Optimal Linear Representations of Images Under Diverse Criteria | Geometric Tools for Finding Linear Projections

Evgenia Rubinshtein

ISBN 10: 3639133994 / ISBN 13: 9783639133998

Published by VDM Verlag Dr. Müller, 2009

About this Item

Optimal Linear Representations of Images Under Diverse Criteria | Geometric Tools for Finding Linear Projections | Evgenia Rubinshtein | Taschenbuch | Englisch | VDM Verlag Dr. Müller | EAN 9783639133998 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu.

Seller Inventory # 101634216

Bibliographic Details

• Title: Optimal Linear Representations of Images Under Diverse Criteria | Geometric Tools for Finding Linear Projections
• Publisher: VDM Verlag Dr. Müller
• Publication Date: 2009
• Language: English
• ISBN 10: 3639133994
• ISBN 13: 9783639133998
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 152W x 7H x 228D millimeters 152 millimeters width by 7 millimeters height by 228 millimeters depth
• Weight: 199 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

Image analysis often requires dimension reduction before statistical analysis, in order to apply sophisticated procedures. Motivated by eventual applications, a variety of criteria have been proposed: reconstruction error, class separation, non-Gaussianity using kurtosis, sparseness, mutual information, recognition of objects, and their combinations. Although some criteria have analytical solutions, the remaining ones require numerical approaches. We present geometric tools for finding linear projections that optimize a given criterion for a given data set. The main idea is to formulate a problem of optimization on a Grassmann or a Stiefel manifold, and to use differential geometry of the underlying space to construct optimization algorithms. Purely deterministic updates lead to local solutions, and addition of random components allows for stochastic gradient searches that eventually lead to global solutions. We demonstrate these results using several image datasets, including natural images and facial images. This book should be useful for professionals, researches and graduate students in Image Analysis field.