(&nar);
numaDestroy(&nam);
numaDestroy(&narbin);
numaDestroy(&nabb);
return ERROR_INT("numa not made", procName, 1);
}
/* We find the intensity value at the right edge of each of
* the rank bins. We also find the median intensity in the bin,
* where approximately half the samples are lower and half are
* higher. This can be considered as a simple approximation
* for the average intensity in the bin. */
start = 0; /* index in nar */
mcount = 0; /* count of median values in rank bins; not to exceed nbins */
for (i = 0; i < nbins; i++) {
midrank = (l_float32)(i + 0.5) / (l_float32)(nbins);
endrank = (l_float32)(i + 1.0) / (l_float32)(nbins);
endrank = L_MAX(0.0, L_MIN(endrank - 0.001, 1.0));
midfound = FALSE;
for (j = start; j < npts; j++) { /* scan up for each bin value */
numaGetFValue(nar, j, &val);
/* Use (j == npts - 1) tests in case all weight is at top end */
if ((!midfound && val >= midrank) ||
(mcount < nbins && j == npts - 1)) {
midfound = TRUE;
numaAddNumber(nam, j);
mcount++;
}
if ((val >= endrank) || (j == npts - 1)) {
numaAddNumber(nabb, j);
if (val == endrank)
start = j;
else
start = j - 1;
break;
}
}
}
numaSetValue(nabb, nbins - 1, npts - 1); /* extend to max */
/* Error checking: did we get data in all bins? */
if (mcount != nbins)
L_WARNING("found data for %d bins; should be %d\n",
procName, mcount, nbins);
/* Generate LUT that maps from intensity to bin number */
start = 0;
for (i = 0; i < nbins; i++) {
numaGetIValue(nabb, i, &rightedge);
for (j = start; j < npts; j++) {
if (j <= rightedge)
numaAddNumber(narbin, i);
if (j > rightedge) {
start = j;
break;
}
if (j == npts - 1) { /* we're done */
start = j + 1;
break;
}
}
}
if (pnarbin)
*pnarbin = narbin;
else
numaDestroy(&narbin);
if (pnam)
*pnam = nam;
else
numaDestroy(&nam);
if (pnar)
*pnar = nar;
else
numaDestroy(&nar);
if (pnabb)
*pnabb = nabb;
else
numaDestroy(&nabb);
return 0;
}
/*!
* \brief numaGetRankBinValues()
*
* \param[in] na an array of values
* \param[in] nbins number of bins at which the rank is divided
* \param[out] pnarbin [optional] rank bin value vs array value
* \param[out] pnam [optional] median intensity in a bin vs rank bin
* value, with %nbins of discretized rank values
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) Simple interface for getting a binned rank representation
* of an input array of values. This returns two mappings:
* array value --> rank bin number (narbin)
* rank bin number --> median array value in each rank bin (nam)
* </pre>
*/
l_ok
numaGetRankBinValues(NUMA *na,
l_int32 nbins,
NUMA **pnarbin,
NUMA **pnam)
{
NUMA *nah, *nan; /* histo and normalized histo */
l_int32 maxbins, discardval;
l_float32 maxval, delx;
PROCNAME("numaGetRankBinValues");
if (pnarbin) *pnarbin = NULL;
if (pnam) *pnam = NULL;
if (!pnarbin && !pnam)
return ERROR_INT("no output requested", procName, 1);
if (!na)
return ERROR_INT("na not defined", procName, 1);
if (numaGetCount(na) == 0)
return ERROR_INT("na is empty", procName, 1);
if (nbins < 2)
return ERROR_INT("nbins must be > 1", procName, 1);
/* Get normalized histogram */
numaGetMax(na, &maxval, NULL);
maxbins = L_MIN(100002, (l_int32)maxval + 2);
nah = numaMakeHistogram(na, maxbins, &discardval, NULL);
nan = numaNormalizeHistogram(nah, 1.0);
/* Warn if there is a scale change. This shouldn't happen
* unless the max value is above 100000. */
numaGetParameters(nan, NULL, &delx);
if (delx > 1.0)
L_WARNING("scale change: delx = %6.2f\n", procName, delx);
/* Rank bin the results */
numaDiscretizeRankAndIntensity(nan, nbins, pnarbin, pnam, NULL, NULL);
numaDestroy(&nah);
numaDestroy(&nan);
return 0;
}
/*----------------------------------------------------------------------*
* Splitting a distribution *
*----------------------------------------------------------------------*/
/*!
* \brief numaSplitDistribution()
*
* \param[in] na histogram
* \param[in] scorefract fraction of the max score, used to determine
* range over which the histogram min is searched
* \param[out] psplitindex [optional] index for splitting
* \param[out] pave1 [optional] average of lower distribution
* \param[out] pave2 [optional] average of upper distribution
* \param[out] pnum1 [optional] population of lower distribution
* \param[out] pnum2 [optional] population of upper distribution
* \param[out] pnascore [optional] for debugging; otherwise use NULL
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) This function is intended to be used on a distribution of
* values that represent two sets, such as a histogram of
* pixel values for an image with a fg and bg, and the goal
* is to determine the averages of the two sets and the
* best splitting point.
* (2) The Otsu method finds a split point that divides the distribution
* into two parts by maximizing a score function that is the
* product of two terms:
* (a) the square of the difference of centroids, (ave1 - ave2)^2
* (b) fract1 * (1 - fract1)
* where fract1 is the fraction in the lower distribution.
* (3) This works well for images where the fg and bg are
* each relatively homogeneous and well-separated in color.
