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velocity_segment.c
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/* Please see velocity_segment.m for documentation.
*
* Author: Gunnar Farnebäck
* Computer Vision Laboratory
* Linköping University, Sweden
*/
#include "mex.h"
#include "matrix.h"
#include <stdlib.h>
#include <float.h>
#include <stdio.h> /* For DumpCandidateHeap */
#include <string.h>
#define MAX_PARAMS 8
#define DEFAULT_MINSIZE 500
#define DEFAULT_MAXSIZE 500
#define DEFAULT_KERNELDIST 4
#define DEFAULT_LAMBDA 0.1 /* Factor to make it harder for new regions. */
#define DEFAULT_COVERAGE 1.0 /* How large part of the image to segment. */
/* Whether to recompute the parameters for a region at the end. */
#define DEFAULT_PARAMETER_RECOMPUTATION 0
/* How many times the initial blocks are regrown. */
#define DEFAULT_NUMBER_OF_INITIAL_ITERATIONS 2
/* Which motion models to use. Default is affine only. */
#define DEFAULT_MOTION_MODELS 2
#define DEFAULT_VERBOSE 0
/* Motion models */
#define CONSTANT_MOTION 1
#define AFFINE_MOTION 2
#define EIGHT_PARAMETER_MOTION 4
struct region
{
double param[MAX_PARAMS];
int motion_model;
int startx;
int starty;
int size;
};
struct candidate
{
double param[MAX_PARAMS];
int motion_model;
double cost;
int x;
int y;
int last_rebuild;
};
static int
number_of_parameters(int motion_model)
{
int n;
switch (motion_model)
{
case CONSTANT_MOTION:
n = 2;
break;
case AFFINE_MOTION:
n = 6;
break;
case EIGHT_PARAMETER_MOTION:
n = 8;
break;
}
return n;
}
static void
clear_quadratic_form(double *Q, int motion_model)
{
int i, j;
int n = number_of_parameters(motion_model);
for (j = 0; j < n+1; j++)
for (i = 0; i < n+1; i++)
Q[j * (MAX_PARAMS+1) + i] = 0.0;
}
static void
add_to_quadratic_form(double *Q, double *T, int x, int y, int xsize,
int ysize, int motion_model, int debug)
{
int index = x + y * xsize;
int N = xsize * ysize;
double T11 = T[index];
double T12 = T[index + N];
double T13 = T[index + 2*N];
double T22 = T[index + 4*N];
double T23 = T[index + 5*N];
double T33 = T[index + 8*N];
double x2, xy, y2;
double x3, x2y, xy2, y3;
double x4, x3y, x2y2, xy3, y4;
if (debug)
mexPrintf("%f %f %f %f %f %f\n", T11, T12, T13, T22, T23, T33);
switch (motion_model)
{
case CONSTANT_MOTION:
Q[0 + 0 * (MAX_PARAMS+1)] += T11;
Q[1 + 1 * (MAX_PARAMS+1)] += T22;
Q[2 + 2 * (MAX_PARAMS+1)] += T33;
Q[0 + 1 * (MAX_PARAMS+1)] += T12;
Q[0 + 2 * (MAX_PARAMS+1)] += T13;
Q[1 + 2 * (MAX_PARAMS+1)] += T23;
Q[1 + 0 * (MAX_PARAMS+1)] += T12;
Q[2 + 0 * (MAX_PARAMS+1)] += T13;
Q[2 + 1 * (MAX_PARAMS+1)] += T23;
break;
case AFFINE_MOTION:
x2 = x * x;
xy = x * y;
y2 = y * y;
Q[0 + 0 * (MAX_PARAMS+1)] += x2 * T11;
Q[1 + 1 * (MAX_PARAMS+1)] += y2 * T11;
Q[2 + 2 * (MAX_PARAMS+1)] += T11;
Q[3 + 3 * (MAX_PARAMS+1)] += x2 * T22;
Q[4 + 4 * (MAX_PARAMS+1)] += y2 * T22;
Q[5 + 5 * (MAX_PARAMS+1)] += T22;
