Optimal partial clique edge covering guided by potential energy minimization

For given integers\ua0k,\ua0n,\ua0r\ua0we aim at families of\ua0k\ua0sub-cliques called blocks, of a clique with\ua0n\ua0vertices, such that every block has\ua0r\ua0vertices, and the blocks together cover a maximum number of edges. We demonstrate a combinatorial optimization method that generates such optimal partial clique edge coverings. It takes certain packages of columns (corresponding to vertices) in the incidence matrix of the blocks, considers the number of uncovered edges as an energy term that has to be minimized by transforming these packages. As a proof of concept we can completely solve the above maximization problem in the case of\ua0k≤4k≤4\ua0blocks and obtain optimal coverings for all integers\ua0n\ua0and\ua0r\ua0with\ua0r/n≥5/9r/n≥5/9. This generalizes known results for total coverings to partial coverings. The method as such is not restricted to\ua0k≤4k≤4\ua0blocks, but a challenge for further research (also on total coverings) is to limit the case distinctions when more blocks are involved

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

Computational Methods for Segmentation of Multi-Modal Multi-Dimensional Cardiac Images

Segmentation of the heart structures helps compute the cardiac contractile function quantified via the systolic and diastolic volumes, ejection fraction, and myocardial mass, representing a reliable diagnostic value. Similarly, quantification of the myocardial mechanics throughout the cardiac cycle, analysis of the activation patterns in the heart via electrocardiography (ECG) signals, serve as good cardiac diagnosis indicators. Furthermore, high quality anatomical models of the heart can be used in planning and guidance of minimally invasive interventions under the assistance of image guidance. The most crucial step for the above mentioned applications is to segment the ventricles and myocardium from the acquired cardiac image data. Although the manual delineation of the heart structures is deemed as the gold-standard approach, it requires significant time and effort, and is highly susceptible to inter- and intra-observer variability. These limitations suggest a need for fast, robust, and accurate semi- or fully-automatic segmentation algorithms. However, the complex motion and anatomy of the heart, indistinct borders due to blood flow, the presence of trabeculations, intensity inhomogeneity, and various other imaging artifacts, makes the segmentation task challenging. In this work, we present and evaluate segmentation algorithms for multi-modal, multi-dimensional cardiac image datasets. Firstly, we segment the left ventricle (LV) blood-pool from a tri-plane 2D+time trans-esophageal (TEE) ultrasound acquisition using local phase based filtering and graph-cut technique, propagate the segmentation throughout the cardiac cycle using non-rigid registration-based motion extraction, and reconstruct the 3D LV geometry. Secondly, we segment the LV blood-pool and myocardium from an open-source 4D cardiac cine Magnetic Resonance Imaging (MRI) dataset by incorporating average atlas based shape constraint into the graph-cut framework and iterative segmentation refinement. The developed fast and robust framework is further extended to perform right ventricle (RV) blood-pool segmentation from a different open-source 4D cardiac cine MRI dataset. Next, we employ convolutional neural network based multi-task learning framework to segment the myocardium and regress its area, simultaneously, and show that segmentation based computation of the myocardial area is significantly better than that regressed directly from the network, while also being more interpretable. Finally, we impose a weak shape constraint via multi-task learning framework in a fully convolutional network and show improved segmentation performance for LV, RV and myocardium across healthy and pathological cases, as well as, in the challenging apical and basal slices in two open-source 4D cardiac cine MRI datasets. We demonstrate the accuracy and robustness of the proposed segmentation methods by comparing the obtained results against the provided gold-standard manual segmentations, as well as with other competing segmentation methods

2D Phase Unwrapping via Graph Cuts

Phase imaging technologies such as interferometric synthetic aperture radar (InSAR), magnetic resonance imaging (MRI), or optical interferometry, are nowadays widespread and with an increasing usage. The so-called phase unwrapping, which consists in the in- ference of the absolute phase from the modulo-2π phase, is a critical step in many of their processing chains, yet still one of its most challenging problems. We introduce an en- ergy minimization based approach to 2D phase unwrapping. In this approach we address the problem by adopting a Bayesian point of view and a Markov random field (MRF) to model the phase. The maximum a posteriori estimation of the absolute phase gives rise to an integer optimization problem, for which we introduce a family of efficient algo- rithms based on existing graph cuts techniques. We term our approach and algorithms PUMA, for Phase Unwrapping MAx flow. As long as the prior potential of the MRF is convex, PUMA guarantees an exact global solution. In particular it solves exactly all the minimum L p norm (p ≥ 1) phase unwrapping problems, unifying in that sense, a set of existing independent algorithms. For non convex potentials we introduce a version of PUMA that, while yielding only approximate solutions, gives very useful phase unwrap- ping results. The main characteristic of the introduced solutions is the ability to blindly preserve discontinuities. Extending the previous versions of PUMA, we tackle denoising by exploiting a multi-precision idea, which allows us to use the same rationale both for phase unwrapping and denoising. Finally, the last presented version of PUMA uses a frequency diversity concept to unwrap phase images having large phase rates. A representative set of experiences illustrates the performance of PUMA

