third-party/leptonica/src/quadtree.c
/*====================================================================*
- 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.
*====================================================================*/
/*
* quadtree.c
*
* Top level quadtree linear statistics
* l_int32 pixQuadtreeMean()
* l_int32 pixQuadtreeVariance()
*
* Statistics in an arbitrary rectangle
* l_int32 pixMeanInRectangle()
* l_int32 pixVarianceInRectangle()
*
* Quadtree regions
* BOXAA *boxaaQuadtreeRegions()
*
* Quadtree access
* l_int32 quadtreeGetParent()
* l_int32 quadtreeGetChildren()
* l_int32 quadtreeMaxLevels()
*
* Display quadtree
* PIX *fpixaDisplayQuadtree()
*
*
* There are many other statistical quantities that can be computed
* in a quadtree, such as rank values, and these can be added as
* the need arises.
*
* Similar results that can approximate a single level of the quadtree
* can be generated by pixGetAverageTiled(). There we specify the
* tile size over which the mean, mean square, and root variance
* are generated; the results are saved in a (reduced size) pix.
* Because the tile dimensions are integers, it is usually not possible
* to obtain tilings that are a power of 2, as required for quadtrees.
*/
#include <math.h>
#include "allheaders.h"
#ifndef NO_CONSOLE_IO
#define DEBUG_BOXES 0
#endif /* !NO_CONSOLE_IO */
/*----------------------------------------------------------------------*
* Top-level quadtree linear statistics *
*----------------------------------------------------------------------*/
/*!
* pixQuadtreeMean()
*
* Input: pixs (8 bpp, no colormap)
* nlevels (in quadtree; max allowed depends on image size)
* *pix_ma (input mean accumulator; can be null)
* *pfpixa (<return> mean values in quadtree)
* Return: 0 if OK, 1 on error
*
* Notes:
* (1) The returned fpixa has @nlevels of fpix, each containing
* the mean values at its level. Level 0 has a
* single value; level 1 has 4 values; level 2 has 16; etc.
*/
l_int32
pixQuadtreeMean(PIX *pixs,
l_int32 nlevels,
PIX *pix_ma,
FPIXA **pfpixa)
{
l_int32 i, j, w, h, size, n;
l_float32 val;
BOX *box;
BOXA *boxa;
BOXAA *baa;
FPIX *fpix;
PIX *pix_mac;
PROCNAME("pixQuadtreeMean");
if (!pfpixa)
return ERROR_INT("&fpixa not defined", procName, 1);
*pfpixa = NULL;
if (!pixs || pixGetDepth(pixs) != 8)
return ERROR_INT("pixs not defined or not 8 bpp", procName, 1);
pixGetDimensions(pixs, &w, &h, NULL);
if (nlevels > quadtreeMaxLevels(w, h))
return ERROR_INT("nlevels too large for image", procName, 1);
if (!pix_ma)
pix_mac = pixBlockconvAccum(pixs);
else
pix_mac = pixClone(pix_ma);
if (!pix_mac)
return ERROR_INT("pix_mac not made", procName, 1);
if ((baa = boxaaQuadtreeRegions(w, h, nlevels)) == NULL) {
pixDestroy(&pix_mac);
return ERROR_INT("baa not made", procName, 1);
}
*pfpixa = fpixaCreate(nlevels);
for (i = 0; i < nlevels; i++) {
boxa = boxaaGetBoxa(baa, i, L_CLONE);
size = 1 << i;
n = boxaGetCount(boxa); /* n == size * size */
fpix = fpixCreate(size, size);
for (j = 0; j < n; j++) {
box = boxaGetBox(boxa, j, L_CLONE);
pixMeanInRectangle(pixs, box, pix_mac, &val);
fpixSetPixel(fpix, j % size, j / size, val);
boxDestroy(&box);
}
fpixaAddFPix(*pfpixa, fpix, L_INSERT);
boxaDestroy(&boxa);
}
pixDestroy(&pix_mac);
boxaaDestroy(&baa);
return 0;
}
/*!
