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/*
Partially based on Yossi Rubner code:
=========================================================================
emd.c
Last update: 3/14/98
An implementation of the Earth Movers Distance.
Based of the solution for the Transportation problem as described in
"Introduction to Mathematical Programming" by F. S. Hillier and
G. J. Lieberman, McGraw-Hill, 1990.
Copyright (C) 1998 Yossi Rubner
Computer Science Department, Stanford University
E-Mail: rubner@cs.stanford.edu URL: http://vision.stanford.edu/~rubner
==========================================================================
*/
#include "_cv.h"
#define MAX_ITERATIONS 500
#define CV_EMD_INF ((float)1e20)
#define CV_EMD_EPS ((float)1e-5)
/* CvNode1D is used for lists, representing 1D sparse array */
typedef struct CvNode1D
{
float val;
struct CvNode1D *next;
}
CvNode1D;
/* CvNode2D is used for lists, representing 2D sparse matrix */
typedef struct CvNode2D
{
float val;
struct CvNode2D *next[2]; /* next row & next column */
int i, j;
}
CvNode2D;
typedef struct CvEMDState
{
int ssize, dsize;
float **cost;
CvNode2D *_x;
CvNode2D *end_x;
CvNode2D *enter_x;
char **is_x;
CvNode2D **rows_x;
CvNode2D **cols_x;
CvNode1D *u;
CvNode1D *v;
int* idx1;
int* idx2;
/* find_loop buffers */
CvNode2D **loop;
char *is_used;
/* russel buffers */
float *s;
float *d;
float **delta;
float weight, max_cost;
char *buffer;
}
CvEMDState;
/* static function declaration */
static CvStatus icvInitEMD( const float *signature1, int size1,
const float *signature2, int size2,
int dims, CvDistanceFunction dist_func, void *user_param,
const float* cost, int cost_step,
CvEMDState * state, float *lower_bound,
char *local_buffer, int local_buffer_size );
static CvStatus icvFindBasicVariables( float **cost, char **is_x,
CvNode1D * u, CvNode1D * v, int ssize, int dsize );
static float icvIsOptimal( float **cost, char **is_x,
CvNode1D * u, CvNode1D * v,
int ssize, int dsize, CvNode2D * enter_x );
static void icvRussel( CvEMDState * state );
static CvStatus icvNewSolution( CvEMDState * state );
static int icvFindLoop( CvEMDState * state );
static void icvAddBasicVariable( CvEMDState * state,
int min_i, int min_j,
CvNode1D * prev_u_min_i,
CvNode1D * prev_v_min_j,
CvNode1D * u_head );
static float icvDistL2( const float *x, const float *y, void *user_param );
static float icvDistL1( const float *x, const float *y, void *user_param );
static float icvDistC( const float *x, const float *y, void *user_param );
/* The main function */
CV_IMPL float
cvCalcEMD2( const CvArr* signature_arr1,
const CvArr* signature_arr2,
int dist_type,
CvDistanceFunction dist_func,
const CvArr* cost_matrix,
CvArr* flow_matrix,
float *lower_bound,
void *user_param )
{
char local_buffer[16384];
char *local_buffer_ptr = (char *)cvAlignPtr(local_buffer,16);
CvEMDState state;
float emd = 0;
CV_FUNCNAME( "cvCalcEMD2" );
memset( &state, 0, sizeof(state));
__BEGIN__;
double total_cost = 0;
CvStatus result = CV_NO_ERR;
float eps, min_delta;
CvNode2D *xp = 0;
CvMat sign_stub1, *signature1 = (CvMat*)signature_arr1;
CvMat sign_stub2, *signature2 = (CvMat*)signature_arr2;
CvMat cost_stub, *cost = &cost_stub;
CvMat flow_stub, *flow = (CvMat*)flow_matrix;
int dims, size1, size2;
CV_CALL( signature1 = cvGetMat( signature1, &sign_stub1 ));
CV_CALL( signature2 = cvGetMat( signature2, &sign_stub2 ));
if( signature1->cols != signature2->cols )
