鬆弛法研究: 應用及類神經網路製作

Abstract

摘要 鬆弛法由於可以使用上下文的資訊來減少局部的含糊，並提昇整體的一致性，因此便 成為解決具有含糊不清與不確定情況的影象分析與電腦視覺問題之一項重要技術。不 過由於鬆弛法須要反覆執行，使得它的速度相當慢。另外，目前多數的細線化方法大 都是使用局部運算，因此其執行結果不穩定且易失真。 本論文中，首先基於鬆弛法提出一個同時適用於灰度與二值影像的新細線化方法。在 這個新方法裡，細線化被視為一種將各個像素分別歸類到骨架或非骨架的一個過程， 因此可以用鬆弛法來做細線化。在這個細線化過程中，用到原始資料中的上下文資訊 ，因此可儘量保持直線的直線性。我們一共用了五種類別，其中四個類分別代表四種 不同方向的骨架，另一個類別則代表非骨架。當所有的點都被歸類到骨架或非骨架時 ，整個鬆弛過程就停止。實驗結果顯示出所提出的這個方法在保持直線性上十分有效 。 接下來，為了加快鬆弛法的執行速度，我們另提出了兩種可以將鬆弛法對映到類神經 網路上的方法。在被對映到的類神經網路中，神經細胞是用來代表原先鬆弛法中的各 種假設，而神經細胞間的連結則用來代表各種假設之間的關係。藉由這兩個對映之方 法，類神經網路技術可以容易地用來解決許多目前已經用鬆弛法處理的問題，類神經 網路的許多優點也因而以發揮到許多鬆弛法的應用之中。藉著定出一個特殊的能量函 數，我們提出第一種對映方法，以使得〞Hopfield類神經網路〞執行鬆弛過程。再者 ，藉由將原本鬆弛法中個別物體的各種可能的假設，放到一種殊的神經細胞〞池〞中 ，我們提出第二種對映方法，使得〞交互激勵與競爭網路〞可以執行鬆弛過程。論文 中所列出的實驗結果驗證了這兩種對映方法之可行性。 /////// ABSTRACT Relaxation is one of the most important techniques for solving image analysis and computer vision problems with ambiguity and uncertainty because the contexual information can be utilized to reduce local ambiguity and achieve global consistency in the relaxation process. Unfortunately, the relaxation process is usually slow in speed because of its iterative nature. On the other hand, most of the existing thinning algorithms are based on local operations and suffered from distortions and unstability. In this thesis, a new thinning algorithm for both gray□scale and binary images based on the relaxation technique is proposed first. In this approcah, thinning is treated as a process of assigning each pixel to either a skeleton' or a nonskeleton category so that relaxation can be used to perform thinning. Contextual information existing in input data is utilized in the thinning process in order to preserve line straightness. Five classes are created to classify each pixel, with four classes belonging to the skeleton category for different orientations and one to the nonskeleton category. The relaxation process is terminated when it converges to a condition in which pixels lying on skeletons achieve high skeleton probability values, while other pixels have unity nonskeleton probability values. Good experimental results show that the proposed approach is effective in keeping line shraighthess. To speed up the relaxation process, two methods for mapping the relaxation process onto neural networks are proposed next. In the mapped networks the neural nodes are used to represent the various possible hypotheses and pieces of evidence in the original relaxation process, and the neural links embody the relationships among them. By these methods, the neural network technology can be easily adapted to solve the many problems which have already been solved by the relaxation process. The advantages of the neural network can thus be injected into the numerous relaxation applications. By defining a special energy function, the first mapping method makes the Hopfield neural network perform the relaxation process. By representing the various possible hypotheses for an object in the original relaxation problem by a special kind of neuron pool, the second mapping method makes the interactive activation and competition network perform the relaxation process. Experimental results demonstrating the feasibility of the proposed methods are also given.