7.2.1 Modeling the natural scene using 【fractals】
Natural scenes, assumed to be defined on a continuous bounded support includedin R2, are supposed to follow a fractal model [33, 34]. This comes from the fact that the power spectrum of most images of natural landscapes (incidentally, it isalso true with European cities) exhibits scale invariance properties [35]. Naturalphenomena are statistically scale-invariant, which means that rescaling objects doesnot affect the measured statistics. This can also be called self-similarity: a sceneresembles a scaled version of itself, or even a subset of itself – of course from a statisticalviewpoint. The stochastic approach is then a convenient way to model theseproperties. Up to a multiplicative factor, the statistic regarded as a function of spatialvariables does not change, whereas the transformed object can exhibit noticeable differences.Commonly used statistics are the expectations of autocorrelation functionsand power spectra, depending on the working space. Let x and y denote the imagespace coordinates, and u and v the normalized spatial frequencies and r = "u2+v2the radial frequency. The normalization is done w.r.t. the Nyquist frequency [36], so that (u,v) # [−1/2,1/2]2.
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分形么这不是！


汗...