This book addresses one of the central problems in computer-aided image analysis; how the shape of structures in an image should be represented to best facilitate quantitative analysis. To accomplish this task requires an understanding of what shape is and how it should be extracted from grey-scale images. In Professor Gauch's book a new shape description for grey-scale images called the intensity axis of symmetry (IAS) and an associated curvature-based description called vertex curves are presented.
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1 Introduction and Background.- 1.1. Shape Description.- 1.2. Image Description.- 1.3. Image Shape Description.- 2 The Intensity Axis of Symmetry.- 2.1. Axes of Symmetry.- 2.2. The Intensity Axis of Symmetry (IAS).- 2.3. Properties of the IAS.- 2.3.1. Axis Topology.- 2.3.2. Axis Bending and Branching.- 2.3.3. Axis Radius Function.- 2.3.4. Axis Inverse Mapping.- 2.3.5. Axis Invariance.- 2.4. Discussion.- 3 Computing the Intensity Axis of Symmetry.- 3.1. Level by Level Calculation of Axes.- 3.2. Simultaneous Calculation of Axes.- 3.2.1. A Review of the Active Contour Model.- 3.2.2. The Active Surface Model.- 3.2.3. The Image Symmetry Function.- 3.2.4. Linking the Active Surface.- 3.2.5. Identifying Individual Axis Sheets.- 3.2.6. Calculating the Radius and Curvature Functions.- 3.3. Discussion.- 4 Segmentation via the Intensity Axis of Symmetry.- 4.1. Displaying the IAS.- 4.2. Image Segmentation.- 4.2.1. Segmentation Method.- 4.2.2. Segmentation Results.- 4.3. Effects of Image Processing.- 4.3.1. Contrast Enhancement.- 4.3.2. Gaussian Blurring.- 4.3.3. Edge Strength Images.- 4.4. Discussion.- 5 Multiresolution Analysis of the Intensity Axis of Symmetry.- 5.1. Early Multiresolution Analysis.- 5.2. The Multiresolution IAS.- 5.3. Multiresolution Vertex Curves.- 5.3.1. Boundary Curvature and Vertices.- 5.3.2. Surface Curvature.- 5.3.3. Level Curve Curvature and Vertex Curves.- 5.3.4. Vertex Curve Topology.- 5.3.5. Multiresolution Properties of Vertex Curves.- 5.4. Multiresolution Watershed Boundaries.- 5.4.1. Watersheds and Their Boundaries.- 5.4.2. Linking Intensity Extrema.- 5.4.3. Displaying Watershed Region Hierarchies.- 5.4.4. Associating Scale with Watershed Boundaries.- 5.4.5. Imposing a Quasi-Hierarchy on IAS Sheets.- 5.5. Discussion.- 6 Conclusions.- 6.1. The Definition of the IAS.- 6.2. An Implementation of the IAS.- 6.3. Image Segmentation Using the IAS.- 6.4. Multiresolution Analysis of the IAS.- 6.5. New Research Directions.
Book by Gauch John M
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