SGP 2013 features a two-day school on geometry processing, specifically targeted towards graduate students at the beginning of their PhD studies. The courses will focus on fundamental concepts and important aspects of digital geometry processing.
This school is intended for those SGP participants, who are not yet that familiar with the overall field and who will thus benefit from a more thorough introduction into the topics dealt with at the following SGP event, where there is no time for much of an introduction in the actual presentations.
Program (tentative)
Day 1 - July 1
09:00 - 09:30 |
Reception, opening, and summary of courses |
09:30 - 10:15 |
Efficient and Effective Mesh Representations for Shape Modeling and Analysis |
10.15 - 10.30 |
Coffe break |
10:30 - 11:15 |
Efficient and Effective Mesh Representations for Shape Modeling and Analysis |
11.15 - 11.30 |
Coffe break |
11:30 - 12:15 |
Mathematical Tools for 3D Shape Analysis and Description |
12.15 - 14.00 |
Lunch |
14.00 - 15:15 |
Mathematical Tools for 3D Shape Analysis and Description |
15.15 - 15.30 |
Coffee break |
15:30 - 16:45 |
Spectral and Diffusion Geometry |
16.45 - 17.00 |
Coffee break |
17:00 - 17:45 |
Spectral and Diffusion Geometry |
Day 2 - July 2
09:00 - 0:45 |
Quad mesh generation and processing |
9:45 - 10:00 |
Coffe break |
10:00 - 10:45 |
Quad mesh generation and processing |
10:45 - 11:00 |
Coffe break |
11:00 - 12:30 |
Fixing Defects in Polygon Meshes - Algorithms and Techniques |
12.30 - 14.00 |
Lunch |
14.00 - 14:45 |
Smooth Differential Geometry |
14.45 - 15.00 |
Coffee break |
15:00 - 15:45 |
Discrete Differential Geometry |
15.45 - 16.00 |
Coffee break |
16:00 - 16:45 |
Discrete Differential Geometry |
16.45 - 17.00 |
Coffee break |
17.00 - 17:45 |
Discrete Exterior Calculus |
Efficient and Effective Mesh Representations for Shape Modeling and Analysis
by Leila De Floriani (presenter), Peter Lindstrom, and Kenneth Weiss
Contact:
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Schedule: July 1, 09:30 - 10:15, 10:30 - 11:15
Abstract
Data structures play a fundamental role in describing the geometry and topology of shapes in computer graphics, scientific visualization and spatial data processing. In this tutorial, we review relevant issues in designing geometric and topological data structures that are efficient (in time and space) and effective (for specific applications). We present a taxonomy on the space of data structures for representing and navigating meshes, which we characterize by the properties of the meshing domain, by the entities and relationships that they encode and by the queries that they support. We review recent contributions on compact representations for structured, unstructured and hierarchical meshes in two, three and higher dimensions, and how they effectively exploit properties of the meshing domain to achieve their efficiency.
Mathematical Tools for 3D Shape Analysis and Description
by Silvia Biasotti (presenter), Andrea Cerri (presenter), and Michela Spagnuolo
Contact:
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Schedule: July 1, 11:30 - 12:15, 14:00 - 15:15
Abstract
This course is meant as an introductory guide for students/researchers who are willing to explore 3D shape analysis, and thus require to manage the rather complex mathematical tools which most methods rely on. The attendees will familiarize with mathematical concepts that span from geometry to topology, and introducing the computational counterparts, always keeping an eye on the concepts effectively used for 3D shape analysis. Examples of applications to shape description and retrieval will be shown to demonstrate how these mathematical notions can be transferred into practical solutions.
Spectral and Diffusion Geometry
by Michael Bronstein (presenter)
Contact:
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Schedule: July 1, 15:30 - 16:45, 17:00 - 17:45
Abstract
Over the last decade, the intersections between 3D shape analysis and image processing have become a topic of increasing interest in the computer graphics community. Nevertheless, when attempting to apply current image analysis methods to 3D shapes (feature-based description, registration, recognition, indexing, etc.) one has to face fundamental differences between images and geometric objects. Shape analysis poses new challenges that are non-existent in image analysis. The purpose of this tutorial is to overview the foundations of shape analysis and to formulate state-of-the-art theoretical and computational methods for shape description based on their intrinsic geometric properties. The emerging field of spectral and diffusion geometry provides a generic framework for many methods in the analysis of geometric shapes and objects. The tutorial will present in a new light the problems of shape analysis based on diffusion geometric constructions such as manifold embeddings using the Laplace-Beltrami and heat operator, 3D feature detectors and descriptors, diffusion and commute-time metrics, functional correspondence, and spectral symmetry.
