Mathematical Models in Computer Vision: Planar Shape Analysis and Its Applications in Image-Based Inferences

ABSTRACT: Shapes of boundaries can play an important role in characterizing objects in images. We describe an approach for statistical analysis of shapes of closed curves using ideas from differential geometry. A fundamental tool in this shape analysis is the construction and implementation of geodesic paths between shapes. We use geodesic paths to accomplish a variety of tasks, including the definition of a metric to compare shapes, the computation of intrinsic statistics for a set of shapes, and the definition of probability models on shape spaces. We demonstrate this approach using three applications: (i) automated clustering of objects in an image database according to their shapes, (ii) interpolation of heart-wall boundaries in echocardiographic image sequences, and (iii) a study of shapes of human silhouettes in infrared surveillance images.

	Main		Mathematical Models in Computer Vision: The Handbook, Springer (2005)
	Editors Preface Contents Contributors References Sample Chapter Order		Planar Shape Analysis and Its Applications in Image-Based Inferences, A. Srivastava, S. Joshi, D. Kaziska and D. Wilson ABSTRACT: Shapes of boundaries can play an important role in characterizing objects in images. We describe an approach for statistical analysis of shapes of closed curves using ideas from differential geometry. A fundamental tool in this shape analysis is the construction and implementation of geodesic paths between shapes. We use geodesic paths to accomplish a variety of tasks, including the definition of a metric to compare shapes, the computation of intrinsic statistics for a set of shapes, and the definition of probability models on shape spaces. We demonstrate this approach using three applications: (i) automated clustering of objects in an image database according to their shapes, (ii) interpolation of heart-wall boundaries in echocardiographic image sequences, and (iii) a study of shapes of human silhouettes in infrared surveillance images.

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