Name
Abstract | ||
|---|---|---|
Abstract In this paper we examine,the problem,of reconstructing a (possibly dynamic) ellipsoid from its (possibly inconsistent) orthogonal silhouette projections. We present a particularly convenient representation of ellipsoids as elements,of the vector space of symmetric,matrices. The relationship between an ellipsoid and its orthogonal projections in this representation is linear, unlike the standard parameterization based on semi-axis length and orientation. This representation is used to completely and simply characterize the solutions to the reconstruction,problem. The representation also allows the straightforward inclusion of geometric,constraints on the reconstructed ellipsoid in the form,of inner and outer bounds,on recovered,ellipsoid shape. The inclusion of a dynamic model with natural behavior, such as stretching, shrinking, and rotation, is similarly straightforward in this framework and results in the possibility of dynamic ellipsoid estimation. For example, the linear reconstruction of a dynamic ellipsoid from a single lower-dimensional projection observed,over time is possible. Numerical,examples,are provided to illustrate these points. 1 INTRODUCTION,3 |
Year | DOI | Venue |
|---|---|---|
1994 | 10.1006/cgip.1994.1012 | CVGIP: Graphical Model and Image Processing |
Keywords | Field | DocType |
reconstructing ellipsoids,symmetric matrices,orthogonal projection,vector space | Vector space,Ellipsoid,Reconstruction problem,Parametrization,Mathematical analysis,Silhouette,Symmetric matrix,Geometry,Ellipsoid method,Mathematics,Geodesics on an ellipsoid | Journal |
Volume | Issue | ISSN |
56 | 2 | 1049-9652 |
Citations | PageRank | References |
19 | 2.31 | 15 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| William C. Karl | 1 | 196 | 20.88 |
| George C. Verghese | 2 | 208 | 26.26 |
| Alan S. Willsky | 3 | 7466 | 847.01 |