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In order to build an edge detector that provides information on the degree of importance spatial features represent in the visual field, I used the wavelet transform applied to two-dimensional signals and performed a multi-resolution multi-oriented edge detection. The wavelets are functions well-localized in spatial domain and in frequency domain. Thus the wavelet decomposition of a signal or an image provides outputs in which you can still extract spatial features and not only frequency components.
In order to detect edges the wavelet I chose is the first derivative of a smoothing function. I decompose the images as many times as I have directions of detection. I decided to work for the moment on the X-direction and the Y-direction only. Each step of the decomposition corresponds to a different scale. I use a discrete scale s = 2j (dyadic wavelet) and a finite number of decomposed images. Instead of scaling the filters at each step I sample the image by 2 (gain in processing time). Then, I extract the extrema, track and link them from the coarsest scale to the finest one. I build a symbolic image in which the edge-pixels are not only localized but labelled too, according to the number of appearances in the different scales and according to the contrast range of the edge. Without any arbitrary threshold I can subsequently classify the edges according to their physical properties in the scene and their degree of importance.
This process is subsequently intended to be part of more general perceptual learning procedures. The context should be: none or as little as possible a priori knowledge, and the ultimate goal is to integrate this detector in a feedback system dealing with color information, texture and smooth surfaces extraction. Then decisions must be taken on symbolic levels in order to make new interpretation or even new edge detection on ambiguous areas of the visual field.
Laurent Peytavin, "Multi-Oriented Multi-Resolution Edge Detection", . February 1990.
Date Posted: 22 August 2007