Gerald Farin

Image Registration Using Hierarchical B-Splines,with X. Zie. IEEE Transactions on Visualization and Computer Graphics 10(1): 85-94. 2004

Abstract: Hierarchical B-splines have been widely used for shape modeling since their discovery by Forsey and Bartels. In this paper, we present an application of this concept to image registration by matching two images at increasing levels of detail. Results using MRI brain data are presented that demonstrate high degrees of matching yet unnecessary distortions are avoided. We compare our results with the nonlinear ICP(IterativeClosestPoint) algorithm (used for landmark-based registration) and optical flow (used for intensity-based registration.
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Shape. G. Farin Abstract: A survey of shape related methods in CAGD. download

 

A geometric interpretation of the diagonal of a tensor-product Bézier volume Abstract: A geometric interpretation of the diagonal of a tensor-product trivariate Bézier volume using degree elevation of Bézier triangles is given. download



Discrete Coons patches Gerald Farin, Dianne Hansford Abstract: We investigate surfaces which interpolate given boundary curves. We show that the discrete bilinearly blended Coons patch can be defined as the solution of a linear system. With the goal of producing better shape than the Coons patch, this idea is generalized, resulting in a new method based on a blend of variational principles. We show that no single blend of variational principles can produce "good" shape for all boundary curve geometries. We also discuss triangular Coons patches and point out the connections to the rectangular case. download

Geometric curve approximation Hans Wolters and Gerald Farin; Abstract: We present a new metric to measure the shape quality of curves. This metric is based upon the concept of total curvature. We then present a rational approximation scheme that minimizes a functional defined in terms of this metric. download

Determination of end conditions for NURB surface interpolation Anshuman Razdan and Gerald Farin download

A transfinite form of Sibson's interpolant L. Gross and G. Farin; Abstract: Sibson's interpolant usesVoronoi diagrams in the plane to interpolate a set of scattered data points. This paper presents an extension of this method to handle the interpolation of a set of functional curves (transfinite surface interpolation). We derive a simple formula for this new surface type which can interpolate to any number of boundary curves. In addition, a unique surface may be created from a set of discontinuous curves. Finally, we present a form of the interpolant which uses convex or concave polygonal domains. download