Device Space Design for Efficient Scale-Space Edge Detection

We present a new approach to the computation of scalable image derivative operators, based on the finite element method, that addresses the issues of method, efficiency and scale-adaptability. The design procedure is applied to the problem of approximating scalable differential operators within the framework of Schwartz distributions. Within this framework, the finite element approach allows us to define a device space in which scalable image derivative operators are implemented using a combination of piecewise-polynomial and Gaussian basis functions.Here we illustrate the approach in relation to the problem of scale-space edge detection, in which significant scale-space edge points are identified by maxima of existing edge-strength measures that are based on combinations of scale-normalised derivatives. We partition the image in order to locally identify approximate ranges of scales within which significant edge points may exist, thereby avoiding unnecessary computation of edge-strength measures across the entire range of scales.