Performance of a New Method of Multicomponent Images Segmentation in the Presence of Noise ()
1. Introduction
Multicomponent images are composed of several plans of images. We can classify them into three main categories [1]: 1) The images of homogeneous components are those consisted of series of images of the same nature, and representing the same scene. The nature of the third dimension depending on the application may be temporal or polarimetric. 2) The images with quasi-homogeneous components are images intrinsically vectorial. Each pixel is characterized by the vector “color” or multispectral. The components are expressed numerically with the same measuring unit, for example energies in different wavebands. The only rigorous approach to treat such images is the vectorial approach. This work interests particularly this category of images. 3) The images with heterogeneous or multiprotocol components are images whose components are not the same nature because the different components of the image are obtained by the use of sources of different nature.
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 [3] based on the analysis of compact nD histogram. We report here how this algorithm proves to be robust to additional noise considered as a harmful corrupting signal with the extraction of the useful signal.
In this work, we first make a brief presentation of our segmentation algorithm, for more details refer to the article [3]. Then we present here the additive noises that are likely considered Gaussian, uniform and so correlated. Finally the robustness of the noise is evaluated on a multicomponent synthetic image whose properties are described.
2. Algorithm of Multicomponent Images Segmentation
The classification of “colours” is carried out in two steps [3]: the learning step and the decision step.
The learning step is a hierarchical decomposition of populations in the compact n-D histogram. For each level of population pn, peaks Pi 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 pn. 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 Figure 2 (drawn in one dimension for clarity). We shall name kernels Ki the peaks corresponding to circled leaves in part (b) of Figure 1. In other words, kernels are significant peaks (part a of figure 1) without descendants in the hierarchical decomposition tree (part (b) of Figure 1) (e.g., Figure 1 shows five significant peaks Pi (i = 0 to 4) and three kernels Ki (i = 2, 3, 4)). The number of classes Nc is taken equal to the number of kernels (the class corresponding to kernel Ki is noted Ci). Therefore Nc 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(Ki) of each kernel Ki is calculated in the feature multidimensional space. Let us denote by ß the color corresponding to the point of coordinates (g1, g2, ∙∙∙, gn) in the feature space. Two cases appear: if (g1, g2, ∙∙∙, gn) belongs to Ki, color ß is attributed to class Ci; if not, let us denote by Pk the peak which belong to (g1, g2, ∙∙∙, gn); color ß is attributed to class Ci corresponding to kernel Ki, son of Pk, knowing that d[µ(Ki), (g1, g2, ∙∙∙, gn)] is minimum, where d[y, z] is the Euclidean distance between y and z.
This method calls HierarchieFuzzy_nD.
Figure 2 shows an example of segmented image of the probe image, inspired by the image Savoise [2,14].