Q[6 + 6 * (MAX_PARAMS+1)] += T33;
Q[0 + 1 * (MAX_PARAMS+1)] += xy * T11;
Q[0 + 2 * (MAX_PARAMS+1)] += x * T11;
Q[0 + 3 * (MAX_PARAMS+1)] += x2 * T12;
Q[0 + 4 * (MAX_PARAMS+1)] += xy * T12;
Q[0 + 5 * (MAX_PARAMS+1)] += x * T12;
Q[0 + 6 * (MAX_PARAMS+1)] += x * T13;
Q[1 + 2 * (MAX_PARAMS+1)] += y * T11;
Q[1 + 3 * (MAX_PARAMS+1)] += xy * T12;
Q[1 + 4 * (MAX_PARAMS+1)] += y2 * T12;
Q[1 + 5 * (MAX_PARAMS+1)] += y * T12;
Q[1 + 6 * (MAX_PARAMS+1)] += y * T13;
Q[2 + 3 * (MAX_PARAMS+1)] += x * T12;
Q[2 + 4 * (MAX_PARAMS+1)] += y * T12;
Q[2 + 5 * (MAX_PARAMS+1)] += T12;
Q[2 + 6 * (MAX_PARAMS+1)] += T13;
Q[3 + 4 * (MAX_PARAMS+1)] += xy * T22;
Q[3 + 5 * (MAX_PARAMS+1)] += x * T22;
Q[3 + 6 * (MAX_PARAMS+1)] += x * T23;
Q[4 + 5 * (MAX_PARAMS+1)] += y * T22;
Q[4 + 6 * (MAX_PARAMS+1)] += y * T23;
Q[5 + 6 * (MAX_PARAMS+1)] += T23;
Q[1 + 0 * (MAX_PARAMS+1)] += xy * T11;
Q[2 + 0 * (MAX_PARAMS+1)] += x * T11;
Q[3 + 0 * (MAX_PARAMS+1)] += x2 * T12;
Q[4 + 0 * (MAX_PARAMS+1)] += xy * T12;
Q[5 + 0 * (MAX_PARAMS+1)] += x * T12;
Q[6 + 0 * (MAX_PARAMS+1)] += x * T13;
Q[2 + 1 * (MAX_PARAMS+1)] += y * T11;
Q[3 + 1 * (MAX_PARAMS+1)] += xy * T12;
Q[4 + 1 * (MAX_PARAMS+1)] += y2 * T12;
Q[5 + 1 * (MAX_PARAMS+1)] += y * T12;
Q[6 + 1 * (MAX_PARAMS+1)] += y * T13;
Q[3 + 2 * (MAX_PARAMS+1)] += x * T12;
Q[4 + 2 * (MAX_PARAMS+1)] += y * T12;
Q[5 + 2 * (MAX_PARAMS+1)] += T12;
Q[6 + 2 * (MAX_PARAMS+1)] += T13;
Q[4 + 3 * (MAX_PARAMS+1)] += xy * T22;
Q[5 + 3 * (MAX_PARAMS+1)] += x * T22;
Q[6 + 3 * (MAX_PARAMS+1)] += x * T23;
Q[5 + 4 * (MAX_PARAMS+1)] += y * T22;
Q[6 + 4 * (MAX_PARAMS+1)] += y * T23;
Q[6 + 5 * (MAX_PARAMS+1)] += T23;
break;
case EIGHT_PARAMETER_MOTION:
x2 = x * x;
xy = x * y;
y2 = y * y;
x3 = x * x2;
x2y = x * xy;
xy2 = x * y2;
y3 = y * y2;
x4 = x * x3;
x3y = x * x2y;
x2y2 = x * xy2;
xy3 = x * y3;
y4 = y * y3;
Q[0 + 0 * (MAX_PARAMS+1)] += T11;
Q[1 + 1 * (MAX_PARAMS+1)] += x2 * T11;
Q[2 + 2 * (MAX_PARAMS+1)] += y2 * T11;
Q[3 + 3 * (MAX_PARAMS+1)] += T22;
Q[4 + 4 * (MAX_PARAMS+1)] += x2 * T22;
Q[5 + 5 * (MAX_PARAMS+1)] += y2 * T22;
Q[6 + 6 * (MAX_PARAMS+1)] += x4 * T11 + 2.0 * x3y * T12 + x2y2 * T22;
Q[7 + 7 * (MAX_PARAMS+1)] += x2y2 * T11 + 2.0 * xy3 * T12 + y4 * T22;
Q[8 + 8 * (MAX_PARAMS+1)] += T33;
Q[0 + 1 * (MAX_PARAMS+1)] += x * T11;
Q[0 + 2 * (MAX_PARAMS+1)] += y * T11;
Q[0 + 3 * (MAX_PARAMS+1)] += T12;
Q[0 + 4 * (MAX_PARAMS+1)] += x * T12;
Q[0 + 5 * (MAX_PARAMS+1)] += y * T12;
Q[0 + 6 * (MAX_PARAMS+1)] += x2 * T11 + xy * T12;
Q[0 + 7 * (MAX_PARAMS+1)] += xy * T11 + y2 * T12;
Q[0 + 8 * (MAX_PARAMS+1)] += T13;
Q[1 + 2 * (MAX_PARAMS+1)] += xy * T11;
Q[1 + 3 * (MAX_PARAMS+1)] += x * T12;
Q[1 + 4 * (MAX_PARAMS+1)] += x2 * T12;
Q[1 + 5 * (MAX_PARAMS+1)] += xy * T12;
Q[1 + 6 * (MAX_PARAMS+1)] += x3 * T11 + x2y * T12;
Q[1 + 7 * (MAX_PARAMS+1)] += x2y * T11 + xy2 * T12;
Q[1 + 8 * (MAX_PARAMS+1)] += x * T13;
