Design of Multi-Steerable Filters and their Application for the Detection of Corners and Junctions

The theory of steerable filters (introduced by Freeman and Adelson in 1991) offers a convenient and computationally efficient method to represent the rotation of a specific class of 2D filters as a linear combination of base filters. In this paper, we generalize this theory to filters which are modeled as point-by-point products of multiple (in our examples: two) base filters which each are rotated by individual rotation angles, thus introducing the term "multi-steerability". While standard steerable filters are useful for the detection of edges or lines (oriented in some unknown direction), our novel extended theory can be applied to the detection of features which are characterized by multiple orientations, for instance corners or line crossings, which greatly increases the applicability of the theory. We conclude our paper with an example for detecting the crossings in a checkerboard image using double-steerable filters.