The Design and Use of Steerable Filters

Oriented lters are useful in many early vision and image processing tasks. One often needs to apply the same lter, rotated to di erent angles under adaptive control, or wishes to calculate the lter response at various orientations. We present an e cient architecture to synthesize lters of arbitrary orientations from linear combinations of basis lters, allowing one to adaptively \steer" a lter to any orientation, and to determine analytically the lter output as a function of orientation. Steerable lters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation. We show how to design and steer the lters, and present examples of their use in several tasks: the analysis of orientation and phase, angularly adaptive ltering, edge detection, and shape-from-shading. One can also build a self-similar steerable pyramid representation which may be used to implement a steerable \wavelet" decomposition. The same concepts can be generalized to the design of 3-D steerable lters, which should be useful in the analysis of image sequences and volumetric data.