影像擷取與網路結構偵測之統計分析與對應關係

Abstract

影像擷取與網路結構偵測之統計分析與 對應關係

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 像物件擷取。其最重要的貢獻是提出了影像到網路的轉換關係，因而影像擷取問題可 以轉為一個網路上分析問題。近年來網路吸引甚多研究注意並且應用在多個領域。群 落結構是網路的基本重要特性，偵測群落結構可以被分析成一個對模組度(modularity) 最大化的問題，此最佳化可進一步化成矩陣分析及譜分割問題。

因此，我們計畫研究影像擷取以及網路群落分析之間的關連性，使得能利用雙方的 好處發展出有效率高品質的影像擷取成果，影像擷取中估測物件通透率的問題，將能 對應到網路分析中的群落偵測問題，結合雙方領域的知識技術，我們期待能發展出比 現存更有效率、更高品質的影像擷取演算法。此外，透過網路群落分析，我們將能解 決譜方法影像擷取中最大的問題：決定多少個影像物件(matting component)。

另外，統計式區塊模型亦是一種分析網路群落的方式，採用統計推論的方式。此模 型的發展能達到重疊群落結構，然而現存文獻中，邊(edge)的假設並不符合影像擷取所 對應到的網路中邊該具備的特性，我們計畫發展適當的模型，並直接達到軟分割結果， 以解決影像擷取最重要的問題。

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.