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Title of Thesis

Rotation and Gray-Scale Invariant Texture Analysis

Author (s)
Abdul Jalil
Institute/University/Department Details
Mohammad Ali Jinnah University, Karachi
Electronic Engineering
Number of Pages
Keywords (Extracted from title, table of contents and abstract of thesis)
 Texture Analysis, Randon Transform, Component Analysis


Texture analysis is an extremely active and useful area of research. In texture analysis the invariance to rotation, scale and translation are the most typical requirements. Moreover, gray-scale invariance is another important issue. It arises due to the reason that a texture may be subject to different levels of illumination. The purpose of this study is to investigate some inexpensive approaches that are rotation and gray scale invariant and to large extent translation invariant as well. There are three different types of approaches, which have been addressed in this dissertation. In the first approach, we have done texture analysis using Radon Transform (RT) based Hidden Markov Model (HMM). We have introduced three different ways to extract feature vectors using RT. All three give rotation invariant features, while the last one gives rotation, as well as, gray scale invariant features. The textures in this case have been taken from Brodatz album. Due to the inherent property of the RT, we are able to capture the directional features of a certain texture having arbitrary orientation. This set of directional features is used for training of an HMM specifically for that particular texture. Once all the HMMs have been trained, the testing is carried out by using any one of these textures at random with arbitrary orientation. The second approach is somewhat similar to the above one except that the modified or Differential Radon Transform (DRT) has been used instead of the ordinary RT. Hence, we are able to capture the features which are not only rotation but are also gray scale invariant. The reason for the later property is that, unlike the ordinary RT, the DRT is based on the differences between adjacent pixels instead of summing up the pixel values. These features have been used for training of HMMs, one for each texture, and finally testing is carried out. Similar experimentation has been done to extract features using both RT and DRT to give low pass and high pass features. The training and testing process using HMM has been done in a similar manner as above. The third approach is quite different from the above two approaches. In this approach, some principal direction of a texture is defined. Once this direction is estimated, discrete wavelet transform is applied in that particular direction to extract features. These features are then used for classification by k-nearest neighbor classifier. There are two definitions of principal direction, which have been proposed in the dissertation. In case of the first definition, Principal Component Analysis (PCA) has been used to estimate this principal direction. In the case of second definition, the direction has been found out by using DRT. This scheme is computationally lighter compared to the previous one. However, the third approach is limited to anisotrpic textures only unlike the previous method Considering the percentage of correct classification as figure of merit, we have carried out the performance evaluation of the above three approaches. The average result has been found to be 95% approximately and the best result has been close to 100% .




1693 KB

S. No. Chapter Title of the Chapters Page Size (KB)
1 1 Introduction 1
  1.1 Problem Statement 1
  1.2 Contributions of the Dissertation 3
  1.3 Organization of the Dissertation 5
445 KB
2 2 Texture Analysis and its Background 7
  2.1 Introduction 7

95 KB


  2.2 Definition of Texture 7
  2.3 Texture Analysis 9
  2.4 Texture Feature extraction 10
3 3 Computing Tools 18
  3.1 Introduction 18
  3.2 Principal Component Analysis 18

634 KB

  3.3 Radon Transform 20
  3.4 Properties of Radon Transform 22
  3.5 Wavelet Transforms 23
  3.6 Classifiers 27
4 4 Texture Analysis using Radon Transform and Hidden Markov Models 52
511 KB








545 KB

  4.1 Introduction 52
  4.2 Background of Invariant Texture Analysis 52
  4.3 Texture Analysis using RT for Case s = 0 56
  4.4 Texture Analysis using RT for Case s ≠ 0 64
  4.5 Texture Analysis using Variance of RT for Case s≠ 0 67
  4.6 Summary 69
5 5 Texture Analysis using Differential Radon Transform and Hidden Markov Models 71
  5.1 Introduction 71
  5.2 Differential Radon Transform 72
  5.3 Texture Analysis using Differential Radon Transforms and Hidden Markov Model 73
  5.4 Texture analysis using Radon and Differential Radon Transform for the Case s = 0.................. 76
  5.5 Texture analysis using Radon and Differential Radon Transform for the Case s ≠ 0 . 78
6 6 Texture Analysis using its Principal Direction and Discrete Wavelet Transform 82
  6.1 Methods using Principal Direction 84
  6.2 Proposed Method using DRT 87
  6.3 Proposed Method using PCA 90
  6.4 Selection of Dataset for Classification 94




39 KB


  6.5 Simulations and Results 97
7 7 Conclusion and Future Direction 102