* However, if the actual fg and bg sets are very different
* in size, and the bg is highly varied, as can occur in some
* scanned document images, this will bias the split point
* into the larger "bump" (i.e., toward the point where the
* (b) term reaches its maximum of 0.25 at fract1 = 0.5.
* To avoid this, we define a range of values near the
* maximum of the score function, and choose the value within
* this range such that the histogram itself has a minimum value.
* The range is determined by scorefract: we include all abscissa
* values to the left and right of the value that maximizes the
* score, such that the score stays above (1 - scorefract) * maxscore.
* The intuition behind this modification is to try to find
* a split point that both has a high variance score and is
* at or near a minimum in the histogram, so that the histogram
* slope is small at the split point.
* (4) We normalize the score so that if the two distributions
* were of equal size and at opposite ends of the numa, the
* score would be 1.0.
* </pre>
*/
l_ok
numaSplitDistribution(NUMA *na,
l_float32 scorefract,
l_int32 *psplitindex,
l_float32 *pave1,
l_float32 *pave2,
l_float32 *pnum1,
l_float32 *pnum2,
NUMA **pnascore)
{
l_int32 i, n, bestsplit, minrange, maxrange, maxindex;
l_float32 ave1, ave2, ave1prev, ave2prev;
l_float32 num1, num2, num1prev, num2prev;
l_float32 val, minval, sum, fract1;
l_float32 norm, score, minscore, maxscore;
NUMA *nascore, *naave1, *naave2, *nanum1, *nanum2;
PROCNAME("numaSplitDistribution");
if (psplitindex) *psplitindex = 0;
if (pave1) *pave1 = 0.0;
if (pave2) *pave2 = 0.0;
if (pnum1) *pnum1 = 0.0;
if (pnum2) *pnum2 = 0.0;
if (pnascore) *pnascore = NULL;
if (!na)
return ERROR_INT("na not defined", procName, 1);
n = numaGetCount(na);
if (n <= 1)
return ERROR_INT("n = 1 in histogram", procName, 1);
numaGetSum(na, &sum);
if (sum <= 0.0)
return ERROR_INT("sum <= 0.0", procName, 1);
norm = 4.0 / ((l_float32)(n - 1) * (n - 1));
ave1prev = 0.0;
numaGetHistogramStats(na, 0.0, 1.0, &ave2prev, NULL, NULL, NULL);
num1prev = 0.0;
num2prev = sum;
maxindex = n / 2; /* initialize with something */
/* Split the histogram with [0 ... i] in the lower part
* and [i+1 ... n-1] in upper part. First, compute an otsu
* score for each possible splitting. */
if ((nascore = numaCreate(n)) == NULL)
return ERROR_INT("nascore not made", procName, 1);
naave1 = (pave1) ? numaCreate(n) : NULL;
naave2 = (pave2) ? numaCreate(n) : NULL;
nanum1 = (pnum1) ? numaCreate(n) : NULL;
nanum2 = (pnum2) ? numaCreate(n) : NULL;
maxscore = 0.0;
for (i = 0; i < n; i++) {
numaGetFValue(na, i, &val);
num1 = num1prev + val;
if (num1 == 0)
ave1 = ave1prev;
else
ave1 = (num1prev * ave1prev + i * val) / num1;
num2 = num2prev - val;
if (num2 == 0)
ave2 = ave2prev;
else
ave2 = (num2prev * ave2prev - i * val) / num2;
fract1 = num1 / sum;
score = norm * (fract1 * (1 - fract1)) * (ave2 - ave1) * (ave2 - ave1);
numaAddNumber(nascore, score);
if (pave1) numaAddNumber(naave1, ave1);
if (pave2) numaAddNumber(naave2, ave2);
if (pnum1) numaAddNumber(nanum1, num1);
if (pnum2) numaAddNumber(nanum2, num2);
if (score > maxscore) {
maxscore = score;
maxindex = i;
}
num1prev = num1;
num2prev = num2;
ave1prev = ave1;
ave2prev = ave2;
}
/* Next, for all contiguous scores within a specified fraction
* of the max, choose the split point as the value with the
* minimum in the histogram. */
minscore = (1. - scorefract) * maxscore;
for (i = maxindex - 1; i >= 0; i--) {
numaGetFValue(nascore, i, &val);
if (val < minscore)
break;
}
minrange = i + 1;
for (i = maxindex + 1; i < n; i++) {
numaGetFValue(nascore, i, &val);
if (val < minscore)
break;
}
maxrange = i - 1;
numaGetFValue(na, minrange, &minval);
bestsplit = minrange;
for (i = minrange + 1; i <= maxrange; i++) {
numaGetFValue(na, i, &val);
if (val < minval) {
minval = val;
bestsplit = i;
}
}
/* Add one to the bestsplit value to get the threshold value,
* because when we take a threshold, as in pixThresholdToBinary(),
* we always choose the set with values below the threshold. */
bestsplit = L_MIN(255, bestsplit + 1);
if (psplitindex) *psplitindex = bestsplit;
if (pave1) numaGetFValue(naave1, bestsplit, pave1);
if (pave2) numaGetFValue(naave2, bestsplit, pave2);
if (pnum1) numaGetFValue(nanum1, bestsplit, pnum1);
if (pnum2) numaGetFValue(nanum2, bestsplit, pnum2);
if (pnascore) { /* debug mode */
fprintf(stderr, "minrange = %d, maxrange = %d\n", minrange, maxrange);
fprintf(stderr, "minval = %10.0f\n", minval);
gplotSimple1(nascore, GPLOT_PNG, "/tmp/lept/nascore",
"Score for split distribution");
*pnascore = nascore;
} else {
numaDestroy(&nascore);
}
if (pave1) numaDestroy(&naave1);
if (pave2) numaDestroy(&naave2);
if (pnum1) numaDestroy(&nanum1);
if (pnum2) numaDestroy(&nanum2);
return 0;
}
/*----------------------------------------------------------------------*
* Comparing histograms *
*----------------------------------------------------------------------*/
/*!
