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Computer Science - Image Processing | Data Segmentation and Model Selection for Computer Vision - A Statistical Approach

Data Segmentation and Model Selection for Computer Vision

A Statistical Approach

Bab-Hadiashar, Alireza, Suter, David (Eds.)

2000, XX, 208 p.

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The primary focus of this book is on techniques for segmentation of visual data. By "visual data," we mean data derived from a single image or from a sequence of images. By "segmentation" we mean breaking the visual data into meaningful parts or segments. However, in general, we do not mean "any old data": but data fundamental to the operation of robotic devices such as the range to and motion of objects in a scene. Having said that, much of what is covered in this book is far more general: The above merely describes our driving interests. The central emphasis of this book is that segmentation involves model­ fitting. We believe this to be true either implicitly (as a conscious or sub­ conscious guiding principle of those who develop various approaches) or explicitly. What makes model-fitting in computer vision especially hard? There are a number of factors involved in answering this question. The amount of data involved is very large. The number of segments and types (models) are not known in advance (and can sometimes rapidly change over time). The sensors we have involve the introduction of noise. Usually, we require fast ("real-time" or near real-time) computation of solutions independent of any human intervention/supervision. Chapter 1 summarizes many of the attempts of computer vision researchers to solve the problem of segmenta­ tion in these difficult circumstances.

Content Level » Research

Keywords » 3D - computer vision - image processing - pattern - pattern recognition

Related subjects » Image Processing

Table of contents 

I Historical Review.- 1 2D and 3D Scene Segmentation for Robotic Vision.- 1.1 Introduction.- 1.2 Binary Image Segmentation.- 1.3 2D Multitonal Image Segmentation.- 1.3.1 Structured Representations.- 1.3.2 Edge Extraction and Linkage.- 1.3.3 Texture Segmentation.- 1.4 2–1D Scene Segmentation.- 1.4.1 Range Enhanced Scene Segmentation.- 1.4.2 Range and Intensity Extraction of Planar Surfaces.- 1.4.3 Multidimensional (Semantic-Free) Clustering.- 1.4.4 Model Recognition-Based Segmentation.- 1.4.5 “Blocks World” Experiments.- 1.4.6 Motion-Based Segmentation.- 1.5 3D Scene Segmentation.- 1.5.1 Multiple Projection Space Cube Analysis.- 1.5.2 Multiple Range-Finder Surface Shape and Color Reconstruction.- 1.6 Discussion and Conclusions.- II Statistical and Geometrical Foundations.- 2 Robust Regression Methods and Model Selection.- 2.1 Introduction.- 2.2 The Influence Function and the Breakdown Point.- 2.3 Robust Estimation and Inference in Linear Models.- 2.3.1 Robust Estimation.- 2.3.2 Robust Inference.- 2.4 Robust Model Selection.- 2.4.1 Robust Akaike’s Criterion — AICR.- 2.4.2 Robust Cross-Validation.- 2.5 Conclusions.- 3 Robust Measures of Evidence for Variable Selection.- 3.1 Introduction.- 3.2 The Akaike Information Criterion.- 3.3 Model Selection Based on the Wald Test.- 3.3.1 The Wald Test Statistic (TP).- 3.3.2 The Wald Test Statistic (TP) in Linear Regression.- 3.3.3 The Robustified Wald Test Statistic (RTP).- 3.3.4 The Role of the Noncentrality Parameter of the Wald Statistic for Variable Selection in Linear Regression.- 3.3.5 Biased Least Squares Estimation and Variable Selection.- 3.4 Hypothesis Testing and Measures of Evidence for Variable Selection.- 3.4.1 Introduction.- 3.4.2 Hypothesis Estimation to Select Variables.- 3.4.3 The Likelihood Ratio Measure of Evidence as a Variable Selection Criterion for Linear Regression.- 3.4.4 More Measures of Evidence Based on the Principle of Invariance.- 3.4.5 Robust Wald Measures of Evidence for Linear Regression.- 3.5 Examples.- 3.5.1 The Hald Data with Outliers.- 3.5.2 Agglomeration in Bayer Precipitation.- 3.5.3 The Coleman Data.- 3.5.4 Order Selection of Autoregressive Models.- 3.5.5 Logistic Regression: Myocardial Infarctions.- 3.5.6 The Food Stamp Data.- 3.5.7 Discussion.- 3.6 Recommendations.- 4 Model Selection Criteria for Geometric Inference.- 4.1 Introduction.- 4.2 Classical Regression.- 4.2.1 Residual of Line Fitting.- 4.2.2 Comparison of Models.- 4.2.3 Expected Residual.- 4.2.4 Model Selection.- 4.2.5 Noise Estimation.- 4.2.6 Generalization.- 4.3 Geometric Line Fitting.- 4.3.1 Residual Analysis.- 4.3.2 Geometric AIC.- 4.4 General Geometric Model Selection.- 4.5 Geometric Cp.- 4.6 Bayesian Approaches.- 4.6.1 MDL.- 4.6.2 BIC.- 4.7 Noise Estimation.- 4.7.1 Source of Noise.- 4.7.2 Trap of MLE.- 4.8 Concluding Remarks.- III Segmentation and Model Selection: Range and Motion.- 5 Range and Motion Segmentation.- 5.1 Introduction.- 5.2 Robust Statistical Segmentation Methods: A Review.- 5.2.1 Principles of Robust Segmentation.- 5.2.2 Range Segmentation.- 5.2.3 Motion Segmentation.- 5.3 Segmentation Using Unbiased Scale Estimate from Ranked Residuals.- 5.4 Range Segmentation.- 5.5 Optic Flow Segmentation.- 5.5.1 Experimental Results.- 5.5.2 Real Image Sequences.- 5.6 Conclusion.- 6 Model Selection for Structure and Motion Recovery from Multiple Images.- 6.1 Introduction.- 6.2 Putative Motion Models.- 6.2.1 Extension to Multiple Views.- 6.3 Maximum Likelihood Estimation (MLE).- 6.4 Model Selection Hypothesis Testing.- 6.5 AIC for Model Selection.- 6.6 Bayes Factors and Bayesian Model Comparison.- 6.6.1 Assessing the Evidence.- 6.6.2 GBIC Modified BIC for Least Squares Problems.- 6.7 GRIC Modified Bayes Factors for Fitting Varieties ..- 6.7.1 Posterior of a Line versus Posterior of a Point Model.- 6.7.2 The General Case.- 6.8 The Quest for the Universal Prior: MDL.- 6.9 Bayesian Model Selection and Model Averaging.- 6.10 Results.- 6.10.1 Dimension Three Examples.- 6.10.2 Dimension Two Examples.- 6.11 Discussion.- 6.12 Conclusion.- Appendices.- A Bundle Adjustment.- B The BIC Approximation.- C GBIC: An Improved Approximation to Bayes Factors for Least Squares Problems.- References.

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