Edge Detection of SAR Images Based on the Fractal Theory

After discussing the SAR images' properties and the principles of image description with discrete Fractional Brownian incremental random field model(DFBR model), this paper presents two new methods of edge detection for SAR images based on the Fractal theory. It is known that the Fractal Brownian random model is valid to describe the image of nature scene.In one tiny region of image, the gray surface is self similar to statistics.But for the edge points, the point located in the boundaries between adjacent regions, this property will be lost.And the Fractal parameters of these points will be out of range.So we can determine whether the point of image is edge point via calculating its Fractal parameters.A new fast method to calculate the Fractal dimension and the principles of determining edge point based on single Fractal dimension are discussed in this paper. Moreover, the Fractal parameters of image points must not depend on the scale.But for the edge points, because they have lost the self similar, their Fractal parameters will change more quickly with the scales than the other points.So we can estimate the points' Fractal parameters in different scales and caculate their difference matrix(edge magnitude map).Then we can obtain binary edge image by thresholding this edge map. In the end, the authors present experimental results of edge detection of a SAR images with the Sobel operator, the Prewitt operator, and these two methods are mentioned above.After analyzing the experimental results in detail, the authors draw the conclusion: these two new methods have better ability to anti noise for SAR images edge detection.And the second method, the Multifractal Method, get better results of edge detection than the first method, the single fractal method.