* pixQuadtreeVariance()
*
* Input: pixs (8 bpp, no colormap)
* nlevels (in quadtree)
* *pix_ma (input mean accumulator; can be null)
* *dpix_msa (input mean square accumulator; can be null)
* *pfpixa_v (<optional return> variance values in quadtree)
* *pfpixa_rv (<optional return> root variance values in quadtree)
* Return: 0 if OK, 1 on error
*
* Notes:
* (1) The returned fpixav and fpixarv have @nlevels of fpix,
* each containing at the respective levels the variance
* and root variance values.
*/
l_int32
pixQuadtreeVariance(PIX *pixs,
l_int32 nlevels,
PIX *pix_ma,
DPIX *dpix_msa,
FPIXA **pfpixa_v,
FPIXA **pfpixa_rv)
{
l_int32 i, j, w, h, size, n;
l_float32 var, rvar;
BOX *box;
BOXA *boxa;
BOXAA *baa;
FPIX *fpixv, *fpixrv;
PIX *pix_mac; /* copy of mean accumulator */
DPIX *dpix_msac; /* msa clone */
PROCNAME("pixQuadtreeVariance");
if (!pfpixa_v && !pfpixa_rv)
return ERROR_INT("neither &fpixav nor &fpixarv defined", procName, 1);
if (pfpixa_v) *pfpixa_v = NULL;
if (pfpixa_rv) *pfpixa_rv = NULL;
if (!pixs || pixGetDepth(pixs) != 8)
return ERROR_INT("pixs not defined or not 8 bpp", procName, 1);
pixGetDimensions(pixs, &w, &h, NULL);
if (nlevels > quadtreeMaxLevels(w, h))
return ERROR_INT("nlevels too large for image", procName, 1);
if (!pix_ma)
pix_mac = pixBlockconvAccum(pixs);
else
pix_mac = pixClone(pix_ma);
if (!pix_mac)
return ERROR_INT("pix_mac not made", procName, 1);
if (!dpix_msa)
dpix_msac = pixMeanSquareAccum(pixs);
else
dpix_msac = dpixClone(dpix_msa);
if (!dpix_msac)
return ERROR_INT("dpix_msac not made", procName, 1);
if ((baa = boxaaQuadtreeRegions(w, h, nlevels)) == NULL) {
pixDestroy(&pix_mac);
dpixDestroy(&dpix_msac);
return ERROR_INT("baa not made", procName, 1);
}
if (pfpixa_v) *pfpixa_v = fpixaCreate(nlevels);
if (pfpixa_rv) *pfpixa_rv = fpixaCreate(nlevels);
for (i = 0; i < nlevels; i++) {
boxa = boxaaGetBoxa(baa, i, L_CLONE);
size = 1 << i;
n = boxaGetCount(boxa); /* n == size * size */
if (pfpixa_v) fpixv = fpixCreate(size, size);
if (pfpixa_rv) fpixrv = fpixCreate(size, size);
for (j = 0; j < n; j++) {
box = boxaGetBox(boxa, j, L_CLONE);
pixVarianceInRectangle(pixs, box, pix_mac, dpix_msac, &var, &rvar);
if (pfpixa_v) fpixSetPixel(fpixv, j % size, j / size, var);
if (pfpixa_rv) fpixSetPixel(fpixrv, j % size, j / size, rvar);
boxDestroy(&box);
}
if (pfpixa_v) fpixaAddFPix(*pfpixa_v, fpixv, L_INSERT);
if (pfpixa_rv) fpixaAddFPix(*pfpixa_rv, fpixrv, L_INSERT);
boxaDestroy(&boxa);
}
pixDestroy(&pix_mac);
dpixDestroy(&dpix_msac);
boxaaDestroy(&baa);
return 0;
}
/*----------------------------------------------------------------------*
* Statistics in an arbitrary rectangle *
*----------------------------------------------------------------------*/
/*!
* pixMeanInRectangle()
*
* Input: pix (8 bpp)
* box (region to compute mean value)
* pixma (mean accumulator)
* &val (<return> mean value
* Return: 0 if OK, 1 on error
*
* Notes:
* (1) This function is intended to be used for many rectangles
* on the same image. It can find the mean within a
* rectangle in O(1), independent of the size of the rectangle.
