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Local Features in Natural Images via Singularity Theory / by James Damon, Peter Giblin, Gareth Haslinger.
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2379,2381-2384 2385-2386,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Damon, James., Author.
- Giblin, Peter., Author.
- Haslinger, Gareth., Author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 2165
- Language:
- English
- Subjects (All):
- Global analysis (Mathematics).
- Manifolds (Mathematics).
- Computer science—Mathematics.
- Computer science--Mathematics.
- Computer science.
- Optical data processing.
- Global Analysis and Analysis on Manifolds.
- Mathematical Applications in Computer Science.
- Computer Imaging, Vision, Pattern Recognition and Graphics.
- Local Subjects:
- Global Analysis and Analysis on Manifolds.
- Mathematical Applications in Computer Science.
- Computer Imaging, Vision, Pattern Recognition and Graphics.
- Physical Description:
- 1 online resource (X, 255 p. 107 illus., 50 illus. in color.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2016.
- Summary:
- This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer’s eye. The goal is to detect geometric features of objects in the image and to separate regions of the objects with distinct visual properties. When the scene is illuminated by a single principal light source, we further include the visual clues resulting from the interaction of the geometric features of objects, the shade/shadow regions on the objects, and the “apparent contours”. We do so by a mathematical analysis using a repertoire of methods in singularity theory. This is applied for generic light directions of both the “stable configurations” for these interactions, whose features remain unchanged under small viewer movement, and the generic changes which occur under changes of view directions. These may then be used to differentiate between objects and determine their shapes and positions.
- Contents:
- Introduction
- Overview
- Part I-Mathematical Basis for Analysis of Feature-Shade/Shadow- Contours
- Abstract Classification of Singularities Preserving Features
- Singularity Equivalence Groups Capturing Interactions
- Methods for Classification of Singularities
- Methods for Topological Classification of Singularities
- Part II-The Classification of Interactions Involving Feature– Shade/Shadow–Contours
- Stratifications of Generically Illuminated Surfaces with Geometric Features
- Realizations of Abstract Mappings Representing Projection Singularities
- Statements of the Main Classification Results
- Part III-Classifications of Interactions of Pairs of Feature– Shade/Shadow–Contours
- Stable View Projections and Transitions involving Shade/Shadow Curves on a Smooth Surface (SC)
- Transitions involving Views of Geometric Features (FC)
- Part IV-Classifications of Multiple Interactions
- Transitions involving Geometric Features and Shade/Shadow Curves (SFC)
- Classifications of Stable Multilocal Configurations and Their Generic Transitions
- Bibliography.
- ISBN:
- 3-319-41471-2
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