Exemplo n.º 1
0
/*!
 *  pixRotateBinaryNice()
 *
 *      Input:  pixs (1 bpp)
 *              angle (radians; clockwise is positive; about the center)
 *              incolor (L_BRING_IN_WHITE, L_BRING_IN_BLACK)
 *      Return: pixd, or null on error
 *
 *  Notes:
 *      (1) For very small rotations, just return a clone.
 *      (2) This does a computationally expensive rotation of 1 bpp images.
 *          The fastest rotators (using shears or subsampling) leave
 *          visible horizontal and vertical shear lines across which
 *          the image shear changes by one pixel.  To ameliorate the
 *          visual effect one can introduce random dithering.  One
 *          way to do this in a not-too-random fashion is given here.
 *          We convert to 8 bpp, do a very small blur, rotate using
 *          linear interpolation (same as area mapping), do a
 *          small amount of sharpening to compensate for the initial
 *          blur, and threshold back to binary.  The shear lines
 *          are magically removed.
 *      (3) This operation is about 5x slower than rotation by sampling.
 */
PIX *
pixRotateBinaryNice(PIX       *pixs,
                    l_float32  angle,
                    l_int32    incolor)
{
PIX  *pixt1, *pixt2, *pixt3, *pixt4, *pixd;

    PROCNAME("pixRotateBinaryNice");

    if (!pixs || pixGetDepth(pixs) != 1)
        return (PIX *)ERROR_PTR("pixs undefined or not 1 bpp", procName, NULL);
    if (incolor != L_BRING_IN_WHITE && incolor != L_BRING_IN_BLACK)
        return (PIX *)ERROR_PTR("invalid incolor", procName, NULL);

    pixt1 = pixConvertTo8(pixs, 0);
    pixt2 = pixBlockconv(pixt1, 1, 1);  /* smallest blur allowed */
    pixt3 = pixRotateAM(pixt2, angle, incolor);
    pixt4 = pixUnsharpMasking(pixt3, 1, 1.0);  /* sharpen a bit */
    pixd = pixThresholdToBinary(pixt4, 128);
    pixDestroy(&pixt1);
    pixDestroy(&pixt2);
    pixDestroy(&pixt3);
    pixDestroy(&pixt4);
    return pixd;
}
Exemplo n.º 2
0
/*!
 *  deskew()
 *
 *      Input:  pixs
 *              redsearch  (for binary search: reduction factor = 1, 2 or 4)
 *      Return: deskewed pix, or NULL on error
 */
PIX *
deskew(PIX     *pixs,
       l_int32  redsearch)
{
l_float32  angle, conf, deg2rad;
PIX       *pixg;  /* gray version */
PIX       *pixb; /* binary version */
PIX       *pixd;  /* destination image */

    PROCNAME("deskew");

    if (!pixs)
	return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);

    /* Calculate a skew angle.  We may need to make a binary version of the
     * image for this calculation.
     */
    if (pixGetDepth(pixs) != 1) {
	/* FIX ME:  We should probably pick a threshold value with more care.  */
	/* Create a grayscale image if we need one.  */
	if (pixGetDepth(pixs) >= 24) {
	    pixg = pixConvertRGBToGray(pixs, 0.0, 0.0, 0.0);
	} else {
	    pixg = pixs;
	}
	    
	pixb = pixThresholdToBinary(pixg, 127);
	if (pixg != pixs) {
	    pixDestroy(&pixg);
	}
	/* Assert:  We are done with any gray image.  */
    } else {
	pixb = pixs;
    }
    /* Assert: We have a valid binary image.  */
    if (redsearch != 1 && redsearch != 2 && redsearch != 4)
	return (PIX *)ERROR_PTR("redsearch not in {1,2,4}", procName, NULL);

    deg2rad = 3.1415926535 / 180.;
    if (pixFindSkewSweepAndSearch(pixb, &angle, &conf,
				  DEFAULT_SWEEP_REDUCTION, redsearch,
				  DEFAULT_SWEEP_RANGE, DEFAULT_SWEEP_DELTA,
				  DEFAULT_MINBS_DELTA)) {
	pixd = pixClone(pixs);
	goto finish;
    }
	
    if (L_ABS(angle) < MIN_DESKEW_ANGLE || conf < MIN_ALLOWED_CONFIDENCE) {
	pixd = pixClone(pixs);
	goto finish;
    }

