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Table of Contents
Intro; Preface; Workshop Participants and Affiliations at the Time of the Workshop; Introduction; Contents; 1 Medial Fragments for Segmentation of Articulating Objects in Images; 1.1 Introduction; 1.2 Background and Related Work; 1.3 Methods; 1.4 Results and Discussion; References; 2 Scaffolding a Skeleton; 2.1 Introduction; 2.2 Related Work; 2.3 Construction Outline; 2.4 Partitioning the Sphere at a Branching Point; 2.4.1 Minimum Number of Vertices of Faces on the Sphere; 2.4.2 Algorithm to Partition the Sphere into Quadrangles; 2.5 Constructing Sleeves Around Skeleton Edges
2.5.1 Algorithm: Creating a Sleeve Along the Branch2.5.1.1 Defining a Frame at v0; 2.5.1.2 Branches Ending at Extremities; 2.5.1.3 Branches Ending at Another Branch Point; 2.5.1.4 Generating the Scaffold Mesh; 2.6 Implementation and Results; 2.7 Conclusion, Limitations, and Future Work; References; 3 Convolution Surfaces with Varying Radius: Formulae for Skeletons Made of Arcs of Circles and Line Segments; 3.1 Introduction; 3.2 Convolution Surfaces; 3.2.1 Kernels; 3.2.2 Notations; 3.2.3 Convolution of Regular Curves; 3.2.4 Discussion on the Choice of a Kernel; 3.2.5 Varying Thickness
3.2.5.1 Varying Radius as Proposed by Hornus et al.3.2.5.2 SCALIS as Proposed by Zanni et al.; 3.3 Determining General Closed-Form Formulae Through Recurrence; 3.3.1 Creative Telescoping; 3.3.2 Practical Use; 3.4 Convolution with Line Segments; 3.4.1 Integrals for Convolution; 3.4.2 Closed Forms Through Recurrence Formulae; 3.5 Convolution with Arcs of Circle; 3.5.1 Rational Parametrization; 3.5.2 Integrals for Convolution; 3.5.3 Closed Forms Through Recurrence Formulae; 3.6 Application and Outlook; 3.7 Conclusion; References; 4 Exploring 2D Shape Complexity; 4.1 Introduction
4.1.1 Prior Work on Shape Complexity4.1.2 Our Contribution; 4.2 Defining Complexity; 4.2.1 Qualitative Complexity; 4.2.1.1 Construction Definition; 4.2.1.2 Predictability Definition; 4.2.2 Evaluating Quantitative Measures of Complexity; 4.3 Measures; 4.3.1 Shape Database; 4.3.2 Global Measures; 4.3.2.1 Skeleton Measures; 4.3.3 Sampling-Based Measures; 4.3.3.1 Boundary Downsampling; 4.3.3.2 Area Downsampling; 4.3.3.3 Boundary Measures; 4.3.3.4 Moment Measures; 4.3.3.5 Area Measures; 4.4 Clustering; 4.5 Discussion; 4.5.1 Discussion of Methodology and Future Work; References
2.5.1 Algorithm: Creating a Sleeve Along the Branch2.5.1.1 Defining a Frame at v0; 2.5.1.2 Branches Ending at Extremities; 2.5.1.3 Branches Ending at Another Branch Point; 2.5.1.4 Generating the Scaffold Mesh; 2.6 Implementation and Results; 2.7 Conclusion, Limitations, and Future Work; References; 3 Convolution Surfaces with Varying Radius: Formulae for Skeletons Made of Arcs of Circles and Line Segments; 3.1 Introduction; 3.2 Convolution Surfaces; 3.2.1 Kernels; 3.2.2 Notations; 3.2.3 Convolution of Regular Curves; 3.2.4 Discussion on the Choice of a Kernel; 3.2.5 Varying Thickness
3.2.5.1 Varying Radius as Proposed by Hornus et al.3.2.5.2 SCALIS as Proposed by Zanni et al.; 3.3 Determining General Closed-Form Formulae Through Recurrence; 3.3.1 Creative Telescoping; 3.3.2 Practical Use; 3.4 Convolution with Line Segments; 3.4.1 Integrals for Convolution; 3.4.2 Closed Forms Through Recurrence Formulae; 3.5 Convolution with Arcs of Circle; 3.5.1 Rational Parametrization; 3.5.2 Integrals for Convolution; 3.5.3 Closed Forms Through Recurrence Formulae; 3.6 Application and Outlook; 3.7 Conclusion; References; 4 Exploring 2D Shape Complexity; 4.1 Introduction
4.1.1 Prior Work on Shape Complexity4.1.2 Our Contribution; 4.2 Defining Complexity; 4.2.1 Qualitative Complexity; 4.2.1.1 Construction Definition; 4.2.1.2 Predictability Definition; 4.2.2 Evaluating Quantitative Measures of Complexity; 4.3 Measures; 4.3.1 Shape Database; 4.3.2 Global Measures; 4.3.2.1 Skeleton Measures; 4.3.3 Sampling-Based Measures; 4.3.3.1 Boundary Downsampling; 4.3.3.2 Area Downsampling; 4.3.3.3 Boundary Measures; 4.3.3.4 Moment Measures; 4.3.3.5 Area Measures; 4.4 Clustering; 4.5 Discussion; 4.5.1 Discussion of Methodology and Future Work; References