透視不變性於電腦視覺之應用

Abstract

電腦視覺的主要目標，是發展能以良好效率及精確性完成特定影像分析工作的穩定系統。其中，基於透視投影幾何的方法，常與參考點所提供的已知資訊有所關連。交比不變性在此類投影轉換中，扮演了一個重要的角色。事實上，它是許多辨識和影像重建方法的基礎，同時也是處理電腦視覺問題最重要的技術之一，例如平面特徵的辨認、三度空間的定位，以及在自動導航領域之應用。在本篇論文中，我們應用交比發展了產生線光源影子的方法，以及利用交比進行臉孔辨識的系統。基於此不變性，我們可以避免大量且繁複的有關三維空間資訊的計算，例如攝影機的校正，和物體完整結構的重建，而直接使用交比去求得物體二維或三維結構的相對量測值。我們也發展了一個新的方法，去預測及描述交比計算過程所產生的定位誤差的特性。此方法並不直接進行整個影像空間的誤差計算。由於此方法可提供我們對此類誤差的傳播較具象的概念，因此能幫助我們有效率地選擇參考點。另外，我們也提出了以影像特徵點間的區域相似度和整體的幾何關係為基礎的影像特徵對應計算方法。此演算法可做為影像分析的前處理運算，並可望適用於包括本論文所提出的各種即時電腦視覺應用。

One of the main purposes of computer vision is to develop a reliable system that can carry out its tasks with satisfactory efficiency and precision in a realistic environment. Approaches based on projective geometry are often associated with reference points given as prior knowledge. As a geometric invariant under projective transformations, cross-ratio is the basis of many recognition and reconstruction algorithms. In fact, cross-ratio-based approaches are important techniques to address various computer vision problems, such as planar feature recognition, 3-D localization and autonomous navigation applications. In this dissertation, applications of cross-ratio in shadow generation and identity verification are investigated. The common idea of these algorithms is to use cross-ratio to determine measurements of object structure without tedious and expensive computation to infer 3-D information, including object modeling and camera calibration. Meanwhile, for error analysis of cross-ratio-based approaches, we derive efficient means to predict and to describe the characteristic of localization error. The approach allows one to select appropriate reference image points by providing corresponding regions of localization error. Finally, an efficient approach for finding correspondences between image features based on local similarity and global constraints is also conducted as an applicable stage of image analysis, which will be suitable for various real-time applications of computer vision, including those developed in this dissertation.