    /* If the pixel depth of pixs is 1, we need to use a bit-depth
     * independent rotate instead of the more accurate area mapping rotate.
     */
    if (pixGetDepth(pixs) == 1) {
	if ((pixd = pixRotateShear(pixs, 0, 0, deg2rad * angle, 0xffffff00)) == NULL) {
	    pixd = pixClone(pixs);
	}
    } else {
#if defined(COLOR_ROTATE)
	if ((pixd = pixRotateAMColorFast(pixs, deg2rad * angle)) == NULL) {
	    pixd = pixClone(pixs);
	}
#else
	if ((pixd = pixRotateAM(pixs, deg2rad * angle, 0xffffff00)) == NULL) {
	    pixd = pixClone(pixs);
	}
#endif
    }

   finish:
    if (pixb != pixs) {
	pixDestroy(&pixb);
    }
    return pixd;
}
Exemplo n.º 3
0
int main(int argc,
         char **argv) {
    l_int32 i, w, h, d, rotflag;
    PIX *pixs, *pixt, *pixd;
    l_float32 angle, deg2rad, pops, ang;
    char *filein, *fileout;
    static char mainName[] = "rotatetest1";

    if (argc != 4)
        return ERROR_INT(" Syntax:  rotatetest1 filein angle fileout",
                         mainName, 1);

    filein = argv[1];
    angle = atof(argv[2]);
    fileout = argv[3];
    deg2rad = 3.1415926535 / 180.;

    if ((pixs = pixRead(filein)) == NULL)
        return ERROR_INT("pix not made", mainName, 1);
    if (pixGetDepth(pixs) == 1) {
        pixt = pixScaleToGray3(pixs);
        pixDestroy(&pixs);
        pixs = pixAddBorderGeneral(pixt, 1, 0, 1, 0, 255);
        pixDestroy(&pixt);
    }

    pixGetDimensions(pixs, &w, &h, &d);
    fprintf(stderr, "w = %d, h = %d\n", w, h);

#if 0
    /* repertory of rotation operations to choose from */
pixd = pixRotateAM(pixs, deg2rad * angle, L_BRING_IN_WHITE);
pixd = pixRotateAMColor(pixs, deg2rad * angle, 0xffffff00);
pixd = pixRotateAMColorFast(pixs, deg2rad * angle, 255);
pixd = pixRotateAMCorner(pixs, deg2rad * angle, L_BRING_IN_WHITE);
pixd = pixRotateShear(pixs, w /2, h / 2, deg2rad * angle,
                      L_BRING_IN_WHITE);
pixd = pixRotate3Shear(pixs, w /2, h / 2, deg2rad * angle,
                       L_BRING_IN_WHITE);
pixRotateShearIP(pixs, w / 2, h / 2, deg2rad * angle); pixd = pixs;
#endif

#if 0
    /* timing of shear rotation */
for (i = 0; i < NITERS; i++) {
    pixd = pixRotateShear(pixs, (i * w) / NITERS,
                          (i * h) / NITERS, deg2rad * angle,
                          L_BRING_IN_WHITE);
    pixDisplay(pixd, 100 + 20 * i, 100 + 20 * i);
    pixDestroy(&pixd);
}
#endif

#if 0
    /* timing of in-place shear rotation */
for (i = 0; i < NITERS; i++) {
    pixRotateShearIP(pixs, w/2, h/2, deg2rad * angle, L_BRING_IN_WHITE);
/*        pixRotateShearCenterIP(pixs, deg2rad * angle, L_BRING_IN_WHITE); */
    pixDisplay(pixs, 100 + 20 * i, 100 + 20 * i);
}
pixd = pixs;
if (pixGetDepth(pixd) == 1)
    pixWrite(fileout, pixd, IFF_PNG);
else
    pixWrite(fileout, pixd, IFF_JFIF_JPEG);
pixDestroy(&pixs);
#endif

