Image processing is used in applications for different fields like medicine, industry or robotics([1] [2] [3] [4] [5]). Segmentation is the first step in image processing and is the supports for the execution of other tasks such as refinement or features identification as referred in [6]. Segmentation is a low-level operation with the objective of dividing homogeneous or heterogeneous regions. The homogeneous regions with borders belong to objects or part of them in the images. The approach for segmentation followed in this paper applies Fuzzy logic, there are some previous efforts executed following this approach, for instance, Lopes in [7] uses an automatic threshold method based on a fuzziness measure; Cheng in [8] uses principles of fuzzy c-partition and the maximum entropy to select threshold values for gray-level images.
Other topic that explores this work is the use of validity indexes. Previously, Gamarra in [9] applied validity indexes to find the optimal number of clusters. Besides, some interesting works have explored the application of validity indexes for image segmentation. Bensaid in [10] proposed a new validity index, the partition index (SC), and introduced a new clustering algorithm, the validity-guided (re) clustering (VGC), in Bensaid´s work the validity index is not used to find the optimal number of clusters, that is already known; the validity index is used to improve the quality of partitions generated by a clustering algorithm. The VGC was applied exclusively for Magnetic Resonance Images (MRI) images. In addition, the work developed for
Velthuizen in [11] applies the VGC algorithm to MRI images for brain tumor segmentation.
This work will explore the application of different validity indexes, which will have their information correlated in order to find an adequate number of clusters for an image segmentation task. The remainder of the paper is as follows. the second section explains the different algorithms used in the paper; the thir