A Self-Referencing Level-Set Method for Image Reconstruction from Sparse Fourier Samples
International Journal of Computer Vision
Shape Estimation from Support and Diameter Functions
Journal of Mathematical Imaging and Vision
MCMC curve sampling for image segmentation
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention
| Hi-index | 754.84 |
We introduce confidence region techniques for analyzing and visualizing the performance of two-dimensional parametric shape estimators. Assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary, Cramer-Rao bounds are used to define an asymptotic confidence region, centered around the true boundary. Computation of the probability that an entire boundary estimate lies within the confidence region is a challenging problem, because the estimate is a two-dimensional nonstationary random process. We derive lower bounds on this probability using level crossing statistics. The same bounds also apply to asymptotic confidence regions formed around the estimated boundaries, lower-bounding the probability that the entire true boundary lies within the confidence region. The results make it possible to generate asymptotic confidence regions for arbitrary prescribed probabilities. These asymptotic global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated object, and facilitate geometric inferences. Numerical simulations suggest that the new bounds are quite tight