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# Description of Three Dimensional Structures

The recognition of complex objects cannot be based on raw image data because of its quantity and inappropriate level of representation. What reduces the data to a manageable level is the process of feature description, that produces symbolic assertions such as "elongation(S,1.2)" or "shape(S,flat)".

Besides providing the data compression that makes recognition computationally tractable, description allows recognition processes to be more independent of the specific type of raw data, thus promoting generality. It may also simplify relationships; for example, an apple is approximately described as a "reddish spheroid".

One might ask: "What is the distinction between recognition and description?", because recognition also reduces sets of data to descriptions. We would be more inclined to say an image curve is "described as straight" than is "recognized as a straight line", whereas the reverse would apply to a person's face. Thus, one criterion is simplicity - descriptions represent simple, consistent, generic phenomena. They are also more exact - "convex" allows approximate local reconstruction of a surface fragment, whereas "face" can hardly be more than representative.

If a description is dependent on a conjunction of properties, then it is probably not suitable for use here (e.g. a "square" is a "curve" with equal length "side"s, each at "right angle"s). Hence, another criterion is general applicability, because "straight" is a useful description to consider for any boundary, whereas "square" is not.

The descriptions presented here are simple unary and binary three dimensional properties of curves, surfaces and volumes such as curvature, area or relative orientation. They are not reducible to subdescriptions (i.e. they are not structured). Because we have three dimensional range data available, it is possible to directly compute these properties, as contrasted to the difficulties encountered when using two dimensional intensity data (though two dimensional data is also useful). The use of three dimensional data also allows richer and more accurate descriptions.

Pattern recognition techniques often estimate properties from two dimensional projections of the structures, but cannot always do so correctly, because of the information lost in the projection process. To overcome this, some researchers have exploited constraints available from the real properties of objects, such as the relationship between area and contour [38], from assuming that curves are locally planar [154] or by assuming that a surface region is a particular model patch [66].

Some of the properties considered below are viewpoint invariant. These properties are important because they further the goal of viewpoint independent recognition. Moreover, the key invariant properties are local (e.g. curvature) as compared to global (e.g. area), because objects in three dimensional scenes are often partially obscured, which affects global properties.

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Next: Some Three Dimensional Structural Up: From Surface To Objects: Previous: Discussion
Bob Fisher 2004-02-26