path: root/editor/pnmnorm.c

/******************************************************************************
                                  Pnmnorm
*******************************************************************************

  This program normalizes the contrast in a Netpbm image.

  by Bryan Henderson bryanh@giraffe-data.com San Jose CA March 2002.
  Adapted from Ppmnorm.

  Ppmnorm is by Wilson H. Bent, Jr. (whb@usc.edu)
  Extensively hacked from pgmnorm.c, which carries the following note:

  Copyright (C) 1989, 1991 by Jef Poskanzer.

  Permission to use, copy, modify, and distribute this software and its
  documentation for any purpose and without fee is hereby granted, provided
  that the above copyright notice appear in all copies and that both that
  copyright notice and this permission notice appear in supporting
  documentation.  This software is provided "as is" without express or
  implied warranty.

  (End of note from pgmnorm.c)

  Pgmnorm's man page also said:

  Partially based on the fbnorm filter in Michael Mauldin's "Fuzzy Pixmap"
  package.
*****************************************************************************/

#include <assert.h>

#include "pm_c_util.h"
#include "mallocvar.h"
#include "nstring.h"
#include "shhopt.h"
#include "matrix.h"
#include "pnm.h"

enum brightMethod {BRIGHT_LUMINOSITY, BRIGHT_COLORVALUE, BRIGHT_SATURATION};

struct CmdlineInfo {
    /* All the information the user supplied in the command line,
       in a form easy for the program to use.
    */
    const char * inputFileName;  /* Name of input file */
    unsigned int bvalueSpec;
    xelval bvalue;
    unsigned int bpercentSpec;
    float bpercent;
    unsigned int wvalueSpec;
    xelval wvalue;
    unsigned int wpercentSpec;
    float wpercent;
    unsigned int bsingle;
    unsigned int wsingle;
    float middle;
    unsigned int midvalueSpec;
    xelval midvalue;
    enum brightMethod brightMethod;
    unsigned int keephues;
    float maxExpansion;
        /* The maximum allowed expansion factor for expansion specified
           by per centile.  This is a factor, not a per cent increase.
           E.g. 50% increase means a factor of 1.50.
        */
    unsigned int verbose;
};



static void
parseCommandLine(int argc, const char ** argv,
                 struct CmdlineInfo * const cmdlineP) {
/*----------------------------------------------------------------------------
   parse program command line described in Unix standard form by argc
   and argv.  Return the information in the options as *cmdlineP.

   If command line is internally inconsistent (invalid options, etc.),
   issue error message to stderr and abort program.

   Note that the strings we return are stored in the storage that
   was passed to us as the argv array.  We also trash *argv.
-----------------------------------------------------------------------------*/
    optEntry *option_def;
        /* Instructions to pm_optParseOptions3 on how to parse our options.
         */
    optStruct3 opt;

    unsigned int luminosity, colorvalue, saturation;
    unsigned int middleSpec, maxexpandSpec;
    float maxexpand;

    unsigned int option_def_index;

    MALLOCARRAY_NOFAIL(option_def, 100);

    option_def_index = 0;   /* incremented by OPTENT3 */
    OPTENT3(0,   "bpercent",      OPT_FLOAT,
            &cmdlineP->bpercent,   &cmdlineP->bpercentSpec, 0);
    OPTENT3(0,   "wpercent",      OPT_FLOAT,
            &cmdlineP->wpercent,   &cmdlineP->wpercentSpec, 0);
    OPTENT3(0,   "bvalue",        OPT_UINT,
            &cmdlineP->bvalue,     &cmdlineP->bvalueSpec, 0);
    OPTENT3(0,   "wvalue",        OPT_UINT,
            &cmdlineP->wvalue,     &cmdlineP->wvalueSpec, 0);
    OPTENT3(0,   "bsingle",       OPT_FLAG,
            NULL,                 &cmdlineP->bsingle, 0);
    OPTENT3(0,   "wsingle",       OPT_FLAG,
            NULL,                 &cmdlineP->wsingle, 0);
    OPTENT3(0,   "middle",        OPT_FLOAT,
            &cmdlineP->middle,     &middleSpec, 0);
    OPTENT3(0,   "midvalue",      OPT_UINT,
            &cmdlineP->midvalue,   &cmdlineP->midvalueSpec, 0);
    OPTENT3(0,   "maxexpand",     OPT_FLOAT,
            &maxexpand,            &maxexpandSpec, 0);
    OPTENT3(0,   "keephues",      OPT_FLAG,
            NULL,                  &cmdlineP->keephues, 0);
    OPTENT3(0,   "luminosity",    OPT_FLAG,
            NULL,                  &luminosity, 0);
    OPTENT3(0,   "colorvalue",    OPT_FLAG,
            NULL,                  &colorvalue, 0);
    OPTENT3(0,   "saturation",    OPT_FLAG,
            NULL,                  &saturation, 0);
    OPTENT3(0,   "brightmax",     OPT_FLAG,
            NULL,                  &colorvalue, 0);
    OPTENT3(0,   "verbose",       OPT_FLAG,
            NULL,                  &cmdlineP->verbose, 0);

