The Application And Research Of Image Segmentation Based On Spectral Method

Image segmentation is an important element of pattern recognition and image processing. There are many different image segmentation methods, one of which is image segmentation based on graph theory, and it is newly developing technique in recent years; It firmly bases on spectral and graph theory, and is widely applied to practice, but the main challenges of the technique are how to construct the similarity matrix, how to reduce the time complexity of the algorithm, and how to judge the number of the clustering automatically.In the paper, it researches the image segmentation based on spectral theory from different angles to remove the obstacles mentioned above. Firstly, it analyzes the algorithm named spectral grouping using the Nystr?m method, compares the performance between the algorithm and traditional spectral segmentation method to summarize the advantages of the algorithm, because the time complexity of the algorithm is lower than the traditional one obviously. Secondly, because it is significant to use the suitable kernel function for computing the similarity matrix in the algorithm, it structures a new kernel function named weighted Mahalanobis distance Gaussian kernel at the first time. Simultaneously, it introduces several kernel functions for computing the affinity matrix, and analyses their effect. It also analyses that weighted Mahalanobis distance is more appropriate for computing the similarity between two pixel than Mahalanobis distance, uses weighted Mahalanobis distance Gaussian kernel for Nystr?m-Ncut segmentation to obtain a better segmentation result. Thirdly, because the number of the segmentation block affects the segmentation directly, in order to judge the number of clustering automatically, it imports a simple clustering method instead of k-means for attaining a better result, but the method must establish related parameters by debugging program. So it's limitations make it only apply to some specific images. However, it supplies a new method that estimate the number of clustering for spectral clustering. At last, it introduces a novel thresholding algorithm based on spectral method which achieves improved image segmentation performance at low computational cost. The algorithm shows the superior performance compared to existing thresholding algorithm. But it needs to adjust parameters for final segmentation. Sometimes, even if it adjusts parameters, the result of the segmentation is not satisfactorily; It conveniently implements the algorithm using the Mahalanobis Gaussian kernel or local Mahalanobis Gaussian kernel structured at the first time, and obtains clear results but not to adjust parameters.