CV_ERROR( CV_StsUnmatchedSizes, "The arrays must have equal number of columns (which is number of dimensions but 1)" );
dims = signature1->cols - 1;
size1 = signature1->rows;
size2 = signature2->rows;
if( !CV_ARE_TYPES_EQ( signature1, signature2 ))
CV_ERROR( CV_StsUnmatchedFormats, "The array must have equal types" );
if( CV_MAT_TYPE( signature1->type ) != CV_32FC1 )
CV_ERROR( CV_StsUnsupportedFormat, "The signatures must be 32fC1" );
if( flow )
{
CV_CALL( flow = cvGetMat( flow, &flow_stub ));
if( flow->rows != size1 || flow->cols != size2 )
CV_ERROR( CV_StsUnmatchedSizes,
"The flow matrix size does not match to the signatures' sizes" );
if( CV_MAT_TYPE( flow->type ) != CV_32FC1 )
CV_ERROR( CV_StsUnsupportedFormat, "The flow matrix must be 32fC1" );
}
cost->data.fl = 0;
cost->step = 0;
if( dist_type < 0 )
{
if( cost_matrix )
{
if( dist_func )
CV_ERROR( CV_StsBadArg,
"Only one of cost matrix or distance function should be non-NULL in case of user-defined distance" );
if( lower_bound )
CV_ERROR( CV_StsBadArg,
"The lower boundary can not be calculated if the cost matrix is used" );
CV_CALL( cost = cvGetMat( cost_matrix, &cost_stub ));
if( cost->rows != size1 || cost->cols != size2 )
CV_ERROR( CV_StsUnmatchedSizes,
"The cost matrix size does not match to the signatures' sizes" );
if( CV_MAT_TYPE( cost->type ) != CV_32FC1 )
CV_ERROR( CV_StsUnsupportedFormat, "The cost matrix must be 32fC1" );
}
else if( !dist_func )
CV_ERROR( CV_StsNullPtr, "In case of user-defined distance Distance function is undefined" );
}
else
{
if( dims == 0 )
CV_ERROR( CV_StsBadSize,
"Number of dimensions can be 0 only if a user-defined metric is used" );
user_param = (void *) (size_t)dims;
switch (dist_type)
{
case CV_DIST_L1:
dist_func = icvDistL1;
break;
case CV_DIST_L2:
dist_func = icvDistL2;
break;
case CV_DIST_C:
dist_func = icvDistC;
break;
default:
CV_ERROR( CV_StsBadFlag, "Bad or unsupported metric type" );
}
}
IPPI_CALL( result = icvInitEMD( signature1->data.fl, size1,
signature2->data.fl, size2,
dims, dist_func, user_param,
cost->data.fl, cost->step,
&state, lower_bound, local_buffer_ptr,
sizeof( local_buffer ) - 16 ));
if( result > 0 && lower_bound )
{
emd = *lower_bound;
EXIT;
}
eps = CV_EMD_EPS * state.max_cost;
/* if ssize = 1 or dsize = 1 then we are done, else ... */
if( state.ssize > 1 && state.dsize > 1 )
{
int itr;
for( itr = 1; itr < MAX_ITERATIONS; itr++ )
{
/* find basic variables */
result = icvFindBasicVariables( state.cost, state.is_x,
state.u, state.v, state.ssize, state.dsize );
if( result < 0 )
break;
/* check for optimality */
min_delta = icvIsOptimal( state.cost, state.is_x,
state.u, state.v,
state.ssize, state.dsize, state.enter_x );
if( min_delta == CV_EMD_INF )
{
CV_ERROR( CV_StsNoConv, "" );
}
/* if no negative deltamin, we found the optimal solution */
if( min_delta >= -eps )
break;
/* improve solution */
IPPI_CALL( icvNewSolution( &state ));
}
}
/* compute the total flow */
for( xp = state._x; xp < state.end_x; xp++ )
{
float val = xp->val;
int i = xp->i;
int j = xp->j;
int ci = state.idx1[i];
int cj = state.idx2[j];
if( xp != state.enter_x && ci >= 0 && cj >= 0 )
{
total_cost += (double)val * state.cost[i][j];
if( flow )
((float*)(flow->data.ptr + flow->step*ci))[cj] = val;
}
}
emd = (float) (total_cost / state.weight);
__END__;
if( state.buffer && state.buffer != local_buffer_ptr )
cvFree( &state.buffer );
return emd;
}
