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

POROUS MEDIUM CONVECTION AT LARGE RAYLEIGH NUMBER: STUDIES OF COHERENT STRUCTURE, TRANSPORT, AND REDUCED DYNAMICS

Buoyancy-driven convection in fluid-saturated porous media is a key environmental and technological process, with applications ranging from carbon dioxide storage in terrestrial aquifers to the design of compact heat exchangers. Porous medium convection is also a paradigm for forced-dissipative infinite-dimensional dynamical systems, exhibiting spatiotemporally chaotic dynamics if not ``true turbulence. The objective of this dissertation research is to quantitatively characterize the dynamics and heat transport in two-dimensional horizontal and inclined porous medium convection between isothermal plane parallel boundaries at asymptotically large values of the Rayleigh number $Ra$ by investigating the emergent, quasi-coherent flow. This investigation employs a complement of direct numerical simulations (DNS), secondary stability and dynamical systems theory, and variational analysis. The DNS confirm the remarkable tendency for the interior flow to self-organize into closely-spaced columnar plumes at sufficiently large $Ra$ (up to $Ra \simeq 10^5$), with more complex spatiotemporal features being confined to boundary layers near the heated and cooled walls. The relatively simple form of the interior flow motivates investigation of unstable steady and time-periodic convective states at large $Ra$ as a function of the domain aspect ratio $L$. To gain insight into the development of spatiotemporally chaotic convection, the (secondary) stability of these fully nonlinear states to small-amplitude disturbances is investigated using a spatial Floquet analysis. The results indicate that there exist two distinct modes of instability at large $Ra$: a bulk instability mode and a wall instability mode. The former usually is excited by long-wavelength disturbances and is generally much weaker than the latter. DNS, strategically initialized to investigate the fully nonlinear evolution of the most dangerous secondary instability modes, suggest that the (long time) mean inter-plume spacing in statistically-steady porous medium convection results from an interplay between the competing effects of these two types of instability. Upper bound analysis is then employed to investigate the dependence of the heat transport enhancement factor, i.e. the Nusselt number $Nu$, on $Ra$ and $L$. To solve the optimization problems arising from the ``background field upper-bound variational analysis, a novel two-step algorithm in which time is introduced into the formulation is developed. The new algorithm obviates the need for numerical continuation, thereby enabling the best available bounds to be computed up to $Ra\approx 2.65\times 10^4$. A mathematical proof is given to demonstrate that the only steady state to which this numerical algorithm can converge is the required global optimal of the variational problem. Using this algorithm, the dependence of the bounds on $L(Ra)$ is explored, and a ``minimal flow unit is identified. Finally, the upper bound variational methodology is also shown to yield quantitatively useful predictions of $Nu$ and to furnish a functional basis that is naturally adapted to the boundary layer dynamics at large $Ra$

Cooperation of Nature and Physiologically Inspired Mechanism in Visualisation

A novel approach of integrating two swarm intelligence algorithms is considered, one simulating the behaviour of birds flocking (Particle Swarm Optimisation) and the other one (Stochastic Diffusion Search) mimics the recruitment behaviour of one species of ants – Leptothorax acervorum. This hybrid algorithm is assisted by a biological mechanism inspired by the behaviour of blood flow and cells in blood vessels, where the concept of high and low blood pressure is utilised. The performance of the nature-inspired algorithms and the biologically inspired mechanisms in the hybrid algorithm is reflected through a cooperative attempt to make a drawing on the canvas. The scientific value of the marriage between the two swarm intelligence algorithms is currently being investigated thoroughly on many benchmarks and the results reported suggest a promising prospect (al-Rifaie, Bishop & Blackwell, 2011). We also discuss whether or not the ‘art works’ generated by nature and biologically inspired algorithms can possibly be considered as ‘computationally creative’