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Any undesirable signal limiting to a degree or another the integrity and the intelligibility of a useful signal can be considered as noise. In the general rule, the good performance of a system is assured only if the level of power of the useful signal exceeds by several orders of magnitude that of the noise (signal to noise of a several tens of decibels). However certain elaborate methods of treatment allow working with very low signal to noise ratio in an optimal way any a priori knowledge available on the signal useful to interpret. In this work, we evaluate the robustness of the noise on a new method of multicomponent image segmentation developed recently. Two types of additional noises are considered, which are the Gaussian noise and the uniform noise, with varying correlation between the different components (or planes) of the image. Quantitative results show the influence of the noise level on the segmentation method.

Multicomponent images are composed of several plans of images. We can classify them into three main categories [

In a multicomponent image, a pixel can be considered as a vector of attributes of n elements (tuple, where n is the number of components of the image) from which each value of the tuple is resulting from a component of the image. Segmenting the images according to their radiometric attributes can be achieved by analyzing multidimensional histogram [2,3]. However, to manipulate a nD histogram (n > = 3) is not easy task because it requires a large memory [4-6]. The difficulty can be overcome by using a compact multidimensional histogram [7-12]. We have recently proposed a segmentation method [

In this work, we first make a brief presentation of our segmentation algorithm, for more details refer to the article [

The classification of “colours” is carried out in two steps [

The learning step is a hierarchical decomposition of populations in the compact n-D histogram. For each level of population p_{n}, peaks P_{i} are identified by the FCCL algorithm for a given value of α, which retains the connected components whose populations are greater than or equal to p_{n}. Each peak is then iteratively decomposed into narrower peaks, beginning from population 0. A peak is labelled as significant if it represents a population greater than or equal to a threshold S (expressed in percent of the total population in the histogram). The procedure is illustrated in part (a) of _{i} the peaks corresponding to circled leaves in part (b) of _{i} (i = 0 to 4) and three kernels K_{i} (i = 2, 3, 4)). The number of classes N_{c} is taken equal to the number of kernels (the class corresponding to kernel K_{i} is noted C_{i}). Therefore N_{c} depends on the threshold S, i.e. on the precision the image colors are analyzed with and the value of α the degree of similarity between the spels.

At the decision step, the mass center µ(K_{i}) of each kernel K_{i} is calculated in the feature multidimensional space. Let us denote by ß the color corresponding to the point of coordinates (g_{1}, g_{2}, ∙∙∙, g_{n}) in the feature space. Two cases appear: if (g_{1}, g_{2}, ∙∙∙, g_{n}) belongs to K_{i}, color ß is attributed to class C_{i}; if not, let us denote by P_{k} the peak which belong to (g_{1}, g_{2}, ∙∙∙, g_{n}); color ß is attributed to class C_{i} corresponding to kernel K_{i}, son of P_{k}, knowing that d[µ(K_{i}), (g_{1}, g_{2}, ∙∙∙, g_{n})] is minimum, where d[y, z] is the Euclidean distance between y and z.

This method calls HierarchieFuzzy_nD.