    /* Note: -brightmax was documented and accepted long before it was
       actually implemented.  By the time we implemented it, we
       decided -colorvalue was a better name for it.
    */

    opt.opt_table = option_def;
    opt.short_allowed = FALSE;  /* We have no short (old-fashioned) options */
    opt.allowNegNum = FALSE;  /* We have no parms that are negative numbers */

    pm_optParseOptions3(&argc, (char **)argv, opt, sizeof(opt), 0);
        /* Uses and sets argc, argv, and some of *cmdline_p and others. */

    if (!cmdlineP->wpercentSpec)
        cmdlineP->wpercent = 1.0;
    if (!cmdlineP->bpercentSpec)
        cmdlineP->bpercent = 2.0;

    if (cmdlineP->wpercent < 0.0)
        pm_error("You specified a negative value for wpercent: %f",
                 cmdlineP->wpercent);
    if (cmdlineP->bpercent < 0.0)
        pm_error("You specified a negative value for bpercent: %f",
                 cmdlineP->bpercent);
    if (cmdlineP->wpercent > 100.0)
        pm_error("You specified a per centage > 100 for wpercent: %f",
                 cmdlineP->wpercent);
    if (cmdlineP->bpercent > 100.0)
        pm_error("You specified a per centage > 100 for bpercent: %f",
                 cmdlineP->bpercent);

    if (cmdlineP->bsingle && (cmdlineP->bpercentSpec || cmdlineP->bvalueSpec))
        pm_error("You cannot specify both -bsingle and -bpercent or -bvalue");

    if (cmdlineP->wsingle && (cmdlineP->wpercentSpec || cmdlineP->wvalueSpec))
        pm_error("You cannot specify both -wsingle and -wpercent or -wvalue");

    if (middleSpec) {
        if (cmdlineP->middle < 0.0 || cmdlineP->middle > 1.0)
            pm_error("-middle is a normalized brightness value; it "
                     "must be in the range 0..1.  You specified %f",
                     cmdlineP->middle);
    } else
        cmdlineP->middle = 0.5;

    if (luminosity + colorvalue + saturation > 1)
        pm_error("You can specify only one of "
                 "-luminosity, -colorvalue, and -saturation");
    else {
        if (colorvalue)
            cmdlineP->brightMethod = BRIGHT_COLORVALUE;
        else if (saturation)
            cmdlineP->brightMethod = BRIGHT_SATURATION;
        else
            cmdlineP->brightMethod = BRIGHT_LUMINOSITY;
    }
    if (maxexpandSpec) {
        if (maxexpand < 0)
            pm_error("-maxexpand must be positive.  You specified %f",
                     maxexpand);
        else
            cmdlineP->maxExpansion = 1 + (float)maxexpand/100;
    } else
        cmdlineP->maxExpansion = 1e6;  /* essentially infinite */

    if (argc-1 > 1)
        pm_error("Program takes at most one argument: the input file "
                 "specification.  "
                 "You specified %d arguments.", argc-1);
    if (argc-1 < 1)
        cmdlineP->inputFileName = "-";
    else
        cmdlineP->inputFileName = argv[1];
}



static void
buildHistogram(FILE *   const ifp,
               int      const cols,
               int      const rows,
               xelval   const maxval,
               int      const format,
               unsigned int   hist[],
               enum brightMethod const brightMethod) {
/*----------------------------------------------------------------------------
   Build the histogram of brightness values for the image that is in file
   'ifp', which is positioned just after the header (at the raster).

   The histogram is the array hist[] such that hist[x] is the number
   of xels in the image that have brightness x.  That brightness is
   either the color value (intensity of most intense component) of the
   xel or it is the luminosity of the xel, depending on
   'brightMethod'.  In either case, it is based on the same maxval as
   the image, which is 'maxval'.  The image is 'cols' columns wide by
   'rows' rows high.

