Design and implementation of multisteerable matched filters

Image analysis problems such as feature tracking, edge detection, image enhancement, or texture analysis require thedetection of multi-oriented patterns which can appear at arbitrary orientations. Direct rotated matched filtering for feature detection is computationally expensive, but can be sped up with steerable filters. So far, steerable filter approaches were limited to only one direction. Many important low-level image features are, however, characterized by more than a single orientation. We therefore present here a framework for efficiently detecting specific multi-oriented patterns with arbitrary orientations in grayscale images. The core idea is to construct multisteerable filters by appropriate combinations of single-steerable filters. We exploit that steerable filters are closed under addition and multiplication. This allows to derive a design guide for multisteerable filters by means of multivariate polynomials. Furthermore, we describe an efficient implementation scheme and discuss the use of weighting functions to reduce angular oscillations. Applications in camera calibration, junction analysis of images from plant roots, and the discrimination of L, T, and X-junctions demonstrate the potential of this approach.