Specify an origin to warpPerspective() function in OpenCV 2.x - opencv

Question

I try to specify a different origin for the warpPerspective() function than the basic (0,0), in order to apply the transform independently of the support image size. I added a CvPoint parameter to the original code, but I can't find where to use these coordinates. I tried to use them in the computation of X0, Y0 and W0 but it didn't work, this only shift the transformed image in the resulting image. Any idea?
Here the code:
void warpPerspective( const Mat& src, Mat& dst, const Mat& M0, Size dsize,
int flags, int borderType, const Scalar& borderValue, CvPoint origin )
{
dst.create( dsize, src.type() );
const int BLOCK_SZ = 32;
short XY[BLOCK_SZ*BLOCK_SZ*2], A[BLOCK_SZ*BLOCK_SZ];
double M[9];
Mat _M(3, 3, CV_64F, M);
int interpolation = flags & INTER_MAX;
if( interpolation == INTER_AREA )
interpolation = INTER_LINEAR;
CV_Assert( (M0.type() == CV_32F || M0.type() == CV_64F) && M0.rows == 3 && M0.cols == 3 );
M0.convertTo(_M, _M.type());
if( !(flags & WARP_INVERSE_MAP) )
invert(_M, _M);
int x, y, x1, y1, width = dst.cols, height = dst.rows;
int bh0 = std::min(BLOCK_SZ/2, height);
int bw0 = std::min(BLOCK_SZ*BLOCK_SZ/bh0, width);
bh0 = std::min(BLOCK_SZ*BLOCK_SZ/bw0, height);
for( y = 0; y < height; y += bh0 )
{
for( x = 0; x < width; x += bw0 )
{
int bw = std::min( bw0, width - x);
int bh = std::min( bh0, height - y);
Mat _XY(bh, bw, CV_16SC2, XY), _A;
Mat dpart(dst, Rect(x, y, bw, bh));
for( y1 = 0; y1 < bh; y1++ )
{
short* xy = XY + y1*bw*2;
double X0 = M[0]*x + M[1]*(y + y1) + M[2];
double Y0 = M[3]*x + M[4]*(y + y1) + M[5];
double W0 = M[6]*x + M[7]*(y + y1) + M[8];
if( interpolation == INTER_NEAREST )
for( x1 = 0; x1 < bw; x1++ )
{
double W = W0 + M[6]*x1;
W = W ? 1./W : 0;
int X = saturate_cast<int>((X0 + M[0]*x1)*W);
int Y = saturate_cast<int>((Y0 + M[3]*x1)*W);
xy[x1*2] = (short)X;
xy[x1*2+1] = (short)Y;
}
else
{
short* alpha = A + y1*bw;
for( x1 = 0; x1 < bw; x1++ )
{
double W = W0 + M[6]*x1;
W = W ? INTER_TAB_SIZE/W : 0;
int X = saturate_cast<int>((X0 + M[0]*x1)*W);
int Y = saturate_cast<int>((Y0 + M[3]*x1)*W);
xy[x1*2] = (short)(X >> INTER_BITS);
xy[x1*2+1] = (short)(Y >> INTER_BITS);
alpha[x1] = (short)((Y & (INTER_TAB_SIZE-1))*INTER_TAB_SIZE +
(X & (INTER_TAB_SIZE-1)));
}
}
}
if( interpolation == INTER_NEAREST )
remap( src, dpart, _XY, Mat(), interpolation, borderType, borderValue );
else
{
Mat _A(bh, bw, CV_16U, A);
remap( src, dpart, _XY, _A, interpolation, borderType, borderValue );
}
}
}
}