   Leave the file positioned arbitrarily.
-----------------------------------------------------------------------------*/
    int row;
    xel * xelrow;

    xelrow = pnm_allocrow(cols);

    {
        unsigned int i;
        for (i = 0; i <= maxval; ++i)
            hist[i] = 0;
    }
    for (row = 0; row < rows; ++row) {
        int col;
        pnm_readpnmrow(ifp, xelrow, cols, maxval, format);
        for (col = 0; col < cols; ++col) {
            xelval brightness;
            xel const p = xelrow[col];
            if (PNM_FORMAT_TYPE(format) == PPM_TYPE) {
                switch(brightMethod) {
                case BRIGHT_LUMINOSITY:
                    brightness = ppm_luminosity(p);
                    break;
                case BRIGHT_COLORVALUE:
                    brightness = ppm_colorvalue(p);
                    break;
                case BRIGHT_SATURATION:
                    brightness = ppm_saturation(p, maxval);
                    break;
                }
            } else
                brightness = PNM_GET1(p);
            ++hist[brightness];
        }
    }
    pnm_freerow(xelrow);
}



static xelval
minimumValue(const unsigned int * const hist,
             unsigned int         const highest) {
/*----------------------------------------------------------------------------
   The minimum brightness in the image, according to histogram 'hist',
   which goes up to 'highest'.

   Abort the program if there are no pixels of any brightness.
-----------------------------------------------------------------------------*/
    xelval i;
    bool foundOne;

    for (i = 0, foundOne = false; !foundOne; ) {
        if (hist[i] > 0)
            foundOne = true;
        else {
            if (i == highest)
                pm_error("INTERNAL ERROR in function 'minimumValue'.  "
                         "No pixels");
            else
                ++i;
        }
    }
    return i;
}



static xelval
maximumValue(const unsigned int * const hist,
             unsigned int         const highest) {
/*----------------------------------------------------------------------------
   The maximum brightness in the image, according to histogram 'hist',
   which goes up to 'highest'.

   Abort the program if there are no pixels of any brightness.
-----------------------------------------------------------------------------*/
    xelval i;
    bool foundOne;

    for (i = highest, foundOne = false; !foundOne; ) {
        if (hist[i] > 0)
            foundOne = true;
        else {
            if (i == 0)
                pm_error("INTERNAL ERROR in function 'maximumValue'.  "
                         "No pixels");
            else
                --i;
        }
    }
    return i;
}



static unsigned int
brightnessCount(const unsigned int * const hist,
                unsigned int         const highest) {
/*----------------------------------------------------------------------------
   The number of distinct brightnesses in the image according to
   histogram 'hist', which goes up to brightness 'highest'.
-----------------------------------------------------------------------------*/
    xelval i;
    unsigned int nonzeroCount;

    for (i = 0, nonzeroCount = 0; i <= highest; ++i) {
        if (hist[i] > 0)
            ++nonzeroCount;
    }

    return nonzeroCount;
}



static void
computeBottomPercentile(const unsigned int * const hist,
                        unsigned int         const highest,
                        unsigned int         const total,
                        float                const percent,
                        unsigned int *       const percentileP) {
/*----------------------------------------------------------------------------
   Compute the lowest index of hist[] such that the sum of the hist[]
   values with that index and lower represent at least 'percent' per cent of
   'total' (which is assumed to be the sum of all the values in hist[],
   given to us to save us the time of computing it).
-----------------------------------------------------------------------------*/
    unsigned int cutoff = total * percent / 100.0;
    unsigned int count;
    unsigned int percentile;

    percentile = 0; /* initial value */
    count = hist[0];  /* initial value */

    while (count < cutoff) {
        if (percentile == highest)
            pm_error("Internal error: computeBottomPercentile() received"
                     "a 'total' value greater than the sum of the hist[]"
                     "values");
        ++percentile;
        count += hist[percentile];
    }
    *percentileP = percentile;
}



static void
computeTopPercentile(const unsigned int * const hist,
                     unsigned int         const highest,
                     unsigned int         const total,
                     float                const percent,
                     unsigned int *       const percentileP) {
/*----------------------------------------------------------------------------
   Compute the highest index of hist[] such that the sum of the hist[]
   values with that index and higher represent 'percent' per cent of
   'total' (which is assumed to be the sum of all the values in hist[],
   given to us to save us the time of computing it).
-----------------------------------------------------------------------------*/
    unsigned int cutoff = total * percent / 100.0;
    unsigned int count;
    unsigned int percentile;

    percentile = highest; /* initial value */
    count = hist[highest];

    while (count < cutoff) {
        --percentile;
        count += hist[percentile];
    }
    *percentileP = percentile;
}



static void
computeAdjustmentForExpansionLimit(xelval   const maxval,
                                   xelval   const unlBvalue,
                                   xelval   const unlWvalue,
                                   float    const maxExpansion,
                                   xelval * const bLowerP,
                                   xelval * const wRaiseP) {
/*----------------------------------------------------------------------------
   Assuming 'unlBvalue' and 'unlWvalue' are the appropriate bvalue and
   wvalue to normalize the image to 0 .. maxval, compute the amount
   by which the bvalue must be raised and the wvalue lowered from that
   in order to cap the expansion factor at 'maxExpansion'.

