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diff --git a/leptonica/src/baseline.c b/leptonica/src/baseline.c
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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 baseline.c
+ * <pre>
+ *
+ * Locate text baselines in an image
+ * NUMA *pixFindBaselines()
+ *
+ * Projective transform to remove local skew
+ * PIX *pixDeskewLocal()
+ *
+ * Determine local skew
+ * l_int32 pixGetLocalSkewTransform()
+ * NUMA *pixGetLocalSkewAngles()
+ *
+ * We have two apparently different functions here:
+ * ~ finding baselines
+ * ~ finding a projective transform to remove keystone warping
+ * The function pixGetLocalSkewAngles() returns an array of angles,
+ * one for each raster line, and the baselines of the text lines
+ * should intersect the left edge of the image with that angle.
+ * </pre>
+ */
+
+#ifdef HAVE_CONFIG_H
+#include <config_auto.h>
+#endif /* HAVE_CONFIG_H */
+
+#include <math.h>
+#include "allheaders.h"
+
+ /* Min to travel after finding max before abandoning peak */
+static const l_int32 MinDistInPeak = 35;
+
+ /* Thresholds for peaks and zeros, relative to the max peak */
+static const l_int32 PeakThresholdRatio = 20;
+static const l_int32 ZeroThresholdRatio = 100;
+
+ /* Default values for determining local skew */
+static const l_int32 DefaultSlices = 10;
+static const l_int32 DefaultSweepReduction = 2;
+static const l_int32 DefaultBsReduction = 1;
+static const l_float32 DefaultSweepRange = 5.; /* degrees */
+static const l_float32 DefaultSweepDelta = 1.; /* degrees */
+static const l_float32 DefaultMinbsDelta = 0.01f; /* degrees */
+
+ /* Overlap slice fraction added to top and bottom of each slice */
+static const l_float32 OverlapFraction = 0.5;
+
+ /* Minimum allowed confidence (ratio) for accepting a value */
+static const l_float32 MinAllowedConfidence = 3.0;
+
+
+/*---------------------------------------------------------------------*
+ * Locate text baselines in an image *
+ *---------------------------------------------------------------------*/
+/*!
+ * \brief pixFindBaselines()
+ *
+ * \param[in] pixs 1 bpp, 300 ppi
+ * \param[out] ppta [optional] pairs of pts corresponding to
+ * approx. ends of each text line
+ * \param[in] pixadb for debug output; use NULL to skip
+ * \return na of baseline y values, or NULL on error
+ *
+ * <pre>
+ * Notes:
+ * (1) Input binary image must have text lines already aligned
+ * horizontally. This can be done by either rotating the
+ * image with pixDeskew(), or, if a projective transform
+ * is required, by doing pixDeskewLocal() first.
+ * (2) Input null for &pta if you don't want this returned.
+ * The pta will come in pairs of points (left and right end
+ * of each baseline).
+ * (3) Caution: this will not work properly on text with multiple
+ * columns, where the lines are not aligned between columns.
+ * If there are multiple columns, they should be extracted
+ * separately before finding the baselines.
+ * (4) This function constructs different types of output
+ * for baselines; namely, a set of raster line values and
+ * a set of end points of each baseline.
+ * (5) This function was designed to handle short and long text lines
+ * without using dangerous thresholds on the peak heights. It does
+ * this by combining the differential signal with a morphological
+ * analysis of the locations of the text lines. One can also
+ * combine this data to normalize the peak heights, by weighting
+ * the differential signal in the region of each baseline
+ * by the inverse of the width of the text line found there.