/************************************************************************************\
* initialize structure, allocate buffers and generate initial golution *
\************************************************************************************/
static CvStatus
icvInitEMD( const float* signature1, int size1,
const float* signature2, int size2,
int dims, CvDistanceFunction dist_func, void* user_param,
const float* cost, int cost_step,
CvEMDState* state, float* lower_bound,
char* local_buffer, int local_buffer_size )
{
float s_sum = 0, d_sum = 0, diff;
int i, j;
int ssize = 0, dsize = 0;
int equal_sums = 1;
int buffer_size;
float max_cost = 0;
char *buffer, *buffer_end;
memset( state, 0, sizeof( *state ));
assert( cost_step % sizeof(float) == 0 );
cost_step /= sizeof(float);
/* calculate buffer size */
buffer_size = (size1+1) * (size2+1) * (sizeof( float ) + /* cost */
sizeof( char ) + /* is_x */
sizeof( float )) + /* delta matrix */
(size1 + size2 + 2) * (sizeof( CvNode2D ) + /* _x */
sizeof( CvNode2D * ) + /* cols_x & rows_x */
sizeof( CvNode1D ) + /* u & v */
sizeof( float ) + /* s & d */
sizeof( int ) + sizeof(CvNode2D*)) + /* idx1 & idx2 */
(size1+1) * (sizeof( float * ) + sizeof( char * ) + /* rows pointers for */
sizeof( float * )) + 256; /* cost, is_x and delta */
if( buffer_size < (int) (dims * 2 * sizeof( float )))
{
buffer_size = dims * 2 * sizeof( float );
}
/* allocate buffers */
if( local_buffer != 0 && local_buffer_size >= buffer_size )
{
buffer = local_buffer;
}
else
{
buffer = (char*)cvAlloc( buffer_size );
if( !buffer )
return CV_OUTOFMEM_ERR;
}
state->buffer = buffer;
buffer_end = buffer + buffer_size;
state->idx1 = (int*) buffer;
buffer += (size1 + 1) * sizeof( int );
state->idx2 = (int*) buffer;
buffer += (size2 + 1) * sizeof( int );
state->s = (float *) buffer;
buffer += (size1 + 1) * sizeof( float );
state->d = (float *) buffer;
buffer += (size2 + 1) * sizeof( float );
/* sum up the supply and demand */
for( i = 0; i < size1; i++ )
{
float weight = signature1[i * (dims + 1)];
if( weight > 0 )
{
s_sum += weight;
state->s[ssize] = weight;
state->idx1[ssize++] = i;
}
else if( weight < 0 )
return CV_BADRANGE_ERR;
}
for( i = 0; i < size2; i++ )
{
float weight = signature2[i * (dims + 1)];
if( weight > 0 )
{
d_sum += weight;
state->d[dsize] = weight;
state->idx2[dsize++] = i;
}
else if( weight < 0 )
return CV_BADRANGE_ERR;
}
if( ssize == 0 || dsize == 0 )
return CV_BADRANGE_ERR;
/* if supply different than the demand, add a zero-cost dummy cluster */
diff = s_sum - d_sum;
if( fabs( diff ) >= CV_EMD_EPS * s_sum )
{
equal_sums = 0;
if( diff < 0 )
{
state->s[ssize] = -diff;
state->idx1[ssize++] = -1;
}
else
{
state->d[dsize] = diff;
state->idx2[dsize++] = -1;
}
}
state->ssize = ssize;
state->dsize = dsize;
state->weight = s_sum > d_sum ? s_sum : d_sum;
if( lower_bound && equal_sums ) /* check lower bound */
{
int sz1 = size1 * (dims + 1), sz2 = size2 * (dims + 1);
float lb = 0;
float* xs = (float *) buffer;
float* xd = xs + dims;
memset( xs, 0, dims*sizeof(xs[0]));
memset( xd, 0, dims*sizeof(xd[0]));
for( j = 0; j < sz1; j += dims + 1 )
{
float weight = signature1[j];
for( i = 0; i < dims; i++ )
xs[i] += signature1[j + i + 1] * weight;
}
for( j = 0; j < sz2; j += dims + 1 )
{
float weight = signature2[j];
for( i = 0; i < dims; i++ )
xd[i] += signature2[j + i + 1] * weight;
}
lb = dist_func( xs, xd, user_param ) / state->weight;
i = *lower_bound <= lb;
*lower_bound = lb;
if( i )
