invcmap.c

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/* $Revision: 1.2 $ */
/*****************************************************************************
 * The routines inv_cmap_2 and inv_cmap are copyrighted as noted below.  
 * They may be freely copied, modified, and redistributed, provided that 
 * the copyright notice is preserved on all copies.
 *
 * There is no warranty or other guarantee of fitness for this software,
 * it is provided solely "as is".  Bug reports or fixes may be sent
 * to the author, who may or may not act on them as he desires.
 *
 * You may not include this software in a program or other software product
 * without supplying the source, or without informing the end-user that the
 * source is available for no extra charge.
 *
 * If you modify this software, you should include a notice giving the
 * name of the person performing the modification, the date of modification,
 * and the reason for such modification.
 */
/*
 * inv_cmap.c - Compute an inverse colormap.
 *
 * Author:	Spencer W. Thomas
 * 		EECS Dept.
 * 		University of Michigan
 * Date:	Thu Sep 20 1990
 * Copyright (c) 1990, University of Michigan
 *
 * $Id: invcmap.c,v 1.2 1996/08/23 02:56:23 eddins Exp $
 *
 * Modified 7-93 by Joseph M. Winograd for use with MATLAB indexing and
 *	quantization.
 *
 * Modified August 96 by Steven L. Eddins to use variable typedefs
 *      from mex.h and ANSI function prototypes; also removed DEBUG code
 */

static char rcsid[] = "$Id: invcmap.c,v 1.2 1996/08/23 02:56:23 eddins Exp $";

#include <math.h>
/* #include <stdio.h> (JMW) */

#include "mex.h"  /* added by SLE */

/* Print some performance stats. */
/* #define INSTRUMENT_IT */
/* Track minimum and maximum in inv_cmap_2. */
#define MINMAX_TRACK

static int32_T bcenter, gcenter, rcenter;
static int32_T gdist, rdist, cdist;
static int32_T cbinc, cginc, crinc;
static uint32_T *gdp, *rdp, *cdp;
static int32_T *grgbp, *rrgbp, *crgbp;
static int32_T gstride, rstride;
static int32_T x, xsqr, colormax;
static int32_T cindex;
#ifdef INSTRUMENT_IT
static int32_T outercount = 0, innercount = 0;
#endif

void
inv_cmap_2( int32_T colors, int32_T *colormap, int32_T qm, int32_T qe, 
            uint32_T *dist_buf, int32_T *rgbmap, uint32_T *flops );

int32_T
redloop(void);

int32_T
greenloop( int32_T restart );

int32_T
blueloop( int32_T restart );

void maxfill( uint32_T *buffer, int32_T side )
{
    register uint32_T maxv = ~((uint32_T) 0);
    register int32_T i;
    register uint32_T *bp;

    for ( i = colormax * colormax * colormax, bp = buffer;
	  i > 0;
	  i--, bp++ )
	*bp = maxv;
}

/*****************************************************************
 * TAG( inv_cmap_2 )
 *
 * Compute an inverse colormap efficiently.
 * Inputs:
 * 	colors:		Number of colors in the forward colormap.
 * 	colormap:	The forward colormap. (In MATLAB order)
 * 	qm:		Number of quantization bits for color space.
 *			The inverse colormap will have (2^bits)^3 entries.
 *	qe:		Number of quantization bits for colormap entries.
 * 	dist_buf:	An array of (2^bits)^3 long integers to be
 * 			used as scratch space.
 *	flops:		FLOP count.
 * Outputs:
 * 	rgbmap:		The output inverse colormap.  The entry
 * 			rgbmap[(r<<(2*bits)) + (g<<bits) + b]
 * 			is the colormap entry that is closest to the
 * 			(quantized) color (r,g,b).
 * Assumptions:
 * 	Quantization is performed by right shift (low order bits are
 * 	truncated).  Thus, the distance to a quantized color is
 * 	actually measured to the color at the center of the cell
 * 	(i.e., to r+.5, g+.5, b+.5, if (r,g,b) is a quantized color).
 * Algorithm:
 * 	Uses a "distance buffer" algorithm:
 * 	The distance from each representative in the forward color map
 * 	to each point in the rgb space is computed.  If it is less
 * 	than the distance currently stored in dist_buf, then the
 * 	corresponding entry in rgbmap is replaced with the current
 * 	representative (and the dist_buf entry is replaced with the
 * 	new distance).
 *
 * 	The distance computation uses an efficient incremental formulation.
 *
 * 	Distances are computed "outward" from each color.  If the
 * 	colors are evenly distributed in color space, the expected
 * 	number of cells visited for color I is N^3/I.
 * 	Thus, the complexity of the algorithm is O(log(K) N^3),
 * 	where K = colors, and N = 2^bits.
 */

