Download Bayesian Modeling of Uncertainty in Low-Level Vision by Richard Szeliski PDF

By Richard Szeliski

Vision has to accommodate uncertainty. The sensors are noisy, the earlier wisdom is doubtful or erroneous, and the issues of recuperating scene details from photographs are frequently ill-posed or underconstrained. This learn monograph, that is according to Richard Szeliski's Ph.D. dissertation at Carnegie Mellon college, offers a Bayesian version for representing and processing uncertainty in low­ point imaginative and prescient. lately, probabilistic types were proposed and utilized in imaginative and prescient. Sze­ liski's process has a number of distinguishing positive aspects that make this monograph im­ portant and tasty. First, he provides a scientific Bayesian probabilistic estimation framework within which we will be able to outline and compute the earlier version, the sensor version, and the posterior version. moment, his process represents and computes explicitly not just the simplest estimates but additionally the extent of uncertainty of these estimates utilizing moment order information, i.e., the variance and covariance. 3rd, the algorithms constructed are computationally tractable for dense fields, comparable to intensity maps made from stereo or variety finder info, instead of simply sparse facts units. eventually, Szeliski demonstrates winning purposes of the tactic to a number of genuine international difficulties, together with the iteration of fractal surfaces, movement estimation with no correspondence utilizing sparse variety facts, and incremental intensity from motion.

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Pk+IApk = O. 2. 12. ::1E(Uk + QkPk). This involves computing the product of the sparse matrix A and the Ph and the inner product of the resulting vector Wk and Pk. On a fine-grained parallel architecture, the matrix operation is computable in constant time (dependent on the size of the neighborhoods or molecules in A) and the inner product summation is computable in log n steps using a summing pyramid. After updating the new state, we compute the new residual rk+1 and find the value of f3k+1 which will make the new and old directions conjugate.

The resulting conjugate gradient descent algorithm is Identical to the usual single-level algorithm except that we use a smoothed version of the residual f = SSTr to choose the new direction (Szeliski 1989). We describe the development of this algorithm below. Conjugate gradient descent is a numerical optimization technique closely related to steepest descent algorithms (Press et al. 1986). At each step k, a direction Pk is selected in the state space, and an optimal sized step is taken in this direction.

14: Algorithm convergence as a function of L Controlled-continuity thin plate. bilinear interpolator. 0316 ~ ... , .... ':"'~".. . "':' ~..... :. 0100 .... . ,. "'".... ~" " .. :\,. \' ~, <.... :: bilinear "'~"'" bilinear with discontinuities , ..... 0010 bicubic ,... 0001 .. ... , ... , ... 15: Algorithm convergence as a function of interpolator Controlled-continuity thin plate, L = 4 or 5. 44 Bayesian Modeling of Uncertainty in Low-Level Vision and continuous membrane are even faster.

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