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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 .
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.
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
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]
Low altitude aerial photograph for use in photogrammetry. Location: Three Arch Bay, Laguna Beach, California. Photogrammetry is the science and technology of obtaining reliable information about physical objects and the environment through the process of recording, measuring and interpreting photographic images and patterns of electromagnetic radiant imagery and other phenomena.
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. [1]
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.
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 .