On optimal linear filtering for edge detection
Tóm tắt
In this paper, we revisit the analytical expressions of the three Canny's (1983) criteria for edge detection quality: good detection, good localization, and low multiplicity of false detections. Our work differs from Canny's work on two essential points. Here, the criteria are given for discrete sampled signals, i.e., for the real, implemented filters. Instead of a single-step edge as input signal, we use pulses of various width. The proximity of other edges affects the quality of the detection process. This is taken into account in the new expressions of these criteria. We derive optimal filters for each of the criteria and for any combination of them. In particular, we define an original filter which maximizes detection and localization and a simple approximation of the optimal filter for the simultaneous maximization of the three criteria. The upper bounds of the criteria are computed which allow users to measure the absolute and relative performance of any filter (exponential, Deriche (1987), and first derivative of Gaussian filters are evaluated). Our criteria can also be used to compute the optimal value of the scale parameter of a given filter when the resolution of the detection is fixed.
Từ khóa
#Maximum likelihood detection #Image edge detection #Nonlinear filters #Finite impulse response filter #Space vector pulse width modulation #Upper bound #Markov random fields #Surface morphology #Mathematical model #KernelTài liệu tham khảo
10.1109/34.134047
10.1109/34.103275
10.1109/34.62607
10.1109/34.297960
10.1109/34.632980
10.1109/ICIP.1995.537441
10.1109/34.41386
pipes, 1971, the calculus of finite differences and linear difference equations with constant coefficients, Applied Mathematics for Engineers and Physicists, 272
demigny, 2001, fast recursive implementation of the gaussian filter, Proc 11th IFIP Int Conf Very Large Scale Integration, 339
prewitt, 1970, object enhancement and extraction, Picture Processing and Psychopictories, 75
10.1109/34.120331
shen, 1990, new edge detection methods based on exponential filter, Proc ICPR, 10
canny, 1983, Finding edges and lines in images
10.1007/BF00123164
10.1016/1049-9652(92)90060-B
10.1109/34.56205
10.1016/0031-3203(93)90135-J
10.1109/TPAMI.1986.4767851