一個基於傅立葉轉換及小波轉換之紋理分析的研究

Abstract

近年來由於多媒體資料之大量增長，使得有效管理多媒體資料庫之議題變得十分重要而富挑戰性。因此多媒體資料之檢索及儲存便成為一個重要之研究領域。在影像檢索方面，系統之設計必須要具備以影像內涵如顏色、形狀及紋理為特徵來檢索之功能及特色。由於紋理是影像檢索中一個重要的特徵，因此紋理分析的研究便顯得重要。 本論文之主要目的在研究紋理分析的主要問題包括紋理分離、紋理分類及紋理元素分析，並運用傅立葉轉換及小波轉換的理論來發展一些解決上述問題的方法。最後並整合部份在上述方法中所提出之演算法以提出一個MPEG-7紋理瀏覽描述子的計算法。 一般而言，基於小波轉換而發展的紋理分離法常發生過度分離的現象。為了解決這個問題，我們將提出一個新的紋理分離法。這個方法主要的重點在於，利用將一個像素分類為屬於紋理區域內，或屬於紋理區域邊界，來達到紋理區域分離的目的。紋理區域邊界上的點則再進一步細分至已分離出之紋理區域內，以達到紋理分離的目的。 接著我們將提出一個紋理元素分析的方法，我們先假設構成紋理的基本元素可用一個平行四邊形來表示，那麼只要求出構成此平行四邊形的兩個向量，便可求出紋理的基本元素。我們先利用一個基於影像對比而發展的判斷值來選擇適當的子影像進行處理。接著我們發展了一個邊緣偵測法來找出子影像的邊緣。基於這些邊緣點，我們用霍夫曼轉換來算出構成紋理元素的向量。我們利用求出的紋理元素合成原圖來驗證方法的效能。 接著我們會提出一個紋理粗分類法及一個紋理檢索之權重法。此二法的主要觀念是基於一個事實，即屬於方向性的紋理，其傅立葉頻譜的反應值會集中在某一個方向，而屬於週期性的紋理，其頻譜的反應值會集中在某幾個方向，而隨機性的紋理，其頻譜的反應值則出現在所有方向。基於上述事實，我們對紋理影像的傅立葉頻譜進行主軸分析以判斷某紋理影像是否屬於方向性的紋理。如果此紋理影像不是方向性的紋理，則我們將紋理影像的頻譜視為一張影像，並再做一次傅立葉轉換，以得到一張加強頻譜，我們接著利用加強頻譜上能量在方向性分佈的變異數來進一步將紋理影像分類為週期性的紋理或隨機性的紋理。 最後，我們將提出一個MPEG-7紋理瀏覽描述子的計算法，包括紋理規律度，紋理方向及紋理大小的計算。我們運用上述將紋理影像分類為週期性或隨機性的方法來計算MPEG-7標準中所規範的紋理規律性。對於高規律紋理，我們則運用在上述紋理元素分析法中所提到的觀念，利用霍夫曼轉換來算出兩個紋理影像的主要排列方向。我們也將說明如何求出在這兩個方向上的紋理大小。此外，我們會利用上述紋理粗分類法中所提到的主軸分析來求出方向性紋理中唯一的方向。 本論文中所提出之方法可應用於紋理檢索及數位圖書館系統之設計。

The recent emerging of multimedia and the tremendous growth of large image and video archives have made the effective management of multimedia image databases become a very important and challenging task. Therefore, retrieval and storage of multimedia are very popular research topics and have drawn lots of attentions recently. For multimedia retrieval, to capture the perceptual properties of visual content, the information retrieval system is required to support the retrieval by visual contents, such as color, shape, or texture. As texture is an essential feature when performing image retrieval, the study of texture analysis becomes critical and important. The goal of this dissertation is to study the major problems of texture analysis, including texture segmentation, texture primitive extraction, coarse classification of textures and propose solutions based on Fourier transform and wavelet transform accordingly. In addition, some algorithms and methods proposed are integrated to compute the texture browsing descriptor specified by MPEG-7. Based on the texture browsing descriptor computed, applications of texture browsing and texture retrieval by query by example are also implemented to demonstrate the effectiveness of the integrated system. For texture segmentation, to deal with the over-segmentation issue which usually occurs in traditional texture segmentation approaches based on wavelet transform, an unsupervised texture segmentation method based on determining the interior of texture regions is proposed. The key idea of the proposed method is that if the pixels of the input image can be classified into interior pixels (pixels within a texture region) and boundary ones, then the segmentation can be achieved by applying region growing on the interior pixels and reclassifying boundary pixels. Next, we will propose a method for texture primitive extraction based on wavelet transform. The main work of the method is to extract the two displacement vectors that form the texture primitive from HL and LH subimages. A contrast-based criterion is used to select appropriate sub-images for detecting displacement vectors. An edge thresholding method is then performed on the sub-images selected to locate edges. Based on these edges, Hough transform is applied to extract the displacement vectors. Synthesized textures are provided to show the effectiveness of the proposed method. Then, we will provide a coarse classification method for textures and a weighting scheme for texture retrieval. The method is based on the fact that for a directional texture image, the magnitudes of its Fourier spectrum will concentrate on a certain direction; for periodic, on several directions; for random, on all directions. To classify a texture image into directional or non-directional, principal component analysis is conducted on the Fourier spectrum to get the ratio of two eigenvalues, which will be used to measure the directionality of the texture image. If the texture image is not a directional one, based on enhanced Fourier spectrum, a spectral measure consists of the variance of the radial wedge distribution is then calculated to further classify the texture image as a periodic or a random one. Finally, an efficient computation method for the texture browsing descriptor of MPEG-7 is provided. Based the above-mentioned method for classifying periodic and random textures, a regularity measure is developed. For regular textures, the two dominant directions of textures are extracted by performing Hough transform on the Fourier spectrum. A scale computation method is then provided to determine the scales corresponding to the two dominant directions. In addition, the principal component analysis developed above is used to detect textures with only one dominant direction. The proposed methods can be used in the applications of texture retrieval and digital library.