return ( CvStatus ) 1;
}
/* assign pointers */
state->is_used = (char *) buffer;
/* init delta matrix */
state->delta = (float **) buffer;
buffer += ssize * sizeof( float * );
for( i = 0; i < ssize; i++ )
{
state->delta[i] = (float *) buffer;
buffer += dsize * sizeof( float );
}
state->loop = (CvNode2D **) buffer;
buffer += (ssize + dsize + 1) * sizeof(CvNode2D*);
state->_x = state->end_x = (CvNode2D *) buffer;
buffer += (ssize + dsize) * sizeof( CvNode2D );
/* init cost matrix */
state->cost = (float **) buffer;
buffer += ssize * sizeof( float * );
/* compute the distance matrix */
for( i = 0; i < ssize; i++ )
{
int ci = state->idx1[i];
state->cost[i] = (float *) buffer;
buffer += dsize * sizeof( float );
if( ci >= 0 )
{
for( j = 0; j < dsize; j++ )
{
int cj = state->idx2[j];
if( cj < 0 )
state->cost[i][j] = 0;
else
{
float val;
if( dist_func )
{
val = dist_func( signature1 + ci * (dims + 1) + 1,
signature2 + cj * (dims + 1) + 1,
user_param );
}
else
{
assert( cost );
val = cost[cost_step*ci + cj];
}
state->cost[i][j] = val;
if( max_cost < val )
max_cost = val;
}
}
}
else
{
for( j = 0; j < dsize; j++ )
state->cost[i][j] = 0;
}
}
state->max_cost = max_cost;
memset( buffer, 0, buffer_end - buffer );
state->rows_x = (CvNode2D **) buffer;
buffer += ssize * sizeof( CvNode2D * );
state->cols_x = (CvNode2D **) buffer;
buffer += dsize * sizeof( CvNode2D * );
state->u = (CvNode1D *) buffer;
buffer += ssize * sizeof( CvNode1D );
state->v = (CvNode1D *) buffer;
buffer += dsize * sizeof( CvNode1D );
/* init is_x matrix */
state->is_x = (char **) buffer;
buffer += ssize * sizeof( char * );
for( i = 0; i < ssize; i++ )
{
state->is_x[i] = buffer;
buffer += dsize;
}
assert( buffer <= buffer_end );
icvRussel( state );
state->enter_x = (state->end_x)++;
return CV_NO_ERR;
}
/****************************************************************************************\
* icvFindBasicVariables *
\****************************************************************************************/
static CvStatus
icvFindBasicVariables( float **cost, char **is_x,
CvNode1D * u, CvNode1D * v, int ssize, int dsize )
{
int i, j, found;
int u_cfound, v_cfound;
CvNode1D u0_head, u1_head, *cur_u, *prev_u;
CvNode1D v0_head, v1_head, *cur_v, *prev_v;
/* initialize the rows list (u) and the columns list (v) */
u0_head.next = u;
for( i = 0; i < ssize; i++ )
{
u[i].next = u + i + 1;
}
u[ssize - 1].next = 0;
u1_head.next = 0;
v0_head.next = ssize > 1 ? v + 1 : 0;
for( i = 1; i < dsize; i++ )
{
v[i].next = v + i + 1;
}
v[dsize - 1].next = 0;
v1_head.next = 0;
/* there are ssize+dsize variables but only ssize+dsize-1 independent equations,
so set v[0]=0 */
v[0].val = 0;
v1_head.next = v;
v1_head.next->next = 0;
/* loop until all variables are found */
u_cfound = v_cfound = 0;
while( u_cfound < ssize || v_cfound < dsize )
{
found = 0;
if( v_cfound < dsize )
{
/* loop over all marked columns */
prev_v = &v1_head;
for( found |= (cur_v = v1_head.next) != 0; cur_v != 0; cur_v = cur_v->next )
{
float cur_v_val = cur_v->val;
j = (int)(cur_v - v);
/* find the variables in column j */
prev_u = &u0_head;
for( cur_u = u0_head.next; cur_u != 0; )
{
i = (int)(cur_u - u);
if( is_x[i][j] )
{
/* compute u[i] */
cur_u->val = cost[i][j] - cur_v_val;
/* ...and add it to the marked list */
prev_u->next = cur_u->next;
cur_u->next = u1_head.next;
u1_head.next = cur_u;
cur_u = prev_u->next;
}
else
{
prev_u = cur_u;
cur_u = cur_u->next;
