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Invariant Methods for Problems in Medical Imaging.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Invariant Methods for Problems in Medical Imaging.
Author:	Tuznik, Stanley Leonard.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2020
Description:	119 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-02, Section: B.
Notes:	Advisor: Tannenbaum, Allen;Sandhu, Romeil.
Contained By:	Dissertations Abstracts International82-02B.
Subject:	Applied mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27964084
ISBN:	9798662469778

Invariant Methods for Problems in Medical Imaging.
Tuznik, Stanley Leonard.

Invariant Methods for Problems in Medical Imaging. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 119 p.

Source: Dissertations Abstracts International, Volume: 82-02, Section: B.

Thesis (Ph.D.)--State University of New York at Stony Brook, 2020.

This item must not be sold to any third party vendors.

Geometric invariance is of utmost importance for image processing algorithms. In this work, we discuss the mathematical theory of differential invariants and the numerical aspects of their application to the low-level image processing problems of object recognition and image registration. In particular, we study the use of differential invariants as a novel feature point detector in 2D and 3D imagery and demonstrate the results of a feature point-based image registration pipeline which is entirely equi-affine-invariant. Along the way, we demonstrate the construction of nonlinear, geometric invariant scale-spaces for image data. A final application of differential invariants to object recognition is the construction of differential invariant signature curves for the invariant representation of 2D shapes. We discuss the practical computation of differential invariant signature curves for object recognition, including several crucial numerical details, and argue that these methods are well-suited for inclusion in practical image data-driven domains such as medical imaging.

ISBN: 9798662469778Subjects--Topical Terms:

377601
Applied mathematics.
Subjects--Index Terms:

Curvature

Invariant Methods for Problems in Medical Imaging.
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245 1 0 $a Invariant Methods for Problems in Medical Imaging.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 119 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-02, Section: B.
500 $a Advisor: Tannenbaum, Allen;Sandhu, Romeil.
502 $a Thesis (Ph.D.)--State University of New York at Stony Brook, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a Geometric invariance is of utmost importance for image processing algorithms. In this work, we discuss the mathematical theory of differential invariants and the numerical aspects of their application to the low-level image processing problems of object recognition and image registration. In particular, we study the use of differential invariants as a novel feature point detector in 2D and 3D imagery and demonstrate the results of a feature point-based image registration pipeline which is entirely equi-affine-invariant. Along the way, we demonstrate the construction of nonlinear, geometric invariant scale-spaces for image data. A final application of differential invariants to object recognition is the construction of differential invariant signature curves for the invariant representation of 2D shapes. We discuss the practical computation of differential invariant signature curves for object recognition, including several crucial numerical details, and argue that these methods are well-suited for inclusion in practical image data-driven domains such as medical imaging.
590 $a School code: 0771.
650 4 $a Applied mathematics. $3 377601
653 $a Curvature
653 $a Differential invariant
653 $a Lie group
653 $a Object recognition
653 $a Plane curve
690 $a 0364
710 2 $a State University of New York at Stony Brook. $b Applied Mathematics and Statistics. $3 857349
773 0 $t Dissertations Abstracts International $g 82-02B.
790 $a 0771
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27964084