Q[2 + 3 * (MAX_PARAMS+1)] += y * T12;
Q[2 + 4 * (MAX_PARAMS+1)] += xy * T12;
Q[2 + 5 * (MAX_PARAMS+1)] += y2 * T12;
Q[2 + 6 * (MAX_PARAMS+1)] += x2y * T11 + xy2 * T12;
Q[2 + 7 * (MAX_PARAMS+1)] += xy2 * T11 + y3 * T12;
Q[2 + 8 * (MAX_PARAMS+1)] += y * T13;
Q[3 + 4 * (MAX_PARAMS+1)] += x * T22;
Q[3 + 5 * (MAX_PARAMS+1)] += y * T22;
Q[3 + 6 * (MAX_PARAMS+1)] += x2 * T12 + xy * T22;
Q[3 + 7 * (MAX_PARAMS+1)] += xy * T12 + y2 * T22;
Q[3 + 8 * (MAX_PARAMS+1)] += T23;
Q[4 + 5 * (MAX_PARAMS+1)] += xy * T22;
Q[4 + 6 * (MAX_PARAMS+1)] += x3 * T12 + x2y * T22;
Q[4 + 7 * (MAX_PARAMS+1)] += x2y * T12 + xy2 * T22;
Q[4 + 8 * (MAX_PARAMS+1)] += x * T23;
Q[5 + 6 * (MAX_PARAMS+1)] += x2y * T12 + xy2 * T22;
Q[5 + 7 * (MAX_PARAMS+1)] += xy2 * T12 + y3 * T22;
Q[5 + 8 * (MAX_PARAMS+1)] += y * T23;
Q[6 + 7 * (MAX_PARAMS+1)] += x3y * T11 + 2.0 * x2y2 * T12 + xy3 * T22;
Q[6 + 8 * (MAX_PARAMS+1)] += x2 * T13 + xy * T23;
Q[7 + 8 * (MAX_PARAMS+1)] += xy * T13 + y2 * T23;
Q[1 + 0 * (MAX_PARAMS+1)] += x * T11;
Q[2 + 0 * (MAX_PARAMS+1)] += y * T11;
Q[3 + 0 * (MAX_PARAMS+1)] += T12;
Q[4 + 0 * (MAX_PARAMS+1)] += x * T12;
Q[5 + 0 * (MAX_PARAMS+1)] += y * T12;
Q[6 + 0 * (MAX_PARAMS+1)] += x2 * T11 + xy * T12;
Q[7 + 0 * (MAX_PARAMS+1)] += xy * T11 + y2 * T12;
Q[8 + 0 * (MAX_PARAMS+1)] += T13;
Q[2 + 1 * (MAX_PARAMS+1)] += xy * T11;
Q[3 + 1 * (MAX_PARAMS+1)] += x * T12;
Q[4 + 1 * (MAX_PARAMS+1)] += x2 * T12;
Q[5 + 1 * (MAX_PARAMS+1)] += xy * T12;
Q[6 + 1 * (MAX_PARAMS+1)] += x3 * T11 + x2y * T12;
Q[7 + 1 * (MAX_PARAMS+1)] += x2y * T11 + xy2 * T12;
Q[8 + 1 * (MAX_PARAMS+1)] += x * T13;
Q[3 + 2 * (MAX_PARAMS+1)] += y * T12;
Q[4 + 2 * (MAX_PARAMS+1)] += xy * T12;
Q[5 + 2 * (MAX_PARAMS+1)] += y2 * T12;
Q[6 + 2 * (MAX_PARAMS+1)] += x2y * T11 + xy2 * T12;
Q[7 + 2 * (MAX_PARAMS+1)] += xy2 * T11 + y3 * T12;
Q[8 + 2 * (MAX_PARAMS+1)] += y * T13;
Q[4 + 3 * (MAX_PARAMS+1)] += x * T22;
Q[5 + 3 * (MAX_PARAMS+1)] += y * T22;
Q[6 + 3 * (MAX_PARAMS+1)] += x2 * T12 + xy * T22;
Q[7 + 3 * (MAX_PARAMS+1)] += xy * T12 + y2 * T22;
Q[8 + 3 * (MAX_PARAMS+1)] += T23;
Q[5 + 4 * (MAX_PARAMS+1)] += xy * T22;
Q[6 + 4 * (MAX_PARAMS+1)] += x3 * T12 + x2y * T22;
Q[7 + 4 * (MAX_PARAMS+1)] += x2y * T12 + xy2 * T22;
Q[8 + 4 * (MAX_PARAMS+1)] += x * T23;
Q[6 + 5 * (MAX_PARAMS+1)] += x2y * T12 + xy2 * T22;
Q[7 + 5 * (MAX_PARAMS+1)] += xy2 * T12 + y3 * T22;
Q[8 + 5 * (MAX_PARAMS+1)] += y * T23;
Q[7 + 6 * (MAX_PARAMS+1)] += x3y * T11 + 2.0 * x2y2 * T12 + xy3 * T22;
Q[8 + 6 * (MAX_PARAMS+1)] += x2 * T13 + xy * T23;
Q[8 + 7 * (MAX_PARAMS+1)] += xy * T13 + y2 * T23;
break;
default:
mexErrMsgTxt("Unknown motion model.");
break;
}
}
static void
compute_optimal_param(double *Q, double *param, int motion_model)
{
/* Here a linear equation system needs to be solved. */
/* Solved by call back to matlab. */
int n = number_of_parameters(motion_model);
mxArray *Qbarmat = mxCreateDoubleMatrix(n, n, mxREAL);
