Two-dimensional shape-adaptive windowing functions for image analysis

Two-dimensional (2D) windowing functions (e.g. Hann's) defined on square (or rectangular) sub-matrices are routinely used in image processing when the local 2D Fourier transform has to be computed. However, in applications where the square-shaped 2D Fourier transform has to be computed from a spatially limited subset of image data of irregular shape (e.g. from an area obtained by segmenting), windowing functions defined on square sub-matrices cannot be used. Therefore, there is a need for 2D weighting functions whose support shape is adaptable to the shape of a given binary object. Several design variants of 2D shape-adaptive windowing functions (SAW) are presented as a proposed solution to this problem. In order to quantitatively assess and compare the design variants, five criteria for measurement of 2D SAW qualities are proposed. Based on extensive testing undertaken on both simulated and real-life data, it can be concluded that qualities of each of the proposed 2D SAW design variants are generally superior to the quality of an evenly-weighting window according to these test criteria. In conclusion, one of these 2D SAW design variants is recommended as superior for generic use in image processing.