*/
l_int32
pixMeanInRectangle(PIX *pixs,
BOX *box,
PIX *pixma,
l_float32 *pval)
{
l_int32 w, h, bx, by, bw, bh;
l_uint32 val00, val01, val10, val11;
l_float32 norm;
BOX *boxc;
PROCNAME("pixMeanInRectangle");
if (!pval)
return ERROR_INT("&val not defined", procName, 1);
*pval = 0.0;
if (!pixs || pixGetDepth(pixs) != 8)
return ERROR_INT("pixs not defined", procName, 1);
if (!box)
return ERROR_INT("box not defined", procName, 1);
if (!pixma)
return ERROR_INT("pixma not defined", procName, 1);
/* Clip rectangle to image */
pixGetDimensions(pixs, &w, &h, NULL);
boxc = boxClipToRectangle(box, w, h);
boxGetGeometry(boxc, &bx, &by, &bw, &bh);
boxDestroy(&boxc);
if (bw == 0 || bh == 0)
return ERROR_INT("no pixels in box", procName, 1);
/* Use up to 4 points in the accumulator */
norm = 1.0 / (bw * bh);
if (bx > 0 && by > 0) {
pixGetPixel(pixma, bx + bw - 1, by + bh - 1, &val11);
pixGetPixel(pixma, bx + bw - 1, by - 1, &val10);
pixGetPixel(pixma, bx - 1, by + bh - 1, &val01);
pixGetPixel(pixma, bx - 1, by - 1, &val00);
*pval = norm * (val11 - val01 + val00 - val10);
} else if (by > 0) { /* bx == 0 */
pixGetPixel(pixma, bw - 1, by + bh - 1, &val11);
pixGetPixel(pixma, bw - 1, by - 1, &val10);
*pval = norm * (val11 - val10);
} else if (bx > 0) { /* by == 0 */
pixGetPixel(pixma, bx + bw - 1, bh - 1, &val11);
pixGetPixel(pixma, bx - 1, bh - 1, &val01);
*pval = norm * (val11 - val01);
} else { /* bx == 0 && by == 0 */
pixGetPixel(pixma, bw - 1, bh - 1, &val11);
*pval = norm * val11;
}
return 0;
}
/*!
* pixVarianceInRectangle()
*
* Input: pix (8 bpp)
* box (region to compute variance and/or root variance)
* pix_ma (mean accumulator)
* dpix_msa (mean square accumulator)
* &var (<optional return> variance)
* &rvar (<optional return> root variance)
* Return: 0 if OK, 1 on error
*
* Notes:
* (1) This function is intended to be used for many rectangles
* on the same image. It can find the variance and/or the
* square root of the variance within a rectangle in O(1),
* independent of the size of the rectangle.
*/
l_int32
pixVarianceInRectangle(PIX *pixs,
BOX *box,
PIX *pix_ma,
DPIX *dpix_msa,
l_float32 *pvar,
l_float32 *prvar)
{
l_int32 w, h, bx, by, bw, bh;
l_uint32 val00, val01, val10, val11;
l_float64 dval00, dval01, dval10, dval11, mval, msval, var, norm;
BOX *boxc;
PROCNAME("pixVarianceInRectangle");
if (!pvar && !prvar)
return ERROR_INT("neither &var nor &rvar defined", procName, 1);
if (pvar) *pvar = 0.0;
if (prvar) *prvar = 0.0;
if (!pixs || pixGetDepth(pixs) != 8)
return ERROR_INT("pixs not defined", procName, 1);
if (!box)
return ERROR_INT("box not defined", procName, 1);
if (!pix_ma)
return ERROR_INT("pix_ma not defined", procName, 1);
if (!dpix_msa)
return ERROR_INT("dpix_msa not defined", procName, 1);
/* Clip rectangle to image */
