迴圈式自信傳遞的收斂性質及影像的應用

Abstract

將自信傳遞用在singly connected 的圖上，我們可以將計算量降低且得出正確的beliefs；但如果圖是有loop的，我們使用自信傳遞就會發生一些問題。在[11]這篇論文中，它給了我們一些結果讓我們可以去解決一種特殊的case叫做single loop所造成的錯誤，我們的論文用[11]這篇的結果做了一些推廣，我們將這些結果拿去解決另外一種case的錯誤，而這種case是把兩個single loop 透過一個singly connected的子圖去把它們連在一起。最後，我們做了一個實驗是找出臉部圖片裡眼睛、鼻子、嘴巴的位置，由於眼睛、鼻子、嘴巴在相對位置上本身就會有一些相對關係，所以它們所形成的分布就會使代表它們的圖出現有迴圈的狀況；接著，我們就使用迴圈式自信傳遞的方法把它們的所在位置找出。

In the case of singly connected graph, the computational complexity for calculating beliefs can be reduced by using the belief propagation. But in the case of loopy graph, it would cause some problem if we use the belief propagation to evaluate beliefs. There are some results for correcting those problems in the case of single loop, and those results were made by Weiss in [11]. In this paper, we use those results in [11] to solve another case, which has two single loops connected by a singly connected sub-graph. In the end, we attempt to apply Loopy belief propagation to an experiment of pose estimation in the face image. In this experiment, a face image can be composed by eyes, nose and mouth. Our purpose is to find the most likely pose of those parts in the face image. Those unknown poses of parts will be unobserved variables of a joint distribution, and the graph of this distribution has a loop. We then use belief propagation to compute the beliefs for this joint distribution so that we can find those poses and plot the locations on the face image.