臺灣博碩士論文加值系統

本篇論文主要研究應用小波轉換於紋路影像分析，包括二維、三維紋路影
像分割與計算紋路影像表面方向。在電腦視覺、影像處理與圖形識別領域
上，紋路扮演了很重要的角色。然而，由於紋路仍沒有統一且唯一的定義
，導致其在分析上的困難。因此，基於人類視覺系統的觀念，我們使用小
波轉換為多重解析/多重尺度做為分析紋路影像之工具。在這論文中，首
先我們針對二維紋路影像分割問題，提出非監督式紋路影像分割法。對於
紋路影像分割法，最困難的是local特徵擷取與分類的數目。我們先利用
小波轉換後的高頻通道(high-frequency channel)計算出local的紋路特
徵。稍後，並使用Wold特徵來表示紋路。在分群方面，通常iterative方
式最常被使用，相同的分割法執行許多次，從中找出分類的數目。這技巧
較浪費時間。我們則提出一直接方式(包含多重界閥法與合併法)決定分類
的數目。實驗結果顯示，我們所提的兩個方法能得到不錯的結果。接著，
我們提出一個在透射投影模式下，計算紋路影像表面方向的方法。投影後
紋路影像的支配頻率變化由連續小波轉換之脊平面來表示。脊點代表在空
間/頻率定義域中能量集中的區域，它是一個四維向量。除了位置向量外
，還有尺度(scale)與角度(rotation)等參數。我們並指出脊平面包含決
定紋路影像表面方向非常重要的資訊。而且，我們也提出兩種擷取脊平面
的方法(單一與多重)。脊平面的尺度與表面方向有關，並且可推導為一拋
物面。我們因此發展出一套close-form solution來計算紋路影像表面方
向。這方法在有、無雜訊環境下評估，都得到蠻不錯的結果。即使在高雜
訊環境下，誤差皆在3度以內。使用一先前方法測試過的一組影像，實驗
結果證實我們的方法較經確。在過去，極少有人針對複雜紋路影像探討計
算複雜平面紋路影像的表面方向。由於，複雜紋路影像在自然界是經常碰
得到，也是不可忽略的。我們另外提出一個在透射投影模式下,基於連續
小波轉換之脊平面來計算複雜紋路影像表面方向。在處理複雜紋路過程
中,經由連續小波轉換後所得的資訊不完全可信。然而，我們觀察到投影
後複雜紋路影像的支配頻率變化的趨勢雖較混亂但仍有脈落可尋。因此，
我們結合robust regression技術於脊平面的fitting，找出一組脊點之最
佳子集來代表複雜紋路之支配頻率變化;從而求出表面方向。所謂脊點之
最佳子集是指這些脊點有類似的特性，在此所指的是脊點方向的一致性與
脊平面fitting後脊點尺度誤差的一致性。從所選出之脊點最佳子集，應
用先前我們所提的方法來計算出複雜紋路影像表面方向。實驗結果證實我
們的方法簡單且有效。最後，我們提出兩個三維紋路影像分割方法，做為
表面方向計算的第一步。先前計算紋路影像之表面方向的方法大都有一共
通的假設，那就是影像主要只包含一種紋路。事實上，我們所看見的影像
經常出現兩種以上的紋路。為了更實際解決表面方向計算的問題，分割三
維紋路影像是不可缺少的第一步。我們以連續小波轉換之脊平面來描述透
射投影模式下紋路影像支配頻率的變化。脊平面可更進一步推導為二次多
項式。在傍一個方法裡，必須計算出local表面方向。我們使用robust
regression技術使得決定local表面方向所需的區域非限定於固定大小。
如此，因較多資訊被使用，所得的local表面方向也較準確。接著，應用
robusat clustering與fusion技術來完成整個分割。我們方法的特點是不
需對每個影像點求其local特徵，結果也不會有鋸齒狀效應。在第二個方
法中，不需計算出local表面方向。一開始，整張影像相對應的脊平面分
為大小形狀相同的小區塊。一個階層式的agglomerative分群法用來合併
特性相似的小區塊，合併之條件由maximum likelihood函數決定。接著，
我們結合不同脊平面所分割出的結果，以完成整個分割。實驗結果顯示，
我們所提的兩個方法能得到不錯的結果。總之，本篇論文基於小波轉換提
供許多有效方法來分析紋路影像。我們所提方法的效益經由Brodatz書上
的影像與實際影像測試得到證實。