pixGetDimensions(pixs, &w, &h, NULL);
boxc = boxClipToRectangle(box, w, h);
boxGetGeometry(boxc, &bx, &by, &bw, &bh);
boxDestroy(&boxc);
if (bw == 0 || bh == 0)
return ERROR_INT("no pixels in box", procName, 1);
/* Use up to 4 points in the accumulators */
norm = 1.0 / (bw * bh);
if (bx > 0 && by > 0) {
pixGetPixel(pix_ma, bx + bw - 1, by + bh - 1, &val11);
pixGetPixel(pix_ma, bx + bw - 1, by - 1, &val10);
pixGetPixel(pix_ma, bx - 1, by + bh - 1, &val01);
pixGetPixel(pix_ma, bx - 1, by - 1, &val00);
dpixGetPixel(dpix_msa, bx + bw - 1, by + bh - 1, &dval11);
dpixGetPixel(dpix_msa, bx + bw - 1, by - 1, &dval10);
dpixGetPixel(dpix_msa, bx - 1, by + bh - 1, &dval01);
dpixGetPixel(dpix_msa, bx - 1, by - 1, &dval00);
mval = norm * (val11 - val01 + val00 - val10);
msval = norm * (dval11 - dval01 + dval00 - dval10);
var = (msval - mval * mval);
if (pvar) *pvar = (l_float32)var;
if (prvar) *prvar = (l_float32)(sqrt(var));
} else if (by > 0) { /* bx == 0 */
pixGetPixel(pix_ma, bw - 1, by + bh - 1, &val11);
pixGetPixel(pix_ma, bw - 1, by - 1, &val10);
dpixGetPixel(dpix_msa, bw - 1, by + bh - 1, &dval11);
dpixGetPixel(dpix_msa, bw - 1, by - 1, &dval10);
mval = norm * (val11 - val10);
msval = norm * (dval11 - dval10);
var = (msval - mval * mval);
if (pvar) *pvar = (l_float32)var;
if (prvar) *prvar = (l_float32)(sqrt(var));
} else if (bx > 0) { /* by == 0 */
pixGetPixel(pix_ma, bx + bw - 1, bh - 1, &val11);
pixGetPixel(pix_ma, bx - 1, bh - 1, &val01);
dpixGetPixel(dpix_msa, bx + bw - 1, bh - 1, &dval11);
dpixGetPixel(dpix_msa, bx - 1, bh - 1, &dval01);
mval = norm * (val11 - val01);
msval = norm * (dval11 - dval01);
var = (msval - mval * mval);
if (pvar) *pvar = (l_float32)var;
if (prvar) *prvar = (l_float32)(sqrt(var));
} else { /* bx == 0 && by == 0 */
pixGetPixel(pix_ma, bw - 1, bh - 1, &val11);
dpixGetPixel(dpix_msa, bw - 1, bh - 1, &dval11);
mval = norm * val11;
msval = norm * dval11;
var = (msval - mval * mval);
if (pvar) *pvar = (l_float32)var;
if (prvar) *prvar = (l_float32)(sqrt(var));
}
return 0;
}
/*----------------------------------------------------------------------*
* Quadtree regions *
*----------------------------------------------------------------------*/
/*!
* boxaaQuadtreeRegions()
*
* Input: w, h (of pix that is being quadtree-ized)
* nlevels (in quadtree)
* Return: baa (for quadtree regions at each level), or null on error
*
* Notes:
* (1) The returned boxaa has @nlevels of boxa, each containing
* the set of rectangles at that level. The rectangle at
* level 0 is the entire region; at level 1 the region is
* divided into 4 rectangles, and at level n there are n^4
* rectangles.
* (2) At each level, the rectangles in the boxa are in "raster"
* order, with LR (fast scan) and TB (slow scan).