Answer 1

Ok, I found it myself! You have 2 things to do:
compute the destination dimensions in source referential, and do the remap using these dimensions ;
increment the computed points coordinates.
Here is the code thus transformed:
void warpPerspective( const Mat& src, Mat& dst, const Mat& M0, Size dsize,
int flags, int borderType, const Scalar& borderValue, CvPoint origin )
{
dst.create( dsize, src.type() );
const int BLOCK_SZ = 32;
short XY[BLOCK_SZ*BLOCK_SZ*2], A[BLOCK_SZ*BLOCK_SZ];
double M[9];
Mat _M(3, 3, CV_64F, M);
int interpolation = flags & INTER_MAX;
if( interpolation == INTER_AREA )
interpolation = INTER_LINEAR;
CV_Assert( (M0.type() == CV_32F || M0.type() == CV_64F) && M0.rows == 3 && M0.cols == 3 );
M0.convertTo(_M, _M.type());
if( !(flags & WARP_INVERSE_MAP) )
invert(_M, _M);
int x, xDest, y, yDest, x1, y1, width = dst.cols, height = dst.rows;
int bh0 = std::min(BLOCK_SZ/2, height);
int bw0 = std::min(BLOCK_SZ*BLOCK_SZ/bh0, width);
bh0 = std::min(BLOCK_SZ*BLOCK_SZ/bw0, height);
for( y = -origin.y, yDest = 0; y < height; y += bh0, yDest += bh0 )
{
for( x = -origin.x, xDest = 0; x < width; x += bw0, xDest += bw0 )
{
int bw = std::min( bw0, width - x);
int bh = std::min( bh0, height - y);
// to avoid dimensions errors
if (bw <= 0 || bh <= 0)
break;
Mat _XY(bh, bw, CV_16SC2, XY), _A;
Mat dpart(dst, Rect(xDest, yDest, bw, bh));
for( y1 = 0; y1 < bh; y1++ )
{
short* xy = XY + y1*bw*2;
double X0 = M[0]*x + M[1]*(y + y1) + M[2];
double Y0 = M[3]*x + M[4]*(y + y1) + M[5];
double W0 = M[6]*x + M[7]*(y + y1) + M[8];
if( interpolation == INTER_NEAREST )
for( x1 = 0; x1 < bw; x1++ )
{
double W = W0 + M[6]*x1;
W = W ? 1./W : 0;
int X = saturate_cast<int>((X0 + M[0]*x1)*W);
int Y = saturate_cast<int>((Y0 + M[3]*x1)*W);
xy[x1*2] = (short)X;
xy[x1*2+1] = (short)Y;
}
else
{
short* alpha = A + y1*bw;
for( x1 = 0; x1 < bw; x1++ )
{
double W = W0 + M[6]*x1;
W = W ? INTER_TAB_SIZE/W : 0;
int X = saturate_cast<int>((X0 + M[0]*x1)*W);
int Y = saturate_cast<int>((Y0 + M[3]*x1)*W);
xy[x1*2] = (short)(X >> INTER_BITS) + origin.x;
xy[x1*2+1] = (short)(Y >> INTER_BITS) + origin.y;
alpha[x1] = (short)((Y & (INTER_TAB_SIZE-1))*INTER_TAB_SIZE +
(X & (INTER_TAB_SIZE-1)));
}
}
}
if( interpolation == INTER_NEAREST )
remap( src, dpart, _XY, Mat(), interpolation, borderType, borderValue );
else
{
Mat _A(bh, bw, CV_16U, A);
remap( src, dpart, _XY, _A, interpolation, borderType, borderValue );
}
}
}
}
with this function:
CvPoint transformPoint(const CvPoint pointToTransform, const CvMat* matrix) {
double coordinates[3] = {pointToTransform.x, pointToTransform.y, 1};
CvMat originVector = cvMat(3, 1, CV_64F, coordinates);
CvMat transformedVector = cvMat(3, 1, CV_64F, coordinates);
cvMatMul(matrix, &originVector, &transformedVector);
CvPoint outputPoint = cvPoint((int)(cvmGet(&transformedVector, 0, 0) / cvmGet(&transformedVector, 2, 0)), (int)(cvmGet(&transformedVector, 1, 0) / cvmGet(&transformedVector, 2, 0)));
return outputPoint;
}

