Developing new algorithms and data structures for efficient processing of geometric shapes. A major goal of this research is to guarantee desired surface properties such as geometric accuracy or topological properties such as being a manifold. An application involves interactive shape modeling and sculpting in virtual environments.

Dissertation

GPU-assisted Surface Reconstruction on Locally-uniform Samples [pdf]
Yong J Kil and Nina Amenta,
Proceedings of International Meshing Roundtable, 2008.

Abstract:
In point-based graphics, surfaces are represented by point clouds without explicit connectivity. If the distribution of the points can be carefully controlled, surface reconstruction becomes a much easier problem. We present a simple, completely local surface reconstruction algorithm for input point distributions that are locally uniform. The locality of the computation lets us handle large point sets using parallel and out-of-core methods. The algorithm can be implemented robustly with floating-point arithmetic. We demonstrate the simplicity, efficiency, and numerical stability of our algorithm with an out-of-core and parallel implementation using graphics hardware.

Laser Scanner Super-resolution
Yong Joo Kil, Boris Mederos, and Nina Amenta
Eurographics Symposium on Point-based Graphics 2006.

Combining Laser Scans
Yong Joo Kil, Boris Mederos, and Nina Amenta
Sketch of ACM SIGGRAPH 2006.

Abstract:
We give a method for improving the resolution of surfaces captured with a laser range scanner by combining many very similar scans. This idea is an application of the 2D image processing technique known as superresolution. The input lower-resolution scans are each randomly shifted, so that each one contributes slightly different information to the final model. Noise is reduced by averaging the input scans.

Evolutionary Morphing [movie]
David F. Wiley, Nina Amenta, Dan A. Alcantara, Deboshmita Ghosh, Yong J Kil,
Eric Delson, Will Harcourt-Smith, F. James Rohlf, Katherine St. John, Bernd Hamann
Proceedings of IEEE Visualization 2005
[More Info].

Abstract:
We introduce a technique to visualize the gradual evolutionary change of the shapes of living things as a morph between known three-dimensional shapes. Given geometric computer models of anatomical shapes for some collection of specimens - here the skulls of the some of the extant members of a family of monkeys - an evolutionary tree for the group implies a hypothesis about the way in which the shape changed through time. We use a statistical method which expresses the value of some variable - in this case the shape - at an internal point in the tree as a weighted average of the values at the leaves. The framework of geometric morphometrics can then be used to define a shape-space, based on the correspondences of landmark points on the surfaces, within which these weighted averages can be realized as actual surfaces. Our software provides tools for performing and visualizing such an analysis in three dimensions. Beginning with laser range surfaces scans of skulls, we use our landmark editor to interactively place landmark points on the surface. We use these to compute a treemorph which smoothly interpolates the shapes across the tree. Each intermediate shape in the morph is a linear combination of all of the input surfaces. We create a surface model for an intermediate shape by warping all the input meshes towards the correct shape and then merging them together. Our merging procedure is novel. Given several similar surface meshes, we compute a weighted average between them by averaging their associated trivariate squared distance functions, and then extract the extremal surface which traces out the "valleys" along which the averaged function is nearly zero.

3D Warp Brush Modeling
Y. Kil, P. Renzulli, O. Kreylos, B. Hamann, G. Monno, O.G. Staadt.
Journal of Computer and Graphics, ELSEVIER, Vol. 30, No. 4, 2006.

3D Warp Brush: Interactive Free-Form Modeling on the Responsive Workbench
Y. Kil, P. Renzulli, O. Kreylos, B. Hamann, G. Monno, O.G. Staadt
Proceedings of IEEE Virtual Reality 2005.

Abstract:
We introduce the 3D warp brush, a method for interactive shape modeling in a immersive virtual reality environment. 3D warp brushes are implicitly-defined tools that operate on triangle meshes. We combine the efficiency of explicit mesh representations with implicit modeling operators. The area of influence of a 3D warp brush can be of arbitrary shape since it has an associated distance field. We define different warp functions including drag, explode, and whittle. A unique feature of our framework is the ability to convert meshes into 3D warp brushes at run time. The use of a Responsive Workbench and two-handed interaction allows the user to exploit the full potential of the modeling system by intuitive and easy modification of a base surface into a desired shape. We present models, which have been created and modified using 3D warp brushes, to demonstrate the usefulness of our framework.

Defining Point Set Surfaces
Nina Amenta and Yong Joo Kil
Journal of ACM SIGGRAPH, pp. 264-270, 2004.
[More Info].

Abstract:
The MLS surface, used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field. This definition reveals connections to research in computer vision and computational topology. Variants of the MLS surface can be created by varying the vector field and the energy function. As an example of such a generalization, we define a point-set surface for surfels (points equipped with normals). We also make an important technical observation: the procedures described in the literature to take points in space onto the MLS surface do not, in fact, produce points of the MLS surface. We describe a simple iterative procedure which does, for any of the variants.

The Domain of a Point Set Surface
Nina Amenta and Yong Joo Kil
Eurographics Symposium on Point-based Graphics, pp. 139-147, 2004.
[More Info].

Abstract:
It is useful to be able to define a two-dimensional point-set surface determined by a point cloud. One popular definition is Levin's MLS surface. This surface is defined on a domain which is a three-dimensional, a narrow region around the input point cloud. If we were to extend the definition outside the domain, we would produce components of the surface which are far from the point cloud. This is important in practice, since when moving points onto the MLS surface, we need to begin with an initial guess which is within the domain. We visualize the domain in two dimensions, and explain why it is so narrow. We also consider two MLS variants which can be defined on a wider domain without producing spurious surface components. One is efficient and works well except near sharp corners. The other is computationally expensive but seems to work well everywhere.

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