   E.g. if 'maxval' is 100, 'unlBvalue' is 20 and 'unlWvalue' is 70, that
   implies an expansion factor of 100/50 (because the range goes from
   70-20, which is 50, to 100 - 0, which is 100).  If 'maxEpansion' is
   1.333, these values are unacceptable.  To get down to the desired 1.333
   factor, we need the span of bvalue to wvalue to be 75, not 50.  So
   we need to raise the bvalue and lower the wvalue by a total of 25.
   We apportion that adjustment to bvalue and wvalue in proportion to
   how close each is already to it's end (which we call the margin).
   'unlBvalue' is 20 from its end, while 'unlWvalue' is 30 from its end,
   so we want to lower the bvalue by 10 and raise the wvalue by 15.
   Ergo we return *bLowerP = 10 and *wRaise = 15.
-----------------------------------------------------------------------------*/
    unsigned int const newRange = maxval - 0;
        /* The range of sample values after normalization, if we used
           the unlimited bvalue and wvalue
        */
    unsigned int const oldRange = unlWvalue - unlBvalue;
        /* The range of sample values in the original image that normalize
           to 0 .. maxval, if we used the unlimited bvalue and wvalue
        */
    float const unlExpansion = (float)newRange/oldRange;

    if (unlExpansion <= maxExpansion) {
        /* No capping is necessary.  Unlimited values are already within
           range.
           */
        *bLowerP = 0;
        *wRaiseP = 0;
    } else {
        unsigned int const totalWidening = newRange/maxExpansion - oldRange;
            /* Amount by which the (bvalue, wvalue) range must be widened
               to limit expansion to 'maxExpansion'
            */
        unsigned int const bMargin = unlBvalue - 0;
        unsigned int const wMargin = maxval - unlWvalue;

        /* Apportion 'totalWidening' between the black and and the
           white end
        */
        *bLowerP =
            ROUNDU((float)bMargin / (bMargin + wMargin) * totalWidening);
        *wRaiseP =
            ROUNDU((float)wMargin / (bMargin + wMargin) * totalWidening);

        pm_message("limiting expansion of %.1f%% to %.1f%%",
                   (unlExpansion - 1) * 100, (maxExpansion -1) * 100);
    }
}



static void
disOverlap(xelval   const reqBvalue,
           xelval   const reqWvalue,
           bool     const bIsFixed,
           bool     const wIsFixed,
           xelval   const maxval,
           xelval * const nonOlapBvalueP,
           xelval * const nonOlapWvalueP) {
/*----------------------------------------------------------------------------
   Compute black and white end values that don't overlap, i.e. the
   black value is darker than the white, from an initial attempt that
   might overlap.

   'req{B|W}value' is that initial attempt.  We return the
   nonoverlapping version as *nonOlap{B|W}valueP.

   '{b|w}IsFixed' means we cannot change that endpoint.

   If both ends are fixed 'reqBvalue' and 'reqWvalue' overlap, we just
   fail the program -- the user asked for the impossible.

   Where one end is fixed and the other is not, we move the unfixed end
   to be one unit above or below the fixed end, as appropriate.

   Where both ends are free, we move them to the point halfway between them,
   the white end being one more than the black end.
-----------------------------------------------------------------------------*/
    assert(maxval > 0);

    if (reqBvalue < reqWvalue) {
        /* No overlap; initial attempt is fine. */
        *nonOlapBvalueP = reqBvalue;
        *nonOlapWvalueP = reqWvalue;
    } else {
        if (bIsFixed && wIsFixed)
            pm_error("The colors which become black (value <= %u) "
                     "would overlap the "
                     "colors which become white (value >= %u).",
                     reqBvalue, reqWvalue);
        else if (bIsFixed) {
            if (reqBvalue >= maxval)
                pm_error("The black value must be less than the maxval");
            else {
                *nonOlapBvalueP = reqBvalue;
                *nonOlapWvalueP = reqBvalue + 1;
            }
        } else if (wIsFixed) {
            if (reqWvalue == 0)
                pm_error("The white value must be greater than 0");
            else {
                *nonOlapBvalueP = reqWvalue - 1;
                *nonOlapWvalueP = reqWvalue;
            }
        } else {
            /* Both ends are free; use the point halfway between them. */
            xelval const midPoint = (reqWvalue + reqBvalue)/2;
            *nonOlapBvalueP = MIN(midPoint, maxval-1);
            *nonOlapWvalueP = *nonOlapBvalueP + 1;
        }
    }
}