#if 0
    /* timing of various rotation operations (choose) */
startTimer();
w = pixGetWidth(pixs);
h = pixGetHeight(pixs);
for (i = 0; i < NTIMES; i++) {
    pixd = pixRotateShearCenter(pixs, deg2rad * angle, L_BRING_IN_WHITE);
    pixDestroy(&pixd);
}
pops = (l_float32)(w * h * NTIMES / 1000000.) / stopTimer();
fprintf(stderr, "vers. 1, mpops: %f\n", pops);
startTimer();
w = pixGetWidth(pixs);
h = pixGetHeight(pixs);
for (i = 0; i < NTIMES; i++) {
    pixRotateShearIP(pixs, w/2, h/2, deg2rad * angle, L_BRING_IN_WHITE);
}
pops = (l_float32)(w * h * NTIMES / 1000000.) / stopTimer();
fprintf(stderr, "shear, mpops: %f\n", pops);
pixWrite(fileout, pixs, IFF_PNG);
for (i = 0; i < NTIMES; i++) {
    pixRotateShearIP(pixs, w/2, h/2, -deg2rad * angle, L_BRING_IN_WHITE);
}
pixWrite("/usr/tmp/junkout", pixs, IFF_PNG);
#endif

#if 0
    /* area-mapping rotation operations */
pixd = pixRotateAM(pixs, deg2rad * angle, L_BRING_IN_WHITE);
/*    pixd = pixRotateAMColorFast(pixs, deg2rad * angle, 255); */
if (pixGetDepth(pixd) == 1)
    pixWrite(fileout, pixd, IFF_PNG);
else
    pixWrite(fileout, pixd, IFF_JFIF_JPEG);
#endif

#if 0
    /* compare the standard area-map color rotation with
     * the fast area-map color rotation, on a pixel basis */
{
PIX    *pix1, *pix2;
NUMA   *nar, *nag, *nab, *naseq;
GPLOT  *gplot;

startTimer();
pix1 = pixRotateAMColor(pixs, 0.12, 0xffffff00);
fprintf(stderr, " standard color rotate: %7.2f sec\n", stopTimer());
pixWrite("junkcolor1", pix1, IFF_JFIF_JPEG);
startTimer();
pix2 = pixRotateAMColorFast(pixs, 0.12, 0xffffff00);
fprintf(stderr, " fast color rotate: %7.2f sec\n", stopTimer());
pixWrite("junkcolor2", pix2, IFF_JFIF_JPEG);
pixd = pixAbsDifference(pix1, pix2);
pixGetColorHistogram(pixd, 1, &nar, &nag, &nab);
naseq = numaMakeSequence(0., 1., 256);
gplot = gplotCreate("junk_absdiff", GPLOT_X11, "Number vs diff",
                    "diff", "number");
gplotAddPlot(gplot, naseq, nar, GPLOT_POINTS, "red");
gplotAddPlot(gplot, naseq, nag, GPLOT_POINTS, "green");
gplotAddPlot(gplot, naseq, nab, GPLOT_POINTS, "blue");
gplotMakeOutput(gplot);
pixDestroy(&pix1);
pixDestroy(&pix2);
pixDestroy(&pixd);
numaDestroy(&nar);
numaDestroy(&nag);
numaDestroy(&nab);
numaDestroy(&naseq);
gplotDestroy(&gplot);
}
#endif

