Statistical Analysis of Correspondence between Image Matting and Network Structure Detection
LU HENRY HORNG-SHING
|關鍵字:||像擷取;譜方法影像擷取;群落結構;模組度;圖分割;向量分劃;統計 式區塊模型;統計推論;譜最佳化;向量分群;Image matting;spectral matting;community structure;modularity;graph partitioning;vector partitioning;stochastic blockmodel;statistical inference;spectral optimization;vector clustering|
影像擷取是一種從影像之中擷取出多個影像物件且伴隨著偵測各物件在各像素上 通透率的程序。譜方法影像擷取(Spectral Matting)是其中一種技術，可以達到多層次影
Statistical analysis of correspondence between image matting and network structure detection Image matting, a process of extracting image components from an image with opacity estimation at each pixel covered by the objects, constitutes an essential task in image editing, video production, computer vision, and fields of image segmentation. Spectral matting is one of the popular image matting techniques and it can extract mattes not only two layers but also multiple layers. The most valuable contribution of spectral matting is that it proposes a useful and convincible mapping relationship from an image to a network. Therefore the image matting problem is linked to the network analysis problem. In recent years, networks have attracted much attention in many fields such as biological pathways, social systems, computer networks, etc. Community structure is a common feature of networks and usually corresponds to basic units in networks. Community detection problem can be considered as an optimization of the benefit function called the “modularity”. The optimization is expressed in terms of eigenvectors of a characteristic matrix called the “modularity matrix” and the optimization leads to a spectral partitioning problem. Hence, we plan to investigate the relationship between the image matting and network community analysis such that we can utilize the advantages of both methods to invent an efficient and high-quality image matting algorithm. Once establishing the relationship between both problems, we expect to share the advantages of both with each other such that the difficulties or limitations of both can be overcome. There are some similarities and analogism between both problems and we expect to explore the relation between the matting Laplacian and modularity matrix. Consequently, the image matting problem can be transformed to a network analysis problem and correspondingly solving the matting components can be regarded as the community structure detection in a network formed by the input image. Combining the domain knowledge of the image processing and network analysis field, we expect to achieve better quality and efficiency of matting results compared with the state of the art in image matting field. Besides, with the assistance of the modularity matrix, we plan to overcome the major limitation of image matting to determine the appropriate number of matting components that is the number of communities from networks’ perspective of views. Alternatively, the stochastic blockmodel has been investigated for community structure detection in networks by statistical analysis of the community structure in a random graph. A series of stochastic blockmodel variants has been investigated for the purpose of achieving accurate vertex degree distribution and overlapping community structures in literature. However, the graph in their analysis has the integer number of edges between vertices, which violates the definition of matting Laplacian in spectral matting. We also plan to develop an accurate stochastic blockmodel for the application of the image matting problem. It is noted that the major challenge of spectral matting is the process of mapping hard segmentation results to soft segmentation results. By incorporating the stochastic blockmodel method, we plan to achieve the soft segmentation results in image matting directly.