Great. Now adapt this to video (:
This results in characters in frame apparently moonwalking around. It's a really cool effect, but not good for actually resizing a film. Might make for a cool bit of a music video.
Might make for a cool bit of a music video
Or maybe doing histogram equalisation for pairs of adjacent frames before the seam cutting might help.
If you visualize a video as a stack of frames, then the seam would cut through the stack, like cutting a cake with a knife, following the minimum-energy path through the stack.
You'd do this by modifying the recurrence relation to add a term for the energy of pixels in the previous frame as well as the previous line in the current frame.
In the single frame case, each pixel is a 0 dimensional point, and for each pixel, you evaluate the 3 adjacent pixels in the row above. Then to find the seam you just pick the lowest energy pixel at the edge of the frame and follow the thread up. So the total runtime of this algorithm is O(pixels).
In the multi-frame case, if you want the video to be totally smooth, you have to think higher-dimensionally.
In the multi frame case, each seam is a 1 dimensional list of pixels, and for each seam, you evaluate the $HUGE_NUMBER of adjacent seams in the previous frame.
That is, the 2D case's runtime is proportional to the image height times the number of adjacent pixels, which is a small constant (3). In the 3D case, the runtime is proportional to the number of frame times the number of adjacent seams, which is massive.
I can imagine some heuristic optimizations that would allow you to guide your search, though. For instance, you could significantly downsample the video in both pixels and framerate and solve that, and then use that low-resolution solution to constrain and prune an approximate high-resolution search.
The problem is that humans watching the video will build a 3D mental model of the scene; any transform that modifies multiple frames must do so in such a way as to maintain global spatial consistency, or it will look odd. Seam carving is too primitive to do this. You will have shots where (for instance) someone is walking obliquely away from a building towards the camera, and yet making no headway because the algorithm is carving away the (low energy, yet perceptually indispensible) pixels that seperate them - the result will be that they appear to be walking in place (and growing).
https://news.ycombinator.com/item?id=20285242#unv_20290891
(HN really should make it easier to make "anchor" links, so people don't have to load a new page just to see a sub-thread. That probably took me almost 5 minutes, which is like a quarter of the "anti-procrastination" budget with the default settings. It should have taken 10 seconds.)
One part I didn't get into is artificial weights. The original paper discusses "painting" certain regions of the image as high energy, driving seams away from those regions. This ties into faces when the paper suggests face detection to automatically paint faces with high energy, avoiding these issues in the first place!
Basically you'd apply a heuristic that because faces are so special to the human visual system, the perceived energy of a face is higher than the pixels would otherwise indicate.
This would make seams avoid altering any faces in the scene.
Great intuition! The original paper actually goes into this, and they come up with that solution.
This solution is a special case of allowing the user to apply positive and negative penalties as they wish. The latter allows targeted object removal.