DPP-PMRF: Rethinking Optimization for a Probabilistic Graphical Model Using Data-Parallel Primitives

We present a new parallel algorithm for probabilistic graphical model optimization. The algorithm relies on data-parallel primitives (DPPs), which provide portable performance over hardware architecture. We evaluate results on CPUs and GPUs for an image segmentation problem. Compared to a serial baseline, we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare our performance to a reference, OpenMP-based algorithm, and find speedups of up to 7X (CPU).Comment: LDAV 2018, October 201

Large-scale Binary Quadratic Optimization Using Semidefinite Relaxation and Applications

In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve large-scale problems. However, general nonsubmodular problems are significantly more challenging to solve. Finding a solution when the problem is of large size to be of practical interest, however, typically requires relaxation. Two standard relaxation methods are widely used for solving general BQPs--spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy to implement, but its bound is loose. Semidefinite relaxation has a tighter bound, but its computational complexity is high, especially for large scale problems. In this work, we present a new SDP formulation for BQPs, with two desirable properties. First, it has a similar relaxation bound to conventional SDP formulations. Second, compared with conventional SDP methods, the new SDP formulation leads to a significantly more efficient and scalable dual optimization approach, which has the same degree of complexity as spectral methods. We then propose two solvers, namely, quasi-Newton and smoothing Newton methods, for the dual problem. Both of them are significantly more efficiently than standard interior-point methods. In practice, the smoothing Newton solver is faster than the quasi-Newton solver for dense or medium-sized problems, while the quasi-Newton solver is preferable for large sparse/structured problems. Our experiments on a few computer vision applications including clustering, image segmentation, co-segmentation and registration show the potential of our SDP formulation for solving large-scale BQPs.Comment: Fixed some typos. 18 pages. Accepted to IEEE Transactions on Pattern Analysis and Machine Intelligenc

Different approaches to community detection

A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in network clustering and blockmodeling, and based on an extended version of The many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4 (2017) by the same author

Two and three dimensional segmentation of multimodal imagery

The role of segmentation in the realms of image understanding/analysis, computer vision, pattern recognition, remote sensing and medical imaging in recent years has been significantly augmented due to accelerated scientific advances made in the acquisition of image data. This low-level analysis protocol is critical to numerous applications, with the primary goal of expediting and improving the effectiveness of subsequent high-level operations by providing a condensed and pertinent representation of image information. In this research, we propose a novel unsupervised segmentation framework for facilitating meaningful segregation of 2-D/3-D image data across multiple modalities (color, remote-sensing and biomedical imaging) into non-overlapping partitions using several spatial-spectral attributes. Initially, our framework exploits the information obtained from detecting edges inherent in the data. To this effect, by using a vector gradient detection technique, pixels without edges are grouped and individually labeled to partition some initial portion of the input image content. Pixels that contain higher gradient densities are included by the dynamic generation of segments as the algorithm progresses to generate an initial region map. Subsequently, texture modeling is performed and the obtained gradient, texture and intensity information along with the aforementioned initial partition map are used to perform a multivariate refinement procedure, to fuse groups with similar characteristics yielding the final output segmentation. Experimental results obtained in comparison to published/state-of the-art segmentation techniques for color as well as multi/hyperspectral imagery, demonstrate the advantages of the proposed method. Furthermore, for the purpose of achieving improved computational efficiency we propose an extension of the aforestated methodology in a multi-resolution framework, demonstrated on color images. Finally, this research also encompasses a 3-D extension of the aforementioned algorithm demonstrated on medical (Magnetic Resonance Imaging / Computed Tomography) volumes

A goal-driven unsupervised image segmentation method combining graph-based processing and Markov random fields

Image segmentation is the process of partitioning a digital image into a set of homogeneous regions (according to some homogeneity criterion) to facilitate a subsequent higher-level analysis. In this context, the present paper proposes an unsupervised and graph-based method of image segmentation, which is driven by an application goal, namely, the generation of image segments associated with a user-defined and application-specific goal. A graph, together with a random grid of source elements, is defined on top of the input image. From each source satisfying a goal-driven predicate, called seed, a propagation algorithm assigns a cost to each pixel on the basis of similarity and topological connectivity, measuring the degree of association with the reference seed. Then, the set of most significant regions is automatically extracted and used to estimate a statistical model for each region. Finally, the segmentation problem is expressed in a Bayesian framework in terms of probabilistic Markov random field (MRF) graphical modeling. An ad hoc energy function is defined based on parametric models, a seed-specific spatial feature, a background-specific potential, and local-contextual information. This energy function is minimized through graph cuts and, more specifically, the alpha-beta swap algorithm, yielding the final goal-driven segmentation based on the maximum a posteriori (MAP) decision rule. The proposed method does not require deep a priori knowledge (e.g., labelled datasets), as it only requires the choice of a goal-driven predicate and a suited parametric model for the data. In the experimental validation with both magnetic resonance (MR) and synthetic aperture radar (SAR) images, the method demonstrates robustness, versatility, and applicability to different domains, thus allowing for further analyses guided by the generated product

Local, multi-resolution detection of network communities by Markovian dynamics

Complex networks are used to represent systems from many disciplines, including biology, physics, medicine, engineering and the social sciences; Many real-world networks are organised into densely connected communi- ties, whose composition gives some insight into the underlying network. Most approaches for nding such communities do so by partitioning the network into disjoint subsets, at the cost of requiring global information and that nodes belong to exactly one community. In recent years, some effort has been devoted towards the development of local methods, but these are either limited in resolution or ignore relevant network features such as directedness. Here we show that introducing a dynamic process onto the network allows us to de ne a community quality function severability which is inherently multi-resolution, takes into account edge-weight and direction, can accommodate overlapping communities and orphan nodes and crucially does not require global knowledge. Both constructive and real-world examples| drawn from elds as diverse as image segmentation, metabolic networks and word association|are used to illustrate the characteristics of this approach. We envision this approach as a starting point for the future analysis of both evolving networks and networks too large to be readily analysed as a whole (e.g. the World Wide Web).Open Acces