TRAITEMENT DE L'IMAGE: FILTRE MÉDIAN EN TEMPS CONSTANT

/*
 * ctmf.c - Constant-time median filtering
 * Copyright (C) 2006  Simon Perreault
 *
 * Reference: S. Perreault and P. Hébert, "Median Filtering in Constant Time",
 * IEEE Transactions on Image Processing, September 2007.
 *
 * This program has been obtained from http://nomis80.org/ctmf.html. No patent
 * covers this program, although it is subject to the following license:
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
 *
 * Contact:
 *  Laboratoire de vision et systèmes numériques
 *  Pavillon Adrien-Pouliot
 *  Université Laval
 *  Sainte-Foy, Québec, Canada
 *  G1K 7P4
 *
 *  perreaul@gel.ulaval.ca
 */

/* Standard C includes */
#include <assert.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>

/* Type declarations */
#ifdef _MSC_VER
#include <basetsd.h>
typedef UINT8 uint8_t;
typedef UINT16 uint16_t;
typedef UINT32 uint32_t;
#pragma warning( disable: 4799 )
#else
#include <stdint.h>
#endif

/* Intrinsic declarations */
#if defined(__SSE2__) || defined(__MMX__)
#if defined(__SSE2__)
#include <emmintrin.h>
#elif defined(__MMX__)
#include <mmintrin.h>
#endif
#if defined(__GNUC__)
#include <mm_malloc.h>
#elif defined(_MSC_VER)
#include <malloc.h>
#endif
#elif defined(__ALTIVEC__)
#include <altivec.h>
#endif

/* Compiler peculiarities */
#if defined(__GNUC__)
#include <stdint.h>
#define inline __inline__
#define align(x) __attribute__ ((aligned (x)))
#elif defined(_MSC_VER)
#define inline __inline
#define align(x) __declspec(align(x))
#else
#define inline
#define align(x)
#endif

#ifndef MIN
#define MIN(a,b) ((a) > (b) ? (b) : (a))
#endif

#ifndef MAX
#define MAX(a,b) ((a) < (b) ? (b) : (a))
#endif

/**
 * This structure represents a two-tier histogram. The first tier (known as the
 * "coarse" level) is 4 bit wide and the second tier (known as the "fine" level)
 * is 8 bit wide. Pixels inserted in the fine level also get inserted into the
 * coarse bucket designated by the 4 MSBs of the fine bucket value.
 *
 * The structure is aligned on 16 bytes, which is a prerequisite for SIMD
 * instructions. Each bucket is 16 bit wide, which means that extra care must be
 * taken to prevent overflow.
 */
typedef struct align(16)
{
    uint16_t coarse[16];
    uint16_t fine[16][16];
} Histogram;

/**
 * HOP is short for Histogram OPeration. This macro makes an operation \a op on
 * histogram \a h for pixel value \a x. It takes care of handling both levels.
 */
#define HOP(h,x,op) \
    h.coarse[x>>4] op; \
    *((uint16_t*) h.fine + x) op;

#define COP(c,j,x,op) \
    h_coarse[ 16*(n*c+j) + (x>>4) ] op; \
    h_fine[ 16 * (n*(16*c+(x>>4)) + j) + (x & 0xF) ] op;

/**
 * Adds histograms \a x and \a y and stores the result in \a y. Makes use of
 * SSE2, MMX or Altivec, if available.
 */
#if defined(__SSE2__)
static inline void histogram_add( const uint16_t x[16], uint16_t y[16] )
{
    *(__m128i*) &y[0] = _mm_add_epi16( *(__m128i*) &y[0], *(__m128i*) &x[0] );
    *(__m128i*) &y[8] = _mm_add_epi16( *(__m128i*) &y[8], *(__m128i*) &x[8] );
}
#elif defined(__MMX__)
static inline void histogram_add( const uint16_t x[16], uint16_t y[16] )
{
    *(__m64*) &y[0]  = _mm_add_pi16( *(__m64*) &y[0],  *(__m64*) &x[0]  );
    *(__m64*) &y[4]  = _mm_add_pi16( *(__m64*) &y[4],  *(__m64*) &x[4]  );
    *(__m64*) &y[8]  = _mm_add_pi16( *(__m64*) &y[8],  *(__m64*) &x[8]  );
    *(__m64*) &y[12] = _mm_add_pi16( *(__m64*) &y[12], *(__m64*) &x[12] );
}
#elif defined(__ALTIVEC__)
static inline void histogram_add( const uint16_t x[16], uint16_t y[16] )
{
    *(vector unsigned short*) &y[0] = vec_add( *(vector unsigned short*) &y[0], *(vector unsigned short*) &x[0] );
    *(vector unsigned short*) &y[8] = vec_add( *(vector unsigned short*) &y[8], *(vector unsigned short*) &x[8] );
}
#else
static inline void histogram_add( const uint16_t x[16], uint16_t y[16] )
{
    int i;
    for ( i = 0; i < 16; ++i ) {
        y[i] += x[i];
    }
}
#endif

