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Synopsis
One of the most natural representations for modelling spatial objects in computers is discrete representations in the form of a 2D square raster and a 3D cubic grid, since these are naturally obtained by segmenting sensor images. However, the main difficulty is that discrete representations are only approximations of the original objects, and can only be as accurate as the cell size allows. If digitisation is done by real sensor devices, then there is the additional difficulty of sensor distortion. To overcome this, digital shape features must be used that abstract from the inaccuracies of digital representation. In order to ensure the correspondence of continuous and digital features, it is necessary to relate shape features of the underlying continuous objects and to determine the necessary resolution of the digital representation.
This volume gives an overview and a classification of the actual approaches to describe the relation between continuous and discrete shape features that are based on digital geometric concepts of discrete structures.
Audience: This book will be of interest to researchers and graduate students whose work involves computer vision, image processing, knowledge representation or representation of spatial objects.
Booknews
At a graduate and research level, describes the relationship between two pictorial representations of real objects, the discrete and the continuous. Examines the properties of both representations thoroughly and makes them explicit in the form of predicates, a process that can be seen as mapping from an analogical representation to a propositional representation in the form of symbolic descriptions. Draws on standard Euclidean geometry and topology for the mathematical tools necessary to describe the continuous representations, and on graph theory for the discrete representations. Explores the graph- based, axiomatic, embedding, and digitization approaches. Annotation c. by Book News, Inc., Portland, Or.