C / C++ / C++.NET : Traitement de l'image: filtre médian en temps constant

Description

Le filtre médian est un filtre, spatial et non linéaire, qui calcule en chaque pixel la médiane des niveaux de gris des pixels de sa fenêtre, ce qui donnera le niveau de gris du pixel dans l'image filtrée.
Imaginons une fenêtre de taille r, pour trouver la médiane, il faut trier les pixels et retenir le pixel médian. Si on programme cette fonction d'une manière naïve, on devra pour chaque pixel trier les r pixels voisins. La complexité de cet algorithme explose lorsque r augmente trop.

Cet algorithme propose une méthode pour calculer le filtre médian avec un temps constant pour tout r ! Quelque soit la taille de la fenêtre, la complexité reste la même!

Cet algorithme n'est pas de moi mais il est tellement performant qu'il devait être sur Codes Sources. Voici le lien du site internet des créateurs:
http://nomis80.org/ctmf.html
Vous trouverez aussi sur ce site internet, le très intéressant document technique de cet algorithme.

Si vous n'êtes pas convaincu, j'ai créé une petite interface graphique qui permet d'appliquer le filtre médian sur des images. Vous pouvez ainsi modifier r (presque) en temps réel.
Le traitement des images couleurs est simple mais pourrait être amélioré: je lance 3 fois l'algorithme suivant les composantes R,G et B. On peut donc choisir de filtrer en couleur ou en niveau de gris. On peut aussi voir le temps de l'exécution de la fonction en bas à droite de la fenêtre.
Pour sélectionner une autre image, il suffit de faire un clic droit sur l'image.

J'insiste, allez visiter leur site internet.

Source / Exemple :

/*

  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;
        }
    }
}

Conclusion :

Sources : http://nomis80.org/ctmf.html

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Codes Sources

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Traitement de l'image: filtre médian en temps constant

Description

Source / Exemple :

Conclusion :

Codes Sources

A voir également

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inscrivez-vous, c'est gratuit et ça prend moins d'une minute !

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Source / Exemple :

Conclusion :

A voir également

Vous n'êtes pas encore membre ? inscrivez-vous, c'est gratuit et ça prend moins d'une minute !

Du même auteur (Pistol_Pete)

Visualisation des images en 3d sans opengl

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