具有雜訊穩健性的改進式邊緣及脊偵測演算法和雙邊濾波器

Abstract

在影像處理領域中，邊緣偵測是一個基礎而重要的問題，因此一直都有受到持續討論。我們觀察到在傳統的邊緣偵測方法中，有一個雖然關鍵卻較少受到關注的子領域：脊偵測：此外有個能在邊緣偵測上派上用場，卻沒那麼常被實際運用到的演算法：雙邊濾波器。 在論文的前半部分中，我們先整理了包含邊緣偵測的三個領域的內容，並簡單介紹了該領域歷年來的發展，以及對該領域內不同的方法按照類別做了總整理。其中也包含了領域中一些方法的介紹和理論說明。 而在後半部分，我們則基於前人提出過的方法，嘗試提出了關於雙邊濾波器以及脊偵測的改進方法。在雙邊濾波器這部分，我們透過影像平滑和線性組合來避免了傳統雙邊濾波器常有的無法保存特徵細節的問題。而在脊偵測這部分，我們則是透過了多尺度的LoG偵測器來求出脊特徵在影像特定位置上的大小，再配合另一個脊偵測演算法來求出該位置周圍的變化幅度來判斷是否為脊特徵，藉此也避開了該方法原有的無法選定脊特徵大小的問題。 最後我們則透過實驗去重現前半部分中部分比較重要的方法，以及我們提出的方法在不同圖像上的效果，以此比較我們的方法的實際表現。

Edge detection is a fundamental and important issue in the image processing field, and thus has been continuously discussed. We observe that among the traditional edge detection methods, there is a sub-domain that has received less attention although it is crucial: ridge detection, and an algorithm that can be useful for edge detection but is not so often used in practice: the bilateral filter. In the first half of the thesis, we first organize the content of the three areas, and give a brief overview of the development of the area over the years, as well as a summary of the different methods in the area. An introduction and theoretical description of some of the methods in the field are also included. In the second half of the thesis, we try to present improved methods for bilateral filters and ridge detection, based on the methods proposed by the previous researchers. In the part of bilateral filter, we avoid the problem of not preserving feature details, which is often found in traditional bilateral filters, by image smoothing and linear combination. For ridge detection, we use a multi-scale LoG detector to determine the size of a ridge feature at a specific location in the image, and then use another ridge detection algorithm to detect ridge by variations, which avoids the problem of not being able to select the size of the ridge feature. Finally, we experimentally reproduce some of the more important methods in the first half of the thesis and compare the performance of our method with the results of our proposed method on different images.