* \brief grayHistogramsToEMD()
*
* \param[in] naa1, naa2 two numaa, each with one or more 256-element
* histograms
* \param[out] pnad nad of EM distances for each histogram
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) The two numaas must be the same size and have corresponding
* 256-element histograms. Pairs do not need to be normalized
* to the same sum.
* (2) This is typically used on two sets of histograms from
* corresponding tiles of two images. The similarity of two
* images can be found with the scoring function used in
* pixCompareGrayByHisto():
* score S = 1.0 - k * D, where
* k is a constant, say in the range 5-10
* D = EMD
* for each tile; for multiple tiles, take the Min(S) over
* the set of tiles to be the final score.
* </pre>
*/
l_ok
grayHistogramsToEMD(NUMAA *naa1,
NUMAA *naa2,
NUMA **pnad)
{
l_int32 i, n, nt;
l_float32 dist;
NUMA *na1, *na2, *nad;
PROCNAME("grayHistogramsToEMD");
if (!pnad)
return ERROR_INT("&nad not defined", procName, 1);
*pnad = NULL;
if (!naa1 || !naa2)
return ERROR_INT("na1 and na2 not both defined", procName, 1);
n = numaaGetCount(naa1);
if (n != numaaGetCount(naa2))
return ERROR_INT("naa1 and naa2 numa counts differ", procName, 1);
nt = numaaGetNumberCount(naa1);
if (nt != numaaGetNumberCount(naa2))
return ERROR_INT("naa1 and naa2 number counts differ", procName, 1);
if (256 * n != nt) /* good enough check */
return ERROR_INT("na sizes must be 256", procName, 1);
nad = numaCreate(n);
*pnad = nad;
for (i = 0; i < n; i++) {
na1 = numaaGetNuma(naa1, i, L_CLONE);
na2 = numaaGetNuma(naa2, i, L_CLONE);
numaEarthMoverDistance(na1, na2, &dist);
numaAddNumber(nad, dist / 255.); /* normalize to [0.0 - 1.0] */
numaDestroy(&na1);
numaDestroy(&na2);
}
return 0;
}
/*!
* \brief numaEarthMoverDistance()
*
* \param[in] na1, na2 two numas of the same size, typically histograms
* \param[out] pdist earthmover distance
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) The two numas must have the same size. They do not need to be
* normalized to the same sum before applying the function.
* (2) For a 1D discrete function, the implementation of the EMD
* is trivial. Just keep filling or emptying buckets in one numa
* to match the amount in the other, moving sequentially along
* both arrays.
* (3) We divide the sum of the absolute value of everything moved
* (by 1 unit at a time) by the sum of the numa (amount of "earth")
* to get the average distance that the "earth" was moved.
* This is the value returned here.
* (4) The caller can do a further normalization, by the number of
* buckets (minus 1), to get the EM distance as a fraction of
* the maximum possible distance, which is n-1. This fraction
* is 1.0 for the situation where all the 'earth' in the first
* array is at one end, and all in the second array is at the
* other end.
* </pre>
*/
l_ok
numaEarthMoverDistance(NUMA *na1,
NUMA *na2,
l_float32 *pdist)
{
l_int32 n, norm, i;
l_float32 sum1, sum2, diff, total;
l_float32 *array1, *array3;
NUMA *na3;
PROCNAME("numaEarthMoverDistance");
if (!pdist)
return ERROR_INT("&dist not defined", procName, 1);
*pdist = 0.0;
if (!na1 || !na2)
return ERROR_INT("na1 and na2 not both defined", procName, 1);
n = numaGetCount(na1);
if (n != numaGetCount(na2))
return ERROR_INT("na1 and na2 have different size", procName, 1);
/* Generate na3; normalize to na1 if necessary */
numaGetSum(na1, &sum1);
numaGetSum(na2, &sum2);
norm = (L_ABS(sum1 - sum2) < 0.00001 * L_ABS(sum1)) ? 1 : 0;
if (!norm)
na3 = numaTransform(na2, 0, sum1 / sum2);
else
na3 = numaCopy(na2);
array1 = numaGetFArray(na1, L_NOCOPY);
array3 = numaGetFArray(na3, L_NOCOPY);
/* Move earth in n3 from array elements, to match n1 */
total = 0;
for (i = 1; i < n; i++) {
diff = array1[i - 1] - array3[i - 1];
array3[i] -= diff;
total += L_ABS(diff);
}
*pdist = total / sum1;
numaDestroy(&na3);
return 0;
}
/*!
* \brief grayInterHistogramStats()
*
* \param[in] naa numaa with two or more 256-element histograms
* \param[in] wc half-width of the smoothing window
* \param[out] pnam [optional] mean values
* \param[out] pnams [optional] mean square values
* \param[out] pnav [optional] variances
* \param[out] pnarv [optional] rms deviations from the mean
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) The %naa has two or more 256-element numa histograms, which
* are to be compared value-wise at each of the 256 gray levels.
* The result are stats (mean, mean square, variance, root variance)
* aggregated across the set of histograms, and each is output
* as a 256 entry numa. Think of these histograms as a matrix,
* where each histogram is one row of the array. The stats are
* then aggregated column-wise, between the histograms.