}
}
prev_v->next = cur_v->next;
v_cfound++;
}
}
if( u_cfound < ssize )
{
/* loop over all marked rows */
prev_u = &u1_head;
for( found |= (cur_u = u1_head.next) != 0; cur_u != 0; cur_u = cur_u->next )
{
float cur_u_val = cur_u->val;
float *_cost;
char *_is_x;
i = (int)(cur_u - u);
_cost = cost[i];
_is_x = is_x[i];
/* find the variables in rows i */
prev_v = &v0_head;
for( cur_v = v0_head.next; cur_v != 0; )
{
j = (int)(cur_v - v);
if( _is_x[j] )
{
/* compute v[j] */
cur_v->val = _cost[j] - cur_u_val;
/* ...and add it to the marked list */
prev_v->next = cur_v->next;
cur_v->next = v1_head.next;
v1_head.next = cur_v;
cur_v = prev_v->next;
}
else
{
prev_v = cur_v;
cur_v = cur_v->next;
}
}
prev_u->next = cur_u->next;
u_cfound++;
}
}
if( !found )
{
return CV_NOTDEFINED_ERR;
}
}
return CV_NO_ERR;
}
/****************************************************************************************\
* icvIsOptimal *
\****************************************************************************************/
static float
icvIsOptimal( float **cost, char **is_x,
CvNode1D * u, CvNode1D * v, int ssize, int dsize, CvNode2D * enter_x )
{
float delta, min_delta = CV_EMD_INF;
int i, j, min_i = 0, min_j = 0;
/* find the minimal cij-ui-vj over all i,j */
for( i = 0; i < ssize; i++ )
{
float u_val = u[i].val;
float *_cost = cost[i];
char *_is_x = is_x[i];
for( j = 0; j < dsize; j++ )
{
if( !_is_x[j] )
{
delta = _cost[j] - u_val - v[j].val;
if( min_delta > delta )
{
min_delta = delta;
min_i = i;
min_j = j;
}
}
}
}
enter_x->i = min_i;
enter_x->j = min_j;
return min_delta;
}
/****************************************************************************************\
* icvNewSolution *
\****************************************************************************************/
static CvStatus
icvNewSolution( CvEMDState * state )
{
int i, j;
float min_val = CV_EMD_INF;
int steps;
CvNode2D head, *cur_x, *next_x, *leave_x = 0;
CvNode2D *enter_x = state->enter_x;
CvNode2D **loop = state->loop;
/* enter the new basic variable */
i = enter_x->i;
j = enter_x->j;
state->is_x[i][j] = 1;
enter_x->next[0] = state->rows_x[i];
enter_x->next[1] = state->cols_x[j];
enter_x->val = 0;
state->rows_x[i] = enter_x;
state->cols_x[j] = enter_x;
/* find a chain reaction */
steps = icvFindLoop( state );
if( steps == 0 )
return CV_NOTDEFINED_ERR;
/* find the largest value in the loop */
for( i = 1; i < steps; i += 2 )
{
float temp = loop[i]->val;
if( min_val > temp )
{
leave_x = loop[i];
min_val = temp;
}
}
/* update the loop */
for( i = 0; i < steps; i += 2 )
{
float temp0 = loop[i]->val + min_val;
float temp1 = loop[i + 1]->val - min_val;
loop[i]->val = temp0;
loop[i + 1]->val = temp1;
}
/* remove the leaving basic variable */
i = leave_x->i;
j = leave_x->j;
state->is_x[i][j] = 0;
head.next[0] = state->rows_x[i];
cur_x = &head;
while( (next_x = cur_x->next[0]) != leave_x )
{
cur_x = next_x;
assert( cur_x );
}
cur_x->next[0] = next_x->next[0];
state->rows_x[i] = head.next[0];
head.next[1] = state->cols_x[j];
cur_x = &head;
while( (next_x = cur_x->next[1]) != leave_x )
{
cur_x = next_x;
assert( cur_x );
}
cur_x->next[1] = next_x->next[1];
state->cols_x[j] = head.next[1];
/* set enter_x to be the new empty slot */
state->enter_x = leave_x;
return CV_NO_ERR;
}
/****************************************************************************************\
* icvFindLoop *
\****************************************************************************************/
