Scale multiplication in odd Gabor transform domain for edge detection

In this paper, we propose an adaptive edge detection technique based on scale multiplication in odd Gabor transform domain (ESMG). With adjacent scale multiplication in odd Gabor transform domain, a sharpened edge response output is obtained, which can more effectively resist the inverse influence from noise contamination on the performance of edge detector. Based on odd Gabor filter with single scale, it is shown that Rayleigh distribution can be feasibly adopted to model the real pdf of edge response. Thus the pdf of sharpened edge response output can be approximately modeled by an exponential distribution since there exists strong correlation between two edge response outputs with two adjacent scale factors. In determining the threshold for the sharpened edge response, an adaptive strategy is applied, in which the nonlinear relation of the threshold with the mean and variance of exponential distribution is exploited. Moreover, an optimization problem is finally formulated to find the adaptive adjustment factor. The experimental results on both synthetic and real world natural images show that our scheme is robust and takes on good edge detection performance.