static xelval
resolvedPctBvalue(const unsigned int * const hist,
                  unsigned int         const totalPixelCt,
                  xelval               const maxval,
                  struct CmdlineInfo   const cmdline) {

    xelval retval;

    if (cmdline.bsingle)
        retval = minimumValue(hist, maxval);
    else if (cmdline.bvalueSpec && !cmdline.bpercentSpec) {
        retval = cmdline.bvalue;
    } else {
        xelval percentBvalue;

        computeBottomPercentile(hist, maxval, totalPixelCt, cmdline.bpercent,
                                &percentBvalue);
        if (cmdline.bvalueSpec)
            retval = MIN(percentBvalue, cmdline.bvalue);
        else
            retval = percentBvalue;
    }
    return retval;
}



static xelval
resolvedPctWvalue(const unsigned int * const hist,
                  unsigned int         const totalPixelCt,
                  xelval               const maxval,
                  struct CmdlineInfo   const cmdline) {

    xelval retval;

    if (cmdline.wsingle)
        retval = maximumValue(hist, maxval);
    else if (cmdline.wvalueSpec && !cmdline.wpercentSpec) {
        retval = cmdline.wvalue;
    } else {
        xelval percentWvalue;

        computeTopPercentile(hist, maxval, totalPixelCt, cmdline.wpercent,
                             &percentWvalue);
        if (cmdline.wvalueSpec)
            retval = MAX(percentWvalue, cmdline.wvalue);
        else
            retval = percentWvalue;
    }

    return retval;
}



static void
resolvePercentParams(FILE *             const ifP,
                     unsigned int       const cols,
                     unsigned int       const rows,
                     xelval             const maxval,
                     int                const format,
                     struct CmdlineInfo const cmdline,
                     xelval *           const bvalueP,
                     xelval *           const wvalueP) {
/*----------------------------------------------------------------------------
   Figure out the endpoint of the stretch (the value that is to be stretched
   to black and the one that is to be stretched to white) as requested
   by the -{b,w}{value,percent,single} options.

   These values may be invalid because of overlapping, and they may exceed
   the maximum allowed stretch; Caller must deal with that.
-----------------------------------------------------------------------------*/
    unsigned int * hist;  /* malloc'ed */

    MALLOCARRAY(hist, PNM_OVERALLMAXVAL+1);

    if (hist == NULL)
        pm_error("Unable to allocate storage for intensity histogram.");
    else {
        buildHistogram(ifP, cols, rows, maxval, format, hist,
                       cmdline.brightMethod);

        if (!cmdline.bvalueSpec && !cmdline.wvalueSpec &&
            brightnessCount(hist, maxval) < 2) {
            /* Special case - you can't stretch a single brightness to both
               ends.  So just don't stretch at all.
            */
            *bvalueP = 0;
            *wvalueP = maxval;
        } else {
            *bvalueP = resolvedPctBvalue(hist, cols * rows, maxval, cmdline);

            *wvalueP = resolvedPctWvalue(hist, cols * rows, maxval, cmdline);
        }
        free(hist);
    }
}



static void
computeEndValues(FILE *             const ifP,
                 int                const cols,
                 int                const rows,
                 xelval             const maxval,
                 int                const format,
                 struct CmdlineInfo const cmdline,
                 xelval *           const bvalueP,
                 xelval *           const wvalueP,
                 bool *             const quadraticP,
                 xelval *           const midvalueP) {
/*----------------------------------------------------------------------------
   Figure out what original values will be translated to full bright and full
   dark and, if user requested, a middle brightness -- thus defining to what
   all the other values get translated.

   This may involve looking at the image.  The image is in the file 'ifP',
   which is positioned just past the header (at the raster).  Leave it
   positioned arbitrarily.