+ * </pre>
+ */
+NUMA *
+pixFindBaselines(PIX *pixs,
+ PTA **ppta,
+ PIXA *pixadb)
+{
+l_int32 h, i, j, nbox, val1, val2, ndiff, bx, by, bw, bh;
+l_int32 imaxloc, peakthresh, zerothresh, inpeak;
+l_int32 mintosearch, max, maxloc, nloc, locval;
+l_int32 *array;
+l_float32 maxval;
+BOXA *boxa1, *boxa2, *boxa3;
+GPLOT *gplot;
+NUMA *nasum, *nadiff, *naloc, *naval;
+PIX *pix1, *pix2;
+PTA *pta;
+
+ PROCNAME("pixFindBaselines");
+
+ if (ppta) *ppta = NULL;
+ if (!pixs || pixGetDepth(pixs) != 1)
+ return (NUMA *)ERROR_PTR("pixs undefined or not 1 bpp", procName, NULL);
+
+ /* Close up the text characters, removing noise */
+ pix1 = pixMorphSequence(pixs, "c25.1 + e15.1", 0);
+
+ /* Estimate the resolution */
+ if (pixadb) pixaAddPix(pixadb, pixScale(pix1, 0.25, 0.25), L_INSERT);
+
+ /* Save the difference of adjacent row sums.
+ * The high positive-going peaks are the baselines */
+ if ((nasum = pixCountPixelsByRow(pix1, NULL)) == NULL) {
+ pixDestroy(&pix1);
+ return (NUMA *)ERROR_PTR("nasum not made", procName, NULL);
+ }
+ h = pixGetHeight(pixs);
+ nadiff = numaCreate(h);
+ numaGetIValue(nasum, 0, &val2);
+ for (i = 0; i < h - 1; i++) {
+ val1 = val2;
+ numaGetIValue(nasum, i + 1, &val2);
+ numaAddNumber(nadiff, val1 - val2);
+ }
+ numaDestroy(&nasum);
+
+ if (pixadb) { /* show the difference signal */
+ lept_mkdir("lept/baseline");
+ gplotSimple1(nadiff, GPLOT_PNG, "/tmp/lept/baseline/diff", "Diff Sig");
+ pix2 = pixRead("/tmp/lept/baseline/diff.png");
+ pixaAddPix(pixadb, pix2, L_INSERT);
+ }
+
+ /* Use the zeroes of the profile to locate each baseline. */
+ array = numaGetIArray(nadiff);
+ ndiff = numaGetCount(nadiff);
+ numaGetMax(nadiff, &maxval, &imaxloc);
+ numaDestroy(&nadiff);
+
+ /* Use this to begin locating a new peak: */
+ peakthresh = (l_int32)maxval / PeakThresholdRatio;
+ /* Use this to begin a region between peaks: */
+ zerothresh = (l_int32)maxval / ZeroThresholdRatio;
+
+ naloc = numaCreate(0);
+ naval = numaCreate(0);
+ inpeak = FALSE;
+ for (i = 0; i < ndiff; i++) {
+ if (inpeak == FALSE) {
+ if (array[i] > peakthresh) { /* transition to in-peak */
+ inpeak = TRUE;
+ mintosearch = i + MinDistInPeak; /* accept no zeros
+ * between i and mintosearch */
+ max = array[i];
+ maxloc = i;
+ }
+ } else { /* inpeak == TRUE; look for max */
+ if (array[i] > max) {
+ max = array[i];
+ maxloc = i;
+ mintosearch = i + MinDistInPeak;
+ } else if (i > mintosearch && array[i] <= zerothresh) { /* leave */
+ inpeak = FALSE;
+ numaAddNumber(naval, max);
+ numaAddNumber(naloc, maxloc);
+ }
+ }
+ }
+ LEPT_FREE(array);
+
+ /* If array[ndiff-1] is max, eg. no descenders, baseline at bottom */
+ if (inpeak) {
+ numaAddNumber(naval, max);
+ numaAddNumber(naloc, maxloc);
+ }
+
+ if (pixadb) { /* show the raster locations for the peaks */
+ gplot = gplotCreate("/tmp/lept/baseline/loc", GPLOT_PNG, "Peak locs",
+ "rasterline", "height");
+ gplotAddPlot(gplot, naloc, naval, GPLOT_POINTS, "locs");
+ gplotMakeOutput(gplot);
+ gplotDestroy(&gplot);
+ pix2 = pixRead("/tmp/lept/baseline/loc.png");
+ pixaAddPix(pixadb, pix2, L_INSERT);
+ }
+ numaDestroy(&naval);
+
+ /* Generate an approximate profile of text line width.
