Data Segmentation and Model Selection for Computer Vision: A Statistical Approach

ISBN-13: 9781468495089 / Angielski / Miękka / 2012 / 208 str.

Alireza Bab-Hadiashar; David Suter

Opis

This edited volume explores several issues relating to parametric segmentation including robust operations, model selection criteria and automatic model selection, plus 2D and 3D scene segmentation. Emphasis is placed on robust model selection with techniques such as robust Mallows Cp, least K-th order statistical model fitting (LKS), and robust regression receiving much attention. With contributions from leading researchers, this is a valuable resource for researchers and graduated students working in computer vision, pattern recognition, image processing and robotics.

Spis treści

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.

O autorze

The problem of range and motion segmentation is of major importance in computer vision, image procession, and intelligent robotics. This edited volume explores several issues relating to parametric segmentation emphasizing robust techniques and model selection. With contributions from leading scientists and engineers in the field, this book is a valuable resource for researchers and graduate students working in computer vision, pattern recognition, image processing and robotics.