USING ORDER STATISTIC FILTERS. An order statistic (OS) filter of window size L is detcrmined by its vector of coefficients [cl, ... cL]; for input and output signals ...
ON THE DETECTION OF EDGES USING ORDER STATISTIC FILTERS Alji-edoRestrepo (Palacios), Gerald Hincapie' and Alfonso Parra Universidad de 10s Andes, A.A. 4976, Bogota, Colombia
for r = 1, ..., ( L - l ) / 2 . Q,::L is the range foi*a sample
Abstract. The class of nonlinear filters known as order statistic filters has been successfully applied for the restoration of images, overcoming difficulties not solvable by the use of linear filters. An adaptive approach for the restoration of images using OS filters was proposed in [l]; it makes use of a moving quasi-range filter for the estimation of edges. We explore further this type of filter for edge detection.
of size L;for small values of r we say that (),-....L is an outer quasirange, and an inner quasirangti, for large values of r. OSED's are linear combiiations of quasiranges, for example, an OSED with c oefficients [-.2, -.8, 0, .8, .2] corresponds to the linear c~mbination
0.2Q1,,5 + 0.8Q2::5. The output of an OSED IS a thresholded version of the output of the corresponding OS filter; at each coordinate, if the output of the OS filter is below a give1 threshold level, the output of the detector is set t , be zero, otherwise. the output of the detector is se to be the output value of the OS filter.
1. A FRAMEWORK FOR EDGE DETECTION USING ORDER STATISTIC FILTERS An order statistic (OS) filter of window size L is detcrmined by its vector of coefficients [cl, ... cL]; for input and output signals x = ( x i ) and y = { y i } ,
1.1 Deterministic Considerations
respectively, each component y i of the output signal is given by [cl, ... cLl[
