Structure from motion using line correspondences
International Journal of Computer Vision
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
The Geometry of Multiple Images: The Laws That Govern The Formation of Images of A Scene and Some of Their Applications
Novel View Synthesis by Cascading Trilinear Tensors
IEEE Transactions on Visualization and Computer Graphics
A Common Framework for Kinetic Depth, Reconstruction and Motion for Deformable Objects
ECCV '94 Proceedings of the Third European Conference-Volume II on Computer Vision - Volume II
Matching constraints and the joint image
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A Differential Geometric Approach to Multiple View Geometry in Spaces of Constant Curvature
International Journal of Computer Vision - Special Issue on Computer Vision Research at the Beckman Institute of Advanced Science and Technology
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
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In this paper, the geometry of a general class of projections from Rn to Rk (k n) is examined, as a generalization of classic multiple view geometry in computer vision. It is shown that geometric constraints that govern multiple images of hyperplanes in Rn, as well as any incidence conditions among these hyperplanes (such as inclusion, intersection, and restriction), can be systematically captured through certain rank conditions on the so-called multiple view matrix. All constraints known or unknown in computer vision for the projection from R3 to R2 are simply instances of this result. It certainly simplifies current efforts to extending classic multiple view geometry to dynamical scenes. It also reveals that since most new constraints in spaces of higher dimension are nonlinear, the rank conditions are a natural replacement for the traditional multilinear analysis. We also demonstrate that the rank conditions encode extremely rich information about dynamical scenes and they give rise to fundamental criteria for purposes such as stereopsis in n-dimensional space, segmentation of dynamical features, detection of spatial and temporal formations, and rejection of occluding T-junctions.