# Catalogue of Artificial Intelligence Techniques

## Curvature Maps

**Keywords:**
Gaussian curvature, mean curvature, principal curvature, umbilic point

### Categories: Vision

Author(s): **R.M. Cameron-Jones**

The representation of the curvatures of an image considered as a surface--usually applied to depth maps. The normal curvature of a surface at a point reaches its maximum and minimum, the principal curvatures, at directions in the surface which are perpendicular. At an umbilic point, e.g., on a plane or sphere, the normal curvature is independent of direction. The Gaussian curvature (frequently denoted ), the product of the principal curvatures, and the mean curvature (frequently denoted ), the mean of the principal curvatures, may be used to classify the surface type into perceptually significant categories according to their sign.

### References:

- Besl, P. and Jain, R.,
*Intrinsic and Extrinsic Surface Characteristics*,*IEEE CS Conference on Computer Vision and Pattern Recognition*, 1985, pp.226--233.

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