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## Di±culties in stereo matching process

It is important to note that the stereo matching problem has been considered as a dif¯cult problem in stereo vision for several reasons like depth discontinuities, illumination variations and lack of texture [Dhond, Aggarwal, 1989].

• Occlusion problem [Dhond, Aggarwal, 1989]: In general, stereo images contain nearly similar contents since they correspond to the same scene. However, there are some areas in one image that are absent in the other image, and they are referred to as occluded areas. The occlusion e®ect is illustrated in Fig. 2.8 where the point m(r) is only visible in the right image.

This occlusion e®ect in stereo images is due to the di®erent viewpoints of the cameras and the presence of discontinuities in the scene. Therefore, the disparity is unde¯ned in occlusion areas because such areas cannot be found in the other image.

• Illumination variations: In real stereoscopic imaging system, the characteristics of the cameras may be slightly di®erent. Consequently, some illumination changes may appear between the captured images. Fig. 2.9 shows an example of a SPOT5 stereo image which has signi¯cant illumination variations. This luminance di®erence is con¯rmed by displaying the histograms of both images. This illumination variation will cause a serious problem in the correspondence process. In order to overcome this problem, a pre-processing step, like the histogram equalization, is often applied to the original stereo images.

### Stereo matching constraints

In order to overcome the ambiguities mentioned above, some matching constraints can be imposed. The most commonly used constraints are the following ones [Miled et al., 2006a; Boufama, Jin, 2002]:

• Epipolar constraint: Given an image point in one image, the corresponding point must lie on an epipolar line in the other image. The main advantage of this constraint is that it reduces the matching problem from a 2D search problem to a 1D one. Furthermore, when the stereo images are recti¯ed, the 1D search problem is further simpli¯ed since the epipolar line will coincide with the image scan line.

• Uniqueness constraint: It imposes that a given pixel in one image can match to no more than one pixel in the other image. However, this constraint fails in the presence of transparent objects.

#### Overview of stereo matching approaches

With an ultimate aim of producing a disparity map that can be used in the di®erent applications mentioned earlier in Chapter 1, stereo matching process has been extensively studied in computer vision. A survey of the state-of-the-art methods can be found in [Scharstein, Szeliski, 2002]. Traditionally, stereo matching algorithms are basically classi¯ed into two categories: local methods and global ones.

**Compression tools**

Generally, compression techniques aim at reducing the number of bits needed to represent an image. Several methods of data reduction are available, the choice of which strongly de- pends on the underlying application requirement [Bovik, 2000]. Traditionally, compression techniques are basically classi¯ed into two categories: lossy techniques and lossless ones. A typical coding scheme is shown in Fig. 3.1. It incorporates three fundamentals steps namely transformation/modelling, quantization and entropy coding.

**Table of contents :**

**A R¶esum¶e en fran»cais **

A.1 Introduction : Contexte de la thµese

A.2 Etat de l’art

A.2.1 M¶ethodes de codage des images st¶er¶eoscopiques

A.2.2 Principe des sch¶emas de lifting

A.3 Contributions

A.3.1 Nouvelles approches bas¶ees sur les sch¶emas de lifting vectoriels

A.3.2 Int¶egration d’une carte de disparit¶e dense dans les sch¶emas de codage d’images st¶er¶eo

A.3.3 Sch¶ema de lifting non s¶eparable et m¶ethodes d’optimisation des ¯ltres xi

A.4 Conclusion et perspectives

Abstract

Acknowledgements

List of Tables

List of Figures

**1 Introduction **

1.1 Thesis context

1.2 Objectives and contributions

1.3 Thesis outline

1.4 Publications

**2 Main concepts in Stereo Vision **

2.1 Introduction

2.2 Acquisition

2.2.1 Pinhole camera model

2.2.2 Stereoscopic imaging system

2.2.3 Epipolar geometry

2.2.4 Epipolar recti¯cation

2.3 Stereo matching process

2.3.1 Disparity information

2.3.2 Depth information

2.3.3 Di±culties in stereo matching process

2.3.4 Stereo matching constraints

2.4 Overview of stereo matching approaches

2.4.1 Local methods

2.4.2 Global methods

2.5 Conclusion

**3 Stereo image coding: state-of-the-art **

3.1 Introduction

3.2 Compression tools

3.2.1 Transformation

3.2.2 Quantization

3.2.3 Entropy coding: examples in wavelet-based codecs

3.3 Stereo image coding: state-of-the-art

3.3.1 Basic approach for joint coding of stereo images

3.3.2 Characteristics of the disparity map and the DCD

3.3.3 Overview of data compression schemes for stereo images

3.4 Conclusion

**4 Vector Lifting Schemes for stereo image coding **

4.1 Introduction

4.2 Proposed Vector Lifting Schemes

4.2.1 Motivation

4.2.2 Generic VLS decompositions

4.2.3 An improved VLS

4.2.4 Coding cost of prediction coe±cients

4.3 Theoretical analysis

4.3.1 Minimum prediction error variance of VLS-I

4.3.2 Minimum prediction error variance of VLS-II

4.3.3 Discussion

4.4 Experimental results

4.5 Conclusion

**5 Dense disparity estimation for stereo image coding **

5.1 Introduction

5.2 Dense disparity estimation: Variational framework

5.2.1 Problem statement

5.2.2 Optimization algorithm

5.3 Proposed dense disparity map coding method

5.3.1 Partition-based segmentation

5.3.2 Entropy coding with H.264 JM software

5.4 Experimental results

5.4.1 In°uence of the parameters

5.4.2 Performances in stereo image coding context

5.4.3 Performances in multiview video coding context

5.5 Conclusion

**6 Non separable lifting scheme with adaptive update step **

6.1 Introduction

6.2 Non separable lifting schemes

6.2.1 Motivation

6.2.2 Principle of the retained 2D NSLS structure

6.2.3 Links with conventional separable lifting structures

6.3 Proposed optimization method

6.3.1 Optimization of the predictors

6.3.2 Optimization of the update operator

6.4 Theoretical analysis

6.4.1 Notations

6.4.2 Optimal prediction coe±cients

6.4.3 Optimal update coe±cients

6.4.4 Adaptation criterion values

6.4.5 Discussion

6.5 Transmission cost of the ¯lter coe±cients

6.6 Experimental results

6.7 Conclusion

**7 Sparse optimization criteria for still and stereo image coding **

7.1 Introduction

7.2 From `2 minimization to `1 minimization

7.3 `1 minimization method

7.4 Global prediction error minimization technique

7.4.1 Motivation

7.4.2 Optimization of the prediction ¯lter p(HH)

7.5 Joint optimization method

7.5.1 Motivation

7.5.2 Proposed algorithms

7.6 Experimental results

7.7 Conclusion

**8 Conclusion and future work **

**Bibliography**