+ * First, filter the boxes of text, where there may be
+ * more than one box for a given textline. */
+ pix2 = pixMorphSequence(pix1, "r11 + c20.1 + o30.1 +c1.3", 0);
+ if (pixadb) pixaAddPix(pixadb, pix2, L_COPY);
+ boxa1 = pixConnComp(pix2, NULL, 4);
+ pixDestroy(&pix1);
+ pixDestroy(&pix2);
+ if (boxaGetCount(boxa1) == 0) {
+ numaDestroy(&naloc);
+ boxaDestroy(&boxa1);
+ L_INFO("no compnents after filtering\n", procName);
+ return NULL;
+ }
+ boxa2 = boxaTransform(boxa1, 0, 0, 4., 4.);
+ boxa3 = boxaSort(boxa2, L_SORT_BY_Y, L_SORT_INCREASING, NULL);
+ boxaDestroy(&boxa1);
+ boxaDestroy(&boxa2);
+
+ /* Optionally, find the baseline segments */
+ pta = NULL;
+ if (ppta) {
+ pta = ptaCreate(0);
+ *ppta = pta;
+ }
+ if (pta) {
+ nloc = numaGetCount(naloc);
+ nbox = boxaGetCount(boxa3);
+ for (i = 0; i < nbox; i++) {
+ boxaGetBoxGeometry(boxa3, i, &bx, &by, &bw, &bh);
+ for (j = 0; j < nloc; j++) {
+ numaGetIValue(naloc, j, &locval);
+ if (L_ABS(locval - (by + bh)) > 25)
+ continue;
+ ptaAddPt(pta, bx, locval);
+ ptaAddPt(pta, bx + bw, locval);
+ break;
+ }
+ }
+ }
+ boxaDestroy(&boxa3);
+
+ if (pixadb && pta) { /* display baselines */
+ l_int32 npts, x1, y1, x2, y2;
+ pix1 = pixConvertTo32(pixs);
+ npts = ptaGetCount(pta);
+ for (i = 0; i < npts; i += 2) {
+ ptaGetIPt(pta, i, &x1, &y1);
+ ptaGetIPt(pta, i + 1, &x2, &y2);
+ pixRenderLineArb(pix1, x1, y1, x2, y2, 2, 255, 0, 0);
+ }
+ pixWriteDebug("/tmp/lept/baseline/baselines.png", pix1, IFF_PNG);
+ pixaAddPix(pixadb, pixScale(pix1, 0.25, 0.25), L_INSERT);
+ pixDestroy(&pix1);
+ }
+
+ return naloc;
+}
+
+
+/*---------------------------------------------------------------------*
+ * Projective transform to remove local skew *
+ *---------------------------------------------------------------------*/
+/*!
+ * \brief pixDeskewLocal()
+ *
+ * \param[in] pixs 1 bpp
+ * \param[in] nslices the number of horizontal overlapping slices;
+ * must be larger than 1 and not exceed 20;
+ * use 0 for default
+ * \param[in] redsweep sweep reduction factor: 1, 2, 4 or 8;
+ * use 0 for default value
+ * \param[in] redsearch search reduction factor: 1, 2, 4 or 8, and
+ * not larger than redsweep; use 0 for default value
+ * \param[in] sweeprange half the full range, assumed about 0; in degrees;
+ * use 0.0 for default value
+ * \param[in] sweepdelta angle increment of sweep; in degrees;
+ * use 0.0 for default value
+ * \param[in] minbsdelta min binary search increment angle; in degrees;
+ * use 0.0 for default value
+ * \return pixd, or NULL on error
+ *
+ * <pre>
+ * Notes:
+ * (1) This function allows deskew of a page whose skew changes
+ * approximately linearly with vertical position. It uses
+ * a projective transform that in effect does a differential
+ * shear about the LHS of the page, and makes all text lines
+ * horizontal.