/*
 * Here's the idea:  scan from the "center" of each cell "out"
 * until we hit the "edge" of the cell -- that is, the point
 * at which some other color is closer -- and stop.  In 1-D,
 * this is simple:
 * 	for i := here to max do
 * 		if closer then buffer[i] = this color
 * 		else break
 * 	repeat above loop with i := here-1 to min by -1
 *
 * In 2-D, it's trickier, because along a "scan-line", the
 * region might start "after" the "center" point.  A picture
 * might clarify:
 *		 |    ...
 *               | ...	.
 *              ...    	.
 *           ... |      .
 *          .    +     	.
 *           .          .
 *            .         .
 *             .........
 *
 * The + marks the "center" of the above region.  On the top 2
 * lines, the region "begins" to the right of the "center".
 *
 * Thus, we need a loop like this:
 * 	detect := false
 * 	for i := here to max do
 * 		if closer then
 * 			buffer[..., i] := this color
 * 			if !detect then
 * 				here = i
 * 				detect = true
 * 		else
 * 			if detect then
 * 				break
 * 				
 * Repeat the above loop with i := here-1 to min by -1.  Note that
 * the "detect" value should not be reinitialized.  If it was
 * "true", and center is not inside the cell, then none of the
 * cell lies to the left and this loop should exit
 * immediately.
 *
 * The outer loops are similar, except that the "closer" test
 * is replaced by a call to the "next in" loop; its "detect"
 * value serves as the test.  (No assignment to the buffer is
 * done, either.)
 *
 * Each time an outer loop starts, the "here", "min", and
 * "max" values of the next inner loop should be
 * re-initialized to the center of the cell, 0, and cube size,
 * respectively.  Otherwise, these values will carry over from
 * one "call" to the inner loop to the next.  This tracks the
 * edges of the cell and minimizes the number of
 * "unproductive" comparisons that must be made.
 *
 * Finally, the inner-most loop can have the "if !detect"
 * optimized out of it by splitting it into two loops: one
 * that finds the first color value on the scan line that is
 * in this cell, and a second that fills the cell until
 * another one is closer:
 *  	if !detect then	    {needed for "down" loop}
 * 	    for i := here to max do
 * 		if closer then
 * 			buffer[..., i] := this color
 * 			detect := true
 * 			break
 *	for i := i+1 to max do
 *		if closer then
 * 			buffer[..., i] := this color
 * 		else
 * 			break
 *
 * In this implementation, each level will require the
 * following variables.  Variables labelled (l) are local to each
 * procedure.  The ? should be replaced with r, g, or b:
 *  	cdist:	    	The distance at the starting point.
 * 	?center:	The value of this component of the color
 *  	c?inc:	    	The initial increment at the ?center position.
 * 	?stride:	The amount to add to the buffer
 * 			pointers (dp and rgbp) to get to the
 * 			"next row".
 * 	min(l):		The "low edge" of the cell, init to 0
 * 	max(l):		The "high edge" of the cell, init to
 * 			colormax-1
 * 	detect(l):    	True if this row has changed some
 * 	    	    	buffer entries.
 *  	i(l): 	    	The index for this row.
 *  	?xx:	    	The accumulated increment value.
 *  	
 *  	here(l):    	The starting index for this color.  The
 *  	    	    	following variables are associated with here,
 *  	    	    	in the sense that they must be updated if here
 *  	    	    	is changed.
 *  	?dist:	    	The current distance for this level.  The
 *  	    	    	value of dist from the previous level (g or r,
 *  	    	    	for level b or g) initializes dist on this
 *  	    	    	level.  Thus gdist is associated with here(b)).
 *  	?inc:	    	The initial increment for the row.
 *
 *  	?dp:	    	Pointer into the distance buffer.  The value
 *  	    	    	from the previous level initializes this level.
 *  	?rgbp:	    	Pointer into the rgb buffer.  The value
 *  	    	    	from the previous level initializes this level.
 * 
 * The blue and green levels modify 'here-associated' variables (dp,
 * rgbp, dist) on the green and red levels, respectively, when here is
 * changed.
 */

void
inv_cmap_2( int32_T colors, int32_T *colormap, int32_T qm, int32_T qe, 
            uint32_T *dist_buf, int32_T *rgbmap, uint32_T *flops )
{
    int32_T nbits = qe - qm;
    register int32_T e;

    colormax = 1 << qm;
    x = 1 << nbits;
    xsqr = 1 << (2 * nbits);

    /* Compute "strides" for accessing the arrays. */
    gstride = colormax;
    rstride = colormax * colormax;