double *Qbar = mxGetPr(Qbarmat);
mxArray *qmat = mxCreateDoubleMatrix(n, 1, mxREAL);
double *q = mxGetPr(qmat);
mxArray *leftargs[1];
mxArray *rightargs[2];
int i, j;
for (j = 0; j < n; j++)
{
for (i = 0; i < n; i++)
Qbar[i + j * n] = Q[i + j * (MAX_PARAMS+1)];
q[j] = -Q[n + j * (MAX_PARAMS+1)];
}
rightargs[0] = Qbarmat;
rightargs[1] = qmat;
mexCallMATLAB(1, leftargs, 2, rightargs, "\\");
for (i = 0; i < n; i++)
param[i] = mxGetPr(leftargs[0])[i];
mxDestroyArray(Qbarmat);
mxDestroyArray(qmat);
mxDestroyArray(leftargs[0]);
}
static double
trace_from_q(double *Q, int motion_model)
{
switch (motion_model)
{
case CONSTANT_MOTION:
return (Q[0 + 0 * (MAX_PARAMS+1)] + Q[1 + 1 * (MAX_PARAMS+1)] +
Q[2 + 2 * (MAX_PARAMS+1)]);
break;
case AFFINE_MOTION:
return (Q[2 + 2 * (MAX_PARAMS+1)] + Q[5 + 5 * (MAX_PARAMS+1)] +
Q[6 + 6 * (MAX_PARAMS+1)]);
break;
case EIGHT_PARAMETER_MOTION:
return (Q[0 + 0 * (MAX_PARAMS+1)] + Q[3 + 3 * (MAX_PARAMS+1)] +
Q[8 + 8 * (MAX_PARAMS+1)]);
break;
}
return 1.0; /* Never reached */
}
static double
compute_normalized_cost(double *Q, double *param, int motion_model)
{
double cost = 0.0;
int i, j;
int n = number_of_parameters(motion_model);
for (j = 0; j < n+1; j++)
for (i = 0; i < n+1; i++)
cost += param[i] * param[j] * Q[i + j * (MAX_PARAMS+1)];
/* Obs, obs, obs! */
cost /= trace_from_q(Q, motion_model);
return cost;
}
static void
compute_velocity(double *vx, double *vy, int x, int y, double *param,
int motion_model)
{
switch (motion_model)
{
case CONSTANT_MOTION:
*vx = param[0];
*vy = param[1];
break;
case AFFINE_MOTION:
*vx = x*param[0] + y*param[1] + param[2];
*vy = x*param[3] + y*param[4] + param[5];
break;
case EIGHT_PARAMETER_MOTION:
*vx = param[0] + x*param[1] + y*param[2] + x*x*param[6] + x*y*param[7];
*vy = param[3] + x*param[4] + y*param[5] + x*y*param[6] + y*y*param[7];
break;
}
}
static double
normalized_distance(double *T, int x, int y, int xsize, int ysize,
double *param, int motion_model)
{
int index = x + y * xsize;
int N = xsize * ysize;
double T11 = T[index];
double T12 = T[index + N];
double T13 = T[index + 2*N];
double T22 = T[index + 4*N];
double T23 = T[index + 5*N];
double T33 = T[index + 8*N];
double trace = T11 + T22 + T33;
double vx;
double vy;
double distance;
double speedsquare;
compute_velocity(&vx, &vy, x, y, param, motion_model);
distance = (vx*T11*vx + 2.0*vx*T12*vy + 2.0*vx*T13 + vy*T22*vy +
2.0*vy*T23 + T33);
speedsquare = vx*vx + vy*vy + 1;
if (trace <= 0.0)
return 1.0 / 3.0; /* Same as for multiple of I. */
else
return distance / (trace * speedsquare);
}
static void
add_to_heap(int *heap, int *heapsize, int index, double *costs)
{
int i = *heapsize;
heap[*heapsize] = index;
(*heapsize)++;
/* Walk up */
while (i > 0)
{
/* This can be improved on by not dropping the moving value
/* until has reached its position.