Answer 2

A much simpler and cleaner solution is to modify the perspective transformation. You can do a translation which moves the origin to the desired position, then do the perspective transformation and finally do the inverse translation.
Here is a small example program in python, which rotates an image by 45 degrees around the point(100, 100):
import cv2
import numpy as np
def translation_mat(dx, dy):
return np.array([1, 0, dx, 0, 1, dy, 0, 0, 1]).reshape((3,3))
def main():
img = cv2.imread(r"pigeon.png", cv2.IMREAD_GRAYSCALE)
# a simple rotation by 45 degrees
rot = np.array([np.sin(np.pi/4), -np.cos(np.pi/4), 0, np.cos(np.pi/4), np.sin(np.pi/4), 0, 0, 0, 1]).reshape((3,3))
t1 = translation_mat(-100, -100)
t2 = translation_mat(100, 100)
rot_shifted = t2.dot(rot.dot(t1))
size = (img.shape[1], img.shape[0])
img1 = cv2.warpPerspective(img, rot, size)
img2 = cv2.warpPerspective(img, rot_shifted, size)
cv2.imshow("Original image", img)
cv2.imshow("Rotated around (0,0)", img1)
cv2.imshow("Rotated around(100, 100)", img2)
cv2.waitKey(0)
if __name__ == '__main__':
main()
Not that you read the order of transformations from right to left.
rot_shifted = t2.dot(rot.dot(t1))
will apply t1 first, then rot, and then t2.

Answer 3

For those of you looking for this piece in Python, here's a start. I'm not 100% sure it works as I've stripped some optimizations from it. Also there is an issue with lineair interpolation, I simply didn't use it but you might want to take a closer look if you do.
import cv2
import numpy as np
def warp_perspective(src, M, (width, height), (origin_x, origin_y),
flags=cv2.INTER_NEAREST, borderMode=cv2.BORDER_CONSTANT,
borderValue=0, dst=None):
"""
Implementation in Python using base code from
http://stackoverflow.com/questions/4279008/specify-an-origin-to-warpperspective-function-in-opencv-2-x
Note there is an issue with linear interpolation.
"""
B_SIZE = 32
if dst == None:
dst = np.zeros((height, width, 3), dtype=src.dtype)
# Set interpolation mode.
interpolation = flags & cv2.INTER_MAX
if interpolation == cv2.INTER_AREA:
raise Exception('Area interpolation is not supported!')
# Prepare matrix.
M = M.astype(np.float64)
if not(flags & cv2.WARP_INVERSE_MAP):
M = cv2.invert(M)[1]
M = M.flatten()
x_dst = y_dst = 0
for y in xrange(-origin_y, height, B_SIZE):
for x in xrange(-origin_x, width, B_SIZE):
print (x, y)
# Block dimensions.
bw = min(B_SIZE, width - x_dst)
bh = min(B_SIZE, height - y_dst)
# To avoid dimension errors.
if bw <= 0 or bh <= 0:
break
# View of the destination array.
dpart = dst[y_dst:y_dst+bh, x_dst:x_dst+bw]
# Original code used view of array here, but we're using numpy array's.
XY = np.zeros((bh, bw, 2), dtype=np.int16)
A = np.zeros((bh, bw), dtype=np.uint16)
for y1 in xrange(bh):
X0 = M[0]*x + M[1]*(y + y1) + M[2]
Y0 = M[3]*x + M[4]*(y + y1) + M[5]
W0 = M[6]*x + M[7]*(y + y1) + M[8]
if interpolation == cv2.INTER_NEAREST:
for x1 in xrange(bw):
W = np.float64(W0 + M[6]*x1);
if W != 0:
W = np.float64(1.0)/W
X = np.int32((X0 + M[0]*x1)*W)
Y = np.int32((Y0 + M[3]*x1)*W)
XY[y1, x1][0] = np.int16(X)
XY[y1, x1][1] = np.int16(Y)
else:
for x1 in xrange(bw):
W = np.float64(W0 + M[6]*x1);
if W != 0:
W = cv2.INTER_TAB_SIZE/W
X = np.int32((X0 + M[0]*x1)*W)
Y = np.int32((Y0 + M[3]*x1)*W)
XY[y1, x1][0] = np.int16((X >> cv2.INTER_BITS) + origin_x)
XY[y1, x1][1] = np.int16((Y >> cv2.INTER_BITS) + origin_y)
A[y1, x1] = np.int16(((Y & (cv2.INTER_TAB_SIZE-1))*cv2.INTER_TAB_SIZE + (X & (cv2.INTER_TAB_SIZE-1))))
if interpolation == cv2.INTER_NEAREST:
cv2.remap(src, XY, None, interpolation, dst=dpart,
borderMode=borderMode, borderValue=borderValue)
else:
cv2.remap(src, XY, A, interpolation, dst=dpart,
borderMode=borderMode, borderValue=borderValue)
x_dst += B_SIZE
x_dst = 0
y_dst += B_SIZE
return dst