Richard Szeliski. Bayesian modeling of uncertainty in low-level vision. Intl. J. Comp. Vis., 5(3):271-301, December 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....using coarse to ne gradient algorithm. The single dots correspond to optical ow vectors of length zero. As we have described, a coarse to ne algorithm can be used to handle problems of temporal aliasing. It is also a technique for imposing a prior smoothness constraint (see, for example, [32]) This basic technique does, however, have a serious drawback. If the coarse scale estimates are incorrect, then the ne scale estimates will have no chance of correcting the errors. To x this, we must have knowledge of the error in the coarse scale estimates. Since we are working in a ....

Richard Szeliski. Bayesian modeling of uncertainty in low-level vision. Intl. J. Comp. Vis., 5(3):271-301, December 1990.

....We can specify conditional probabilities for particular configurations. However, calculating p(u) such that all the marginal distributions are correct is a difficult problem, in general. There is a single way of specifying a probability distribution whose conditional probabilities are Markovian [9]. We can use a Gibbs (or Boltzman) distribution of the form: p(u) 1=Z p exp( GammaE p (u) T p ) 17) where T p is the temperature of the model and Z p the partition function: Z p = X u exp( GammaE p (u) T p ) The energy function E p (u) can be written as: E p (u) X c2C E c (u) where ....

....respect the parameters could be computed from the dependence of m on d j : ln(p(jY ) d j = X i ( ff 2 ( Gamma m) t R( Gamma m) m i m i d j where the sum is over all the points. But this approach is very restrictive when dealing with the representation of visible surfaces [9]. In this case, the most useful techniques to model visibles surfaces have been spline based representations and MRF. Both of these approaches are examples of locally parameterized models of shape. In a first aproximation we have not considered any prior model for visible surfaces. Surfaces are ....

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R.Szelisky, Bayesian Modeling of Uncertainty in Low-Level Vision. Kluwer Academic Pub. 1989.

....a scalar confidence measure, but a two dimensional probability distribution, capable of representing inhomogeneous directional uncertainties. Anandan [3] computed two dimensional confidences based on a block matching histogram, and Heeger [4] estimated twodimensional covariances. Szeliski [5] has discussed the use of Bayesian techniques for a variety of problems in low level vision. The goal, then, is to compute an expression for the probability of the image velocity conditional on the image sequence. For the purposes of this paper, we will more specifically be concerned with a ....

Richard Szeliski. Bayesian modeling of uncertainty in low-level vision. International Journal of Computer Vision, 5(3):271--301, December 1990.

....mathematical structure known as a Markov Random Field (MRF) 31. A Markov Random Field is a probability distribution defined over a discrete field where the probability of a particular variable u i depends only on a neighborhood N i , that is P (u i ju j ; j 2 N i ) P (u i ju j ; for all j [18]) 32. Regularization [1] is another term for imposing constraints onto a system (or a process) by defining energy functions to be minimized. The constraints are often imposed in form of a smoothing term added to the energy function. 33. Bayesian estimation provides a formalism for information ....

Richard Szelisky. Bayesian Modeling of Uncertainty in Low-level Vision. Kluwer Academic Publishers, 1989.

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