Download Functional and Shape Data Analysis by Anuj Srivastava PDF

By Anuj Srivastava

ISBN-10: 149394018X

ISBN-13: 9781493940189

ISBN-10: 1493940201

ISBN-13: 9781493940202

This textbook for classes on functionality info research and form info research describes how to find, examine, and mathematically symbolize shapes, with a spotlight on statistical modeling and inference. it's aimed toward graduate scholars in research in facts, engineering, utilized arithmetic, neuroscience, biology, bioinformatics, and different comparable components. The interdisciplinary nature of the wide variety of rules covered—from introductory idea to algorithmic implementations and a few statistical case studies—is intended to familiarize graduate scholars with an array of instruments which are proper in constructing computational recommendations for form and similar analyses. those instruments, gleaned from geometry, algebra, facts, and computational technology, are characteristically scattered throughout various classes, departments, and disciplines; Functional and form information research offers a unified, complete resolution through integrating the registration challenge into form research, greater getting ready graduate scholars for dealing with destiny clinical challenges.

Recently, a data-driven and application-oriented specialise in form research has been trending. this article deals a self-contained therapy of this new iteration of tools suit research of curves. Its major concentration is form research of capabilities and curves—in one, , and better dimensions—both closed and open. It develops dependent Riemannian frameworks that offer either quantification of form alterations and registration of curves while. also, those tools are used for statistically summarizing given curve information, appearing size relief, and modeling saw variability. it is strongly recommended that the reader have a historical past in calculus, linear algebra, numerical research, and computation.

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Extra info for Functional and Shape Data Analysis

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5 Organization of this Textbook This textbook is organized as follows. In Chap. 2, we briefly summarize some of the commonly used techniques in shape analysis, along with discussions on their strengths and limitations. In Chap. 3 and Appendix A, we provide a concise summary of mathematical concepts that are relevant to understanding our approach. Specifically, they cover basic material from differential geometry, algebra, and functional analysis. We have tried to highlight definitions and examples that are particularly important in shape analysis.

An important property of a signed-distance function φ : [0, ]12 → R is that ∇φ(x) = 1 for all x ∈ [0, 1]2 . It is easy to see that, for a τ ∈ (0, 1), ∇ψ(τ )(x) = (1 − τ )∇φ1 (x) + τ ∇φ2 (x) is not necessarily equal to one. Hence, an intermediate point in the path ψ is not a proper signed-distance function, and it becomes difficult to talk about the level sets of this function as a shape. Although this framework is not ideally suited for shape analysis of objects, it has been used extensively for extracting boundaries of contours in images.

36 2 Previous Techniques in Shape Analysis Fig. 13 (a) Image I1 , (b) Image I2 , (c) Deformed image is I1 (γ), (d) deformation vector field generating γ, (e) deformed grid γ(D) Associated with an image I, there is an equivalence class of images that can be reached by deforming that I. [I] = {γ · I : γ ∈ Γ } . Similar to the previous section, this is defined to be the equivalence class of shapes associated with I. A transformation between two images I1 and I2 can be modeled by diffeomorphically aligning I1 to I2 .

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