Some Recent Papers

1. A Wavelet Approach to Foveating Images
   (with E.C.Chang) Motivated by applications of foveated images in visualization, we introduce the \dt{foveation transform} of an image. We study the basic properties of these transforms using the multiresolution framework of Mallat. We also consider practical methods of realizing such transforms. In particular, we introduce a new method for foveating images based on wavelets. Preliminary experimental results are shown.
2. A Complete Roundness Classification Procedure
   (with K. Mehlhorn and T. Shermer) This is an update/extension of item 2 above. We describe a {\em roundness classification procedure}, that is, a procedure to determine if the roundness of a planar object $I$ is within some $\epsilon_0$ from an ideal circle. The procedure consists of a probing strategy and an evaluation algorithm working in a feedback loop. This approach of combining probing with evaluation is new in computational metrology. For several definitions of roundness, our procedure uses $O(1/\qual{I})$ probes and runs in time $O(1/\qual{I}^2)$. Here, the quality $\qual{I}$ of $I$ measures how far the roundness of $I$ is from the $\epsilon_0$ accept-reject criterion. Hence our algorithms are ``quality sensitive''. Of independent interest is a 6-probe method to compute a ``near center'' of an almost round object.
3. Issues in the Metrology of Geometric Tolerancing
   (with E.C. Chang) We address some fundamental issues arising in the "standard methodology" for classification problems in geometric tolerancing. By standard methodology, we mean the three steps of ``sampling'', ``computation'' and ``decision'' involved in deciding to accept or reject a manufactured part. We use a simple 1-dimensional problem as case study.
4. Precision-sensitive Euclidean Shortest Path in $3$-Space
   (with J.S.Choi and J.Sellen) We introduce the concept of precision-sensitive algorithms and apply this to the Euclideans shortest path problem in $3$-space. (appeared in 11th ACM Symp.CG'95, and the PhD thesis of Joonsoo Choi)
5. NSF Workshop on Manufacturing and Computational Geometry
   Report on a workshop on April 1-2, 1994, held at the Courant Institute, New York University. (appeared in IEEE Computational Sciences and Engineering, Summer 1995, Vol.2,No.2, pp.82--84)

Last Update: Jan 10, 1997