Algebraic Functions For Recognition
By Amnon Shashua. 1995
In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment-yielding a direct reprojection method that cuts through the computations of camera transformation, scene structure and epipolar geometry. Moreover, the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection. The proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks. >
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Richard I. Hartley
- E. T. Rolls
- Gustavo Deco
- Morten L. Kringelbach
- R. Kesner
- John P. O'Doherty
- Nora D. Volkow
- Kent C. Berridge
Citations in the corpus
- Invariant Visual Object and Face Recognition: Neural and Computational Bases, and a Model, VisNet (2012, background): “This alignment approach is the main theme of the book by Ullman (1996), and there are a number of computer implementations (Lowe, 1985; Grimson, 1990; Huttenlocher and Ullman, 1990; Shashua, 1995).”
- Lines and Points in Three Views and the Trifocal Tensor (1997, methodology): “The importance of this result is that it allows an amalgamation of the linear algorithms for points (Shashua, 1995) and for lines (Hartley, 1994b).”