Chapter 14: Shape computation by scale-space operations

Chapter 14 in Scale-Space Theory in Computer Vision addresses the problem of scale in shape-from-texture. The need for (at least) two scale parameters is emphasized; a local scale describing the amount of smoothing used for suppressing noise and irrelevant details when computing primitive texture descriptors from image data, and an integration scale describing the size of the region in space over which the statistics of the local descriptors is accumulated.

The mechanism for scale selection outlined in chapter~13 is used for adaptive determination of the two scale parameters in a multi-scale texture descriptor, the windowed second moment matrix, which is defined in terms of Gaussian smoothing, first-order derivatives, and non-linear pointwise combinations of these. This texture description can then be combined with various assumptions about surface texture in order to estimate local surface orientation. Two specific assumptions, ``weak isotropy'' and ``constant area,'' are explored in more detail. Experiments on real and synthetic reference data with known geometry demonstrate the viability of the approach.