The Science of Fractal Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The aim of this paper is to apply a new multidirectional resolution analysis to obtain boundaries between areas with different grades of "roughness". To this end, the image texture is parameterized with respect to direction, based on the model of isotropic two dimensional fractional Brownian Motion (2-d-FBM). This model underlies many different investigations in the literature even though some theoretical aspects are not clarified yet. However, in the first part of this paper, we provide some of the crucial missing links in the theory of 2-d-FBM and provide a concrete realisation of this stochastic process. In addition, we derive a formula for its spectral behaviour. In the second part we describe in detail the segmentation procedure. At first, we present a suboptimal, but fast estimation algorithm to obtain angle-dependent fractal parameter-subimages, and compare its performance to the Cramer-Rao bound. Afterwards, we apply matched edge-detection procedures to each subimage separately, and finally combine the angle-dependent boundary pixels to obtain the texture boundaries of the entire scene.