合成仿射不變函數之起點不變性與平面圖形辨識之研究

Abstract

仿射不變函數對平移、旋轉、縮放和切變等仿射轉換具有不變性，是圖形辨識的必要技術之一，「小波合成不變函數」用「合成特徵訊號」套入仿射轉換模型，因而達到保存全部輪廓資訊的目的，使圖形辨識正確率大幅提昇。「小波合成不變函數」可以分辨輪廓的細部資訊，但是也會把起始點的變動當作輪廓變異訊號，因此如何使一個輪廓對映到唯一的「小波合成不變函數」曲線就是本研究的核心課題。本論文提出「框內自然定點法」用以決定輪廓的唯一起始點，該法結合「自然軸定點」的唯一性、圖形骨架化的不變性、和區域內「最遠距離法」的準確性，本論文藉由數個實驗分析和驗證「框內自然定點法」的可用性，並且對照既有的起始點決定法，確認「框內自然定點法」在大部份情況下都可以達成決定唯一起始點的目標。

Affine invariant function (AIF) which is independent of affine transformations such as rotation, translation, scaling, and skewing, is a useful tool of shape recognition. Synthesized Affine Invariant Function (SAIF) which receives synthesized feature signals to determine the parametric curve features no information loss in representing the shape for recognition. While SAIF can represent the detailed contour signals, it is very sensitive to the starting point of the contour signal. By taking the advantages of the uniqueness of natural axis, the invariance of contour skeletonization, and the localization furthest centroid distance of contour, this thesis proposes the constrained natural axis method. The constrained natural axis under almost all conditions can determine a unique starting point on the contour; in turn the SAIF curve refers to the starting point is unique. That makes shape recognition based on SAIF practical and useful. Experimental results show and confirm the feasibility of the innovative method.