Elastic Shape Analysis Of Three Dimensional Objects

Author : Ian H. Jermyn
Publisher : Springer Nature
ISBN 13 : 3031018192
Total Pages : 169 pages
Book Rating : 4.0/5 (31 download)

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Download or read book Elastic Shape Analysis of Three-Dimensional Objects written by Ian H. Jermyn and published by Springer Nature. This book was released on 2022-05-31 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in ℝ, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations. The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L2 metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities. These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis. This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.

Author : Hà Quang Minh
Publisher : Springer Nature
ISBN 13 : 3031018206
Total Pages : 156 pages
Book Rating : 4.0/5 (31 download)

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Download or read book Covariances in Computer Vision and Machine Learning written by Hà Quang Minh and published by Springer Nature. This book was released on 2022-05-31 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covariance matrices play important roles in many areas of mathematics, statistics, and machine learning, as well as their applications. In computer vision and image processing, they give rise to a powerful data representation, namely the covariance descriptor, with numerous practical applications. In this book, we begin by presenting an overview of the {\it finite-dimensional covariance matrix} representation approach of images, along with its statistical interpretation. In particular, we discuss the various distances and divergences that arise from the intrinsic geometrical structures of the set of Symmetric Positive Definite (SPD) matrices, namely Riemannian manifold and convex cone structures. Computationally, we focus on kernel methods on covariance matrices, especially using the Log-Euclidean distance. We then show some of the latest developments in the generalization of the finite-dimensional covariance matrix representation to the {\it infinite-dimensional covariance operator} representation via positive definite kernels. We present the generalization of the affine-invariant Riemannian metric and the Log-Hilbert-Schmidt metric, which generalizes the Log-Euclidean distance. Computationally, we focus on kernel methods on covariance operators, especially using the Log-Hilbert-Schmidt distance. Specifically, we present a two-layer kernel machine, using the Log-Hilbert-Schmidt distance and its finite-dimensional approximation, which reduces the computational complexity of the exact formulation while largely preserving its capability. Theoretical analysis shows that, mathematically, the approximate Log-Hilbert-Schmidt distance should be preferred over the approximate Log-Hilbert-Schmidt inner product and, computationally, it should be preferred over the approximate affine-invariant Riemannian distance. Numerical experiments on image classification demonstrate significant improvements of the infinite-dimensional formulation over the finite-dimensional counterpart. Given the numerous applications of covariance matrices in many areas of mathematics, statistics, and machine learning, just to name a few, we expect that the infinite-dimensional covariance operator formulation presented here will have many more applications beyond those in computer vision.

Author : Salman Khan
Publisher : Springer Nature
ISBN 13 : 3031018214
Total Pages : 187 pages
Book Rating : 4.0/5 (31 download)

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Download or read book A Guide to Convolutional Neural Networks for Computer Vision written by Salman Khan and published by Springer Nature. This book was released on 2022-06-01 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer vision has become increasingly important and effective in recent years due to its wide-ranging applications in areas as diverse as smart surveillance and monitoring, health and medicine, sports and recreation, robotics, drones, and self-driving cars. Visual recognition tasks, such as image classification, localization, and detection, are the core building blocks of many of these applications, and recent developments in Convolutional Neural Networks (CNNs) have led to outstanding performance in these state-of-the-art visual recognition tasks and systems. As a result, CNNs now form the crux of deep learning algorithms in computer vision. This self-contained guide will benefit those who seek to both understand the theory behind CNNs and to gain hands-on experience on the application of CNNs in computer vision. It provides a comprehensive introduction to CNNs starting with the essential concepts behind neural networks: training, regularization, and optimization of CNNs. The book also discusses a wide range of loss functions, network layers, and popular CNN architectures, reviews the different techniques for the evaluation of CNNs, and presents some popular CNN tools and libraries that are commonly used in computer vision. Further, this text describes and discusses case studies that are related to the application of CNN in computer vision, including image classification, object detection, semantic segmentation, scene understanding, and image generation. This book is ideal for undergraduate and graduate students, as no prior background knowledge in the field is required to follow the material, as well as new researchers, developers, engineers, and practitioners who are interested in gaining a quick understanding of CNN models.