The Salmon Algorithm - A New Population Based Search Metaheuristic

This thesis introduces the Salmon Algorithm, a search meta-heuristic which can be used for a variety of combinatorial optimization problems. This algorithm is loosely based on the path finding behaviour of salmon swimming upstream to spawn. There are a number of tunable parameters in the algorithm, so experiments were conducted to find the optimum parameter settings for different search spaces. The algorithm was tested on one instance of the Traveling Salesman Problem and found to have superior performance to an Ant Colony Algorithm and a Genetic Algorithm. It was then tested on three coding theory problems - optimal edit codes, optimal Hamming distance codes, and optimal covering codes. The algorithm produced improvements on the best known values for five of six of the test cases using edit codes. It matched the best known results on four out of seven of the Hamming codes as well as three out of three of the covering codes. The results suggest the Salmon Algorithm is competitive with established guided random search techniques, and may be superior in some search spaces

Doctor of Philosophy in Computing

dissertationImage segmentation is the problem of partitioning an image into disjoint segments that are perceptually or semantically homogeneous. As one of the most fundamental computer vision problems, image segmentation is used as a primary step for high-level vision tasks, such as object recognition and image understanding, and has even wider applications in interdisciplinary areas, such as longitudinal brain image analysis. Hierarchical models have gained popularity as a key component in image segmentation frameworks. By imposing structures, a hierarchical model can efficiently utilize features from larger image regions and make optimal inference for final segmentation feasible. We develop a hierarchical merge tree (HMT) model for image segmentation. Motivated by the application in large-scale segmentation of neuronal structures in electron microscopy (EM) images, our model provides a compact representation of region merging hypotheses and utilizes higher order information for efficient segmentation inference. Taking advantage of supervised learning, our model is free from parameter tuning and outperforms previous state-of-the-art methods on both two-dimensional (2D) and three-dimensional EM image data sets without any change. We also extend HMT to the hierarchical merge forest (HMF) model. By identifying region correspondences, HMF utilizes inter-section information to correct intra-section errors and improves 2D EM segmentation accuracy. HMT is a generic segmentation model. We demonstrate this by applying it to natural image segmentation problems. We propose a constrained conditional model formulation with a globally optimal inference algorithm for HMT and an iterative merge tree sampling algorithm that significantly improves its performance. Experimental results show our approach achieves state-of-the-art accuracy for object-independent image segmentation. Finally, we propose a semi-supervised HMT (SSHMT) model to reduce the high demand for labeled data by supervised learning. We introduce a differentiable unsupervised loss term that enforces consistent boundary predictions and develop a Bayesian learning model that combines supervised and unsupervised information. We show that with a very small amount of labeled data, SSHMT consistently performs close to the supervised HMT with full labeled data sets and significantly outperforms HMT trained with the same labeled subsets

Going beyond semantic image segmentation, towards holistic scene understanding, with associative hierarchical random fields

In this thesis we exploit the generality and expressive power of the Associative Hierarchical Random Field (AHRF) graphical model to take its use beyond that of semantic image segmentation, into object-classes, towards a framework for holistic scene understanding. We provide a working definition for the holistic approach to scene understanding, which allows for the integration of existing, disparate, applications into an unifying ensemble. We believe that modelling such an ensemble as an AHRF is both a principled and pragmatic solution. We present a hierarchy that shows several methods for fusing applications together with the AHRF graphical model. Each of the three; feature, potential and energy, layers subsumes its predecessor in generality and together give rise to many options for integration. With applications on street scenes we demonstrate an implementation of each layer. The first layer application joins appearance and geometric features. For our second layer we implement a things and stuff co-junction using higher order AHRF potentials for object detectors, with the goal of answering the classic questions: What? Where? and How many? A holistic approach to recognition-and-reconstruction is realised within our third layer by linking two energy based formulations of both applications. Each application is evaluated qualitatively and quantitatively. In all cases our holistic approach shows improvement over baseline methods