    /* Do a succession of 180 7-degree rotations in a cw
     * direction, and unwind the result with another set in
     * a ccw direction.  Although there is a considerable amount
     * of distortion after successive rotations, after all
     * 360 rotations, the resulting image is restored to
     * its original pristine condition! */
#if 1
    rotflag = L_ROTATE_AREA_MAP;
/*    rotflag = L_ROTATE_SHEAR;     */
/*    rotflag = L_ROTATE_SAMPLING;   */
    ang = 7.0 * deg2rad;
    pixGetDimensions(pixs, &w, &h, NULL);
    pixd = pixRotate(pixs, ang, rotflag, L_BRING_IN_WHITE, w, h);
    pixWrite("junkrot7", pixd, IFF_PNG);
    for (i = 1; i < 180; i++) {
        pixs = pixd;
        pixd = pixRotate(pixs, ang, rotflag, L_BRING_IN_WHITE, w, h);
        if ((i % 30) == 0) pixDisplay(pixd, 600, 0);
        pixDestroy(&pixs);
    }

    pixWrite("junkspin", pixd, IFF_PNG);
    pixDisplay(pixd, 0, 0);

    for (i = 0; i < 180; i++) {
        pixs = pixd;
        pixd = pixRotate(pixs, -ang, rotflag, L_BRING_IN_WHITE, w, h);
        if (i && (i % 30) == 0) pixDisplay(pixd, 600, 500);
        pixDestroy(&pixs);
    }

    pixWrite("junkunspin", pixd, IFF_PNG);
    pixDisplay(pixd, 0, 500);
    pixDestroy(&pixd);
#endif

    return 0;
}
Exemplo n.º 4
0
main(int    argc,
     char **argv)
{
l_int32      i, n, ws, hs, w, h, rval, gval, bval, order;
l_float32   *mat1, *mat2, *mat3;
l_float32    matd[9];
BOX         *box, *boxt;
BOXA        *boxa, *boxat, *boxa1, *boxa2, *boxa3, *boxa4, *boxa5;
PIX         *pix, *pixs, *pixb, *pixc, *pixt, *pixt1, *pixt2, *pixt3;
PIXA        *pixa;
static char  mainName[] = "xformbox_reg";

    /* ----------------------------------------------------------- *
     *                Test hash rendering in 3 modes               *
     * ----------------------------------------------------------- */
    pixs = pixRead("feyn.tif");
    box = boxCreate(461, 429, 1393, 342);
    pixt1 = pixClipRectangle(pixs, box, NULL);
    boxa = pixConnComp(pixt1, NULL, 8);
    n = boxaGetCount(boxa);
    pixt2 = pixConvertTo8(pixt1, 1);
    pixt3 = pixConvertTo32(pixt1);
    for (i = 0; i < n; i++) {
        boxt = boxaGetBox(boxa, i, L_CLONE);
	rval = (1413 * i) % 256;
	gval = (4917 * i) % 256;
	bval = (7341 * i) % 256;
	pixRenderHashBox(pixt1, boxt, 8, 2, i % 4, 1, L_SET_PIXELS);
	pixRenderHashBoxArb(pixt2, boxt, 7, 2, i % 4, 1, rval, gval, bval);
	pixRenderHashBoxBlend(pixt3, boxt, 7, 2, i % 4, 1, rval, gval, bval,
                              0.5);
	boxDestroy(&boxt);
    }
    pixDisplay(pixt1, 0, 0);
    pixDisplay(pixt2, 0, 300);
    pixDisplay(pixt3, 0, 570);
    pixWrite("/tmp/junkpixt1.png", pixt1, IFF_PNG);
    pixWrite("/tmp/junkpixt2.png", pixt2, IFF_PNG);
    pixWrite("/tmp/junkpixt3.png", pixt3, IFF_PNG);

    boxaDestroy(&boxa);
    boxDestroy(&box);
    pixDestroy(&pixs);
    pixDestroy(&pixt1);
    pixDestroy(&pixt2);
    pixDestroy(&pixt3);


