Direct methods in the calculus of variations
Direct methods in the calculus of variations
Recognition by Linear Combinations of Models
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Graphics Gems III
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Pattern Analysis and Machine Intelligence
Transformation-Invariant Clustering Using the EM Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Principal Component Analysis over Continuous Subspaces and Intersection of Half-Spaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
Multidimensional Morphable Models
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Robust parameterized component analysis: theory and applications to 2D facial appearance models
Computer Vision and Image Understanding - Special issue on Face recognition
Automatic Construction of Active Appearance Models as an Image Coding Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
Data Driven Image Models through Continuous Joint Alignment
IEEE Transactions on Pattern Analysis and Machine Intelligence
2D face recognition based on supervised subspace learning from 3D models
Pattern Recognition
Representing cyclic human motion using functional analysis
Image and Vision Computing
Image and Vision Computing
Learning a generic 3D face model from 2D image databases using incremental Structure-from-Motion
Image and Vision Computing
Global optimization for optimal generalized procrustes analysis
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
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Two-dimensional shape models have been successfully applied to solve many problems in computer vision, such as object tracking, recognition, and segmentation. Typically, 2D shape models are learned from a discrete set of image landmarks (corresponding to projection of 3D points of an object), after applying Generalized Procustes Analysis (GPA) to remove 2D rigid transformations. However, the standard GPA process suffers from three main limitations. Firstly, the 2D training samples do not necessarily cover a uniform sampling of all the 3D transformations of an object. This can bias the estimate of the shape model. Secondly, it can be computationally expensive to learn the shape model by sampling 3D transformations. Thirdly, standard GPA methods use only one reference shape, which can might be insufficient to capture large structural variability of some objects. To address these drawbacks, this paper proposes continuous generalized Procrustes analysis (CGPA). CGPA uses a continuous formulation that avoids the need to generate 2D projections from all the rigid 3D transformations. It builds an efficient (in space and time) non-biased 2D shape model from a set of 3D model of objects. A major challenge in CGPA is the need to integrate over the space of 3D rotations, especially when the rotations are parameterized with Euler angles. To address this problem, we introduce the use of the Haar measure. Finally, we extended CGPA to incorporate several reference shapes. Experimental results on synthetic and real experiments show the benefits of CGPA over GPA.