* (2) These stats are:
* ~ average value: <v> (nam)
* ~ average squared value: <v*v> (nams)
* ~ variance: <(v - <v>)*(v - <v>)> = <v*v> - <v>*<v> (nav)
* ~ square-root of variance: (narv)
* where the brackets < .. > indicate that the average value is
* to be taken over each column of the array.
* (3) The input histograms are optionally smoothed before these
* statistical operations.
* (4) The input histograms are normalized to a sum of 10000. By
* doing this, the resulting numbers are independent of the
* number of samples used in building the individual histograms.
* (5) A typical application is on a set of histograms from tiles
* of an image, to distinguish between text/tables and photo
* regions. If the tiles are much larger than the text line
* spacing, text/table regions typically have smaller variance
* across tiles than photo regions. For this application, it
* may be useful to ignore values near white, which are large for
* text and would magnify the variance due to variations in
* illumination. However, because the variance of a drawing or
* a light photo can be similar to that of grayscale text, this
* function is only a discriminator between darker photos/drawings
* and light photos/text/line-graphics.
* </pre>
*/
l_ok
grayInterHistogramStats(NUMAA *naa,
l_int32 wc,
NUMA **pnam,
NUMA **pnams,
NUMA **pnav,
NUMA **pnarv)
{
l_int32 i, j, n, nn;
l_float32 **arrays;
l_float32 mean, var, rvar;
NUMA *na1, *na2, *na3, *na4;
PROCNAME("grayInterHistogramStats");
if (pnam) *pnam = NULL;
if (pnams) *pnams = NULL;
if (pnav) *pnav = NULL;
if (pnarv) *pnarv = NULL;
if (!pnam && !pnams && !pnav && !pnarv)
return ERROR_INT("nothing requested", procName, 1);
if (!naa)
return ERROR_INT("naa not defined", procName, 1);
n = numaaGetCount(naa);
for (i = 0; i < n; i++) {
nn = numaaGetNumaCount(naa, i);
if (nn != 256) {
L_ERROR("%d numbers in numa[%d]\n", procName, nn, i);
return 1;
}
}
if (pnam) *pnam = numaCreate(256);
if (pnams) *pnams = numaCreate(256);
if (pnav) *pnav = numaCreate(256);
if (pnarv) *pnarv = numaCreate(256);
/* First, use mean smoothing, normalize each histogram,
* and save all results in a 2D matrix. */
arrays = (l_float32 **)LEPT_CALLOC(n, sizeof(l_float32 *));
for (i = 0; i < n; i++) {
na1 = numaaGetNuma(naa, i, L_CLONE);
na2 = numaWindowedMean(na1, wc);
na3 = numaNormalizeHistogram(na2, 10000.);
arrays[i] = numaGetFArray(na3, L_COPY);
numaDestroy(&na1);
numaDestroy(&na2);
numaDestroy(&na3);
}
/* Get stats between histograms */
for (j = 0; j < 256; j++) {
na4 = numaCreate(n);
for (i = 0; i < n; i++) {
numaAddNumber(na4, arrays[i][j]);
}
numaSimpleStats(na4, 0, -1, &mean, &var, &rvar);
if (pnam) numaAddNumber(*pnam, mean);
if (pnams) numaAddNumber(*pnams, mean * mean);
if (pnav) numaAddNumber(*pnav, var);
if (pnarv) numaAddNumber(*pnarv, rvar);
numaDestroy(&na4);
}
for (i = 0; i < n; i++)
LEPT_FREE(arrays[i]);
LEPT_FREE(arrays);
return 0;
}
/*----------------------------------------------------------------------*
* Extrema finding *
*----------------------------------------------------------------------*/
/*!
* \brief numaFindPeaks()
*
* \param[in] nas source numa
* \param[in] nmax max number of peaks to be found
* \param[in] fract1 min fraction of peak value
* \param[in] fract2 min slope
* \return peak na, or NULL on error.
*
* <pre>
* Notes:
* (1) The returned na consists of sets of four numbers representing
* the peak, in the following order:
* left edge; peak center; right edge; normalized peak area
* </pre>
*/
NUMA *
numaFindPeaks(NUMA *nas,
l_int32 nmax,
l_float32 fract1,
l_float32 fract2)
{
l_int32 i, k, n, maxloc, lloc, rloc;
l_float32 fmaxval, sum, total, newtotal, val, lastval;
l_float32 peakfract;
NUMA *na, *napeak;
PROCNAME("numaFindPeaks");
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
n = numaGetCount(nas);
numaGetSum(nas, &total);
/* We munge this copy */
if ((na = numaCopy(nas)) == NULL)
return (NUMA *)ERROR_PTR("na not made", procName, NULL);
if ((napeak = numaCreate(4 * nmax)) == NULL) {
numaDestroy(&na);
return (NUMA *)ERROR_PTR("napeak not made", procName, NULL);
}
for (k = 0; k < nmax; k++) {
numaGetSum(na, &newtotal);
if (newtotal == 0.0) /* sanity check */
break;
numaGetMax(na, &fmaxval, &maxloc);
sum = fmaxval;
lastval = fmaxval;
lloc = 0;
for (i = maxloc - 1; i >= 0; --i) {
numaGetFValue(na, i, &val);
if (val == 0.0) {
lloc = i + 1;
break;
}
if (val > fract1 * fmaxval) {
sum += val;
lastval = val;
continue;
}
if (lastval - val > fract2 * lastval) {
sum += val;
lastval = val;
continue;
}
lloc = i;
break;
}
lastval = fmaxval;
rloc = n - 1;
for (i = maxloc + 1; i < n; ++i) {
numaGetFValue(na, i, &val);
if (val == 0.0) {
rloc = i - 1;
break;
}
if (val > fract1 * fmaxval) {
sum += val;
lastval = val;
continue;
}
if (lastval - val > fract2 * lastval) {
sum += val;
lastval = val;
continue;
}
rloc = i;
break;
}
peakfract = sum / total;
numaAddNumber(napeak, lloc);
numaAddNumber(napeak, maxloc);
numaAddNumber(napeak, rloc);
numaAddNumber(napeak, peakfract);
for (i = lloc; i <= rloc; i++)
numaSetValue(na, i, 0.0);
}
numaDestroy(&na);
return napeak;
}
/*!