*/
BOXAA *
boxaaQuadtreeRegions(l_int32 w,
l_int32 h,
l_int32 nlevels)
{
l_int32 i, j, k, maxpts, nside, nbox, bw, bh;
l_int32 *xstart, *xend, *ystart, *yend;
BOX *box;
BOXA *boxa;
BOXAA *baa;
PROCNAME("boxaaQuadtreeRegions");
if (nlevels < 1)
return (BOXAA *)ERROR_PTR("nlevels must be >= 1", procName, NULL);
if (w < (1 << (nlevels - 1)))
return (BOXAA *)ERROR_PTR("w doesn't support nlevels", procName, NULL);
if (h < (1 << (nlevels - 1)))
return (BOXAA *)ERROR_PTR("h doesn't support nlevels", procName, NULL);
baa = boxaaCreate(nlevels);
maxpts = 1 << (nlevels - 1);
xstart = (l_int32 *)CALLOC(maxpts, sizeof(l_int32));
xend = (l_int32 *)CALLOC(maxpts, sizeof(l_int32));
ystart = (l_int32 *)CALLOC(maxpts, sizeof(l_int32));
yend = (l_int32 *)CALLOC(maxpts, sizeof(l_int32));
for (k = 0; k < nlevels; k++) {
nside = 1 << k; /* number of boxes in each direction */
for (i = 0; i < nside; i++) {
xstart[i] = (w - 1) * i / nside;
if (i > 0) xstart[i]++;
xend[i] = (w - 1) * (i + 1) / nside;
ystart[i] = (h - 1) * i / nside;
if (i > 0) ystart[i]++;
yend[i] = (h - 1) * (i + 1) / nside;
#if DEBUG_BOXES
fprintf(stderr,
"k = %d, xs[%d] = %d, xe[%d] = %d, ys[%d] = %d, ye[%d] = %d\n",
k, i, xstart[i], i, xend[i], i, ystart[i], i, yend[i]);
#endif /* DEBUG_BOXES */
}
nbox = 1 << (2 * k);
boxa = boxaCreate(nbox);
for (i = 0; i < nside; i++) {
bh = yend[i] - ystart[i] + 1;
for (j = 0; j < nside; j++) {
bw = xend[j] - xstart[j] + 1;
box = boxCreate(xstart[j], ystart[i], bw, bh);
boxaAddBox(boxa, box, L_INSERT);
}
}
boxaaAddBoxa(baa, boxa, L_INSERT);
}
FREE(xstart);
FREE(xend);
FREE(ystart);
FREE(yend);
return baa;
}
/*----------------------------------------------------------------------*
* Quadtree access *
*----------------------------------------------------------------------*/
/*!
* quadtreeGetParent()
*
* Input: fpixa (mean, variance or root variance)
* level, x, y (of current pixel)
* &val (<return> parent pixel value), or 0.0 on error.
* Return: 0 if OK, 1 on error
*
* Notes:
* (1) Check return value for error. On error, val is returned as 0.0.
* (2) The parent is located at:
* level - 1
* (x/2, y/2)
*/
l_int32
quadtreeGetParent(FPIXA *fpixa,
l_int32 level,
l_int32 x,
l_int32 y,
l_float32 *pval)
{
l_int32 n;
PROCNAME("quadtreeGetParent");
if (!pval)
return ERROR_INT("&val not defined", procName, 1);
*pval = 0.0;
if (!fpixa)
return ERROR_INT("fpixa not defined", procName, 1);
n = fpixaGetCount(fpixa);
if (level < 1 || level >= n)
return ERROR_INT("invalid level", procName, 1);
if (fpixaGetPixel(fpixa, level - 1, x / 2, y / 2, pval) != 0)
return ERROR_INT("invalid coordinates", procName, 1);
return 0;
}
/*!
* quadtreeGetChildren()
*
* Input: fpixa (mean, variance or root variance)
* level, x, y (of current pixel)
* &val00, val01, val10, val11 (<return> child pixel values)
* Return: 0 if OK, 1 on error
*
* Notes:
* (1) Check return value for error. On error, all return vals are 0.0.