Quad mesh generation and processing
by David Bommes, Bruno Lévy, Nico Pietroni, Enrico Puppo, Claudio Silva, Marco Tarini, Denis Zorin
Contact:
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Schedule: July 2, 09:00 - 09:45, 10:00 - 10:45
Abstract
Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this course, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing.
Fixing Defects in Polygon Meshes - Algorithms and Techniques
by Marcel Campen (presenter), Marco Attene (presenter), and Leif Kobbelt
Contact:
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Schedule: July 2, 11:00 - 12:30
Abstract
Due to their flexibility, expressiveness and hardware support, polygon meshes have become a de facto standard for model representation in many domains. Each application, however, has its own quality requirements that restrict the class of acceptable and supported models. In practice real meshes often have a number of defects and flaws that make them incompatible with such requirements. Hence, repairing these defects in order to achieve compatibility is a highly important task - a task whose complexity and level of difficulty is commonly underestimated by non-experts in the field. This course provides a comprehensive overview of mesh repair concepts and techniques in all their diversity. We consider the 3D model lifecycle from production to exploitation and look at the combinatorics of classes of upstream applications (that create a mesh), repair methods, and downstream applications (that use the model) based on their specific characteristics. This ultimately allows to decide which repair approaches are best suited for the data-link within any particular application scenario - bridging the corresponding compatibility gap.
Smooth Differential Geometry
by Keenan Crane
Contact:
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Schedule: July 2, 14:00 - 14:45
Abstract
In this segment, we will discuss basic concepts from smooth differential geometry and exterior calculus that will later be used to develop geometry processing algorithms. Formulating algorithms first in the smooth setting helps ensure that numerical discretization is consistent and does not depend heavily on mesh tessellation; it also helps us connect discrete algorithms to classical ideas in the smooth setting. This material should be accessible to anyone with some exposure to basic linear algebra and vector calculus, though most of the key concepts are reviewed as needed. Associated coding exercises depend on a basic knowledge of C++, though knowledge of any programming language is likely sufficient: we do not make heavy use of paradigms like inheritance, templates, etc. Accompanying notes also provide guided written exercises that can be used to deepen understanding of the material.
Discrete Differential Geometry
by Etienne Vouga
Contact:
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Schedule: July 2, 15:00 - 15:45, 16:00 - 16:45
Abstract
In this segment, we will discuss basic concepts from smooth differential geometry and exterior calculus that will later be used to develop geometry processing algorithms. Formulating algorithms first in the smooth setting helps ensure that numerical discretization is consistent and does not depend heavily on mesh tessellation; it also helps us connect discrete algorithms to classical ideas in the smooth setting. This material should be accessible to anyone with some exposure to basic linear algebra and vector calculus, though most of the key concepts are reviewed as needed. Associated coding exercises depend on a basic knowledge of C++, though knowledge of any programming language is likely sufficient: we do not make heavy use of paradigms like inheritance, templates, etc. Accompanying notes also provide guided written exercises that can be used to deepen understanding of the material.
Discrete Exterior Calculus
by Keenan Crane
Contact:
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Schedule: July 2, 17:00 - 17:45
Abstract
The exterior calculus of differential forms is, to a large degree, the modern language of differential geometry and mathematical physics. By learning to speak this language we can draw on a wealth of existing knowledge to develop new algorithms, and better understand current algorithms in terms of a well-developed theory. It also allows us to easily write down and implement many seemingly disparate algorithms in a single, unified framework. This course provides an introduction to working with real-world geometric data, expressed in the language of exterior calculus. In particular, we’ll see how a large number of basic geometry processing tasks (smoothing, parameterization, vector field design, etc.) can be expressed in only a few lines of code, typically by solving a simple Poisson equation. The course provides essential mathematical background as well as a large array of real-world examples, with an emphasis on applications and implementation.