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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Empirical Analysis Of Computational And Accuracy Tradeoffs Using Compactly Supported Radial Basis Functions For Surface Reconstruction, Weiming Liu, Bryan S. Morse, Lauralea Otis
Empirical Analysis Of Computational And Accuracy Tradeoffs Using Compactly Supported Radial Basis Functions For Surface Reconstruction, Weiming Liu, Bryan S. Morse, Lauralea Otis
Faculty Publications
Implicit surfaces can be constructed from scattered surface points using radial basis functions (RBFs) to interpolate the surface’s embedding function. Many researchers have used thin-plate spline RBFs for this because of their desirable smoothness properties. Others have used compactly supported RBFs, leading to a sparse matrix solution with lower computational complexity and better conditioning. However, the limited radius of support introduces a free parameter that leads to varying solutions as well as varying computational requirements: a larger radius of support leads to smoother and more accurate solutions but requires more computation. This paper presents an empirical analysis of this radius …
Image Magnification Using Level-Set Reconstruction, Bryan S. Morse, Duane Schwartzwald
Image Magnification Using Level-Set Reconstruction, Bryan S. Morse, Duane Schwartzwald
Faculty Publications
Image magnification is a common problem in imaging applications, requiring interpolation to “read between the pixels”. Although many magnification/interpolation algorithms have been proposed in the literature, all methods must suffer to some degree the effects of impefect reconstruction―false high-frequency content introduced by the underlying original sampling. Most often, these effects manifest themselves as jagged contours in the image. This paper presents a method for constrained smoothing of such artifacts that attempts to produce smooth reconstructions of the image’s level curves while still maintaining image fidelity. This is similar to other iterative reconstruction algorithms and to Bayesian restoration techniques, but instead …
Interpolating Implicit Surfaces From Scattered Surface Data Using Compactly Supported Radial Basis Functions, Bryan S. Morse, David T. Chen, Penny Rheingans, Kalpathi Subramanian, Terry S. Yoo
Interpolating Implicit Surfaces From Scattered Surface Data Using Compactly Supported Radial Basis Functions, Bryan S. Morse, David T. Chen, Penny Rheingans, Kalpathi Subramanian, Terry S. Yoo
Faculty Publications
We describe algebraic methods for creating implicit surfaces using linear combinations of radial basis interpolants to form complex models from scattered surface points. Shapes with arbitrary topology are easily represented without the usual interpolation or aliasing errors arising from discrete sampling. These methods were first applied to implicit surfaces by Savchenko, et al. and later developed independently by Turk and O'Brien as a means of performing shape interpolation. Earlier approaches were limited as a modeling mechanism because of the order of the computational complexity involved. We explore and extend these implicit interpolating methods to make them suitable for systems of …
Isophote-Based Interpolation, Bryan S. Morse, Duane Schwartzwald
Isophote-Based Interpolation, Bryan S. Morse, Duane Schwartzwald
Faculty Publications
Standard methods for image interpolation are based on smoothly fitting the image intensity surface. Recent edge-directed interpolation methods add limited geometric information (edge maps) to build more accurate and visually appealing interpolations at key contours in the image. This paper presents a method for geometry-based interpolation that smoothly fits the isophote (intensity level curve) contours at all points in the image rather than just at selected contours. By using level set methods for curve evolution, no explicit extraction or representation of these contours is required (unlike earlier edge-directed methods). The method uses existing interpolation techniques as an initial approximation and …
Faster Ray Tracing Using Adaptive Grids, Thomas W. Sederberg, Krysztof S. Klimaszewski
Faster Ray Tracing Using Adaptive Grids, Thomas W. Sederberg, Krysztof S. Klimaszewski
Faculty Publications
A new hybrid approach is presented which outperforms the regular grid technique in scenes with highly irregular object distributions by a factor of hundreds, and combined with an area interpolator, by a factor of thousands. Much has been said about scene independence of different acceleration techniques and the alleged superiority of one approach over another. Several theoretical and practical studies conducted in the past have led to the same conclusion: a space partitioning method that allows the fastest rendering of one scene often fails with another. Specialization may be the answer. This has always been pursued, consciously or not, in …
Techniques For Cubic Algebraic Surfaces Ii, Thomas W. Sederberg
Techniques For Cubic Algebraic Surfaces Ii, Thomas W. Sederberg
Faculty Publications
A survey of some techniques that may have potential for free-form modeling with algebraic surfaces is continued. Classical results as well as several recent innovations are included. Specific attention is paid to cubic algebraic surfaces, although many of the ideas presented have application to algebraic surfaces of any degree. Topics addressed include piecewise constructions, interpolation to points and space curves, and parameterization.
Techniques For Cubic Algebraic Surfaces I, Thomas W. Sederberg
Techniques For Cubic Algebraic Surfaces I, Thomas W. Sederberg
Faculty Publications
The tutorial presents some tools for free-form modeling with algebraic surfaces, that is, surfaces that can be defined using an implicit polynomial equation f(x, y, z )=0. Cubic algebraic surfaces (defined by an implicit equation of degree 3) are emphasized. While much of this material applies only to cubic surfaces, some applies to algebraic surfaces of any degree. This area of the tutorial introduces terminology, presents different methods for defining and modeling with cubic surfaces, and examines the power basis representation of algebraic surfaces. Methods of forcing an algebraic surface to interpolate a set of points or a space curve …
A Parallel-Processing Subsystem For Rapid 3-D Interpolation Of Ct Images, William A. Barrett, Stephen J. Allan, Scott R. Cannon
A Parallel-Processing Subsystem For Rapid 3-D Interpolation Of Ct Images, William A. Barrett, Stephen J. Allan, Scott R. Cannon
Faculty Publications
An inexpensive parallel-processing subsystem for the rapid interpolation of CT image planes is demonstrated with a variety of node topologies. The subsystem is based on a tree network of INMOS T414 Transputer processors and is hosted by an AT-based image workstation. The subsystem accepts a stack of eight arbitrarily-spaced 256 x 256 image planes from the host. Subsystem output to the host consists of a stack of 32 scaled and evenly-spaced image planes (256 x 256 x 32 with cubic voxels). Benchmark execution times ranged from 12.3 seconds for three nodes to 5.8 seconds for eight nodes.