+ * (2) The origin of the keystoning can be either a cheap document
+ * feeder that rotates the page as it is passed through, or a
+ * camera image taken from either the left or right side
+ * of the vertical.
+ * (3) The image transformation is a projective warping,
+ * not a rotation. Apart from this function, the text lines
+ * must be properly aligned vertically with respect to each
+ * other. This can be done by pre-processing the page; e.g.,
+ * by rotating or horizontally shearing it.
+ * Typically, this can be achieved by vertically aligning
+ * the page edge.
+ * </pre>
+ */
+PIX *
+pixDeskewLocal(PIX *pixs,
+ l_int32 nslices,
+ l_int32 redsweep,
+ l_int32 redsearch,
+ l_float32 sweeprange,
+ l_float32 sweepdelta,
+ l_float32 minbsdelta)
+{
+l_int32 ret;
+PIX *pixd;
+PTA *ptas, *ptad;
+
+ PROCNAME("pixDeskewLocal");
+
+ if (!pixs || pixGetDepth(pixs) != 1)
+ return (PIX *)ERROR_PTR("pixs undefined or not 1 bpp", procName, NULL);
+
+ /* Skew array gives skew angle (deg) as fctn of raster line
+ * where it intersects the LHS of the image */
+ ret = pixGetLocalSkewTransform(pixs, nslices, redsweep, redsearch,
+ sweeprange, sweepdelta, minbsdelta,
+ &ptas, &ptad);
+ if (ret != 0)
+ return (PIX *)ERROR_PTR("transform pts not found", procName, NULL);
+
+ /* Use a projective transform */
+ pixd = pixProjectiveSampledPta(pixs, ptad, ptas, L_BRING_IN_WHITE);
+
+ ptaDestroy(&ptas);
+ ptaDestroy(&ptad);
+ return pixd;
+}
+
+
+/*---------------------------------------------------------------------*
+ * Determine the local skew *
+ *---------------------------------------------------------------------*/
+/*!
+ * \brief pixGetLocalSkewTransform()
+ *
+ * \param[in] pixs
+ * \param[in] nslices the number of horizontal overlapping slices;
+ * must be larger than 1 and not exceed 20;
+ * use 0 for default
+ * \param[in] redsweep sweep reduction factor: 1, 2, 4 or 8;
+ * use 0 for default value
+ * \param[in] redsearch search reduction factor: 1, 2, 4 or 8, and not
+ * larger than redsweep; use 0 for default value
+ * \param[in] sweeprange half the full range, assumed about 0;
+ * in degrees; use 0.0 for default value
+ * \param[in] sweepdelta angle increment of sweep; in degrees;
+ * use 0.0 for default value
+ * \param[in] minbsdelta min binary search increment angle; in degrees;
+ * use 0.0 for default value
+ * \param[out] pptas 4 points in the source
+ * \param[out] pptad the corresponding 4 pts in the dest
+ * \return 0 if OK, 1 on error
+ *
+ * <pre>
+ * Notes:
+ * (1) This generates two pairs of points in the src, each pair
+ * corresponding to a pair of points that would lie along
+ * the same raster line in a transformed (dewarped) image.
+ * (2) The sets of 4 src and 4 dest points returned by this function
+ * can then be used, in a projective or bilinear transform,
+ * to remove keystoning in the src.