*/
if (costs[heap[i]] < costs[heap[(i+1)/2-1]])
{
int j = (i+1)/2-1;
int tmp = heap[j];
heap[j] = heap[i];
heap[i] = tmp;
i = j;
}
else
break;
}
}
static int
get_top_of_heap(int *heap, int *heapsize, double *costs)
{
int first = heap[0];
int last;
int i, j;
(*heapsize)--;
last = heap[*heapsize];
i = 0;
while (2*i+1 < *heapsize)
{
j = 2*i+1;
if (j+1 < *heapsize && costs[heap[j+1]] < costs[heap[j]])
j++;
if (costs[heap[j]] < costs[last])
{
heap[i] = heap[j];
i = j;
}
else
break;
}
heap[i] = last;
return first;
}
static void
order_candidate_heap(int *heap, int n, struct candidate *candidates)
{
int i, j, k;
int current;
for (k = (n+1)/2-1; k >= 0; k--)
{
current = heap[k];
i = k;
while (2*i+1 < n)
{
j = 2*i+1;
if (j+1 < n
&& candidates[heap[j+1]].cost < candidates[heap[j]].cost)
j++;
if (candidates[heap[j]].cost < candidates[current].cost)
{
heap[i] = heap[j];
i = j;
}
else
break;
}
heap[i] = current;
}
}
static void
dump_candidate_heap(int *heap, int n, struct candidate *candidates,
char *filename)
{
FILE *fd = fopen(filename, "w");
int i;
for (i = 0; i < n; i++)
fprintf(fd, "%5d %5d %g\n", i+1, heap[i], candidates[heap[i]].cost);
fclose(fd);
}
static void
reorder_candidate_heap(int *heap, int n, struct candidate *candidates)
{
int current = heap[0];
int i, j;
i = 0;
while (2*i+1 < n)
{
j = 2*i+1;
if (j+1 < n && candidates[heap[j+1]].cost < candidates[heap[j]].cost)
j++;
if (candidates[heap[j]].cost < candidates[current].cost)
{
heap[i] = heap[j];
i = j;
}
else
break;
}
heap[i] = current;
}
static int
get_first_candidate(int *heap, int *n, struct candidate* candidates)
{
int first = heap[0];
(*n)--;
heap[0] = heap[*n];
reorder_candidate_heap(heap, *n, candidates);
return first;
}
static int
rebuild_candidate(struct candidate *candidate, int *map,
int minsize, int maxsize, int xsize, int ysize,
int *heap, double *costs, int *pixels, double *T,
double *Q, int debug)
{
int size = 0;
int heapsize = 0;
int x = candidate->x;
int y = candidate->y;
int index = x + y*xsize;
double largest_cost = 0.0;
int i;
if (map[index] != 0)
{
candidate->cost = 0.0; /* Should never be used in this case. */
return 0;
}
costs[index] = normalized_distance(T, x, y, xsize, ysize, candidate->param,
candidate->motion_model);
add_to_heap(heap, &heapsize, index, costs);
while (size < maxsize && heapsize > 0)
{
index = get_top_of_heap(heap, &heapsize, costs);
if (map[index] != 0)
continue;
pixels[size] = index;
size++;
map[index] = -1;
if (largest_cost < costs[index])
largest_cost = costs[index];
x = index % xsize;
y = index / xsize;
if (x+1 < xsize) /* South */
{
int newindex = index + 1;
if (map[newindex] == 0)
{
costs[newindex] = normalized_distance(T, x+1, y, xsize, ysize,
candidate->param,
candidate->motion_model);
add_to_heap(heap, &heapsize, newindex, costs);
}
}
if (x-1 >= 0) /* North */
{
int newindex = index - 1;
if (map[newindex] == 0)
{
costs[newindex] = normalized_distance(T, x-1, y, xsize, ysize,
candidate->param,
candidate->motion_model);
add_to_heap(heap, &heapsize, newindex, costs);
}
}
if (y+1 < ysize) /* East */
{
int newindex = index + xsize;
if (map[newindex] == 0)
{
costs[newindex] = normalized_distance(T, x, y+1, xsize, ysize,
candidate->param,
candidate->motion_model);
add_to_heap(heap, &heapsize, newindex, costs);
}
}
if (y-1 >= 0) /* West */
{
int newindex = index - xsize;
if (map[newindex] == 0)
{