static int
icvFindLoop( CvEMDState * state )
{
int i, steps = 1;
CvNode2D *new_x;
CvNode2D **loop = state->loop;
CvNode2D *enter_x = state->enter_x, *_x = state->_x;
char *is_used = state->is_used;
memset( is_used, 0, state->ssize + state->dsize );
new_x = loop[0] = enter_x;
is_used[enter_x - _x] = 1;
steps = 1;
do
{
if( (steps & 1) == 1 )
{
/* find an unused x in the row */
new_x = state->rows_x[new_x->i];
while( new_x != 0 && is_used[new_x - _x] )
new_x = new_x->next[0];
}
else
{
/* find an unused x in the column, or the entering x */
new_x = state->cols_x[new_x->j];
while( new_x != 0 && is_used[new_x - _x] && new_x != enter_x )
new_x = new_x->next[1];
if( new_x == enter_x )
break;
}
if( new_x != 0 ) /* found the next x */
{
/* add x to the loop */
loop[steps++] = new_x;
is_used[new_x - _x] = 1;
}
else /* didn't find the next x */
{
/* backtrack */
do
{
i = steps & 1;
new_x = loop[steps - 1];
do
{
new_x = new_x->next[i];
}
while( new_x != 0 && is_used[new_x - _x] );
if( new_x == 0 )
{
is_used[loop[--steps] - _x] = 0;
}
}
while( new_x == 0 && steps > 0 );
is_used[loop[steps - 1] - _x] = 0;
loop[steps - 1] = new_x;
is_used[new_x - _x] = 1;
}
}
while( steps > 0 );
return steps;
}
/****************************************************************************************\
* icvRussel *
\****************************************************************************************/
static void
icvRussel( CvEMDState * state )
{
int i, j, min_i = -1, min_j = -1;
float min_delta, diff;
CvNode1D u_head, *cur_u, *prev_u;
CvNode1D v_head, *cur_v, *prev_v;
CvNode1D *prev_u_min_i = 0, *prev_v_min_j = 0, *remember;
CvNode1D *u = state->u, *v = state->v;
int ssize = state->ssize, dsize = state->dsize;
float eps = CV_EMD_EPS * state->max_cost;
float **cost = state->cost;
float **delta = state->delta;
/* initialize the rows list (ur), and the columns list (vr) */
u_head.next = u;
for( i = 0; i < ssize; i++ )
{
u[i].next = u + i + 1;
}
u[ssize - 1].next = 0;
v_head.next = v;
for( i = 0; i < dsize; i++ )
{
v[i].val = -CV_EMD_INF;
v[i].next = v + i + 1;
}
v[dsize - 1].next = 0;
/* find the maximum row and column values (ur[i] and vr[j]) */
for( i = 0; i < ssize; i++ )
{
float u_val = -CV_EMD_INF;
float *cost_row = cost[i];
for( j = 0; j < dsize; j++ )
{
float temp = cost_row[j];
if( u_val < temp )
u_val = temp;
if( v[j].val < temp )
v[j].val = temp;
}
u[i].val = u_val;
}
/* compute the delta matrix */
for( i = 0; i < ssize; i++ )
{
float u_val = u[i].val;
float *delta_row = delta[i];
float *cost_row = cost[i];
for( j = 0; j < dsize; j++ )
{
delta_row[j] = cost_row[j] - u_val - v[j].val;
}
}
/* find the basic variables */
do
{
/* find the smallest delta[i][j] */
min_i = -1;
min_delta = CV_EMD_INF;
prev_u = &u_head;
for( cur_u = u_head.next; cur_u != 0; cur_u = cur_u->next )
{
i = (int)(cur_u - u);
float *delta_row = delta[i];
prev_v = &v_head;
for( cur_v = v_head.next; cur_v != 0; cur_v = cur_v->next )
{
j = (int)(cur_v - v);
if( min_delta > delta_row[j] )
{
min_delta = delta_row[j];
min_i = i;
min_j = j;
prev_u_min_i = prev_u;
prev_v_min_j = prev_v;
}
prev_v = cur_v;
}
prev_u = cur_u;
}
if( min_i < 0 )
break;
/* add x[min_i][min_j] to the basis, and adjust supplies and cost */
remember = prev_u_min_i->next;
icvAddBasicVariable( state, min_i, min_j, prev_u_min_i, prev_v_min_j, &u_head );
/* update the necessary delta[][] */