   We return *quadraticP == true iff the normalization is to be via a
   quadratic transfer function fixed at 3 points - full bright, full dark, and
   something in between.  In that case, the original brightnesses of those
   three points are *bvalueP, *midvalueP, and *wvalueP.  We return *quadraticP
   == false iff the normalization is to be via a linear function fixed at 2
   points - full bright and full dark.  In that case, *midvalueP is
   meaningless.
-----------------------------------------------------------------------------*/
    xelval reqBvalue, reqWvalue, nonOlapBvalue, nonOlapWvalue;
    unsigned int bLower, wRaise;

    resolvePercentParams(ifP, cols, rows, maxval, format, cmdline,
                         &reqBvalue, &reqWvalue);

    disOverlap(reqBvalue, reqWvalue,
               cmdline.bvalueSpec, cmdline.wvalueSpec, maxval,
               &nonOlapBvalue, &nonOlapWvalue);

    computeAdjustmentForExpansionLimit(
        maxval, nonOlapBvalue, nonOlapWvalue, cmdline.maxExpansion,
        &bLower, &wRaise);

    *bvalueP = nonOlapBvalue - bLower;
    *wvalueP = nonOlapWvalue + wRaise;

    if (cmdline.midvalueSpec) {
        if (cmdline.midvalue > *bvalueP && cmdline.midvalue < *wvalueP) {
            *quadraticP = true;
            *midvalueP = cmdline.midvalue;
        } else
            *quadraticP = false;
    } else
        *quadraticP = false;
}



static void
computeLinearTransfer(xelval   const bvalue,
                      xelval   const wvalue,
                      xelval   const maxval,
                      xelval * const newBrightness) {
/*----------------------------------------------------------------------------
   Map the middle brightnesses (the ones that don't get clipped to full dark
   or full bright, i.e. from 'bvalue' to 'wvalue') linearly onto 0..maxval.
   Set this mapping in newBrightness[].
-----------------------------------------------------------------------------*/
    unsigned int const range = wvalue - bvalue;

    xelval i;
    unsigned int val;
    /* The following for structure is a hand optimization of this one:
       for (i = bvalue; i <= wvalue; ++i)
           newBrightness[i] = (i-bvalue)*maxval/range);
       (with proper rounding)
    */
    for (i = bvalue, val = range/2;
         i <= wvalue;
         ++i, val += maxval)
        newBrightness[i] = MIN(val / range, maxval);

    assert(newBrightness[bvalue] == 0);
    assert(newBrightness[wvalue] == maxval);
}



typedef struct {
/*----------------------------------------------------------------------------
   A quadratic polynomial function
-----------------------------------------------------------------------------*/
    double a;  /* x^2 coefficient */
    double b;  /* x^1 coefficient */
    double c;  /* x^0 coefficient */
} Quadfn;



static void
computeQuadraticFunction(xelval   const bvalue,
                         xelval   const midvalue,
                         xelval   const wvalue,
                         xelval   const middle,
                         xelval   const maxval,
                         Quadfn * const functionP) {

    /* The matrix equation we solve (for varMatrix) is

       a * x = c
    */
    double ** a;
    double c[3];
    double x[3];
    const char * error;

    MALLOCARRAY2_NOFAIL(a, 3, 3);

    a[0][0] = SQR(bvalue);   a[0][1] = bvalue;   a[0][2] = 1.0;
    a[1][0] = SQR(midvalue); a[1][1] = midvalue; a[1][2] = 1.0;
    a[2][0] = SQR(wvalue);   a[2][1] = wvalue;   a[2][2] = 1.0;

    c[0] = 0.0;
    c[1] = middle;
    c[2] = maxval;

    pm_solvelineareq(a, x, c, 3, &error);

    if (error) {
        pm_error("Cannot fit a quadratic function to the points "
                 "(%u, %u), (%u, %u), and (%u, %u).  %s",
                 bvalue, 0, midvalue, middle, wvalue, maxval, error);
        pm_strfree(error);
    } else {
        functionP->a = x[0];
        functionP->b = x[1];
        functionP->c = x[2];
    }

    pm_freearray2((void **)a);
}



static void
computeQuadraticTransfer(xelval   const bvalue,
                         xelval   const midvalue,
                         xelval   const wvalue,
                         float    const middleNorm,
                         xelval   const maxval,
                         bool     const verbose,
                         xelval * const newBrightness) {
/*----------------------------------------------------------------------------
   Map the middle brightnesses (the ones that don't get clipped to full dark
   or full bright, i.e. from 'bvalue' to 'wvalue') quadratically onto
   0..maxval, such that 'bvalue' maps to 0, 'wvalue' maps to 'maxval, and
   'midvalue' maps to the normalized value 'middleNorm' (i.e. the actual
   xelval middleNorm * maxval).