This thesis focuses on the applications of wavelet transform to
textured imagesin the topics of 2D texture segmentation, shape
from texture, and 3D texture segmentation.Textures play an
important role in the fields of image processing, pattern
recognition, and computer vision.However, there is no universal
definition for textures leading to the difficulty in texture
related work.As a result, we introduce the wavelet transform as
the tool for multiresolution/multiscale representation of
textured images based on the concept of human vision system.In
this thesis, the 2D texture segmentation is firstly concerned.
The main difficulties of texture segmentation are (i).
determination of the number of clusters; (ii). extraction of
reliable local features.In the literature, one method of finding
the number of clusters is usually iterative to meet some
criteria.Usually, it is time consuming since the same
segmentation process are repeated many times.Here, we propose an
unsupervised texture segmentation algorithm in which this
determination is embedded in the clustering process and
therefore the segmentation time is saved.In addition, we suggest
the perceptually significant features, Wold features, as the
description of textures.Some examples have been illustrated to
confirm our idea.It is found by experimental results that
textured images with large number of classes can be successfully
segmented to a certain degree.Next, we consider the shape from
texture problem which recovers visual perception of three
dimensional structures from a monocular image by texture cue
only.We use continuous wavelet transform to characterize the
frequency variations as the ridge surface.The ridge surface is
further derived to be parabolic.This is the first method to
obtain this form in terms of the frequency variations.Also, a
close form solution is proposed for the estimation of tilt and
slant angles.Comparative study with a previous method by a same
set of images demonstrate the superior ability of our approach.
Furthermore, the complex (weakly ordered and disordered)
textures in the shape from texture problem often obviated by
most researchers are also considered in this thesis.A hybrid of
ridge surface fitting and a robust regression techniques is
developed for this problem.Experimental results demonstrate that
our simple method is powerful in solving shape from complex
texture.Finally, the 3D texture segmentation is taken into
account as the first step of shape from texture problem.This
problem is seldom noticed in the past.We present two algorithms
to eliminate the usual assumption of shape from texture problem.
The first one needs extraction of local features but the non-
blocky effects can be achieved without needing to estimate the
local features for every pixel.The second one has the
characteristics of getting rid of extracting local features.Both
methods are demonstrated by many natural images.In sum, this
thesis provides efficient approaches for 2D texture
segmentation, for shape from texture problem by considering
various ordered textures, and for 3D texture segmentation as the
first step of shape from texture problem.The performance of our
methods have been demonstrated by a variety of Brodatz textures
and real-world images.

Cover
Contents
List of Figures
List of Tablesx
1 Introduction
1.1 Related Work on Textures
1.1.1 Survey of 2D Texture Segmentation
1.1.2 Survey of Shape From Texture
1.1.3 Survey of 3D Texture Segmentation
1.2 Thesis Organization
2 Review of Wavelet Transform
2.1 Discrete Wavelet Transform
2.1.1 Critical-Sampled Wavelet Transform
2.1.2 Over-Sampled Wavelet Transform
2.2 Continuous Wavelet Transform
3 Unsupervised Texture Segmentation Via Discrete Wavelet Transform
3.1 Introduction
3.2 Wavelet Filters: Which wavelet to choose?
3.3 Unsupervised Texture Segmentation Algorithm
3.3.1 Texture Feature Extraction from Wavelet Coefficients
3.3.2 Coarse Segmentation
3.3.3 Feature Reduction
3.3.4 Combination/Fusion
3.3.5 Fine segmentation
3.3.6 Multiscale Segmentation and the Estimation of Number of Tex-ture Classes
3.4 Experimental Results
3.5 Conclusions
4 Unsupervised Texture Segmentation by Wold Features
4.1 Introduction
4.2 Wold Features
4.2.1 2D Wold Decomposition
4.2.2 Feature Extraction
4.3 Feature Selection and Coarse Segmentation by Histogram-Based Clus-tering
4.4 Fusion: Integration of Coarsely Segmented Results
4.5 Fine Segmentation
4.6 Experimental Results
4.7 Conclusions
5 Shape From Texture: Direct Estimation of Planar Surface Orientation Using Continuous Wavelet Transform
5.1 Introduction
5.1.1 Problem of Shape From Texture
5.1.2 Our Method
5.2 Nonstationary Image Analysis Using Morlet Wavelet
5.3 Texture Model and Ridge Surface Extraction
5.3.1 MultiComponent Texture Model without Interference
5.3.2 Ridge Points
5.3.3 Ridge Surface Extraction Algorithms
5.4 Frequency Variations From Projection Effects
5.4.1 The Viewing Geometry
5.4.2 Relation of Surface Orientation and Dominate Frequency Varia-tions
5.4.3 Surface Cue: Ridge Surface
5.5 Analytical Solution of Surface Orientation Estimation
5.5.1 Computing the tilt angle
5.5.2 Computing the slant angle
5.6 Detailed Implementation and Experimental Results
5.6.1 Implementation
5.6.2 Experiments
5.7 Conclusions ?
6 Shape From Complex Texture by Ridge Points Consensus of Contin-uous Wavelet Transform
6.1 Introduction
6.2 Difficulty of Characterizing Complex Textures by Ridge Surfaces
6.3 Estimating the Surface Orientations of Complex Textures by Ridge Points Consensus
6.3.1 Observations of Frequency Variations of Various Textures
6.3.2 Selection of Useful Ridge Points by a Robust Regression Technique
6.4 Experiments
6.5 Conclusions
7 3D Texture Segmentation Via Continuous Wavelet Transform
7.1 Introduction
7.2 3D Textured Image Segmentation Algorithm 1: Using Local Features
7.2.1 Multiple ridge surfaces detection
7.2.2 Estimation of Local Surface Orientation
7.2.3 Coarse segmentation
7.2.4 Fusion
7.2.5 Fine Segmentation
7.3 3DTextured Image Segmentation Algorithm 2: Without Using Local Features
7.3.1 Coarse Segmentation through Maximum Likelihood Clustering
7.4 Experimental Results
7.4.1 Experimental Results of The First Method: With Local Features
7.4.2 Experimental Results for the Second Method: Without Local Features
7.5 Conclusions
8 Conclusions and Future Research
8.1 Conclusions
8.2 Future Research
Bibliography