Adaptive mesh refinement techniques for high-order finite-volume WENO schemes

This paper demonstrates the capabilities of Adaptive Mesh Refinement Techniques (AMR) on 2D hybrid unstructured meshes, for high order finite volume WENO methods. The AMR technique developed is a conformal adapting unstructured hybrid quadrilaterals and triangles (quads & tris) technique for resolving sharp flow features in accurate manner for steady-state and time dependent flow problems. In this method, the mesh can be refined or coarsened which depends on an error estimator, making decision at the parent level whilst maintaining a conformal mesh, the unstructured hybrid mesh refinement is done hierarchically.When a numerical method can work on a fixed conformal mesh this can be applied to do dynamic mesh adaptation. Two Refinement strategies have been devised both following a H-P refinement technique, which can be applied for providing better resolution to strong gradient dominated problems. The AMR algorithm has been tested on cylindrical explosion test and forward facing step problems

Automatically Score Tissue Images Like a Pathologist by Transfer Learning

Cancer is the second leading cause of death in the world. Diagnosing cancer early on can save many lives. Pathologists have to look at tissue microarray (TMA) images manually to identify tumors, which can be time-consuming, inconsistent and subjective. Existing algorithms that automatically detect tumors have either not achieved the accuracy level of a pathologist or require substantial human involvements. A major challenge is that TMA images with different shapes, sizes, and locations can have the same score. Learning staining patterns in TMA images requires a huge number of images, which are severely limited due to privacy concerns and regulations in medical organizations. TMA images from different cancer types may have common characteristics that could provide valuable information, but using them directly harms the accuracy. By selective transfer learning from multiple small auxiliary sets, the proposed algorithm is able to extract knowledge from tissue images showing a ``similar" scoring pattern but with different cancer types. Remarkably, transfer learning has made it possible for the algorithm to break the critical accuracy barrier -- the proposed algorithm reports an accuracy of 75.9% on breast cancer TMA images from the Stanford Tissue Microarray Database, achieving the 75\% accuracy level of pathologists. This will allow pathologists to confidently use automatic algorithms to assist them in recognizing tumors consistently with a higher accuracy in real time.Comment: 19 pages, 6 figure

Computer vision for real-time orbital operations. Center directors discretionary fund

Machine vision research is examined as it relates to the NASA Space Station program and its associated Orbital Maneuvering Vehicle (OMV). Initial operation of OMV for orbital assembly, docking, and servicing are manually controlled from the ground by means of an on board TV camera. These orbital operations may be accomplished autonomously by machine vision techniques which use the TV camera as a sensing device. Classical machine vision techniques are described. An alternate method is developed and described which employs a syntactic pattern recognition scheme. It has the potential for substantial reduction of computing and data storage requirements in comparison to the Two-Dimensional Fast Fourier Transform (2D FFT) image analysis. The method embodies powerful heuristic pattern recognition capability by identifying image shapes such as elongation, symmetry, number of appendages, and the relative length of appendages

New algorithmic developments in maximum consensus robust fitting

In many computer vision applications, the task of robustly estimating the set of parameters of a geometric model is a fundamental problem. Despite the longstanding research efforts on robust model fitting, there remains significant scope for investigation. For a large number of geometric estimation tasks in computer vision, maximum consensus is the most popular robust fitting criterion. This thesis makes several contributions in the algorithms for consensus maximization. Randomized hypothesize-and-verify algorithms are arguably the most widely used class of techniques for robust estimation thanks to their simplicity. Though efficient, these randomized heuristic methods do not guarantee finding good maximum consensus estimates. To improve the randomize algorithms, guided sampling approaches have been developed. These methods take advantage of additional domain information, such as descriptor matching scores, to guide the sampling process. Subsets of the data that are more likely to result in good estimates are prioritized for consideration. However, these guided sampling approaches are ineffective when good domain information is not available. This thesis tackles this shortcoming by proposing a new guided sampling algorithm, which is based on the class of LP-type problems and Monte Carlo Tree Search (MCTS). The proposed algorithm relies on a fundamental geometric arrangement of the data to guide the sampling process. Specifically, we take advantage of the underlying tree structure of the maximum consensus problem and apply MCTS to efficiently search the tree. Empirical results show that the new guided sampling strategy outperforms traditional randomized methods. Consensus maximization also plays a key role in robust point set registration. A special case is the registration of deformable shapes. If the surfaces have the same intrinsic shapes, their deformations can be described accurately by a conformal model. The uniformization theorem allows the shapes to be conformally mapped onto a canonical domain, wherein the shapes can be aligned using a M¨obius transformation. The problem of correspondence-free M¨obius alignment of two sets of noisy and partially overlapping point sets can be tackled as a maximum consensus problem. Solving for the M¨obius transformation can be approached by randomized voting-type methods which offers no guarantee of optimality. Local methods such as Iterative Closest Point can be applied, but with the assumption that a good initialization is given or these techniques may converge to a bad local minima. When a globally optimal solution is required, the literature has so far considered only brute-force search. This thesis contributes a new branch-and-bound algorithm that solves for the globally optimal M¨obius transformation much more efficiently. So far, the consensus maximization problems are approached mainly by randomized algorithms, which are efficient but offer no analytical convergence guarantee. On the other hand, there exist exact algorithms that can solve the problem up to global optimality. The global methods, however, are intractable in general due to the NP-hardness of the consensus maximization. To fill the gap between the two extremes, this thesis contributes two novel deterministic algorithms to approximately optimize the maximum consensus criterion. The first method is based on non-smooth penalization supported by a Frank-Wolfe-style optimization scheme, and another algorithm is based on Alternating Direction Method of Multipliers (ADMM). Both of the proposed methods are capable of handling the non-linear geometric residuals commonly used in computer vision. As will be demonstrated, our proposed methods consistently outperform other heuristics and approximate methods.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Computer Science, 201