Surfaces in range image understanding
Surfaces in range image understanding
Solid shape
Representation and recognition of surface shapes in range images: a differential geometry approach
Computer Vision, Graphics, and Image Processing
COSMOS-A Representation Scheme for 3D Free-Form Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Support Cone: A Representational Tool for the Analysis of Boundaries and Their Interactions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Error in Curvature Computation on Multi-Scale Free-Form Surfaces
International Journal of Computer Vision
3D object recognition: Representation and matching
Statistics and Computing
Gauss map computation for free-form surfaces
Computer Aided Geometric Design
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Orientation-based representations (OBR's) have many advantages. Three orientation-based differential geometric representations in computer vision literature are critically examined. The three representations are the extended Gaussian image (EGI), the support-function-based representation (SFBR), and the generalized Gaussian image (GGI). The scope of unique representation, invariant properties from matching considerations, computation and storage requirements, and relations between the three representations are analyzed. A constructive proof of the uniqueness of the SFBR for smooth surfaces is given. It is shown that an OBR using any combination of locally defined descriptors is insufficient to uniquely characterize a surface. It must contain either global descriptors or ordering information to uniquely characterize a surface. The GGI as it was originally introduced requires the recording of one principle vector. It is shown in this paper that this is unnecessary. This reduces the storage requirement of a GGI, therefore making it a more attractive representation. The key ideas of the GGI are to represent the multiple folds of a Gaussian image separately; the use of linked data structures to preserve ordering at all levels and between the folds; and the indexing of the data structures by the unit normal. It extends the EGI approach to a much wider range of applications.