Using border-aligned block functions for image compression

An apparatus for encoding a block of a frame, the apparatus comprising:

• a processor configured to:
• receive the block, wherein the block is in a spatial domain;
• select, based on a shape that partitions the block, a set of basis functions for transforming the block to a transform domain,
• wherein the set of basis functions is selected from a set of candidate sets of basis functions, and
• wherein each of at least some of the candidate sets of basis functions corresponds to a respective direction of a block-crossing shape of a to-be-encoded block and a respective displacement of the block-crossing shape within the to-be-encoded block;
• transform the block using the set of basis functions to obtain a transform block;
• encode, in a compressed bitstream, an indication of the set of basis functions;
• and
• encode, in the compressed bitstream, the transform block.

An apparatus for decoding a block of a frame, the apparatus comprising:

• a processor configured to:
• decode, from a compressed bitstream, an indication of a set of basis functions for inverse transforming a transform block of the block,
• wherein the set of basis functions is one of a set of available candidate sets of basis functions, each available candidate set of at least some of the available candidate sets corresponds to a respective displacement of a shape and a respective direction of the shape within the block;
• wherein the block includes a shape,
• wherein the set of basis functions corresponds to the shape;
• and
• wherein the set of basis functions corresponds to eigenfunctions of a graph Laplacian that is formed based on the shape;
• decode, from the compressed bitstream, the transform block;
• and
• inverse-transform the transform block using the set of basis functions to obtain the block.