If a block with adaptive size is to be replaced by a more versatile adaptive-shape region, two problems immediately arise.

1. How to efficiently transform the data within a region which is not a square?
2. How to find these adaptive-shape regions from the noisy observations?

Two solutions

1. Shape-Adaptive DCT (Sikora & Makai, 1995). A 2D (orthonormal) transform based on 1D DCTs that can be applied on arbitrarily-shaped regions. Good energy-compaction, low complexity, part of MPEG4 standard, can be thought as a generalization of the 2D block DCT.
2. Anisotropic LPA-ICI (our team, 2004). Defines, for every point in the image, and adaptive starshaped neighborhood in which the underlying signal is uniform (in polynomial sense). Very accurate, allows adaptation to the finest structures in the image. Based on convolutions, it is among the fastest pointwise-adaptive methods for robust anisotropic filtering.