What Is the Set of Images of an Object Under All Possible Illumination Conditions?
International Journal of Computer Vision
Affine Structure and Motion from Points, Lines and Conics
International Journal of Computer Vision
International Journal of Computer Vision
Introduction: Computer Vision Research at NECI
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
A Multi-Frame Structure-from-Motion Algorithm under Perspective Projection
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
Classification with Nonmetric Distances: Image Retrieval and Class Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Linear Multi View Reconstruction and Camera Recovery Using a Reference Plane
International Journal of Computer Vision
Shadow Graphs and Surface Reconstruction
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Structure from Many Perspective Images with Occlusions
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Specularities Reduce Ambiguity of Uncalibrated Photometric Stereo
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Linear Multi View Reconstruction with Missing Data
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
A Six Point Solution for Structure and Motion
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Representations for Recognition Under Variable Illumination
Shape, Contour and Grouping in Computer Vision
Illumination Cones for Recognition under Variable Lighting: Faces
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
International Journal of Computer Vision - Special Issue on Texture Analysis and Synthesis
Shadow Graphs and 3D Texture Reconstruction
International Journal of Computer Vision - Special Issue on Texture Analysis and Synthesis
Reconstructing camera projection matrices from multiple pairwise overlapping views
Computer Vision and Image Understanding
Object Level Grouping for Video Shots
International Journal of Computer Vision
Affine Approximation for Direct Batch Recovery of Euclidian Structure and Motion from Sparse Data
International Journal of Computer Vision
A convenient multicamera self-calibration for virtual environments
Presence: Teleoperators and Virtual Environments
Journal of Mathematical Imaging and Vision
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Estimating 3D shape from degenerate sequences with missing data
Computer Vision and Image Understanding
Reconstructing camera projection matrices from multiple pairwise overlapping views
Computer Vision and Image Understanding
Conditional solutions for the affine reconstruction of N-views
Image and Vision Computing
Consistent multi-view reconstruction from epipolar geometries with outliers
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Automatic feature point correspondences and shape analysis with missing data and outliers using MDL
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Learning a generic 3D face model from 2D image databases using incremental Structure-from-Motion
Image and Vision Computing
Successively alternate least square for low-rank matrix factorization with bounded missing data
Computer Vision and Image Understanding
Exploiting loops in the graph of trifocal tensors for calibrating a network of cameras
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Uniqueness of Low-Rank Matrix Completion by Rigidity Theory
SIAM Journal on Matrix Analysis and Applications
Line reconstruction from many perspective images by factorization
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
On aligning sets of points reconstructed from uncalibrated affine cameras
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Handling missing data in the computation of 3d affine transformations
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
On Camera Calibration with Linear Programming and Loop Constraint Linearization
International Journal of Computer Vision
SLSFS'05 Proceedings of the 2005 international conference on Subspace, Latent Structure and Feature Selection
Fast 3d structure from motion with missing points from registration of partial reconstructions
AMDO'12 Proceedings of the 7th international conference on Articulated Motion and Deformable Objects
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Several vision problems can be reduced to the problem of fitting a linear surface of low dimension to data, including the problems of structure-from-affine-motion, and of characterizing the intensity images of a Lambertian scene by constructing the {\em intensity manifold}. For these problems, one must deal with a data matrix with some missing elements. In structure-from-motion, missing elements will occur if some point features are not visible in some frames. To construct the intensity manifold missing matrix elements will arise when the surface normals of some scene points do not face the light source in some images. We propose a novel method for fitting a low rank matrix to a matrix with missing elements. We show experimentally that our method produces good results in the presence of noise. These results can be either used directly, or can serve as an excellent starting point for an iterative method.