By Phillipe Réfrégier, François Goudail

Statistical Processing thoughts for Noisy photos offers a statistical framework to layout algorithms for objective detection, monitoring, segmentation and type (identification). Its major objective is to supply the reader with effective instruments for constructing algorithms that resolve his/her personal picture processing functions. specifically, such issues as speculation test-based detection, quick lively contour segmentation and set of rules layout for non-conventional imaging platforms are comprehensively handled, from theoretical foundations to functional implementations. With a wide variety of illustrations and useful examples, this booklet serves as an first-class textbook or reference publication for senior or graduate point classes on statistical signal/image processing, in addition to a reference for researchers in similar fields.

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**Additional resources for Statistical image processing techniques for noisy images: an application-oriented approach**

**Example text**

In addition, scale invariance is easily seen from Equ. 4 where a scaling of the distances is compensated by the corresponding scaling of the total area. Observe that chord complexity is bigger for small chord lengths and for angles near to zero. Thus, regions corresponding to corners or narrow spaces will contribute more to mutual information (shape complexity). As we have previously seen (Sec. 3), for the interior of an empty sphere, the result obtained is I c = 0 since any pair (x, y) fulfills F (x, y) = 1/AT .

3 with global lines (see Equ. 4) where N is the total number of segments of the global lines or the number of pairs of points considered, which is the total number of intersections divided by two (see Fig. 1). The term of the summatory is the contribution of each chord to the complexity, and we call it chord complexity. Continuous mutual information is invariant to translations, rotations and a change of scale. As we have seen in Sec. 1, point-to-point form factor gives the density of uniformly distributed lines crossing differential areas with centre at these points, and by definition, this density is invariant under translations and rotations.

But, what is complexity? According to W. Li [73], the meaning of this quantity should be very close to certain measures of difficulty concerning the object or the system in question: the difficulty in constructing an object, the difficulty in describing a system, the difficulty in reaching a goal, the difficulty in performing a task, and so on. Many definitions of complexity, corresponding to the different ways of quantifying these difficulties, can be found. In the two last decades, diverse complexity measures, as for instance the mutual information, have been proposed to quantify the degree of structure, dependence, or correlation of a system [50, 73, 36].