Name
Abstract | ||
|---|---|---|
Deformable template representations of observed imagery, model the variability of target pose via the actions of the matrix Lie groups on rigid templates. In this paper, we study the construction of minimum mean squared error estimators on the special orthogonal group, SO(n), for pose estimation. Due to the nonflat geometry of SO(n), the standard Bayesian formulation, of optimal estimators and their characteristics, requires modifications. By utilizing Hilbert-Schmidt metric defined on GL(n), a larger group containing SO(n), a mean squared criterion is defined on SO(n). The Hilbert-Schmidt estimate (HSE) is defined to be a minimum mean squared error estimator, restricted to SO(n). The expected error associated with the HSE is shown to be a lower bound, called the Hilbert-Schmidt bound (HSB), on the error incurred by any other estimator. Analysis and algorithms are presented for evaluating the HSE and the HSB in case of both ground-based and airborne targets. |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1109/34.709572 | IEEE Trans. Pattern Anal. Mach. Intell. |
Keywords | Field | DocType |
deformable template representation,special orthogonal group,matrix lie group,optimal estimator,expected error,error estimator,matrix lie groups,larger group,utilizing hilbert-schmidt,hilbert-schmidt estimate,hilbert-schmidt lower bounds,airborne target,optimal estimation,bayesian methods,lower bound,lie group,estimation theory,geometry,layout,lie groups,object recognition,algorithm design and analysis,indexing terms,minimum mean square error,automatic target recognition,bayesian approach,pose estimation,orthogonal group | Lie group,Combinatorics,Square (algebra),Upper and lower bounds,Matrix (mathematics),Minimum mean square error,Orthogonal group,Estimation theory,Mathematics,Estimator | Journal |
Volume | Issue | ISSN |
20 | 8 | 0162-8828 |
Citations | PageRank | References |
49 | 9.98 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulf Grenander | 1 | 308 | 80.59 |
| Michael I Miller | 2 | 3123 | 422.82 |
| Anuj Srivastana | 3 | 49 | 9.98 |