costs[newindex] = normalized_distance(T, x, y-1, xsize, ysize,
candidate->param,
candidate->motion_model);
add_to_heap(heap, &heapsize, newindex, costs);
}
}
}
if (debug)
mexPrintf("Startpoint: %d %d\n", candidate->x, candidate->y);
candidate->cost = largest_cost;
for (i = 0; i < size; i++)
{
map[pixels[i]] = 0;
if (debug)
mexPrintf("%d\n", pixels[i]);
}
if (size >= minsize)
{
int motion_model = candidate->motion_model;
clear_quadratic_form(Q, motion_model);
for (i = 0; i < size; i++)
add_to_quadratic_form(Q, T, pixels[i] % xsize, pixels[i] / xsize,
xsize, ysize, motion_model, 0);
compute_optimal_param(Q, candidate->param, motion_model);
if (debug)
{
for (i=0; i<number_of_parameters(motion_model); i++)
mexPrintf("%f ", candidate->param[i]);
mexPrintf("\n");
}
}
return size;
}
static int
get_cheapest_pixel(int *heap, int *heapsize, double *costs,
int *heap_position)
{
int first = heap[0];
int last;
int i, j;
(*heapsize)--;
last = heap[*heapsize];
i = 0;
while (2*i+1 < *heapsize)
{
j = 2*i+1;
if (j+1 < *heapsize && costs[heap[j+1]] < costs[heap[j]])
j++;
if (costs[heap[j]] < costs[last])
{
heap[i] = heap[j];
heap_position[heap[i]] = i;
i = j;
}
else
break;
}
heap[i] = last;
heap_position[heap[i]] = i;
return first;
}
static void
remove_from_pixel_heap(int *heap, int *heapsize, double *costs,
int *heap_position, int index)
{
int last;
int i, j;
(*heapsize)--;
last = heap[*heapsize];
i = heap_position[index];
while (2*i+1 < *heapsize)
{
j = 2*i+1;
if (j+1 < *heapsize && costs[heap[j+1]] < costs[heap[j]])
j++;
if (costs[heap[j]] < costs[last])
{
heap[i] = heap[j];
heap_position[heap[i]] = i;
i = j;
}
else
break;
}
heap[i] = last;
heap_position[heap[i]] = i;
}
static void
add_to_pixel_heap(int *heap, int *heapsize, double *costs,
int *heap_position, int index)
{
int i = *heapsize;
heap[*heapsize] = index;
heap_position[index] = *heapsize;
(*heapsize)++;
/* Walk up */
while (i > 0)
{
/* This can be improved on by not dropping the moving value */
/* until has reached its position. */
if (costs[heap[i]] < costs[heap[(i+1)/2-1]])
{
int j = (i+1)/2-1;
int tmp = heap[j];
heap[j] = heap[i];
heap[i] = tmp;
heap_position[heap[i]] = i;
heap_position[heap[j]] = j;
i = j;
}
else
break;
}
}
static void
ascend_in_pixel_heap(int *heap, int heapsize, double *costs,
int *heap_position, int index)
{
int i = heap_position[index];
/* Walk up */
while (i > 0)
{
/* This can be improved on by not dropping the moving value */
/* until has reached its position. */
if (costs[heap[i]] < costs[heap[(i+1)/2-1]])
{
int j = (i+1)/2-1;
int tmp = heap[j];
heap[j] = heap[i];
heap[i] = tmp;
heap_position[heap[i]] = i;
heap_position[heap[j]] = j;
i = j;
}
else
break;
}
}
static void
maybe_add_boundary_pixel(double *T, int x, int y, int xsize, int ysize,
struct region *regions, int n,
int *pixels_heap, int *pixels_heap_size,
double *pixel_costs, int *pixel_heap_position,
int newindex, int *pixel_claimed_by)
{
double cost = normalized_distance(T, x, y, xsize, ysize, regions[n].param,
regions[n].motion_model);
int new_boundary_pixel = (pixel_claimed_by[newindex] == 0);
if (new_boundary_pixel || cost < pixel_costs[newindex])
{
pixel_costs[newindex] = cost;
pixel_claimed_by[newindex] = n;
}
else
return;
if (new_boundary_pixel)
add_to_pixel_heap(pixels_heap, pixels_heap_size, pixel_costs,
pixel_heap_position, newindex);
else