   Set this mapping in newBrightness[].
-----------------------------------------------------------------------------*/
    xelval const middle = pnm_unnormalize(middleNorm, maxval);

    /* Computing this function is just the task of finding a parabola that
       passes through 3 given points:

           (bvalue, 0)
           (midvalue, middle)
           (wvalue, maxval)

       We do that by solving the system of three linear equations in
       in 3 variables.  The 3 variables are the coefficients of the
       quadratic function we're looking for -- A, B, and C in this:

           NEWVAL = A * OLDVAL^2 + B * OLDVAL + C

       The three equations of the system are:

           0      = A * bvalue^2   + B * bvalue   + C
           middle = A * midvalue^2 + B * midvalue + C
           maxval = A * wvalue^2   + B * wvalue   + C

       Expressed in matrix form:

          [ bvalue^2   bvalue   1 ]   [ A ]   [ 0      ]
          [ midvalue^2 midvalue 1 ] * [ B ] = [ middle ]
          [ wvalue^2   wvalue   1 ]   [ C ]   [ maxval ]

       So we solve that for A, B, and C.

       With those coefficients, we have the quadratic function, and we
       simple apply it to every old sample value I in the range to get the
       new:

           newBrightness[I] = A * I^2 + B * I + C
    */

    Quadfn xfer;

    computeQuadraticFunction(bvalue, midvalue, wvalue, middle, maxval,
                             &xfer);


    if (verbose)
        pm_message("Transfer function is %f * s^2 + %f * s + %f",
                   xfer.a, xfer.b, xfer.c);

    {
        xelval i;
        for (i = bvalue; i <= wvalue; ++i)
            newBrightness[i] =
                MIN(ROUNDU(xfer.a * SQR(i) + xfer.b * i + xfer.c), maxval);
    }
}



static void
computeTransferFunction(bool      const quadratic,
                        xelval    const bvalue,
                        xelval    const midvalue,
                        xelval    const wvalue,
                        float     const middle,
                        xelval    const maxval,
                        bool      const verbose,
                        xelval ** const newBrightnessP) {
/*----------------------------------------------------------------------------
   Compute the transfer function, i.e. the array *newBrightnessP such that
   (*newBrightnessP)[x] is the brightness of the xel that should replace a
   xel with brightness x.  Brightness in this case means either luminosity
   or color value (and it doesn't matter to us which).

   'bvalue' is the highest brightness that should map to zero brightness;
   'wvalue' is the lowest brightness that should map to full brightness.

   If 'quadratic' is false, brightnesses in between should be stretched
   linearly.  Otherwise, brightness 'midvalue' should map to brightness
   'middle' (which is expressed on a 0..1 normalized scale) and brightnesses
   should be stretched according to a quadratic polynomial that includes those
   3 points.

   This stretching could conceivably result in more brightnesses mapping to
   zero and full brightness that 'bvalue' and 'wvalue' demand, because of
   rounding.

   Define function only for values 0..maxval.
-----------------------------------------------------------------------------*/
    xelval * newBrightness;
    xelval i;

    MALLOCARRAY(newBrightness, maxval+1);

    if (newBrightness == NULL)
        pm_error("Unable to allocate memory for transfer function.");

    /* Clip the lowest brightnesses to zero */
    if (bvalue > 0)
        for (i = 0; i < bvalue; ++i)
            newBrightness[i] = 0;

    /* Map the middle brightnesses onto 0..maxval */

    if (quadratic)
        computeQuadraticTransfer(bvalue, midvalue, wvalue, middle, maxval,
                                 verbose, newBrightness);
    else
        computeLinearTransfer(bvalue, wvalue, maxval, newBrightness);

    /* Clip the highest brightnesses to maxval */
    for (i = wvalue+1; i <= maxval; ++i)
        newBrightness[i] = maxval;

    *newBrightnessP = newBrightness;
}



static float
brightScaler(xel               const p,
             pixval            const maxval,
             xelval            const newBrightness[],
             enum brightMethod const brightMethod) {
/*----------------------------------------------------------------------------
  Return the multiple by which the brightness pixel of color 'p' (based
  on maxval 'maxval') should be changed according to the transfer
  function newBrightness[], using the 'brightMethod' measure of
  brightness.