* \brief numaFindExtrema()
*
* \param[in] nas input values
* \param[in] delta relative amount to resolve peaks and valleys
* \param[out] pnav [optional] values of extrema
* \return nad (locations of extrema, or NULL on error
*
* <pre>
* Notes:
* (1) This returns a sequence of extrema (peaks and valleys).
* (2) The algorithm is analogous to that for determining
* mountain peaks. Suppose we have a local peak, with
* bumps on the side. Under what conditions can we consider
* those 'bumps' to be actual peaks? The answer: if the
* bump is separated from the peak by a saddle that is at
* least 500 feet below the bump.
* (3) Operationally, suppose we are looking for a peak.
* We are keeping the largest value we've seen since the
* last valley, and are looking for a value that is delta
* BELOW our current peak. When we find such a value,
* we label the peak, use the current value to label the
* valley, and then do the same operation in reverse (looking
* for a valley).
* </pre>
*/
NUMA *
numaFindExtrema(NUMA *nas,
l_float32 delta,
NUMA **pnav)
{
l_int32 i, n, found, loc, direction;
l_float32 startval, val, maxval, minval;
NUMA *nav, *nad;
PROCNAME("numaFindExtrema");
if (pnav) *pnav = NULL;
if (!nas)
return (NUMA *)ERROR_PTR("nas not defined", procName, NULL);
if (delta < 0.0)
return (NUMA *)ERROR_PTR("delta < 0", procName, NULL);
n = numaGetCount(nas);
nad = numaCreate(0);
nav = NULL;
if (pnav) {
nav = numaCreate(0);
*pnav = nav;
}
/* We don't know if we'll find a peak or valley first,
* but use the first element of nas as the reference point.
* Break when we deviate by 'delta' from the first point. */
numaGetFValue(nas, 0, &startval);
found = FALSE;
for (i = 1; i < n; i++) {
numaGetFValue(nas, i, &val);
if (L_ABS(val - startval) >= delta) {
found = TRUE;
break;
}
}
if (!found)
return nad; /* it's empty */
/* Are we looking for a peak or a valley? */
if (val > startval) { /* peak */
direction = 1;
maxval = val;
} else {
direction = -1;
minval = val;
}
loc = i;
/* Sweep through the rest of the array, recording alternating
* peak/valley extrema. */
for (i = i + 1; i < n; i++) {
numaGetFValue(nas, i, &val);
if (direction == 1 && val > maxval ) { /* new local max */
maxval = val;
loc = i;
} else if (direction == -1 && val < minval ) { /* new local min */
minval = val;
loc = i;
} else if (direction == 1 && (maxval - val >= delta)) {
numaAddNumber(nad, loc); /* save the current max location */
if (nav) numaAddNumber(nav, maxval);
direction = -1; /* reverse: start looking for a min */
minval = val;
loc = i; /* current min location */
} else if (direction == -1 && (val - minval >= delta)) {
numaAddNumber(nad, loc); /* save the current min location */
if (nav) numaAddNumber(nav, minval);
direction = 1; /* reverse: start looking for a max */
maxval = val;
loc = i; /* current max location */
}
}
/* Save the final extremum */
/* numaAddNumber(nad, loc); */
return nad;
}
/*!
* \brief numaCountReversals()
*
* \param[in] nas input values
* \param[in] minreversal relative amount to resolve peaks and valleys
* \param[out] pnr [optional] number of reversals
* \param[out] prd [optional] reversal density: reversals/length
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) The input numa is can be generated from pixExtractAlongLine().
* If so, the x parameters can be used to find the reversal
* frequency along a line.
* (2) If the input numa was generated from a 1 bpp pix, the
* values will be 0 and 1. Use %minreversal == 1 to get
* the number of pixel flips. If the only values are 0 and 1,
* but %minreversal > 1, set the reversal count to 0 and
* issue a warning.
* </pre>
*/
l_ok
numaCountReversals(NUMA *nas,
l_float32 minreversal,
l_int32 *pnr,
l_float32 *prd)
{
l_int32 i, n, nr, ival, binvals;
l_int32 *ia;
l_float32 fval, delx, len;
NUMA *nat;
PROCNAME("numaCountReversals");
if (pnr) *pnr = 0;
if (prd) *prd = 0.0;
if (!pnr && !prd)
return ERROR_INT("neither &nr nor &rd are defined", procName, 1);
if (!nas)
return ERROR_INT("nas not defined", procName, 1);
if ((n = numaGetCount(nas)) == 0) {
L_INFO("nas is empty\n", procName);
return 0;
}
if (minreversal < 0.0)
return ERROR_INT("minreversal < 0", procName, 1);
/* Decide if the only values are 0 and 1 */
binvals = TRUE;
for (i = 0; i < n; i++) {
numaGetFValue(nas, i, &fval);
if (fval != 0.0 && fval != 1.0) {
binvals = FALSE;
break;
}
}
nr = 0;
if (binvals) {
if (minreversal > 1.0) {
L_WARNING("binary values but minreversal > 1\n", procName);
} else {
ia = numaGetIArray(nas);
ival = ia[0];
for (i = 1; i < n; i++) {
if (ia[i] != ival) {
nr++;
ival = ia[i];
}
}
LEPT_FREE(ia);
}
} else {
nat = numaFindExtrema(nas, minreversal, NULL);
nr = numaGetCount(nat);
numaDestroy(&nat);
}
if (pnr) *pnr = nr;
if (prd) {
numaGetParameters(nas, NULL, &delx);
len = delx * n;
*prd = (l_float32)nr / len;
}
return 0;
}
/*----------------------------------------------------------------------*
* Threshold crossings and frequency analysis *
*----------------------------------------------------------------------*/
/*!
