ccv_decimal_point_t ccv_perspective_transform_apply(ccv_decimal_point_t point, ccv_size_t size, float m00, float m01, float m02, float m10, float m11, float m12, float m20, float m21, float m22)
{
m00 *= 1.0 / ccv_max(size.width, size.height);
m01 *= 1.0 / ccv_max(size.width, size.height);
m02 *= 1.0 / ccv_max(size.width, size.height);
m10 *= 1.0 / ccv_max(size.width, size.height);
m11 *= 1.0 / ccv_max(size.width, size.height);
m12 *= 1.0 / ccv_max(size.width, size.height);
m20 *= 1.0 / (ccv_max(size.width, size.height) * ccv_max(size.width, size.height));
m21 *= 1.0 / (ccv_max(size.width, size.height) * ccv_max(size.width, size.height));
m22 *= 1.0 / ccv_max(size.width, size.height);
point.x -= size.width * 0.5;
point.y -= size.height * 0.5;
float wz = 1.0 / (point.x * m20 + point.y * m21 + m22);
float wx = size.width * 0.5 + (point.x * m00 + point.y * m01 + m02) * wz;
float wy = size.height * 0.5 + (point.x * m10 + point.y * m11 + m12) * wz;
return ccv_decimal_point(wx, wy);
}
/* this code is a rewrite from OpenCV's legendary Lucas-Kanade optical flow implementation */
void ccv_optical_flow_lucas_kanade(ccv_dense_matrix_t* a, ccv_dense_matrix_t* b, ccv_array_t* point_a, ccv_array_t** point_b, ccv_size_t win_size, int level, double min_eigen)
{
assert(a && b && a->rows == b->rows && a->cols == b->cols);
assert(CCV_GET_CHANNEL(a->type) == CCV_GET_CHANNEL(b->type) && CCV_GET_DATA_TYPE(a->type) == CCV_GET_DATA_TYPE(b->type));
assert(CCV_GET_CHANNEL(a->type) == 1);
assert(CCV_GET_DATA_TYPE(a->type) == CCV_8U);
assert(point_a->rnum > 0);
level = ccv_clamp(level + 1, 1, (int)(log((double)ccv_min(a->rows, a->cols) / ccv_max(win_size.width * 2, win_size.height * 2)) / log(2.0) + 0.5));
ccv_declare_derived_signature(sig, a->sig != 0 && b->sig != 0 && point_a->sig != 0, ccv_sign_with_format(128, "ccv_optical_flow_lucas_kanade(%d,%d,%d,%la)", win_size.width, win_size.height, level, min_eigen), a->sig, b->sig, point_a->sig, CCV_EOF_SIGN);
ccv_array_t* seq = *point_b = ccv_array_new(sizeof(ccv_decimal_point_with_status_t), point_a->rnum, sig);
ccv_object_return_if_cached(, seq);
seq->rnum = point_a->rnum;
ccv_dense_matrix_t** pyr_a = (ccv_dense_matrix_t**)malloc(sizeof(ccv_dense_matrix_t*) * level);
ccv_dense_matrix_t** pyr_a_dx = (ccv_dense_matrix_t**)malloc(sizeof(ccv_dense_matrix_t*) * level);
ccv_dense_matrix_t** pyr_a_dy = (ccv_dense_matrix_t**)malloc(sizeof(ccv_dense_matrix_t*) * level);
ccv_dense_matrix_t** pyr_b = (ccv_dense_matrix_t**)malloc(sizeof(ccv_dense_matrix_t*) * level);
int i, j, t, x, y;
/* generating image pyramid */
pyr_a[0] = a;
pyr_a_dx[0] = pyr_a_dy[0] = 0;
ccv_sobel(pyr_a[0], &pyr_a_dx[0], 0, 3, 0);
ccv_sobel(pyr_a[0], &pyr_a_dy[0], 0, 0, 3);
pyr_b[0] = b;
for (i = 1; i < level; i++)
{
pyr_a[i] = pyr_a_dx[i] = pyr_a_dy[i] = pyr_b[i] = 0;
ccv_sample_down(pyr_a[i - 1], &pyr_a[i], 0, 0, 0);
ccv_sobel(pyr_a[i], &pyr_a_dx[i], 0, 3, 0);
ccv_sobel(pyr_a[i], &pyr_a_dy[i], 0, 0, 3);
ccv_sample_down(pyr_b[i - 1], &pyr_b[i], 0, 0, 0);
}