if( remember == prev_u_min_i->next ) /* line min_i was deleted */
{
for( cur_v = v_head.next; cur_v != 0; cur_v = cur_v->next )
{
j = (int)(cur_v - v);
if( cur_v->val == cost[min_i][j] ) /* column j needs updating */
{
float max_val = -CV_EMD_INF;
/* find the new maximum value in the column */
for( cur_u = u_head.next; cur_u != 0; cur_u = cur_u->next )
{
float temp = cost[cur_u - u][j];
if( max_val < temp )
max_val = temp;
}
/* if needed, adjust the relevant delta[*][j] */
diff = max_val - cur_v->val;
cur_v->val = max_val;
if( fabs( diff ) < eps )
{
for( cur_u = u_head.next; cur_u != 0; cur_u = cur_u->next )
delta[cur_u - u][j] += diff;
}
}
}
}
else /* column min_j was deleted */
{
for( cur_u = u_head.next; cur_u != 0; cur_u = cur_u->next )
{
i = (int)(cur_u - u);
if( cur_u->val == cost[i][min_j] ) /* row i needs updating */
{
float max_val = -CV_EMD_INF;
/* find the new maximum value in the row */
for( cur_v = v_head.next; cur_v != 0; cur_v = cur_v->next )
{
float temp = cost[i][cur_v - v];
if( max_val < temp )
max_val = temp;
}
/* if needed, adjust the relevant delta[i][*] */
diff = max_val - cur_u->val;
cur_u->val = max_val;
if( fabs( diff ) < eps )
{
for( cur_v = v_head.next; cur_v != 0; cur_v = cur_v->next )
delta[i][cur_v - v] += diff;
}
}
}
}
}
while( u_head.next != 0 || v_head.next != 0 );
}
/****************************************************************************************\
* icvAddBasicVariable *
\****************************************************************************************/
static void
icvAddBasicVariable( CvEMDState * state,
int min_i, int min_j,
CvNode1D * prev_u_min_i, CvNode1D * prev_v_min_j, CvNode1D * u_head )
{
float temp;
CvNode2D *end_x = state->end_x;
if( state->s[min_i] < state->d[min_j] + state->weight * CV_EMD_EPS )
{ /* supply exhausted */
temp = state->s[min_i];
state->s[min_i] = 0;
state->d[min_j] -= temp;
}
else /* demand exhausted */
{
temp = state->d[min_j];
state->d[min_j] = 0;
state->s[min_i] -= temp;
}
/* x(min_i,min_j) is a basic variable */
state->is_x[min_i][min_j] = 1;
end_x->val = temp;
end_x->i = min_i;
end_x->j = min_j;
end_x->next[0] = state->rows_x[min_i];
end_x->next[1] = state->cols_x[min_j];
state->rows_x[min_i] = end_x;
state->cols_x[min_j] = end_x;
state->end_x = end_x + 1;
/* delete supply row only if the empty, and if not last row */
if( state->s[min_i] == 0 && u_head->next->next != 0 )
prev_u_min_i->next = prev_u_min_i->next->next; /* remove row from list */
else
prev_v_min_j->next = prev_v_min_j->next->next; /* remove column from list */
}
/****************************************************************************************\
* standard metrics *
\****************************************************************************************/
static float
icvDistL1( const float *x, const float *y, void *user_param )
{
int i, dims = (int)(size_t)user_param;
double s = 0;
for( i = 0; i < dims; i++ )
{
double t = x[i] - y[i];
s += fabs( t );
}
return (float)s;
}
static float
icvDistL2( const float *x, const float *y, void *user_param )
{
int i, dims = (int)(size_t)user_param;
double s = 0;
for( i = 0; i < dims; i++ )
{
double t = x[i] - y[i];
s += t * t;
}
return cvSqrt( (float)s );
}
static float
icvDistC( const float *x, const float *y, void *user_param )
{
int i, dims = (int)(size_t)user_param;
double s = 0;
for( i = 0; i < dims; i++ )
{
double t = fabs( x[i] - y[i] );
if( s < t )
s = t;
}
return (float)s;
}
/* End of file. */