* \brief numaSelectCrossingThreshold()
*
* \param[in] nax [optional] numa of abscissa values; can be NULL
* \param[in] nay signal
* \param[in] estthresh estimated pixel threshold for crossing:
* e.g., for images, white <--> black; typ. ~120
* \param[out] pbestthresh robust estimate of threshold to use
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) When a valid threshold is used, the number of crossings is
* a maximum, because none are missed. If no threshold intersects
* all the crossings, the crossings must be determined with
* numaCrossingsByPeaks().
* (2) %estthresh is an input estimate of the threshold that should
* be used. We compute the crossings with 41 thresholds
* (20 below and 20 above). There is a range in which the
* number of crossings is a maximum. Return a threshold
* in the center of this stable plateau of crossings.
* This can then be used with numaCrossingsByThreshold()
* to get a good estimate of crossing locations.
* </pre>
*/
l_ok
numaSelectCrossingThreshold(NUMA *nax,
NUMA *nay,
l_float32 estthresh,
l_float32 *pbestthresh)
{
l_int32 i, inrun, istart, iend, maxstart, maxend, runlen, maxrunlen;
l_int32 val, maxval, nmax, count;
l_float32 thresh, fmaxval, fmodeval;
NUMA *nat, *nac;
PROCNAME("numaSelectCrossingThreshold");
if (!pbestthresh)
return ERROR_INT("&bestthresh not defined", procName, 1);
*pbestthresh = 0.0;
if (!nay)
return ERROR_INT("nay not defined", procName, 1);
/* Compute the number of crossings for different thresholds */
nat = numaCreate(41);
for (i = 0; i < 41; i++) {
thresh = estthresh - 80.0 + 4.0 * i;
nac = numaCrossingsByThreshold(nax, nay, thresh);
numaAddNumber(nat, numaGetCount(nac));
numaDestroy(&nac);
}
/* Find the center of the plateau of max crossings, which
* extends from thresh[istart] to thresh[iend]. */
numaGetMax(nat, &fmaxval, NULL);
maxval = (l_int32)fmaxval;
nmax = 0;
for (i = 0; i < 41; i++) {
numaGetIValue(nat, i, &val);
if (val == maxval)
nmax++;
}
if (nmax < 3) { /* likely accidental max; try the mode */
numaGetMode(nat, &fmodeval, &count);
if (count > nmax && fmodeval > 0.5 * fmaxval)
maxval = (l_int32)fmodeval; /* use the mode */
}
inrun = FALSE;
iend = 40;
maxrunlen = 0, maxstart = 0, maxend = 0;
for (i = 0; i < 41; i++) {
numaGetIValue(nat, i, &val);
if (val == maxval) {
if (!inrun) {
istart = i;
inrun = TRUE;
}
continue;
}
if (inrun && (val != maxval)) {
iend = i - 1;
runlen = iend - istart + 1;
inrun = FALSE;
if (runlen > maxrunlen) {
maxstart = istart;
maxend = iend;
maxrunlen = runlen;
}
}
}
if (inrun) {
runlen = i - istart;
if (runlen > maxrunlen) {
maxstart = istart;
maxend = i - 1;
maxrunlen = runlen;
}
}
*pbestthresh = estthresh - 80.0 + 2.0 * (l_float32)(maxstart + maxend);
#if DEBUG_CROSSINGS
fprintf(stderr, "\nCrossings attain a maximum at %d thresholds, between:\n"
" thresh[%d] = %5.1f and thresh[%d] = %5.1f\n",
nmax, maxstart, estthresh - 80.0 + 4.0 * maxstart,
maxend, estthresh - 80.0 + 4.0 * maxend);
fprintf(stderr, "The best choice: %5.1f\n", *pbestthresh);
fprintf(stderr, "Number of crossings at the 41 thresholds:");
numaWriteStream(stderr, nat);
#endif /* DEBUG_CROSSINGS */
numaDestroy(&nat);
return 0;
}
/*!
* \brief numaCrossingsByThreshold()
*
* \param[in] nax [optional] numa of abscissa values; can be NULL
* \param[in] nay numa of ordinate values, corresponding to nax
* \param[in] thresh threshold value for nay
* \return nad abscissa pts at threshold, or NULL on error
*
* <pre>
* Notes:
* (1) If nax == NULL, we use startx and delx from nay to compute
* the crossing values in nad.