+ * </pre>
+ */
+l_ok
+pixGetLocalSkewTransform(PIX *pixs,
+ l_int32 nslices,
+ l_int32 redsweep,
+ l_int32 redsearch,
+ l_float32 sweeprange,
+ l_float32 sweepdelta,
+ l_float32 minbsdelta,
+ PTA **pptas,
+ PTA **pptad)
+{
+l_int32 w, h, i;
+l_float32 deg2rad, angr, angd, dely;
+NUMA *naskew;
+PTA *ptas, *ptad;
+
+ PROCNAME("pixGetLocalSkewTransform");
+
+ if (!pptas || !pptad)
+ return ERROR_INT("&ptas and &ptad not defined", procName, 1);
+ *pptas = *pptad = NULL;
+ if (!pixs || pixGetDepth(pixs) != 1)
+ return ERROR_INT("pixs not defined or not 1 bpp", procName, 1);
+ if (nslices < 2 || nslices > 20)
+ nslices = DefaultSlices;
+ if (redsweep < 1 || redsweep > 8)
+ redsweep = DefaultSweepReduction;
+ if (redsearch < 1 || redsearch > redsweep)
+ redsearch = DefaultBsReduction;
+ if (sweeprange == 0.0)
+ sweeprange = DefaultSweepRange;
+ if (sweepdelta == 0.0)
+ sweepdelta = DefaultSweepDelta;
+ if (minbsdelta == 0.0)
+ minbsdelta = DefaultMinbsDelta;
+
+ naskew = pixGetLocalSkewAngles(pixs, nslices, redsweep, redsearch,
+ sweeprange, sweepdelta, minbsdelta,
+ NULL, NULL, 0);
+ if (!naskew)
+ return ERROR_INT("naskew not made", procName, 1);
+
+ deg2rad = 3.14159265f / 180.f;
+ w = pixGetWidth(pixs);
+ h = pixGetHeight(pixs);
+ ptas = ptaCreate(4);
+ ptad = ptaCreate(4);
+ *pptas = ptas;
+ *pptad = ptad;
+
+ /* Find i for skew line that intersects LHS at i and RHS at h / 20 */
+ for (i = 0; i < h; i++) {
+ numaGetFValue(naskew, i, &angd);
+ angr = angd * deg2rad;
+ dely = w * tan(angr);
+ if (i - dely > 0.05 * h)
+ break;
+ }
+ ptaAddPt(ptas, 0, i);
+ ptaAddPt(ptas, w - 1, i - dely);
+ ptaAddPt(ptad, 0, i);
+ ptaAddPt(ptad, w - 1, i);
+
+ /* Find i for skew line that intersects LHS at i and RHS at 19h / 20 */
+ for (i = h - 1; i > 0; i--) {
+ numaGetFValue(naskew, i, &angd);
+ angr = angd * deg2rad;
+ dely = w * tan(angr);
+ if (i - dely < 0.95 * h)
+ break;
+ }
+ ptaAddPt(ptas, 0, i);
+ ptaAddPt(ptas, w - 1, i - dely);
+ ptaAddPt(ptad, 0, i);
+ ptaAddPt(ptad, w - 1, i);
+
+ numaDestroy(&naskew);
+ return 0;
+}
+
+
+/*!
+ * \brief pixGetLocalSkewAngles()
+ *
+ * \param[in] pixs 1 bpp
+ * \param[in] nslices the number of horizontal overlapping slices;
+ * must be larger than 1 and not exceed 20;
+ * use 0 for default
+ * \param[in] redsweep sweep reduction factor: 1, 2, 4 or 8;
+ * use 0 for default value
+ * \param[in] redsearch search reduction factor: 1, 2, 4 or 8, and not
+ * larger than redsweep; use 0 for default value
+ * \param[in] sweeprange half the full range, assumed about 0;
+ * in degrees; use 0.0 for default value
+ * \param[in] sweepdelta angle increment of sweep; in degrees;
+ * use 0.0 for default value
+ * \param[in] minbsdelta min binary search increment angle; in degrees;
+ * use 0.0 for default value
+ * \param[out] pa [optional] slope of skew as fctn of y
+ * \param[out] pb [optional] intercept at y = 0 of skew,
+ 8 as a function of y
+ * \param[in] debug 1 for generating plot of skew angle vs. y;
+ * 0 otherwise
+ * \return naskew, or NULL on error
+ *
+ * <pre>
+ * Notes:
+ * (1) The local skew is measured in a set of overlapping strips.
+ * We then do a least square linear fit parameters to get
+ * the slope and intercept parameters a and b in
+ * skew-angle = a * y + b (degrees)
+ * for the local skew as a function of raster line y.
+ * This is then used to make naskew, which can be interpreted
+ * as the computed skew angle (in degrees) at the left edge
+ * of each raster line.
