Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

Generalized sequential tree-reweighted message passing

This paper addresses the problem of approximate MAP-MRF inference in general graphical models. Following [36], we consider a family of linear programming relaxations of the problem where each relaxation is specified by a set of nested pairs of factors for which the marginalization constraint needs to be enforced. We develop a generalization of the TRW-S algorithm [9] for this problem, where we use a decomposition into junction chains, monotonic w.r.t. some ordering on the nodes. This generalizes the monotonic chains in [9] in a natural way. We also show how to deal with nested factors in an efficient way. Experiments show an improvement over min-sum diffusion, MPLP and subgradient ascent algorithms on a number of computer vision and natural language processing problems

HST-MRF: Heterogeneous Swin Transformer with Multi-Receptive Field for Medical Image Segmentation

The Transformer has been successfully used in medical image segmentation due to its excellent long-range modeling capabilities. However, patch segmentation is necessary when building a Transformer class model. This process may disrupt the tissue structure in medical images, resulting in the loss of relevant information. In this study, we proposed a Heterogeneous Swin Transformer with Multi-Receptive Field (HST-MRF) model based on U-shaped networks for medical image segmentation. The main purpose is to solve the problem of loss of structural information caused by patch segmentation using transformer by fusing patch information under different receptive fields. The heterogeneous Swin Transformer (HST) is the core module, which achieves the interaction of multi-receptive field patch information through heterogeneous attention and passes it to the next stage for progressive learning. We also designed a two-stage fusion module, multimodal bilinear pooling (MBP), to assist HST in further fusing multi-receptive field information and combining low-level and high-level semantic information for accurate localization of lesion regions. In addition, we developed adaptive patch embedding (APE) and soft channel attention (SCA) modules to retain more valuable information when acquiring patch embedding and filtering channel features, respectively, thereby improving model segmentation quality. We evaluated HST-MRF on multiple datasets for polyp and skin lesion segmentation tasks. Experimental results show that our proposed method outperforms state-of-the-art models and can achieve superior performance. Furthermore, we verified the effectiveness of each module and the benefits of multi-receptive field segmentation in reducing the loss of structural information through ablation experiments

MRF-based background initialisation for improved foreground detection in cluttered surveillance videos

Robust foreground object segmentation via background modelling is a difficult problem in cluttered environments, where obtaining a clear view of the background to model is almost impossible. In this paper, we propose a method capable of robustly estimating the background and detecting regions of interest in such environments. In particular, we propose to extend the background initialisation component of a recent patch-based foreground detection algorithm with an elaborate technique based on Markov Random Fields, where the optimal labelling solution is computed using iterated conditional modes. Rather than relying purely on local temporal statistics, the proposed technique takes into account the spatial continuity of the entire background. Experiments with several tracking algorithms on the CAVIAR dataset indicate that the proposed method leads to considerable improvements in object tracking accuracy, when compared to methods based on Gaussian mixture models and feature histograms

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Biomarker for tracking progression of Alzheimer's disease in clinical trials

Currently, there are no treatments available for mitigating the neurological effects of Alzheimer's disease. All clinical trials of disease-modifying treatments, which showed promise in animal models, have failed to show a significant treatment effect in human trials. The lack of a sensitive outcome measure and the focus on the dementia stage for investigating treatments are believed to be the primary reasons behind the failure of all clinical trials till date. The currently used outcome measure, the Alzheimer's Disease Assessment Scale-Cognitive subscale (ADAS-Cog), suffers from low sensitivity in tracking progression of cognitive impairment in clinical trials. A shift in the focus to the prodromal mild cognitive impairment (MCI) stage may help improve the efficiency of clinical trials. However, even lower sensitivity of the ADAS-Cog and an inability to specifically select progressive MCI patients limit the efficiency of clinical trials in the MCI stage. Cerebral atrophy measured on structural magnetic resonance (MR) imaging is highly promising for tracking disease progression in clinical trials. However, cerebral atrophy has not been yet approved as a valid biomarker due to the lack of an understanding behind its relationship with cognitive impairment. The focus of this dissertation spans across the two research areas of (i) developing automatic algorithms for analysis of patients' brain MR volumes, and (ii) improving the efficiency of clinical trials of disease-modifying treatments. This dissertation presents a novel knowledge-driven decision theory approach for automatic tissue segmentation of brain MR volumes, which shows better segmentation performance than the existing approaches. The remaining dissertation contributions focus at improving the efficiency of clinical trials of disease-modifying treatments. An improved scoring methodology is presented for the ADAS-Cog outcome measure, which measures cognitive impairment with better accuracy and significantly improves the sensitivity of the ADAS-Cog in the mild-to-moderate Alzheimer's disease stage. However, the ADAS-Cog continues to suffers from low sensitivity in the MCI stage due to inherent limitations of its items. For improving the efficiency of clinical trials in the MCI stage, a biomarker has been developed that combines the ADAS-Cog with cerebral atrophy for more accurate tracking of Alzheimer's progression and facilitating selection of MCI patients in clinical trials.Biomedical Engineerin