goals

schedule

references

previous years

Schedule

Abstracts

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Recovering the geometry of an object from sequence of images
by Jeffrey Ho

In this talk, we present a new geometry reconstruction algorithm from a sequence of images of a rigid object. The main idea of the algorithm is the following. For a moving object in a constantly illuminated environment, the relative motion between the object and the illumination source will produce a variation in intensity values, and this provides an important cue for solving the reconstruction problem. In particular, it allows us to compute the normal vector field of the object's surface, and hence, the depth (3D structure) relative to the camera can be recovered by integrating the normal vectors. The iterative algorithm we proposed is quite simple and yet effective. Using some differential geometry, we will discuss the algorithm's convergence in the second part of this talk.

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Rapidly Incorporating Real Objects into Mixed Environments
by John Quarles

A method is presented to rapidly incorporate real objects into virtual environments using laser scanned 3D models with color-based marker tracking. Both the real objects and their geometric models are put into a Mixed Environment (ME). In the ME, users can manipulate the scanned, articulated real objects, such as tools, parts, and physical correlates to complex computer-aided design (CAD) models. Our aim is to allow engineering teams to effectively conduct hands-on assembly design verification. This task would be simulated at a high degree of fidelity, and would benefit from the natural interaction afforded by a ME with many specific real objects.

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Quadrilateral Remeshing of Arbitrary Manifolds
by Michael Garland

In this talk, I will discuss our work on remeshing manifolds of arbitrary genus. In particular, I will focus on the problem of remeshing 2-manifold surfaces with quadrilaterals. This is a problem of fundamental importance in surface parameterization, subdivision surface modelling, and computational fluid dynamics, among other applications. Our current work aims to efficiently produce meshes that faithfully preserve the structure of the original shape while maintaining good element quality. We also seek to provide the user with the flexibility to control the flow of the mesh over the surface. The key to our work is our use of smooth scalar fields defined over an initial mesh to induce the global structure of the final remeshed output. We rely heavily on the discrete Laplace- Beltrami operator and its eigenfunctions in this construction, and discrete Morse theory provides the linkage between our scalar fields and the topology of the surface.

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Computational modeling of knee mechanics
by B.J. Fregly

Imagine a world where orthopedic surgeries are custom tailored to the patient, similar to how suits can be custom tailored to the business executive. Rather than basing surgical decisions on population studies or crude anatomic measurements, orthopedic surgeons interact with patient-specific computer models developed from medical imaging data and tuned to movement data collected from the patient prior to surgery. They use these models to predict the patient's unctional outcome for various combinations of surgical procedures, surgical parameters, and/or implant designs under consideration. The virtual human models use state-of-the art imaging, computational, simulation, and optimization technologies to allow the surgeon to optimize the surgical design variables. The end result is greatly improved functional outcome, more reliable surgical procedures, and millions of patients whose quality of life is improved through these technologies.
This seminar will discuss the Computational Biomechanics Lab's efforts to make this futuristic scenario a reality. With an initial focus on the knee, current research efforts in three synergistic directions will be summarized: Dynamic modeling and simulation of patient-specific 1) joint mechanics, 2) human movement, and 3) joint mechanics during human movement. The first and third areas in particular contain a number of challenging geometric modeling issues. Current applications include prediction of in vivo wear in total knee replacements and prediction of patient-specific gait modifications to treat knee joint osteoarthritis. Engineering technologies involved in these projects include multibody dynamics, elastic contact theory, local and global optimization, parallel processing, numerical methods, geometric modeling, and image processing.

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Local corner cutting
by Harmut Prautzch, Universtat Karlsruhe

Corner cutting refers to a class of algorithms which are used to smooth polygons so as to obtain differentiable curves and surfaces in the limit. It is a particular subclass of so called non-stationary sudivision schemes. Local corner cutting methods are dual to interpolatory subdivision schemes where we add corners to a polygon so as to obtain smooth curves or surfaces in the limit. In this talk, I will present conditions that are necessary and sufficient for the differentiability of the limiting curves and surfaces obtained by local corner cutting and their dual schemes. With these results, all existing corner cutting schemes can be analyzed as is shown in the talk. While curve schemes are completely understood, some questions remain for surface schemes.

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Well-formed incidence systems for rigid bodies and seam forest matroids
by Meera Sitharam, CSE, UF

Abstract (see www.cise.ufl.edu/~sitharam/overlap.pdf for paper): We formalize a common problem that arises in several applications that require relative positioning/orienting rigid bodies constrained by incidences at points (joints) or linesegments (hinges): How to pick a maximal set of incidences that are independent? We first formalize the notion of a well-formed system of incidences. We then isolate an underlying graph and equate the problem of finding an well-formed set of incidences to the problem of finding a type of maximal forest which we call the seam forests, which form a matroid structure. A simple greedy algorithm for finding maximal seam forests seam trees immediately follows. The challenge is in equating well-formed systems of incidences incidences to the seam tree, which involves computing the rank of this new matroid structure. I hope to give an intuitive idea of the problem and definitions using examples, and an intuitive explanation of why the algorithm works.

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Exact Computation in Geometric Modeling
by John Keyser, TAMU

Robustness problems due to numerical errors and degeneracies are well-known in the geometric and solid modeling community. Slight errors in numerical computations, as well as unexpected degenerate geometric configurations can cause serious inconsistencies in representations, resulting in program failure. Exact geometric computation offers a route for eliminating numerical error, and is extremely useful when handling degenerate geometric data. However, exact computation brings with it a number of drawbacks, chiefly a tremendous lack of efficiency. This talk will discuss some of the main issues involved in practical implementations of exact geometric computation. Many geometric computations can be reduced to algebraic operations, so much exact geometric computation boils down to performing exact algebraic operations. This talk will include an overview of these operations, along with the current best solutions, and some of the recent work that holds promise for significant advances in the future. Only a limited amount of mathematics background should be needed. Extensions to non-algebraic geometric computation will be discussed. This talk will also give an overview of techniques for improving efficiency, while maintaining exactness, as well as some of the implementations of exact geometric computation being developed. Finally, some other geometric computation problems of current interest to the speaker will be mentioned.

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References

References from the talks as well as the presentation materials will be available here (upon speakers approval).

Previous years

Spring05	Fall04	Spring04	Fall03	Spring03	Fall02
Spring02	Fall01	Spring01	Fall00	Spring00	Fall99	Spring99

goals

schedule

references

previous years

Alper Üngör (ungoratcisedotufldotedu) August 2005