  For example, if 'brightMethod' is BRIGHT_LUMINOSITY, p is has
  luminosity 50, and newBrightness[50] is 75, we would return 1.5.
-----------------------------------------------------------------------------*/
    xelval oldBrightness;
    float scaler;

    switch (brightMethod) {
    case BRIGHT_LUMINOSITY:
        oldBrightness = ppm_luminosity(p);
        break;
    case BRIGHT_COLORVALUE:
        oldBrightness = ppm_colorvalue(p);
        break;
    case BRIGHT_SATURATION:
        oldBrightness = ppm_saturation(p, maxval);
        break;
    }
    if (oldBrightness == 0) {
        assert(newBrightness[oldBrightness] == 0);
        /* Doesn't matter what we scale by.  zero times anything is zero. */
        scaler = 1.0;
    } else
        scaler = (float)newBrightness[oldBrightness]/oldBrightness;

    return scaler;
}



static void
writeRowNormalized(xel *             const xelrow,
                   int               const cols,
                   xelval            const maxval,
                   int               const format,
                   enum brightMethod const brightMethod,
                   bool              const keephues,
                   xelval            const newBrightness[],
                   xel *             const rowbuf) {
/*----------------------------------------------------------------------------
   Write to Standard Output a normalized version of the xel row
   'xelrow'.  Normalize it via the transfer function newBrightness[].

   Use 'rowbuf' as a work buffer.  It is at least 'cols' columns wide.
-----------------------------------------------------------------------------*/
    xel * const outrow = rowbuf;

    unsigned int col;
    for (col = 0; col < cols; ++col) {
        xel const p = xelrow[col];

        if (PPM_FORMAT_TYPE(format) == PPM_TYPE) {
            if (keephues) {
                float const scaler =
                    brightScaler(p, maxval, newBrightness, brightMethod);

                xelval const r = MIN(ROUNDU(PPM_GETR(p)*scaler), maxval);
                xelval const g = MIN(ROUNDU(PPM_GETG(p)*scaler), maxval);
                xelval const b = MIN(ROUNDU(PPM_GETB(p)*scaler), maxval);
                PNM_ASSIGN(outrow[col], r, g, b);
            } else
                PNM_ASSIGN(outrow[col],
                           newBrightness[PPM_GETR(p)],
                           newBrightness[PPM_GETG(p)],
                           newBrightness[PPM_GETB(p)]);
        } else
            PNM_ASSIGN1(outrow[col], newBrightness[PNM_GET1(p)]);
    }
    pnm_writepnmrow(stdout, outrow, cols, maxval, format, 0);
}



static void
reportTransferParm(bool   const quadratic,
                   xelval const bvalue,
                   xelval const midvalue,
                   xelval const wvalue,
                   xelval const maxval,
                   float  const middle) {

    if (quadratic)
        pm_message("remapping %u..%u..%u to %u..%u..%u",
                   bvalue, midvalue, wvalue,
                   0, pnm_unnormalize(middle, maxval), maxval);
    else
        pm_message("remapping %u..%u to %u..%u",
                   bvalue, wvalue, 0, maxval);
}



int
main(int argc, const char *argv[]) {

    struct CmdlineInfo cmdline;
    FILE * ifP;
    pm_filepos imagePos;
    xelval maxval;
    int rows, cols, format;
    bool quadratic;
    xelval bvalue, midvalue, wvalue;

    pm_proginit(&argc, argv);

    parseCommandLine(argc, argv, &cmdline);

    ifP = pm_openr_seekable(cmdline.inputFileName);

    /* Rescale so that bvalue maps to 0, wvalue maps to maxval. */
    pnm_readpnminit(ifP, &cols, &rows, &maxval, &format);
    pm_tell2(ifP, &imagePos, sizeof(imagePos));

    computeEndValues(ifP, cols, rows, maxval, format, cmdline,
                     &bvalue, &wvalue, &quadratic, &midvalue);
    {
        xelval * newBrightness;
        int row;
        xel * xelrow;
        xel * rowbuf;

        assert(wvalue > bvalue);

        xelrow = pnm_allocrow(cols);

        reportTransferParm(quadratic, bvalue, midvalue, wvalue, maxval,
                           cmdline.middle);


        computeTransferFunction(quadratic, bvalue, midvalue, wvalue,
                                cmdline.middle, maxval, cmdline.verbose,
                                &newBrightness);

        pm_seek2(ifP, &imagePos, sizeof(imagePos));
        pnm_writepnminit(stdout, cols, rows, maxval, format, 0);

        rowbuf = pnm_allocrow(cols);

        for (row = 0; row < rows; ++row) {
            pnm_readpnmrow(ifP, xelrow, cols, maxval, format);
            writeRowNormalized(xelrow, cols, maxval, format,
                               cmdline.brightMethod, cmdline.keephues,
                               newBrightness, rowbuf);
        }
        free(newBrightness);
        pnm_freerow(rowbuf);
        pnm_freerow(xelrow);
    }
    pm_close(ifP);
    return 0;
}