    /* ----------------------------------------------------------- *
     *    Test box transforms with either translation or scaling   *
     *    combined with rotation, using the simple 'ordered'       *
     *    function.  Show that the order of the operations does    *
     *    not matter; different hashing schemes end up in the      *
     *    identical boxes.                                         *
     * ----------------------------------------------------------- */
    pix = pixRead("feyn.tif");
    box = boxCreate(420, 360, 1500, 465);
    pixt = pixClipRectangle(pix, box, NULL);
    pixs = pixAddBorderGeneral(pixt, 0, 200, 0, 0, 0);
    boxDestroy(&box);
    pixDestroy(&pix);
    pixDestroy(&pixt);
    boxa = pixConnComp(pixs, NULL, 8);
    n = boxaGetCount(boxa);
    pixa = pixaCreate(0);

    pixt = pixConvertTo32(pixs);
    for (i = 0; i < 3; i++) {
        if (i == 0)
            order = L_TR_SC_RO;
        else if (i == 1)
            order = L_TR_RO_SC;
        else
            order = L_SC_TR_RO;
        boxat = boxaTransformOrdered(boxa, SHIFTX_2, SHIFTY_2, 1.0, 1.0,
                                     450, 250, ROTATION_2, order);
        RenderTransformedBoxa(pixt, boxat, i);
        boxaDestroy(&boxat);
    }
    pixSaveTiled(pixt, pixa, 1, 1, 30, 32);
    pixDestroy(&pixt);

    pixt = pixConvertTo32(pixs);
    for (i = 0; i < 3; i++) {
        if (i == 0)
            order = L_RO_TR_SC;
        else if (i == 1)
            order = L_RO_SC_TR;
        else
            order = L_SC_RO_TR;
        boxat = boxaTransformOrdered(boxa, SHIFTX_2, SHIFTY_2, 1.0, 1.0,
                                     450, 250, ROTATION_2, order);
        RenderTransformedBoxa(pixt, boxat, i + 4);
        boxaDestroy(&boxat);
    }
    pixSaveTiled(pixt, pixa, 1, 1, 30, 0);
    pixDestroy(&pixt);

    pixt = pixConvertTo32(pixs);
    for (i = 0; i < 3; i++) {
        if (i == 0)
            order = L_TR_SC_RO;
        else if (i == 1)
            order = L_SC_RO_TR;
        else
            order = L_SC_TR_RO;
        boxat = boxaTransformOrdered(boxa, 0, 0, SCALEX_2, SCALEY_2,
                                     450, 250, ROTATION_2, order);
        RenderTransformedBoxa(pixt, boxat, i + 8);
        boxaDestroy(&boxat);
    }
    pixSaveTiled(pixt, pixa, 1, 1, 30, 0);
    pixDestroy(&pixt);

    pixt = pixConvertTo32(pixs);
    for (i = 0; i < 3; i++) {
        if (i == 0)
            order = L_RO_TR_SC;
        else if (i == 1)
            order = L_RO_SC_TR;
        else
            order = L_TR_RO_SC;
        boxat = boxaTransformOrdered(boxa, 0, 0, SCALEX_2, SCALEY_2,
                                     450, 250, ROTATION_2, order);
        RenderTransformedBoxa(pixt, boxat, i + 16);
        boxaDestroy(&boxat);
    }
    pixSaveTiled(pixt, pixa, 1, 1, 30, 0);
    pixDestroy(&pixt);

    pixt = pixaDisplay(pixa, 0, 0);
    pixWrite("/tmp/junkxform1.png", pixt, IFF_PNG);
    pixDisplay(pixt, 1000, 0);
    pixDestroy(&pixt);
    pixDestroy(&pixs);
    boxaDestroy(&boxa);
    pixaDestroy(&pixa);


    /* ----------------------------------------------------------- *
     *    Do more testing of box and pta transforms.  Show that    *
     *    resulting boxes are identical by three methods.          *
     * ----------------------------------------------------------- */
        /* Set up pix and boxa */
    pixa = pixaCreate(0);
    pix = pixRead("lucasta.1.300.tif");
    pixTranslate(pix, pix, 70, 0, L_BRING_IN_WHITE);
    pixt = pixCloseBrick(NULL, pix, 14, 5);
    pixOpenBrick(pixt, pixt, 1, 2);
    boxa = pixConnComp(pixt, NULL, 8);
    pixs = pixConvertTo32(pix);
    pixc = pixCopy(NULL, pixs);
    RenderTransformedBoxa(pixc, boxa, 113);
    pixSaveTiled(pixc, pixa, 2, 1, 30, 32);
    pixDestroy(&pix);
    pixDestroy(&pixc);
    pixDestroy(&pixt);

