I have scale down the number of columns in image. and on another copy of the original image I have scale down the number of rows. Now I want to find the intersection region between these two images
Not sure what you mean by "scale down" but suppose you do the column reduction first; then you could do the row reduction on the REDUCED column matrix. This would mean that you have compressed the columns first and then the row compression is applied to that. You could then maybe do some exploration to see if the order of operations (column, followed by row) OR (row followed by column) gives the same result.
I am using image retargeting technique called seam carving .. which resize the image by removing vertical seams and horizontal seams to reach the specific dimension.
I want to remove vertical seams .. and then find the common region (common pixels)between the retageted image and the otiginal image
Nour Alhuda Sir, we can try to find the feature point matching techniques easily naa?? I don't have the deep knowledge in seam carving techniques, but I know it's useful to keep important regions in the image by removing rows and/or columns which are not conveying much information. So your question is that you have two versions say I1 and I2 of of original image I, I have less number of rows and I2 have less number of columns as compared to I. In my opinion use feature point matching between I1 and I2, find the region with more points are match in I1 and I2. SURF keypoint matching is already available in matlab, so you can blindly go for it for a test run.
If you are looking for something new we will think of it. The problem is really interesting and some algorithms working in spatial domain itself can be found out....I hope so....
I have thought a bit more about your problem. In some ways if you can do good bookkeeping you can know exactly what original cell contributed to the new reduced cell. In the attached sketch the pink columns are to be dropped. So column 5 is to go. So the grey columns simply have to be indexed by both their new coordinate and their original coordinates.