/**
 * Subtracts histogram \a x from \a y and stores the result in \a y. Makes use
 * of SSE2, MMX or Altivec, if available.
 */
#if defined(__SSE2__)
static inline void histogram_sub( const uint16_t x[16], uint16_t y[16] )
{
    *(__m128i*) &y[0] = _mm_sub_epi16( *(__m128i*) &y[0], *(__m128i*) &x[0] );
    *(__m128i*) &y[8] = _mm_sub_epi16( *(__m128i*) &y[8], *(__m128i*) &x[8] );
}
#elif defined(__MMX__)
static inline void histogram_sub( const uint16_t x[16], uint16_t y[16] )
{
    *(__m64*) &y[0]  = _mm_sub_pi16( *(__m64*) &y[0],  *(__m64*) &x[0]  );
    *(__m64*) &y[4]  = _mm_sub_pi16( *(__m64*) &y[4],  *(__m64*) &x[4]  );
    *(__m64*) &y[8]  = _mm_sub_pi16( *(__m64*) &y[8],  *(__m64*) &x[8]  );
    *(__m64*) &y[12] = _mm_sub_pi16( *(__m64*) &y[12], *(__m64*) &x[12] );
}
#elif defined(__ALTIVEC__)
static inline void histogram_sub( const uint16_t x[16], uint16_t y[16] )
{
    *(vector unsigned short*) &y[0] = vec_sub( *(vector unsigned short*) &y[0], *(vector unsigned short*) &x[0] );
    *(vector unsigned short*) &y[8] = vec_sub( *(vector unsigned short*) &y[8], *(vector unsigned short*) &x[8] );
}
#else
static inline void histogram_sub( const uint16_t x[16], uint16_t y[16] )
{
    int i;
    for ( i = 0; i < 16; ++i ) {
        y[i] -= x[i];
    }
}
#endif

static inline void histogram_muladd( const uint16_t a, const uint16_t x[16],
        uint16_t y[16] )
{
    int i;
    for ( i = 0; i < 16; ++i ) {
        y[i] += a * x[i];
    }
}

static void ctmf_helper(
        const unsigned char* const src, unsigned char* const dst,
        const int width, const int height,
        const int src_step, const int dst_step,
        const int r, const int cn,
        const int pad_left, const int pad_right
        )
{
    const int m = height, n = width;
    int i, j, k, c;
    const unsigned char *p, *q;

    Histogram H[4];
    uint16_t *h_coarse, *h_fine, luc[4][16];

    assert( src );
    assert( dst );
    assert( r >= 0 );
    assert( width >= 2*r+1 );
    assert( height >= 2*r+1 );
    assert( src_step != 0 );
    assert( dst_step != 0 );

    /* SSE2 and MMX need aligned memory, provided by _mm_malloc(). */
#if defined(__SSE2__) || defined(__MMX__)
    h_coarse = (uint16_t*) _mm_malloc(  1 * 16 * n * cn * sizeof(uint16_t), 16 );
    h_fine   = (uint16_t*) _mm_malloc( 16 * 16 * n * cn * sizeof(uint16_t), 16 );
    memset( h_coarse, 0,  1 * 16 * n * cn * sizeof(uint16_t) );
    memset( h_fine,   0, 16 * 16 * n * cn * sizeof(uint16_t) );
#else
    h_coarse = (uint16_t*) calloc(  1 * 16 * n * cn, sizeof(uint16_t) );
    h_fine   = (uint16_t*) calloc( 16 * 16 * n * cn, sizeof(uint16_t) );
#endif