+ * (2) naskew can then be used to find the baselines of text, because
+ * each text line has a baseline that should intersect
+ * the left edge of the image with the angle given by this
+ * array, evaluated at the raster line of intersection.
+ * </pre>
+ */
+NUMA *
+pixGetLocalSkewAngles(PIX *pixs,
+ l_int32 nslices,
+ l_int32 redsweep,
+ l_int32 redsearch,
+ l_float32 sweeprange,
+ l_float32 sweepdelta,
+ l_float32 minbsdelta,
+ l_float32 *pa,
+ l_float32 *pb,
+ l_int32 debug)
+{
+l_int32 w, h, hs, i, ystart, yend, ovlap, npts;
+l_float32 angle, conf, ycenter, a, b;
+BOX *box;
+GPLOT *gplot;
+NUMA *naskew, *nax, *nay;
+PIX *pix;
+PTA *pta;
+
+ PROCNAME("pixGetLocalSkewAngles");
+
+ if (!pixs || pixGetDepth(pixs) != 1)
+ return (NUMA *)ERROR_PTR("pixs undefined or not 1 bpp", procName, NULL);
+ if (nslices < 2 || nslices > 20)
+ nslices = DefaultSlices;
+ if (redsweep < 1 || redsweep > 8)
+ redsweep = DefaultSweepReduction;
+ if (redsearch < 1 || redsearch > redsweep)
+ redsearch = DefaultBsReduction;
+ if (sweeprange == 0.0)
+ sweeprange = DefaultSweepRange;
+ if (sweepdelta == 0.0)
+ sweepdelta = DefaultSweepDelta;
+ if (minbsdelta == 0.0)
+ minbsdelta = DefaultMinbsDelta;
+
+ pixGetDimensions(pixs, &w, &h, NULL);
+ hs = h / nslices;
+ ovlap = (l_int32)(OverlapFraction * hs);
+ pta = ptaCreate(nslices);
+ for (i = 0; i < nslices; i++) {
+ ystart = L_MAX(0, hs * i - ovlap);
+ yend = L_MIN(h - 1, hs * (i + 1) + ovlap);
+ ycenter = (l_float32)(ystart + yend) / 2;
+ box = boxCreate(0, ystart, w, yend - ystart + 1);
+ pix = pixClipRectangle(pixs, box, NULL);
+ pixFindSkewSweepAndSearch(pix, &angle, &conf, redsweep, redsearch,
+ sweeprange, sweepdelta, minbsdelta);
+ if (conf > MinAllowedConfidence)
+ ptaAddPt(pta, ycenter, angle);
+ pixDestroy(&pix);
+ boxDestroy(&box);
+ }
+
+ /* Do linear least squares fit */
+ if ((npts = ptaGetCount(pta)) < 2) {
+ ptaDestroy(&pta);
+ return (NUMA *)ERROR_PTR("can't fit skew", procName, NULL);
+ }
+ ptaGetLinearLSF(pta, &a, &b, NULL);
+ if (pa) *pa = a;
+ if (pb) *pb = b;
+
+ /* Make skew angle array as function of raster line */
+ naskew = numaCreate(h);
+ for (i = 0; i < h; i++) {
+ angle = a * i + b;
+ numaAddNumber(naskew, angle);
+ }
+
+ if (debug) {
+ lept_mkdir("lept/baseline");
+ ptaGetArrays(pta, &nax, &nay);
+ gplot = gplotCreate("/tmp/lept/baseline/skew", GPLOT_PNG,
+ "skew as fctn of y", "y (in raster lines from top)",
+ "angle (in degrees)");
+ gplotAddPlot(gplot, NULL, naskew, GPLOT_POINTS, "linear lsf");
+ gplotAddPlot(gplot, nax, nay, GPLOT_POINTS, "actual data pts");
+ gplotMakeOutput(gplot);
+ gplotDestroy(&gplot);
+ numaDestroy(&nax);
+ numaDestroy(&nay);
+ }
+
+ ptaDestroy(&pta);
+ return naskew;
+}