* </pre>
*/
NUMA *
numaCrossingsByThreshold(NUMA *nax,
NUMA *nay,
l_float32 thresh)
{
l_int32 i, n;
l_float32 startx, delx;
l_float32 xval1, xval2, yval1, yval2, delta1, delta2, crossval, fract;
NUMA *nad;
PROCNAME("numaCrossingsByThreshold");
if (!nay)
return (NUMA *)ERROR_PTR("nay not defined", procName, NULL);
n = numaGetCount(nay);
if (nax && (numaGetCount(nax) != n))
return (NUMA *)ERROR_PTR("nax and nay sizes differ", procName, NULL);
nad = numaCreate(0);
numaGetFValue(nay, 0, &yval1);
numaGetParameters(nay, &startx, &delx);
if (nax)
numaGetFValue(nax, 0, &xval1);
else
xval1 = startx;
for (i = 1; i < n; i++) {
numaGetFValue(nay, i, &yval2);
if (nax)
numaGetFValue(nax, i, &xval2);
else
xval2 = startx + i * delx;
delta1 = yval1 - thresh;
delta2 = yval2 - thresh;
if (delta1 == 0.0) {
numaAddNumber(nad, xval1);
} else if (delta2 == 0.0) {
numaAddNumber(nad, xval2);
} else if (delta1 * delta2 < 0.0) { /* crossing */
fract = L_ABS(delta1) / L_ABS(yval1 - yval2);
crossval = xval1 + fract * (xval2 - xval1);
numaAddNumber(nad, crossval);
}
xval1 = xval2;
yval1 = yval2;
}
return nad;
}
/*!
* \brief numaCrossingsByPeaks()
*
* \param[in] nax [optional] numa of abscissa values
* \param[in] nay numa of ordinate values, corresponding to nax
* \param[in] delta parameter used to identify when a new peak can be found
* \return nad abscissa pts at threshold, or NULL on error
*
* <pre>
* Notes:
* (1) If nax == NULL, we use startx and delx from nay to compute
* the crossing values in nad.
* </pre>
*/
NUMA *
numaCrossingsByPeaks(NUMA *nax,
NUMA *nay,
l_float32 delta)
{
l_int32 i, j, n, np, previndex, curindex;
l_float32 startx, delx;
l_float32 xval1, xval2, yval1, yval2, delta1, delta2;
l_float32 prevval, curval, thresh, crossval, fract;
NUMA *nap, *nad;
PROCNAME("numaCrossingsByPeaks");
if (!nay)
return (NUMA *)ERROR_PTR("nay not defined", procName, NULL);
n = numaGetCount(nay);
if (nax && (numaGetCount(nax) != n))
return (NUMA *)ERROR_PTR("nax and nay sizes differ", procName, NULL);
/* Find the extrema. Also add last point in nay to get
* the last transition (from the last peak to the end).
* The number of crossings is 1 more than the number of extrema. */
nap = numaFindExtrema(nay, delta, NULL);
numaAddNumber(nap, n - 1);
np = numaGetCount(nap);
L_INFO("Number of crossings: %d\n", procName, np);
/* Do all computation in index units of nax or the delx of nay */
nad = numaCreate(np); /* output crossing locations, in nax units */
previndex = 0; /* prime the search with 1st point */
numaGetFValue(nay, 0, &prevval); /* prime the search with 1st point */
numaGetParameters(nay, &startx, &delx);
for (i = 0; i < np; i++) {
numaGetIValue(nap, i, &curindex);
numaGetFValue(nay, curindex, &curval);
thresh = (prevval + curval) / 2.0;
if (nax)
numaGetFValue(nax, previndex, &xval1);
else
xval1 = startx + previndex * delx;
numaGetFValue(nay, previndex, &yval1);
for (j = previndex + 1; j <= curindex; j++) {
if (nax)
numaGetFValue(nax, j, &xval2);
else
xval2 = startx + j * delx;
numaGetFValue(nay, j, &yval2);
delta1 = yval1 - thresh;
delta2 = yval2 - thresh;
if (delta1 == 0.0) {
numaAddNumber(nad, xval1);
break;
} else if (delta2 == 0.0) {
numaAddNumber(nad, xval2);
break;
} else if (delta1 * delta2 < 0.0) { /* crossing */
fract = L_ABS(delta1) / L_ABS(yval1 - yval2);
crossval = xval1 + fract * (xval2 - xval1);
numaAddNumber(nad, crossval);
break;
}
xval1 = xval2;
yval1 = yval2;
}
previndex = curindex;
prevval = curval;
}
numaDestroy(&nap);
return nad;
}
/*!
* \brief numaEvalBestHaarParameters()
*
* \param[in] nas numa of non-negative signal values
* \param[in] relweight relative weight of (-1 comb) / (+1 comb)
* contributions to the 'convolution'. In effect,
* the convolution kernel is a comb consisting of
* alternating +1 and -weight.
* \param[in] nwidth number of widths to consider
* \param[in] nshift number of shifts to consider for each width
* \param[in] minwidth smallest width to consider
* \param[in] maxwidth largest width to consider
* \param[out] pbestwidth width giving largest score
* \param[out] pbestshift shift giving largest score
* \param[out] pbestscore [optional] convolution with "Haar"-like comb
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) This does a linear sweep of widths, evaluating at %nshift
* shifts for each width, computing the score from a convolution
* with a long comb, and finding the (width, shift) pair that
* gives the maximum score. The best width is the "half-wavelength"
* of the signal.
* (2) The convolving function is a comb of alternating values
* +1 and -1 * relweight, separated by the width and phased by
* the shift. This is similar to a Haar transform, except
* there the convolution is performed with a square wave.
* (3) The function is useful for finding the line spacing
* and strength of line signal from pixel sum projections.
* (4) The score is normalized to the size of nas divided by
* the number of half-widths. For image applications, the input is
* typically an array of pixel projections, so one should
* normalize by dividing the score by the image width in the
* pixel projection direction.