ascend_in_pixel_heap(pixels_heap, *pixels_heap_size, pixel_costs,
pixel_heap_position, newindex);
}
static void
recompute_all_parameters(int *map, struct region *regions, int
number_of_regions, double *T, int xsize,
int ysize)
{
double *Qs;
int x, y;
int index;
int region;
Qs = mxCalloc((MAX_PARAMS+1) * (MAX_PARAMS+1) * number_of_regions,
sizeof(*Qs));
for (y = 0; y < ysize; y++)
for (x = 0; x < xsize; x++)
{
index = x + y * xsize;
region = map[index];
if (region > 0)
add_to_quadratic_form(&(Qs[((MAX_PARAMS+1) *
(MAX_PARAMS+1) *
(region-1))]),
T, x, y, xsize, ysize,
regions[region].motion_model, 0);
}
for (region = 1; region <= number_of_regions; region++)
{
compute_optimal_param(&(Qs[(MAX_PARAMS+1)*(MAX_PARAMS+1)*(region-1)]),
regions[region].param,
regions[region].motion_model);
}
mxFree(Qs);
}
void
mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
int minsize = DEFAULT_MINSIZE;
int maxsize = DEFAULT_MAXSIZE;
int kerneldist = DEFAULT_KERNELDIST;
double lambda = DEFAULT_LAMBDA;
double coverage = DEFAULT_COVERAGE;
int parameter_recomputation = DEFAULT_PARAMETER_RECOMPUTATION;
int number_of_initial_iterations = DEFAULT_NUMBER_OF_INITIAL_ITERATIONS;
int motion_models = DEFAULT_MOTION_MODELS;
int verbose = DEFAULT_VERBOSE;
int number_of_candidates = 0;
struct candidate *candidates;
const int *dims;
int xsize;
int ysize;
int i, j;
int x, y;
double Q[(MAX_PARAMS+1) * (MAX_PARAMS+1)];
double *T;
int *map;
int *candidate_build_heap;
double *candidate_build_costs;
int *candidate_build_pixels;
int *candidate_heap;
int *pixels_heap;
double *pixel_costs;
int *pixel_heap_position;
int *pixel_claimed_by;
int pixels_heap_size;
int number_of_regions;
int number_of_occupied_pixels;
struct region *regions;
int number_of_models;
/* Check the number of input and output arguments. */
if (nrhs < 1)
mexErrMsgTxt("Too few input arguments.");
if (nrhs > 2)
mexErrMsgTxt("Too many input arguments.");
if (nlhs > 4)
mexErrMsgTxt("Too many output arguments.");
/* Check the formats of the input arguments. */
if (!mxIsNumeric(prhs[0]) || mxIsComplex(prhs[0]) ||
mxIsSparse(prhs[0]) || !mxIsDouble(prhs[0]) ||
mxGetNumberOfDimensions(prhs[0]) != 4)
{
mexErrMsgTxt("T must be a real and full four-dimensional array, stored as doubles.");
}
if (nrhs == 2)
if (!mxIsStruct(prhs[1]) || mxGetM(prhs[1]) * mxGetN(prhs[1]) > 1)
mexErrMsgTxt("OPTIONS must be a scalar structure.");
/* We won't deal with an empty tensor field. */
if (mxIsEmpty(prhs[0]))
mexErrMsgTxt("T must not be empty.");
dims = mxGetDimensions(prhs[0]);
if (dims[2] != 3 || dims[3] != 3)
mexErrMsgTxt("T must be M x N x 3 x 3.");
xsize = dims[0];
ysize = dims[1];
T = mxGetPr(prhs[0]);
/* Check if there are any options set. */
if (nrhs == 2)
{
for (i = 0; i < mxGetNumberOfFields(prhs[1]); i++)
{
const mxArray *fieldvalue = mxGetFieldByNumber(prhs[1], 0, i);
const char *fieldname = mxGetFieldNameByNumber(prhs[1], i);
if (strcmp(fieldname, "lambda") == 0)
lambda = mxGetScalar(fieldvalue);
else if (strcmp(fieldname, "minsize") == 0)
minsize = (int) mxGetScalar(fieldvalue);
else if (strcmp(fieldname, "maxsize") == 0)
maxsize = (int) mxGetScalar(fieldvalue);
else if (strcmp(fieldname, "kerneldist") == 0)
kerneldist = (int) mxGetScalar(fieldvalue);
else if (strcmp(fieldname, "coverage") == 0)
coverage = mxGetScalar(fieldvalue);
else if (strcmp(fieldname, "parameter_recomputation") == 0)