Author : Michael Teutsch
Publisher : Springer Nature
ISBN 13 : 3031018265
Total Pages : 128 pages
Book Rating : 4.0/5 (31 download)

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Download or read book Computer Vision in the Infrared Spectrum written by Michael Teutsch and published by Springer Nature. This book was released on 2022-06-01 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Human visual perception is limited to the visual-optical spectrum. Machine vision is not. Cameras sensitive to the different infrared spectra can enhance the abilities of autonomous systems and visually perceive the environment in a holistic way. Relevant scene content can be made visible especially in situations, where sensors of other modalities face issues like a visual-optical camera that needs a source of illumination. As a consequence, not only human mistakes can be avoided by increasing the level of automation, but also machine-induced errors can be reduced that, for example, could make a self-driving car crash into a pedestrian under difficult illumination conditions. Furthermore, multi-spectral sensor systems with infrared imagery as one modality are a rich source of information and can provably increase the robustness of many autonomous systems. Applications that can benefit from utilizing infrared imagery range from robotics to automotive and from biometrics to surveillance. In this book, we provide a brief yet concise introduction to the current state-of-the-art of computer vision and machine learning in the infrared spectrum. Based on various popular computer vision tasks such as image enhancement, object detection, or object tracking, we first motivate each task starting from established literature in the visual-optical spectrum. Then, we discuss the differences between processing images and videos in the visual-optical spectrum and the various infrared spectra. An overview of the current literature is provided together with an outlook for each task. Furthermore, available and annotated public datasets and common evaluation methods and metrics are presented. In a separate chapter, popular applications that can greatly benefit from the use of infrared imagery as a data source are presented and discussed. Among them are automatic target recognition, video surveillance, or biometrics including face recognition. Finally, we conclude with recommendations for well-fitting sensor setups and data processing algorithms for certain computer vision tasks. We address this book to prospective researchers and engineers new to the field but also to anyone who wants to get introduced to the challenges and the approaches of computer vision using infrared images or videos. Readers will be able to start their work directly after reading the book supported by a highly comprehensive backlog of recent and relevant literature as well as related infrared datasets including existing evaluation frameworks. Together with consistently decreasing costs for infrared cameras, new fields of application appear and make computer vision in the infrared spectrum a great opportunity to face nowadays scientific and engineering challenges.

Author : Kristin J. Dana
Publisher : Springer Nature
ISBN 13 : 3031018230
Total Pages : 99 pages
Book Rating : 4.0/5 (31 download)

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Download or read book Computational Texture and Patterns written by Kristin J. Dana and published by Springer Nature. This book was released on 2022-05-31 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: Visual pattern analysis is a fundamental tool in mining data for knowledge. Computational representations for patterns and texture allow us to summarize, store, compare, and label in order to learn about the physical world. Our ability to capture visual imagery with cameras and sensors has resulted in vast amounts of raw data, but using this information effectively in a task-specific manner requires sophisticated computational representations. We enumerate specific desirable traits for these representations: (1) intraclass invariance—to support recognition; (2) illumination and geometric invariance for robustness to imaging conditions; (3) support for prediction and synthesis to use the model to infer continuation of the pattern; (4) support for change detection to detect anomalies and perturbations; and (5) support for physics-based interpretation to infer system properties from appearance. In recent years, computer vision has undergone a metamorphosis with classic algorithms adapting to new trends in deep learning. This text provides a tour of algorithm evolution including pattern recognition, segmentation and synthesis. We consider the general relevance and prominence of visual pattern analysis and applications that rely on computational models.

Author : Michael Felsberg
Publisher : Springer Nature
ISBN 13 : 3031018222
Total Pages : 89 pages
Book Rating : 4.0/5 (31 download)

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Download or read book Probabilistic and Biologically Inspired Feature Representations written by Michael Felsberg and published by Springer Nature. This book was released on 2022-05-31 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under the title "Probabilistic and Biologically Inspired Feature Representations," this text collects a substantial amount of work on the topic of channel representations. Channel representations are a biologically motivated, wavelet-like approach to visual feature descriptors: they are local and compact, they form a computational framework, and the represented information can be reconstructed. The first property is shared with many histogram- and signature-based descriptors, the latter property with the related concept of population codes. In their unique combination of properties, channel representations become a visual Swiss army knife—they can be used for image enhancement, visual object tracking, as 2D and 3D descriptors, and for pose estimation. In the chapters of this text, the framework of channel representations will be introduced and its attributes will be elaborated, as well as further insight into its probabilistic modeling and algorithmic implementation will be given. Channel representations are a useful toolbox to represent visual information for machine learning, as they establish a generic way to compute popular descriptors such as HOG, SIFT, and SHOT. Even in an age of deep learning, they provide a good compromise between hand-designed descriptors and a-priori structureless feature spaces as seen in the layers of deep networks.