Data Segmentation and Model Selection for Computer Vision

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.