int* wi = (int*)malloc(sizeof(int) * win_size.width * win_size.height);
int* widx = (int*)malloc(sizeof(int) * win_size.width * win_size.height);
int* widy = (int*)malloc(sizeof(int) * win_size.width * win_size.height);
ccv_decimal_point_t half_win = ccv_decimal_point((win_size.width - 1) * 0.5f, (win_size.height - 1) * 0.5f);
const int W_BITS14 = 14, W_BITS7 = 7, W_BITS9 = 9;
const float FLT_SCALE = 1.0f / (1 << 25);
// clean up status to 1
for (i = 0; i < point_a->rnum; i++)
{
ccv_decimal_point_with_status_t* point_with_status = (ccv_decimal_point_with_status_t*)ccv_array_get(seq, i);
point_with_status->status = 1;
}
int prev_rows, prev_cols;
for (t = level - 1; t >= 0; t--)
{
ccv_dense_matrix_t* a = pyr_a[t];
ccv_dense_matrix_t* adx = pyr_a_dx[t];
ccv_dense_matrix_t* ady = pyr_a_dy[t];
assert(CCV_GET_DATA_TYPE(adx->type) == CCV_32S);
assert(CCV_GET_DATA_TYPE(ady->type) == CCV_32S);
ccv_dense_matrix_t* b = pyr_b[t];
for (i = 0; i < point_a->rnum; i++)
{
ccv_decimal_point_t prev_point = *(ccv_decimal_point_t*)ccv_array_get(point_a, i);
ccv_decimal_point_with_status_t* point_with_status = (ccv_decimal_point_with_status_t*)ccv_array_get(seq, i);
prev_point.x = prev_point.x / (float)(1 << t);
prev_point.y = prev_point.y / (float)(1 << t);
ccv_decimal_point_t next_point;
if (t == level - 1)
next_point = prev_point;
else {
next_point.x = point_with_status->point.x * 2 + (a->cols - prev_cols * 2) * 0.5;
next_point.y = point_with_status->point.y * 2 + (a->rows - prev_rows * 2) * 0.5;
}
point_with_status->point = next_point;
prev_point.x -= half_win.x;
prev_point.y -= half_win.y;
ccv_point_t iprev_point = ccv_point((int)prev_point.x, (int)prev_point.y);
if (iprev_point.x < 0 || iprev_point.x >= a->cols - win_size.width - 1 ||
iprev_point.y < 0 || iprev_point.y >= a->rows - win_size.height - 1)
{
if (t == 0)
point_with_status->status = 0;
continue;
}
float xd = prev_point.x - iprev_point.x;
float yd = prev_point.y - iprev_point.y;
int iw00 = (int)((1 - xd) * (1 - yd) * (1 << W_BITS14) + 0.5);
int iw01 = (int)(xd * (1 - yd) * (1 << W_BITS14) + 0.5);
int iw10 = (int)((1 - xd) * yd * (1 << W_BITS14) + 0.5);
int iw11 = (1 << W_BITS14) - iw00 - iw01 - iw10;
float a11 = 0, a12 = 0, a22 = 0;
unsigned char* a_ptr = (unsigned char*)ccv_get_dense_matrix_cell_by(CCV_C1 | CCV_8U, a, iprev_point.y, iprev_point.x, 0);
int* adx_ptr = (int*)ccv_get_dense_matrix_cell_by(CCV_C1 | CCV_32S, adx, iprev_point.y, iprev_point.x, 0);
int* ady_ptr = (int*)ccv_get_dense_matrix_cell_by(CCV_C1 | CCV_32S, ady, iprev_point.y, iprev_point.x, 0);
int* wi_ptr = wi;
int* widx_ptr = widx;
int* widy_ptr = widy;
for (y = 0; y < win_size.height; y++)
{
for (x = 0; x < win_size.width; x++)
{
wi_ptr[x] = ccv_descale(a_ptr[x] * iw00 + a_ptr[x + 1] * iw01 + a_ptr[x + a->step] * iw10 + a_ptr[x + a->step + 1] * iw11, W_BITS7);
// because we use 3x3 sobel, which scaled derivative up by 4
widx_ptr[x] = ccv_descale(adx_ptr[x] * iw00 + adx_ptr[x + 1] * iw01 + adx_ptr[x + adx->cols] * iw10 + adx_ptr[x + adx->cols + 1] * iw11, W_BITS9);
