Image Segmentation Based On Completely Positive Decomposition

With the development of science and technology,it is possible for us to obtain a large number of images. As a result, the request for image processing is becoming so high that it is hard to use a uniform way or model to describe all these images.In traditional clustering algorithms we do not consider the influence of similarity matrix on the segmented result where it is just used as an input matrix. In this paper, we use completely positive factorization to unify NMF, K-means clustering as well as spectral clustering: they are different prescriptions of the same problem with slightly different constraints. Namely, we show that clustering a data set is equivalent to finding a completely positive (systematic nonnegative matrix) factorization of the input similarity matrix under some constraints which simplify the determination of the number of the clusters, a long hanging issue in unsupervised case for all the classic clustering, and the computation of the eigenvalues and eigenvectors for a large data set. Our method greatly reduces the computational complexity of these clusterings and avoid the problem of large images processing, improve the recognition accuracy too.In the first part of the paper, we introduce cluster,feature extraction,similarity matrix and definition of completely positive matrix , then gives completely positive factorization of similarity matrix in detail. In experiments, we introduce this way to image recognition of forest to achieve the information of forestry classification and distribution, thus reducing the much work of ground measurements.From those experiments we have summarized a list of conclusions. They are listed in the conclusion section. The analysis presented in this paper is not enough. There also many other aspects should be considered. We listed these future works in the conclusion section.