形態骨架法與篩選法理論及應用之研究

Abstract

在圖形識別與電腦視覺系統□，影像中物件的幾何性質是非常有用的特徵，要顯示物件的特徵常常需要簡潔的表示方式，一個常用的幾何形狀表示方法就是骨架法，骨架法能簡化物件形狀成中軸線表示法，同時能夠保留物件的幾何訊息。近年來，形態影像處理已經成為影像處理的一個重要研究領域，數學型態學能提供有用的工具來探索物件的幾何性質，其中一個重要的形狀表示方法就是形態骨架法。 形態骨架法是以〝野火〞模式為基礎來定義的，在這篇論文□，我們簡短地回顧了形態骨架法與數學形態學的基礎理論，並在L-影像表示法的幫助下，將二元的形態骨架法擴展到灰階影像上。之後，我們比較研究了形態骨架法與乏晰中軸轉換法，為了簡化比較的過程，灰階形態骨架法的一個特殊情形被選擇來與乏晰中軸轉換法作比較，同時提出了在形態骨架與乏晰中軸之間作轉換的方法。對於將形態骨架轉換到乏晰中軸的情形來說，實驗的結果透露出我們提出的方法能夠有效率地將形態骨架轉換成凸乏晰中軸，特別是針對平滑影像，我們提出的方法比原來的方法更有效率。 我們也探索了形態骨架法的相關課題，其中一個就是SKIZ。SKIZ是形態骨架的變形，它發生在當我們考慮影像背景骨架的時候，一個有效計算SKIZ的方法就是使用分水嶺運算法則。基於SKIZ的概念，我們發展了一個新的方法來辨識影像中切割出來的物件間或區域間的空間關係，同時也和累加法與相容法做比較，實驗結果顯示我們所提出的方法是較快且較有效率的。另外一個我們探索的相關課題是形態篩選法，也稱作圖型頻普法。形態篩選法將影像視為由各種不同形狀、大小的顆粒所組成，並模擬篩子的篩選動作對影像上的顆粒作篩選。最近，有人提出了區域形態篩選法，當這方法應用到像素分類的時候，就會遇到視窗的大小需用多大的問題。因此，我們提供了一個預測的方法，這方法適用於具結構化的紋路影像，它是根據結構化的紋路影像具有週期這個概念所發展出來的。這個方法建議我們在一個紋路影像集合中，找出這個紋路影像集合的最大週期，然後選擇一個不小於最大週期的最小奇數來作為視窗的大小。

Geometrical properties of objects in an image are very useful features for pattern recognition and computer vision systems. To represent and characterize the objects, a compact and approximate representation is often needed. A generally used geometrical shape representation is the skeleton representation. It reduces object shape to an axial representation and preserves most of its geometrical information. In recent years, morphological image processing has grown to a major area of study within image processing. Mathematical morphology provides a useful tool for inspecting the geometrical properties of objects. One important shape representation method is morphological skeletonization. Morphological skeletonization is defined based on the concept of grassfire. In this dissertation, we briefly review the morphological skeleton transformation and the mathematical morphology. With the help of the notion of l-images, we extend the binary morphological skeletonization to gray scale images. Therefore, we make a comparative study between morphological skeletonization (MSK) and fuzzy medial axis transformation (FMAT). To simplify the comparison, a special case of our extension is selected. The methods are proposed to perform the translation between MSK and FMAT. For the case of the translation from MSK to the convex FMAT, the experimental results reveal that the proposed method can effectively produce the convex FMAT. In particular, the proposed method is faster than the original method for smoothed images. The relevant topics of the morphological skeleton transformation are also investigated. One of them is the skeleton by influence zones (or SKIZ). The skeleton by influence zones is a variant of the skeleton when we consider the skeleton of the background of an image. An effective method to find the SKIZ is using the watershed algorithm. Based on the concept of SKIZ, we propose a new approach for recognizing the primitive spatial relations between objects or regions in a segmented image. The approach is compared with the aggregation and compatibility methods. The experimental result shows the proposed approach is effective and fast. The other relative topic is called granulometry, or called pattern spectrum by Maragos. Morphological granulometry is introduced by Matheron and is modeled as a sieving process of a random binary image based on the size and shape of grains within the image. Recently, Dougherty and his colleagues introduced the concept of local size distribution. When it is applied to pixel classification, the problem of window size arises. Thus, we present a method to predict the window size when determining the local granulometry for a structural texture image set. The proposed method is based on the concept of periodicity property of structural texture images. It suggests that one may choose the minimum odd number not less than the maximum periods of texture images as a window size.