We can divide a rectangle orthogonally into two rectangles by specifying the position and axis of the cut. This can be repeated recursively.
Given a rectangular image, is it ever beneficial for image compression to cut it into pieces and compress each piece separately? Assuming so, given an image, determine the cuts which maximize compression.
There is an additional subtlety of the order the pieces get compressed. Older pieces may affect the context of neighboring newer pieces across an edge.
There seems a similarity between this decomposition of space and decomposition of layers.