Achievements And Challenges In The Field Of Convolution Operators
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Achievements and Challenges in the Field of Convolution Operators
This volume, which is dedicated to Yuri Karlovich on the occasion of his 75th birthday, includes biographical material, personal reminiscences, and carefully selected papers. The contributions constituting the core of this volume are written by mathematicians who have collaborated with Yuri or have been influenced by his vast mathematical work. They are devoted to topics of Yuri Karlovich's work for five decades, starting with his work on singular integral operators with shift, then broadened to include Toeplitz, Wiener-Hopf, Fourier and Mellin convolution and pseudodifferential operators, factorisation of almost periodic matrix functions, and local trajectory methods for the study of algebras of convolution and singular integral operators.
Learning Convolution Operators for Visual Tracking
Author: Martin Danelljan
language: en
Publisher: Linköping University Electronic Press
Release Date: 2018-05-03
Visual tracking is one of the fundamental problems in computer vision. Its numerous applications include robotics, autonomous driving, augmented reality and 3D reconstruction. In essence, visual tracking can be described as the problem of estimating the trajectory of a target in a sequence of images. The target can be any image region or object of interest. While humans excel at this task, requiring little effort to perform accurate and robust visual tracking, it has proven difficult to automate. It has therefore remained one of the most active research topics in computer vision. In its most general form, no prior knowledge about the object of interest or environment is given, except for the initial target location. This general form of tracking is known as generic visual tracking. The unconstrained nature of this problem makes it particularly difficult, yet applicable to a wider range of scenarios. As no prior knowledge is given, the tracker must learn an appearance model of the target on-the-fly. Cast as a machine learning problem, it imposes several major challenges which are addressed in this thesis. The main purpose of this thesis is the study and advancement of the, so called, Discriminative Correlation Filter (DCF) framework, as it has shown to be particularly suitable for the tracking application. By utilizing properties of the Fourier transform, a correlation filter is discriminatively learned by efficiently minimizing a least-squares objective. The resulting filter is then applied to a new image in order to estimate the target location. This thesis contributes to the advancement of the DCF methodology in several aspects. The main contribution regards the learning of the appearance model: First, the problem of updating the appearance model with new training samples is covered. Efficient update rules and numerical solvers are investigated for this task. Second, the periodic assumption induced by the circular convolution in DCF is countered by proposing a spatial regularization component. Third, an adaptive model of the training set is proposed to alleviate the impact of corrupted or mislabeled training samples. Fourth, a continuous-space formulation of the DCF is introduced, enabling the fusion of multiresolution features and sub-pixel accurate predictions. Finally, the problems of computational complexity and overfitting are addressed by investigating dimensionality reduction techniques. As a second contribution, different feature representations for tracking are investigated. A particular focus is put on the analysis of color features, which had been largely overlooked in prior tracking research. This thesis also studies the use of deep features in DCF-based tracking. While many vision problems have greatly benefited from the advent of deep learning, it has proven difficult to harvest the power of such representations for tracking. In this thesis it is shown that both shallow and deep layers contribute positively. Furthermore, the problem of fusing their complementary properties is investigated. The final major contribution of this thesis regards the prediction of the target scale. In many applications, it is essential to track the scale, or size, of the target since it is strongly related to the relative distance. A thorough analysis of how to integrate scale estimation into the DCF framework is performed. A one-dimensional scale filter is proposed, enabling efficient and accurate scale estimation.
Statistical Atlases and Computational Models of the Heart. ACDC and MMWHS Challenges
This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on Statistical Atlases and Computational Models of the Heart: ACDC and MMWHS Challenges 2017, held in conjunction with MICCAI 2017, in Quebec, Canada, in September 2017. The 27 revised full workshop papers were carefully reviewed and selected from 35 submissions. The papers cover a wide range of topics computational imaging and modelling of the heart, as well as statistical cardiac atlases. The topics of the workshop included: cardiac imaging and image processing, atlas construction, statistical modelling of cardiac function across different patient populations, cardiac computational physiology, model customization, atlas based functional analysis, ontological schemata for data and results, integrated functional and structural analyses, as well as the pre-clinical and clinical applicability of these methods. Besides regular contributing papers, additional efforts of STACOM workshop were also focused on two challenges: ACDC and MM-WHS.