* </pre>
*/
l_ok
numaEvalBestHaarParameters(NUMA *nas,
l_float32 relweight,
l_int32 nwidth,
l_int32 nshift,
l_float32 minwidth,
l_float32 maxwidth,
l_float32 *pbestwidth,
l_float32 *pbestshift,
l_float32 *pbestscore)
{
l_int32 i, j;
l_float32 delwidth, delshift, width, shift, score;
l_float32 bestwidth, bestshift, bestscore;
PROCNAME("numaEvalBestHaarParameters");
if (pbestscore) *pbestscore = 0.0;
if (pbestwidth) *pbestwidth = 0.0;
if (pbestshift) *pbestshift = 0.0;
if (!pbestwidth || !pbestshift)
return ERROR_INT("&bestwidth and &bestshift not defined", procName, 1);
if (!nas)
return ERROR_INT("nas not defined", procName, 1);
bestscore = bestwidth = bestshift = 0.0;
delwidth = (maxwidth - minwidth) / (nwidth - 1.0);
for (i = 0; i < nwidth; i++) {
width = minwidth + delwidth * i;
delshift = width / (l_float32)(nshift);
for (j = 0; j < nshift; j++) {
shift = j * delshift;
numaEvalHaarSum(nas, width, shift, relweight, &score);
if (score > bestscore) {
bestscore = score;
bestwidth = width;
bestshift = shift;
#if DEBUG_FREQUENCY
fprintf(stderr, "width = %7.3f, shift = %7.3f, score = %7.3f\n",
width, shift, score);
#endif /* DEBUG_FREQUENCY */
}
}
}
*pbestwidth = bestwidth;
*pbestshift = bestshift;
if (pbestscore)
*pbestscore = bestscore;
return 0;
}
/*!
* \brief numaEvalHaarSum()
*
* \param[in] nas numa of non-negative signal values
* \param[in] width distance between +1 and -1 in convolution comb
* \param[in] shift phase of the comb: location of first +1
* \param[in] relweight relative weight of (-1 comb) / (+1 comb)
* contributions to the 'convolution'. In effect,
* the convolution kernel is a comb consisting of
* alternating +1 and -weight.
* \param[out] pscore convolution with "Haar"-like comb
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) This does a convolution with a comb of alternating values
* +1 and -relweight, separated by the width and phased by the shift.
* This is similar to a Haar transform, except that for Haar,
* (1) the convolution kernel is symmetric about 0, so the
* relweight is 1.0, and
* (2) the convolution is performed with a square wave.
* (2) The score is normalized to the size of nas divided by
* twice the "width". For image applications, the input is
* typically an array of pixel projections, so one should
* normalize by dividing the score by the image width in the
* pixel projection direction.
* (3) To get a Haar-like result, use relweight = 1.0. For detecting
* signals where you expect every other sample to be close to
* zero, as with barcodes or filtered text lines, you can
* use relweight > 1.0.
* </pre>
*/
l_ok
numaEvalHaarSum(NUMA *nas,
l_float32 width,
l_float32 shift,
l_float32 relweight,
l_float32 *pscore)
{
l_int32 i, n, nsamp, index;
l_float32 score, weight, val;
PROCNAME("numaEvalHaarSum");
if (!pscore)
return ERROR_INT("&score not defined", procName, 1);
*pscore = 0.0;
if (!nas)
return ERROR_INT("nas not defined", procName, 1);
if ((n = numaGetCount(nas)) < 2 * width)
return ERROR_INT("nas size too small", procName, 1);
score = 0.0;
nsamp = (l_int32)((n - shift) / width);
for (i = 0; i < nsamp; i++) {
index = (l_int32)(shift + i * width);
weight = (i % 2) ? 1.0 : -1.0 * relweight;
numaGetFValue(nas, index, &val);
score += weight * val;
}
*pscore = 2.0 * width * score / (l_float32)n;
return 0;
}
/*----------------------------------------------------------------------*
* Generating numbers in a range under constraints *
*----------------------------------------------------------------------*/
/*!
* \brief genConstrainedNumaInRange()
*
* \param[in] first first number to choose; >= 0
* \param[in] last biggest possible number to reach; >= first
* \param[in] nmax maximum number of numbers to select; > 0
* \param[in] use_pairs 1 = select pairs of adjacent numbers;
* 0 = select individual numbers
* \return 0 if OK, 1 on error
*
* <pre>
* Notes:
* (1) Selection is made uniformly in the range. This can be used
* to select pages distributed as uniformly as possible
* through a book, where you are constrained to:
* ~ choose between [first, ... biggest],
* ~ choose no more than nmax numbers, and
* and you have the option of requiring pairs of adjacent numbers.
* </pre>
*/
NUMA *
genConstrainedNumaInRange(l_int32 first,
l_int32 last,
l_int32 nmax,
l_int32 use_pairs)
{
l_int32 i, nsets, val;
l_float32 delta;
NUMA *na;
PROCNAME("genConstrainedNumaInRange");
first = L_MAX(0, first);
if (last < first)
return (NUMA *)ERROR_PTR("last < first!", procName, NULL);
if (nmax < 1)
return (NUMA *)ERROR_PTR("nmax < 1!", procName, NULL);
nsets = L_MIN(nmax, last - first + 1);
if (use_pairs == 1)
nsets = nsets / 2;
if (nsets == 0)
return (NUMA *)ERROR_PTR("nsets == 0", procName, NULL);
/* Select delta so that selection covers the full range if possible */
if (nsets == 1) {
delta = 0.0;
} else {
if (use_pairs == 0)
delta = (l_float32)(last - first) / (nsets - 1);
else
delta = (l_float32)(last - first - 1) / (nsets - 1);
}
na = numaCreate(nsets);
for (i = 0; i < nsets; i++) {
val = (l_int32)(first + i * delta + 0.5);
numaAddNumber(na, val);
if (use_pairs == 1)
numaAddNumber(na, val + 1);
}
return na;
}
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