* (2) The returned child pixels are located at:
* level + 1
* (2x, 2y), (2x+1, 2y), (2x, 2y+1), (2x+1, 2y+1)
*/
l_int32
quadtreeGetChildren(FPIXA *fpixa,
l_int32 level,
l_int32 x,
l_int32 y,
l_float32 *pval00,
l_float32 *pval10,
l_float32 *pval01,
l_float32 *pval11)
{
l_int32 n;
PROCNAME("quadtreeGetChildren");
if (!pval00 || !pval01 || !pval10 || !pval11)
return ERROR_INT("&val* not all defined", procName, 1);
*pval00 = *pval10 = *pval01 = *pval11 = 0.0;
if (!fpixa)
return ERROR_INT("fpixa not defined", procName, 1);
n = fpixaGetCount(fpixa);
if (level < 0 || level >= n - 1)
return ERROR_INT("invalid level", procName, 1);
if (fpixaGetPixel(fpixa, level + 1, 2 * x, 2 * y, pval00) != 0)
return ERROR_INT("invalid coordinates", procName, 1);
fpixaGetPixel(fpixa, level + 1, 2 * x + 1, 2 * y, pval10);
fpixaGetPixel(fpixa, level + 1, 2 * x, 2 * y + 1, pval01);
fpixaGetPixel(fpixa, level + 1, 2 * x + 1, 2 * y + 1, pval11);
return 0;
}
/*!
* quadtreeMaxLevels()
*
* Input: w, h (of image)
* Return: maxlevels (maximum number of levels allowed), or -1 on error
*
* Notes:
* (1) The criterion for maxlevels is that the subdivision not
* go down below the single pixel level. The 1.5 factor
* is intended to keep any rectangle from accidentally
* having zero dimension due to integer truncation.
*/
l_int32
quadtreeMaxLevels(l_int32 w,
l_int32 h)
{
l_int32 i, minside;
minside = L_MIN(w, h);
for (i = 0; i < 20; i++) { /* 2^10 = one million */
if (minside < (1.5 * (1 << i)))
return i - 1;
}
return -1; /* fail if the image has over a trillion pixels! */
}
/*----------------------------------------------------------------------*
* Display quadtree *
*----------------------------------------------------------------------*/
/*!
* fpixaDisplayQuadtree()
*
* Input: fpixa (mean, variance or root variance)
* factor (replication factor at lowest level)
* fontdir (directory for text fonts; e.g., ./fonts)
* Return: pixd (8 bpp, mosaic of quadtree images), or null on error
*
* Notes:
* (1) The mean and root variance fall naturally in the 8 bpp range,
* but the variance is typically outside the range. This
* function displays 8 bpp pix clipped to 255, so the image
* pixels will mostly be 255 (white).
*/
PIX *
fpixaDisplayQuadtree(FPIXA *fpixa,
l_int32 factor,
const char *fontdir)
{
char buf[256];
l_int32 nlevels, i, mag, w;
L_BMF *bmf;
FPIX *fpix;
PIX *pixt1, *pixt2, *pixt3, *pixt4, *pixd;
PIXA *pixat;
PROCNAME("fpixaDisplayQuadtree");
if (!fpixa)
return (PIX *)ERROR_PTR("fpixa not defined", procName, NULL);
if ((nlevels = fpixaGetCount(fpixa)) == 0)
return (PIX *)ERROR_PTR("pixas empty", procName, NULL);
if ((bmf = bmfCreate(fontdir, 6)) == NULL)
L_ERROR("bmf not made; text will not be added", procName);
pixat = pixaCreate(nlevels);
for (i = 0; i < nlevels; i++) {
fpix = fpixaGetFPix(fpixa, i, L_CLONE);
pixt1 = fpixConvertToPix(fpix, 8, L_CLIP_TO_ZERO, 0);
mag = factor * (1 << (nlevels - i - 1));
pixt2 = pixExpandReplicate(pixt1, mag);
pixt3 = pixConvertTo32(pixt2);
snprintf(buf, sizeof(buf), "Level %d\n", i);
pixt4 = pixAddSingleTextblock(pixt3, bmf, buf, 0xff000000,
L_ADD_BELOW, NULL);
pixaAddPix(pixat, pixt4, L_INSERT);
fpixDestroy(&fpix);
pixDestroy(&pixt1);
pixDestroy(&pixt2);
pixDestroy(&pixt3);
}
w = pixGetWidth(pixt4);
pixd = pixaDisplayTiledInRows(pixat, 32, nlevels * (w + 80), 1.0, 0, 30, 2);
pixaDestroy(&pixat);
bmfDestroy(&bmf);
return pixd;
}