    /* First row initialization */
    for ( j = 0; j < n; ++j ) {
        for ( c = 0; c < cn; ++c ) {
            COP( c, j, src[cn*j+c], += r+1 );
        }
    }
    for ( i = 0; i < r; ++i ) {
        for ( j = 0; j < n; ++j ) {
            for ( c = 0; c < cn; ++c ) {
                COP( c, j, src[src_step*i+cn*j+c], ++ );
            }
        }
    }

    for ( i = 0; i < m; ++i ) {

        /* Update column histograms for entire row. */
        p = src + src_step * MAX( 0, i-r-1 );
        q = p + cn * n;
        for ( j = 0; p != q; ++j ) {
            for ( c = 0; c < cn; ++c, ++p ) {
                COP( c, j, *p, -- );
            }
        }

        p = src + src_step * MIN( m-1, i+r );
        q = p + cn * n;
        for ( j = 0; p != q; ++j ) {
            for ( c = 0; c < cn; ++c, ++p ) {
                COP( c, j, *p, ++ );
            }
        }

        /* First column initialization */
        memset( H, 0, cn*sizeof(H[0]) );
        memset( luc, 0, cn*sizeof(luc[0]) );
        if ( pad_left ) {
            for ( c = 0; c < cn; ++c ) {
                histogram_muladd( r, &h_coarse[16*n*c], H[c].coarse );
            }
        }
        for ( j = 0; j < (pad_left ? r : 2*r); ++j ) {
            for ( c = 0; c < cn; ++c ) {
                histogram_add( &h_coarse[16*(n*c+j)], H[c].coarse );
            }
        }
        for ( c = 0; c < cn; ++c ) {
            for ( k = 0; k < 16; ++k ) {
                histogram_muladd( 2*r+1, &h_fine[16*n*(16*c+k)], &H[c].fine[k][0] );
            }
        }

        for ( j = pad_left ? 0 : r; j < (pad_right ? n : n-r); ++j ) {
            for ( c = 0; c < cn; ++c ) {
                const uint16_t t = 2*r*r + 2*r;
                uint16_t sum = 0, *segment;
                int b;

                histogram_add( &h_coarse[16*(n*c + MIN(j+r,n-1))], H[c].coarse );

                /* Find median at coarse level */
                for ( k = 0; k < 16 ; ++k ) {
                    sum += H[c].coarse[k];
                    if ( sum > t ) {
                        sum -= H[c].coarse[k];
                        break;
                    }
                }
                assert( k < 16 );

                /* Update corresponding histogram segment */
                if ( luc[c][k] <= j-r ) {
                    memset( &H[c].fine[k], 0, 16 * sizeof(uint16_t) );
                    for ( luc[c][k] = j-r; luc[c][k] < MIN(j+r+1,n); ++luc[c][k] ) {
                        histogram_add( &h_fine[16*(n*(16*c+k)+luc[c][k])], H[c].fine[k] );
                    }
                    if ( luc[c][k] < j+r+1 ) {
                        histogram_muladd( j+r+1 - n, &h_fine[16*(n*(16*c+k)+(n-1))], &H[c].fine[k][0] );
                        luc[c][k] = j+r+1;
                    }
                }
                else {
                    for ( ; luc[c][k] < j+r+1; ++luc[c][k] ) {
                        histogram_sub( &h_fine[16*(n*(16*c+k)+MAX(luc[c][k]-2*r-1,0))], H[c].fine[k] );
                        histogram_add( &h_fine[16*(n*(16*c+k)+MIN(luc[c][k],n-1))], H[c].fine[k] );
                    }
                }

                histogram_sub( &h_coarse[16*(n*c+MAX(j-r,0))], H[c].coarse );

                /* Find median in segment */
                segment = H[c].fine[k];
                for ( b = 0; b < 16 ; ++b ) {
                    sum += segment[b];
                    if ( sum > t ) {
                        dst[dst_step*i+cn*j+c] = 16*k + b;
                        break;
                    }
                }
                assert( b < 16 );
            }
        }
    }