widy_ptr[x] = ccv_descale(ady_ptr[x] * iw00 + ady_ptr[x + 1] * iw01 + ady_ptr[x + ady->cols] + iw10 + ady_ptr[x + ady->cols + 1] * iw11, W_BITS9);
a11 += (float)(widx_ptr[x] * widx_ptr[x]);
a12 += (float)(widx_ptr[x] * widy_ptr[x]);
a22 += (float)(widy_ptr[x] * widy_ptr[x]);
}
a_ptr += a->step;
adx_ptr += adx->cols;
ady_ptr += ady->cols;
wi_ptr += win_size.width;
widx_ptr += win_size.width;
widy_ptr += win_size.width;
}
a11 *= FLT_SCALE;
a12 *= FLT_SCALE;
a22 *= FLT_SCALE;
float D = a11 * a22 - a12 * a12;
float eigen = (a22 + a11 - sqrtf((a11 - a22) * (a11 - a22) + 4.0f * a12 * a12)) / (2 * win_size.width * win_size.height);
if (eigen < min_eigen || D < FLT_EPSILON)
{
if (t == 0)
point_with_status->status = 0;
continue;
}
D = 1.0f / D;
next_point.x -= half_win.x;
next_point.y -= half_win.y;
ccv_decimal_point_t prev_delta;
for (j = 0; j < LK_MAX_ITER; j++)
{
ccv_point_t inext_point = ccv_point((int)next_point.x, (int)next_point.y);
if (inext_point.x < 0 || inext_point.x >= a->cols - win_size.width - 1 ||
inext_point.y < 0 || inext_point.y >= a->rows - win_size.height - 1)
break;
float xd = next_point.x - inext_point.x;
float yd = next_point.y - inext_point.y;
int iw00 = (int)((1 - xd) * (1 - yd) * (1 << W_BITS14) + 0.5);
int iw01 = (int)(xd * (1 - yd) * (1 << W_BITS14) + 0.5);
int iw10 = (int)((1 - xd) * yd * (1 << W_BITS14) + 0.5);
int iw11 = (1 << W_BITS14) - iw00 - iw01 - iw10;
float b1 = 0, b2 = 0;
unsigned char* b_ptr = (unsigned char*)ccv_get_dense_matrix_cell_by(CCV_C1 | CCV_8U, b, inext_point.y, inext_point.x, 0);
int* wi_ptr = wi;
int* widx_ptr = widx;
int* widy_ptr = widy;
for (y = 0; y < win_size.height; y++)
{
for (x = 0; x < win_size.width; x++)
{
int diff = ccv_descale(b_ptr[x] * iw00 + b_ptr[x + 1] * iw01 + b_ptr[x + b->step] * iw10 + b_ptr[x + b->step + 1] * iw11, W_BITS7) - wi_ptr[x];
b1 += (float)(diff * widx_ptr[x]);
b2 += (float)(diff * widy_ptr[x]);
}
b_ptr += b->step;
wi_ptr += win_size.width;
widx_ptr += win_size.width;
widy_ptr += win_size.width;
}
b1 *= FLT_SCALE;
b2 *= FLT_SCALE;
ccv_decimal_point_t delta = ccv_decimal_point((a12 * b2 - a22 * b1) * D, (a12 * b1 - a11 * b2) * D);
next_point.x += delta.x;
next_point.y += delta.y;
if (delta.x * delta.x + delta.y * delta.y < LK_EPSILON)
break;
if (j > 0 && fabs(prev_delta.x - delta.x) < 0.01 && fabs(prev_delta.y - delta.y) < 0.01)
{
next_point.x -= delta.x * 0.5;
next_point.y -= delta.y * 0.5;
break;
}
prev_delta = delta;
}
ccv_point_t inext_point = ccv_point((int)next_point.x, (int)next_point.y);
if (inext_point.x < 0 || inext_point.x >= a->cols - win_size.width - 1 ||
inext_point.y < 0 || inext_point.y >= a->rows - win_size.height - 1)
point_with_status->status = 0;
else {
point_with_status->point.x = next_point.x + half_win.x;
point_with_status->point.y = next_point.y + half_win.y;
}
}
prev_rows = a->rows;
prev_cols = a->cols;
ccv_matrix_free(adx);
ccv_matrix_free(ady);
if (t > 0)
{
ccv_matrix_free(a);
ccv_matrix_free(b);
}
}
free(widy);
free(widx);
free(wi);
free(pyr_b);
free(pyr_a_dy);
free(pyr_a_dx);
free(pyr_a);
}