        /* (a) Do successive discrete operations: shift, scale, rotate */
    pixt1 = pixTranslate(NULL, pixs, SHIFTX_3, SHIFTY_3, L_BRING_IN_WHITE);
    boxa1 = boxaTranslate(boxa, SHIFTX_3, SHIFTY_3);
    pixc = pixCopy(NULL, pixt1);
    RenderTransformedBoxa(pixc, boxa1, 213);
    pixSaveTiled(pixc, pixa, 2, 0, 30, 32);
    pixDestroy(&pixc);

    pixt2 = pixScale(pixt1, SCALEX_3, SCALEY_3);
    boxa2 = boxaScale(boxa1, SCALEX_3, SCALEY_3);
    pixc = pixCopy(NULL, pixt2);
    RenderTransformedBoxa(pixc, boxa2, 313);
    pixSaveTiled(pixc, pixa, 2, 1, 30, 32);
    pixDestroy(&pixc);

    pixGetDimensions(pixt2, &w, &h, NULL);
    pixt3 = pixRotateAM(pixt2, ROTATION_3, L_BRING_IN_WHITE);
    boxa3 = boxaRotate(boxa2, w / 2, h / 2, ROTATION_3);
    pixc = pixCopy(NULL, pixt3);
    RenderTransformedBoxa(pixc, boxa3, 413);
    pixSaveTiled(pixc, pixa, 2, 0, 30, 32);
    pixDestroy(&pixc);

        /* (b) Set up and use the composite transform */
    mat1 = createMatrix2dTranslate(SHIFTX_3, SHIFTY_3);
    mat2 = createMatrix2dScale(SCALEX_3, SCALEY_3);
    mat3 = createMatrix2dRotate(w / 2, h / 2, ROTATION_3);
    l_productMat3(mat3, mat2, mat1, matd, 3);
    boxa4 = boxaAffineTransform(boxa, matd);
    pixc = pixCopy(NULL, pixt3);
    RenderTransformedBoxa(pixc, boxa4, 513);
    pixSaveTiled(pixc, pixa, 2, 1, 30, 32);
    pixDestroy(&pixc);

        /* (c) Use the special 'ordered' function */
    pixGetDimensions(pixs, &ws, &hs, NULL);
    boxa5 = boxaTransformOrdered(boxa, SHIFTX_3, SHIFTY_3,
                                 SCALEX_3, SCALEY_3,
                                 ws / 2, hs / 2, ROTATION_3, L_TR_SC_RO);
    pixc = pixCopy(NULL, pixt3);
    RenderTransformedBoxa(pixc, boxa5, 613);
    pixSaveTiled(pixc, pixa, 2, 0, 30, 32);
    pixDestroy(&pixc);

    pixDestroy(&pixt1);
    pixDestroy(&pixt2);
    pixDestroy(&pixt3);
    boxaDestroy(&boxa1);
    boxaDestroy(&boxa2);
    boxaDestroy(&boxa3);
    boxaDestroy(&boxa4);
    boxaDestroy(&boxa5);
    lept_free(mat1);
    lept_free(mat2);
    lept_free(mat3);

    pixt = pixaDisplay(pixa, 0, 0);
    pixWrite("/tmp/junkxform2.png", pixt, IFF_PNG);
    pixDisplay(pixt, 1000, 300);
    pixDestroy(&pixt);
    pixDestroy(&pixs);
    boxaDestroy(&boxa);
    pixaDestroy(&pixa);
    return 0;
}
Exemplo n.º 5
0
main(int    argc,
     char **argv)
{
l_int32      i;
l_float32    pi, scale, angle;
PIX         *pixc, *pixm, *pix1, *pix2, *pix3;
PIXA        *pixa;
PTA         *pta1, *pta2, *pta3, *pta4;
static char  mainName[] = "smallpix_reg";

