Topics in matrix analysis
Feature-based correspondence: an eigenvector approach
Image and Vision Computing - Special issue: BMVC 1991
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
3D motion recovery via affine epipolar geometry
International Journal of Computer Vision
The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
Applied numerical linear algebra
Applied numerical linear algebra
Automatic Construction of 2D Shape Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Active Appearance Models Revisited
International Journal of Computer Vision
Overview of the Face Recognition Grand Challenge
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
A Closed-Form Solution to Non-Rigid Shape and Motion Recovery
International Journal of Computer Vision
2D vs. 3D Deformable Face Models: Representational Power, Construction, and Real-Time Fitting
International Journal of Computer Vision
Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
A review of active appearance models
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Real-time combined 2D+3D active appearance models
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Rigid and Articulated Point Registration with Expectation Conditional Maximization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Face alignment using statistical models and wavelet features
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Robust Point Set Registration Using Gaussian Mixture Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Automatic gait recognition based on statistical shape analysis
IEEE Transactions on Image Processing
| Hi-index | 0.00 |
Aligning shapes is essential in many computer vision problems and generalized Procrustes analysis (GPA) is one of the most popular algorithms to align shapes. However, if some of the shape data are missing, GPA cannot be applied. In this paper, we propose EM-GPA, which extends GPA to handle shapes with hidden (missing) variables by using the expectation-maximization (EM) algorithm. For example, 2D shapes can be considered as 3D shapes with missing depth information due to the projection of 3D shapes into the image plane. For a set of 2D shapes, EM-GPA finds scales, rotations and 3D shapes along with their mean and covariance matrix for 3D shape modeling. A distinctive characteristic of EM-GPA is that it does not enforce any rank constraint often appeared in other work and instead uses GPA constraints to resolve the ambiguity in finding scales, rotations, and 3D shapes. The experimental results show that EM-GPA can recover depth information accurately even when the noise level is high and there are a large number of missing variables. By using the images from the FRGC database, we show that EM-GPA can successfully align 2D shapes by taking the missing information into consideration. We also demonstrate that the 3D mean shape and its covariance matrix are accurately estimated. As an application of EM-GPA, we construct a 2D+3D AAM (active appearance model) using the 3D shapes obtained by EM-GPA, and it gives a similar success rate in model fitting compared to the method using real 3D shapes. EM-GPA is not limited to the case of missing depth information, but it can be easily extended to more general cases.