Disparity and Optical Flow Partitioning Using Extended Potts Priors

This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notation of asymptotically level stable functions we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of minimizers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method

Disparity and optical flow partitioning using extended Potts priors

This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notion of asymptotically level stable (als) functions, we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of multipliers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method

A primal dual active set with continuation algorithm for the l0-regularized optimization problem

We develop a primal dual active set with continuation algorithm for solving the ℓ0-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it first identifies the active set from both primal and dual variables, and then updates the primal variable by solving a (typically small) least-squares problem defined on the active set, from which the dual variable can be updated explicitly. Under certain conditions on the sensing matrix, i.e., mutual incoherence property or restricted isometry property, and the noise level, a finite step global convergence of the overall algorithm is established. Extensive numerical examples are presented to illustrate the efficiency and accuracy of the algorithm and its convergence behavior

Stochastic-optimization of equipment productivity in multi-seam formations

Short and long range planning and execution for multi-seam coal formations (MSFs) are challenging with complex extraction mechanisms. Stripping equipment selection and scheduling are functions of the physical dynamics of the mine and the operational mechanisms of its components, thus its productivity is dependent on these parameters. Previous research studies did not incorporate quantitative relationships between equipment productivities and extraction dynamics in MSFs. The intrinsic variability of excavation and spoiling dynamics must also form part of existing models. This research formulates quantitative relationships of equipment productivities using Branch-and-Bound algorithms and Lagrange Parameterization approaches. The stochastic processes are resolved via Monte Carlo/Latin Hypercube simulation techniques within @RISK framework. The model was presented with a bituminous coal mining case in the Appalachian field. The simulated results showed a 3.51% improvement in mining cost and 0.19% increment in net present value. A 76.95yd³ drop in productivity per unit change in cycle time was recorded for sub-optimal equipment schedules. The geologic variability and equipment operational parameters restricted any possible change in the cost function. A 50.3% chance of the mining cost increasing above its current value was driven by the volume of material re-handled with 0.52 regression coefficient. The study advances the optimization process in mine planning and scheduling algorithms, to efficiently capture future uncertainties surrounding multivariate random functions. The main novelty includes the application of stochastic-optimization procedures to improve equipment productivity in MSFs --Abstract, page iii