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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]
Given a group of 3D points viewed by N cameras with matrices {} = …, define to be the homogeneous coordinates of the projection of the point onto the camera. The reconstruction problem can be changed to: given the group of pixel coordinates {}, find the corresponding set of camera matrices {} and the scene structure {} such that
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) ...
[1] [2] The expenditure for managing the data is great. The second and simpler concept is the marching method. [3] [4] [5] The triangulation starts with a triangulated hexagon at a starting point. This hexagon is then surrounded by new triangles, following given rules, until the surface of consideration is triangulated.
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 .