A geometric approach to edge detection

This paper describes edge detection as a composition of four steps: conditioning, feature extraction, blending, and scaling. We examine the role of geometry in determining good features for edge detection and in setting parameters for functions to blend the features. We find that: 1) statistical features such as the range and standard deviation of window intensities can be as effective as more traditional features such as estimates of digital gradients; 2) blending functions that are roughly concave near the origin of feature space can provide visually better edge images than traditional choices such as the city-block and Euclidean norms; 3) geometric considerations can be used to specify the parameters of generalized logistic functions and Takagi–Sugeno input–output systems that yield a rich variety of edge images; and 4) understanding the geometry of the feature extraction and blending functions is the key to using models based on computational learning algorithms such as neural networks and fuzzy systems for edge detection. Edge images derived from a digitized mammogram are given to illustrate various facets of our approach.