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Structure from motion (SfM) [1] is a photogrammetric range imaging technique for estimating three-dimensional structures from two-dimensional image sequences that may be coupled with local motion signals. It is studied in the fields of computer vision and visual perception.
In computer vision, triangulation refers to the process of determining a point in 3D space given its projections onto two, or more, images. In order to solve this problem it is necessary to know the parameters of the camera projection function from 3D to 2D for the cameras involved, in the simplest case represented by the camera matrices .
Biological motion demonstration: dots representing a person walking. In a 1953 study on SFM done by Wallach and O'Connell the kinetic depth effect was tested. They found that by turning shadow images of a three dimensional object can be used as a cue to recover the structure of the physical object quite well. [4]
All points X e.g. X 1, X 2, X 3 on the O L –X L line will verify that constraint. It means that it is possible to test if two points correspond to the same 3D point. Epipolar constraints can also be described by the fundamental matrix , [ 1 ] or in the case of noramlized image coordatinates, the essential matrix [ 2 ] between the two cameras.
Structure from motion may refer to: Structure from motion, a photogrammetric range imaging technique; Structure from motion (psychophysics), how humans recover shape ...
A kinetic triangulation data structure is a kinetic data structure that maintains a triangulation of a set of moving points. Maintaining a kinetic triangulation is important for applications that involve motion planning , such as video games, virtual reality, dynamic simulations and robotics.
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
In mathematics, triangulation describes the replacement of topological spaces with simplicial complexes by the choice of an appropriate homeomorphism. A space that admits such a homeomorphism is called a triangulable space. Triangulations can also be used to define a piecewise linear structure for a space, if one exists. Triangulation has ...