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Image Retargeting
Change of image dimensions without stretching / cropping in regions where there is interesting content.

We first need a salience measure that tells us which areas of an image are interesting or important and should be preserved. Generally involves some kind of gradient filter / Laplace filter / sobel filter, or similar.

Seam Carving
Assuming we want to reduce the width of the image.
Find continuous, monotonic path from top to bottom through the image (seam) which has minimal total salience. Remove this seam.
Repeat until target width reached.

We denote by the lowest cost of a seam starting at pixel and running to the bottom of the image ().
Of course, for the bottom line pixels, this is just the local salience value:

For all other pixels, the minimum cost is computed as

A solution to this can be computed using Dynamic Programming.

An alternative solution approach is to formulate the seam search as a min-cost graph cut problem.