parameter_recomputation = (int) mxGetScalar(fieldvalue);
else if (strcmp(fieldname, "number_of_initial_iterations") == 0)
number_of_initial_iterations = (int) mxGetScalar(fieldvalue);
else if (strcmp(fieldname, "motion_models") == 0)
motion_models = (int) mxGetScalar(fieldvalue);
else if (strcmp(fieldname, "verbose") == 0)
verbose = (int) mxGetScalar(fieldvalue);
else
{
const char *prefix = "Unknown option: ";
char *buf = mxCalloc(strlen(prefix) + strlen(fieldname) + 1,
sizeof(*buf));
sprintf(buf, "%s%s", prefix, fieldname);
mexWarnMsgTxt(buf);
mxFree(buf);
}
/* We can't have minsize larger than maxsize. */
if (minsize > maxsize)
minsize = maxsize;
/* Verify that the field value really is a scalar. */
if (!mxIsNumeric(fieldvalue) || mxIsComplex(fieldvalue) ||
mxIsSparse(fieldvalue) || !mxIsDouble(fieldvalue) ||
mxGetM(fieldvalue)*mxGetN(fieldvalue) > 1)
{
mexErrMsgTxt("The value for the options must be real scalars, stored as a doubles and not in sparse arrays.");
}
}
}
map = mxCalloc(xsize * ysize, sizeof(*map));
candidate_build_heap = mxCalloc(xsize * ysize,
sizeof(*candidate_build_heap));
candidate_build_costs = mxCalloc(xsize * ysize,
sizeof(*candidate_build_costs));
candidate_build_pixels = mxCalloc(xsize * ysize,
sizeof(*candidate_build_pixels));
/* Count the number of initial candidate regions. */
number_of_candidates = 0;
for (y = 7; y < ysize-7; y += kerneldist)
for (x = 7; x < xsize-7; x += kerneldist)
number_of_candidates++;
if (motion_models < 1 || motion_models > 7)
motion_models = DEFAULT_MOTION_MODELS;
number_of_models = (((motion_models&1) != 0) + ((motion_models&2) != 0)
+ ((motion_models&4) != 0));
number_of_candidates *= number_of_models;
candidates = mxCalloc(number_of_candidates, sizeof(*candidates));
if (verbose)
mexPrintf("%d\n", number_of_candidates);
i = 0;
for (y = 7; y < ysize-7; y += kerneldist)
for (x = 7; x < xsize-7; x += kerneldist)
for (j = 0; j < 3; j++)
if (motion_models & (1<<j))
{
candidates[i].x = x;
candidates[i].y = y;
candidates[i].motion_model = 1<<j;
i++;
}
for (i = 0; i < number_of_candidates; i++)
{
int xx = candidates[i].x;
int yy = candidates[i].y;
int motion_model = candidates[i].motion_model;
clear_quadratic_form(Q, motion_model);
for (y = yy-10; y <= yy+10; y++)
for (x = xx-10; x <= xx+10; x++)
if (x >= 0 && x < xsize && y >= 0 && y < ysize)
add_to_quadratic_form(Q, T, x, y, xsize, ysize,
motion_model, 0);
compute_optimal_param(Q, candidates[i].param, motion_model);
/* This value is actually not used, unless the subsequent loop is */
/* removed. */
if (number_of_initial_iterations == 0)
candidates[i].cost = compute_normalized_cost(Q,
candidates[i].param,
motion_model);
/* Improve the parameters a specified number of times */
/* (default 2) by regrowing the region and recomputing the */
/* parameters. */
for (j = 0; j < number_of_initial_iterations; j++)
{
(void)rebuild_candidate(&candidates[i], map, minsize, maxsize,
xsize, ysize, candidate_build_heap,
candidate_build_costs,
candidate_build_pixels, T, Q, 0);
}
candidates[i].last_rebuild = 0;
if (i % 200 == 0)
{
if (verbose)
{
mexPrintf("%d\n", i);
#if 0
for (j = 0; j < number_of_parameters(motion_model); j++)
mexPrintf("%f ", candidates[i].param[j]);
mexPrintf("\n");
#endif
}
}
}
candidate_heap = mxCalloc(number_of_candidates, sizeof(*candidate_heap));
for (i = 0; i < number_of_candidates; i++)
{
candidate_heap[i] = i;