#if defined(__SSE2__) || defined(__MMX__)
    _mm_empty();
    _mm_free(h_coarse);
    _mm_free(h_fine);
#else
    free(h_coarse);
    free(h_fine);
#endif
}

/**
 * \brief Constant-time median filtering
 *
 * This function does a median filtering of an 8-bit image. The source image is
 * processed as if it was padded with zeros. The median kernel is square with
 * odd dimensions. Images of arbitrary size may be processed.
 *
 * To process multi-channel images, you must call this function multiple times,
 * changing the source and destination adresses and steps such that each channel
 * is processed as an independent single-channel image.
 *
 * Processing images of arbitrary bit depth is not supported.
 *
 * The computing time is O(1) per pixel, independent of the radius of the
 * filter. The algorithm's initialization is O(r*width), but it is negligible.
 * Memory usage is simple: it will be as big as the cache size, or smaller if
 * the image is small. For efficiency, the histograms' bins are 16-bit wide.
 * This may become too small and lead to overflow as \a r increases.
 *
 * \param src           Source image data.
 * \param dst           Destination image data. Must be preallocated.
 * \param width         Image width, in pixels.
 * \param height        Image height, in pixels.
 * \param src_step      Distance between adjacent pixels on the same column in
 *                      the source image, in bytes.
 * \param dst_step      Distance between adjacent pixels on the same column in
 *                      the destination image, in bytes.
 * \param r             Median filter radius. The kernel will be a 2*r+1 by
 *                      2*r+1 square.
 * \param cn            Number of channels. For example, a grayscale image would
 *                      have cn=1 while an RGB image would have cn=3.
 * \param memsize       Maximum amount of memory to use, in bytes. Set this to
 *                      the size of the L2 cache, then vary it slightly and
 *                      measure the processing time to find the optimal value.
 *                      For example, a 512 kB L2 cache would have
 *                      memsize=512*1024 initially.
 */
void ctmf(
        const unsigned char* const src, unsigned char* const dst,
        const int width, const int height,
        const int src_step, const int dst_step,
        const int r, const int cn, const long unsigned int memsize
        )
{
    /*
     * Processing the image in vertical stripes is an optimization made
     * necessary by the limited size of the CPU cache. Each histogram is 544
     * bytes big and therefore I can fit a limited number of them in the cache.
     * That number may sometimes be smaller than the image width, which would be
     * the number of histograms I would need without stripes.
     *
     * I need to keep histograms in the cache so that they are available
     * quickly when processing a new row. Each row needs access to the previous
     * row's histograms. If there are too many histograms to fit in the cache,
     * thrashing to RAM happens.
     *
     * To solve this problem, I figure out the maximum number of histograms
     * that can fit in cache. From this is determined the number of stripes in
     * an image. The formulas below make the stripes all the same size and use
     * as few stripes as possible.
     *
     * Note that each stripe causes an overlap on the neighboring stripes, as
     * when mowing the lawn. That overlap is proportional to r. When the overlap
     * is a significant size in comparison with the stripe size, then we are not
     * O(1) anymore, but O(r). In fact, we have been O(r) all along, but the
     * initialization term was neglected, as it has been (and rightly so) in B.
     * Weiss, "Fast Median and Bilateral Filtering", SIGGRAPH, 2006. Processing
     * by stripes only makes that initialization term bigger.
     *
     * Also, note that the leftmost and rightmost stripes don't need overlap.
     * A flag is passed to ctmf_helper() so that it treats these cases as if the
     * image was zero-padded.
     */
    int stripes = (int) ceil( (double) (width - 2*r) / (memsize / sizeof(Histogram) - 2*r) );
    int stripe_size = (int) ceil( (double) ( width + stripes*2*r - 2*r ) / stripes );

    int i;

    for ( i = 0; i < width; i += stripe_size - 2*r ) {
        int stripe = stripe_size;
        /* Make sure that the filter kernel fits into one stripe. */
        if ( i + stripe_size - 2*r >= width || width - (i + stripe_size - 2*r) < 2*r+1 ) {
            stripe = width - i;
        }

        ctmf_helper( src + cn*i, dst + cn*i, stripe, height, src_step, dst_step, r, cn,
                i == 0, stripe == width - i );

        if ( stripe == width - i ) {
            break;
        }
    }
}