#ifdef INSTRUMENT_IT
	outercount = 0;
	innercount = 0;
#endif

    maxfill( dist_buf, colormax );

    e = 0;
    for ( cindex = 0; cindex < colors; cindex++ )
    {
	/*
	 * Distance formula is
	 * (red - map[0])^2 + (green - map[1])^2 + (blue - map[2])^2
	 *
	 * Because of quantization, we will measure from the center of
	 * each quantized "cube", so blue distance is
	 * 	(blue + x/2 - map[2])^2,
	 * where x = 2^(8 - bits).
	 * The step size is x, so the blue increment is
	 * 	2*x*blue - 2*x*map[2] + 2*x^2
	 *
	 * Now, b in the code below is actually blue/x, so our
	 * increment will be 2*(b*x^2 + x^2 - x*map[2]).  For
	 * efficiency, we will maintain this quantity in a separate variable
	 * that will be updated incrementally by adding 2*x^2 each time.
	 */
	/* The initial position is the cell containing the colormap
	 * entry.  We get this by quantizing the colormap values.
	 */
	rcenter = colormap[e] >> nbits;
	rdist = colormap[e] - (rcenter * x + x/2);
	crinc = 2 * ((rcenter + 1) * xsqr - (colormap[e] * x));

        e += colors;
	gcenter = colormap[e] >> nbits;
	gdist = colormap[e] - (gcenter * x + x/2);
	cginc = 2 * ((gcenter + 1) * xsqr - (colormap[e] * x));

	e += colors;
	bcenter = colormap[e] >> nbits;
	cdist = colormap[e] - (bcenter * x + x/2);
	cbinc = 2 * ((bcenter + 1) * xsqr - (colormap[e] * x));

	cdist = rdist*rdist + gdist*gdist + cdist*cdist;

	/* Array starting points. */
	cdp = dist_buf + rcenter * rstride + gcenter * gstride + bcenter;
	crgbp = rgbmap + rcenter * rstride + gcenter * gstride + bcenter;

	(void)redloop();
	e += 1 - 2*colors;
    }
#ifdef INSTRUMENT_IT
    printf( "\nK = %d, N = %d, outer count = %ld, inner count = %ld\n",
	     colors, colormax, outercount, innercount );
#endif
    *flops += 30 * colors;	/* roughly... */
}

/* redloop -- loop up and down from red center. */
int32_T
redloop(void)
{
    int32_T detect;
    int32_T r, i = cindex;
    int32_T first;
    int32_T txsqr = xsqr + xsqr;
    static int32_T here, min, max;
    static int32_T rxx;

    detect = 0;

    /* Basic loop up. */
    for ( r = rcenter, rdist = cdist, rxx = crinc,
	  rdp = cdp, rrgbp = crgbp, first = 1;
	  r < colormax;
	  r++, rdp += rstride, rrgbp += rstride,
	  rdist += rxx, rxx += txsqr, first = 0 )
    {
	if ( greenloop( first ) )
	    detect = 1;
	else if ( detect )
	    break;
    }
    
    /* Basic loop down. */
    for ( r = rcenter - 1, rxx = crinc - txsqr, rdist = cdist - rxx,
	  rdp = cdp - rstride, rrgbp = crgbp - rstride, first = 1;
	  r >= 0;
	  r--, rdp -= rstride, rrgbp -= rstride,
	  rxx -= txsqr, rdist -= rxx, first = 0 )
    {
	if ( greenloop( first ) )
	    detect = 1;
	else if ( detect )
	    break;
    }
    
    return detect;
}

/* greenloop -- loop up and down from green center. */
int32_T
greenloop( int32_T restart )
{
    int32_T detect;
    int32_T g, i = cindex;
    int32_T first;
    int32_T txsqr = xsqr + xsqr;
    static int32_T here, min, max;
#ifdef MINMAX_TRACK
    static int32_T prevmax, prevmin;
    int32_T thismax, thismin;
#endif
    static int32_T ginc, gxx, gcdist;	/* "gc" variables maintain correct */
    static uint32_T *gcdp;		/*  values for bcenter position, */
    static int32_T *gcrgbp;	/*  despite modifications by blueloop */
					/*  to gdist, gdp, grgbp. */

    if ( restart )
    {
	here = gcenter;
	min = 0;
	max = colormax - 1;
	ginc = cginc;
#ifdef MINMAX_TRACK
	prevmax = 0;
	prevmin = colormax;
#endif
    }

#ifdef MINMAX_TRACK
    thismin = min;
    thismax = max;
#endif
    detect = 0;

    /* Basic loop up. */
    for ( g = here, gcdist = gdist = rdist, gxx = ginc,