Shape Detection in Computer Vision Using the Hough Transform

1 Computer Vision: Shape Detection.- 1.1 Why Computer Vision?.- 1.1.1 Industrial Applications.- 1.1.2 Medical Applications.- 1.1.3 Social Applications.- 1.1.4 Military Applications.- 1.2 Why This Book?.- 1.3 Why the Hough Transform?.- 1.4 Representing Shape Symbolically.- 2 Transforms Without Tears.- 2.1 Beginning to See.- 2.2 What about Shape?.- 2.3 Tackling the Maths.- 2.4 Beginning to Compute.- 3 Preprocessing.- 3.1 The Real World.- 3.2 Spot the Difference.- 3.3 Convolution, a Necessary Tool.- 3.4 Edge Detection.- 3.5 Which Parametrisation?.- 3.6 Getting Started.- 3.7 Quantization.- 3.8 Test Images.- 4 Postprocessing.- 4.1 Results of the Transformation.- 4.2 The Butterfly Filter.- 4.3 Designer Butterflies.- 4.4 Putting Things to Work.- 4.5 Reconstruction.- 4.6 Summary.- 5 Representing Shape.- 5.1 From Lines to Circles.- 5.2 Double Houghing.- 5.3 Towards a Representation of Shape.- 5.3.1 Decomposition.- 5.3.2 Geometric and Spatial Relations.- 5.3.3 Saliency.- 5.3.4 Invariance.- 5.3.5 Stability.- 5.3.6 Accessibility.- 5.4 Summary.- 6 Which Hough?.- 6.1 Background.- 6.1.1 Historical.- 6.1.2 Whole Shape Detection.- 6.2 Refinements.- 6.2.1 Preprocessing Considerations.- 6.2.2 Postprocessing Considerations.- 6.3 Software Solutions.- 6.3.1 Computer Friendly Algorithms.- 6.3.2 Dynamically Quantised Accumulators.- 6.3.3 Constraints on Parameter Calculation.- 6.3.4 Parameter Space Decomposition.- 6.3.5 Segmenting the Image.- 6.4 Parallel Processing.- 6.4.1 SIMD Implementations.- 6.4.2 MIMD Implementations.- 6.5 Dedicated Hardware.- 6.6 The Probabilistic Houghs: A Review.- 7 A Case Study: Circles and Ellipses.- 7.1 Preprocessing the Image Data.- 7.2 The Dynamic Generalized Hough Transform.- 7.2.1 Connectivity Detection.- 7.2.2 Segmentation.- 7.2.3 Sampling of Data Points.- 7.2.4 Calculating the Parameters.- 7.2.5 Accumulation of the Parameters.- 7.2.6 Statistical Information and a Robust Stopping Criterion.- 7.2.7 Removal of Features from the Image.- 7.3 A Case Study.- 7.3.1 Edge Intensity Threshold and Connectivity Detection.- 7.3.2 Segmentation.- 7.3.3 Automatic Stopping Criterion.- 7.3.4 Results.- 7.3.5 Coping with the Unexpected.- 7.4 Discussion.- 7.5 Conclusions.- Appendix 1.- 1.1 The Radon Transform.- 1.2 Generalized Function Concentrated on a Line.- 1.3 The General Case.- 1.4 Application to an Ellipse.- Appendix 2.- Appendix 3.- Appendix 4.- References.