        /* Make a small test image, the hard way! */
    pi = 3.1415926535;
    pixc = pixCreate(9, 9, 32);
    pixm = pixCreate(9, 9, 1);
    pta1 = generatePtaLineFromPt(4, 4, 3.1, 0.0);
    pta2 = generatePtaLineFromPt(4, 4, 3.1, 0.5 * pi);
    pta3 = generatePtaLineFromPt(4, 4, 3.1, pi);
    pta4 = generatePtaLineFromPt(4, 4, 3.1, 1.5 * pi);
    ptaJoin(pta1, pta2, 0, 0);
    ptaJoin(pta1, pta3, 0, 0);
    ptaJoin(pta1, pta4, 0, 0);
    pixRenderPta(pixm, pta1, L_SET_PIXELS);
    pixPaintThroughMask(pixc, pixm, 0, 0, 0x00ff0000);
    ptaDestroy(&pta1);
    ptaDestroy(&pta2);
    ptaDestroy(&pta3);
    ptaDestroy(&pta4);
    pixDestroy(&pixm);

        /* Results differ for scaleSmoothLow() w/ and w/out + 0.5.
         * Neither is properly symmetric (with symm pattern on odd-sized
         * pix, because the smoothing is destroying the symmetry. */
    pixa = pixaCreate(11);
    pix1 = pixExpandReplicate(pixc, 2);
    for (i = 0; i < 11; i++) {
        scale = 0.30 + 0.035 * (l_float32)i;
        pix2 = pixScaleSmooth(pix1, scale, scale);
        pix3 = pixExpandReplicate(pix2, 6);
        pixSaveTiled(pix3, pixa, 1, (i == 0), 20, 32);
        pixDestroy(&pix2);
        pixDestroy(&pix3);
    }
    pixDestroy(&pix1);
    DisplayPix(&pixa, 100, 100, NULL);

        /* Results same for pixScaleAreaMap w/ and w/out + 0.5 */
    pixa = pixaCreate(11);
    pix1 = pixExpandReplicate(pixc, 2);
    for (i = 0; i < 11; i++) {
        scale = 0.30 + 0.035 * (l_float32)i;
        pix2 = pixScaleAreaMap(pix1, scale, scale);
        pix3 = pixExpandReplicate(pix2, 6);
        pixSaveTiled(pix3, pixa, 1, (i == 0), 20, 32);
        pixDestroy(&pix2);
        pixDestroy(&pix3);
    }
    pixDestroy(&pix1);
    DisplayPix(&pixa, 100, 200, NULL);

        /* Results better for pixScaleBySampling with + 0.5, for small,
         * odd-dimension pix.  */
    pixa = pixaCreate(11);
    pix1 = pixExpandReplicate(pixc, 2);
    for (i = 0; i < 11; i++) {
        scale = 0.30 + 0.035 * (l_float32)i;
        pix2 = pixScaleBySampling(pix1, scale, scale);
        pix3 = pixExpandReplicate(pix2, 6);
        pixSaveTiled(pix3, pixa, 1, (i == 0), 20, 32);
        pixDestroy(&pix2);
        pixDestroy(&pix3);
    }
    pixDestroy(&pix1);
    DisplayPix(&pixa, 100, 300, NULL);

        /* Results same for pixRotateAM w/ and w/out + 0.5 */
    pixa = pixaCreate(11);
    pix1 = pixExpandReplicate(pixc, 1);
    for (i = 0; i < 11; i++) {
        angle = 0.10 + 0.05 * (l_float32)i;
        pix2 = pixRotateAM(pix1, angle, L_BRING_IN_BLACK);
        pix3 = pixExpandReplicate(pix2, 8);
        pixSaveTiled(pix3, pixa, 1, (i == 0), 20, 32);
        pixDestroy(&pix2);
        pixDestroy(&pix3);
    }
    pixDestroy(&pix1);
    DisplayPix(&pixa, 100, 400, NULL);

