Line and Edge Detection by Symmetry Filters

Sequential (search) methods for edge and line detection and parallel (filter) methods for edge detection are wellknown. Filter methods for line detection are generally based on direction-by-direction filtering: each filter is parallel, but only special hardware architectures allow filtering in different directions simultaneously. We present a class of isotropic edge and line detection filters that work in arbitrary dimension: symmetry filters. The principle of the method is correlation of the filter window content with a mapped version. The mapping may be point inversion, blow or rotation, all relative to the window center. Covariance is used as correlation measure. In this paper only point inversion is considered. Moreover, the filter may contain weighting coefficients e.g. to emphasize contributions from the central part. For point inversion, lines give a positive correlation and edges a negative correlation (twofold symmetry and anti-symmetry).