        /* If the size is odd, we express the center exactly, and the
         * results are better for pixRotateBySampling() w/out 0.5
         * However, if the size is even, the center value is not
         * exact, and if we choose it 0.5 smaller than the actual
         * center, we get symmetrical results with +0.5. 
         * So we choose not to include + 0.5. */
    pixa = pixaCreate(11);
    pix1 = pixExpandReplicate(pixc, 1);
    for (i = 0; i < 11; i++) {
        angle = 0.10 + 0.05 * (l_float32)i;
        pix2 = pixRotateBySampling(pix1, 4, 4, angle, L_BRING_IN_BLACK);
        pix3 = pixExpandReplicate(pix2, 8);
        pixSaveTiled(pix3, pixa, 1, (i == 0), 20, 32);
        pixDestroy(&pix2);
        pixDestroy(&pix3);
    }
    pixDestroy(&pix1);
    DisplayPix(&pixa, 100, 500, NULL);

        /* Results same for pixRotateAMCorner w/ and w/out + 0.5 */
    pixa = pixaCreate(11);
    pix1 = pixExpandReplicate(pixc, 1);
    for (i = 0; i < 11; i++) {
        angle = 0.10 + 0.05 * (l_float32)i;
        pix2 = pixRotateAMCorner(pix1, angle, L_BRING_IN_BLACK);
        pix3 = pixExpandReplicate(pix2, 8);
        pixSaveTiled(pix3, pixa, 1, (i == 0), 20, 32);
        pixDestroy(&pix2);
        pixDestroy(&pix3);
    }
    pixDestroy(&pix1);
    DisplayPix(&pixa, 100, 600, NULL);

        /* Results better for pixRotateAMColorFast without + 0.5 */
    pixa = pixaCreate(11);
    pix1 = pixExpandReplicate(pixc, 1);
    for (i = 0; i < 11; i++) {
        angle = 0.10 + 0.05 * (l_float32)i;
        pix2 = pixRotateAMColorFast(pix1, angle, 0);
        pix3 = pixExpandReplicate(pix2, 8);
        pixSaveTiled(pix3, pixa, 1, (i == 0), 20, 32);
        pixDestroy(&pix2);
        pixDestroy(&pix3);
    }
    pixDestroy(&pix1);
    DisplayPix(&pixa, 100, 700, NULL);

        /* Results slightly better for pixScaleColorLI() w/out + 0.5 */
    pixa = pixaCreate(11);
    pix1 = pixExpandReplicate(pixc, 1);
    for (i = 0; i < 11; i++) {
        scale = 1.0 + 0.2 * (l_float32)i;
        pix2 = pixScaleColorLI(pix1, scale, scale);
        pix3 = pixExpandReplicate(pix2, 4);
        pixSaveTiled(pix3, pixa, 1, (i == 0), 20, 32);
        pixDestroy(&pix2);
        pixDestroy(&pix3);
    }
    pixDestroy(&pix1);
    DisplayPix(&pixa, 100, 800, NULL);

        /* Results slightly better for pixScaleColorLI() w/out + 0.5 */
    pixa = pixaCreate(11);
    pix1 = pixExpandReplicate(pixc, 1);
    for (i = 0; i < 11; i++) {
        scale = 1.0 + 0.2 * (l_float32)i;
        pix2 = pixScaleLI(pix1, scale, scale);
        pix3 = pixExpandReplicate(pix2, 4);
        pixSaveTiled(pix3, pixa, 1, (i == 0), 20, 32);
        pixDestroy(&pix2);
        pixDestroy(&pix3);
    }
    pixDestroy(&pix1);
    DisplayPix(&pixa, 100, 940, NULL);

    pixDestroy(&pixc);
    return 0;
}