Shape from texture from a multi-scale perspective

The problem of scale in shape from texture is addressed. 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. A novel mechanism for automatic scale selection is proposed, based on normalized derivatives. It is used for adaptive determination of the two scale parameters in a multi-scale texture descriptor, the windowed second moment matrix, which is de ned in terms of Gaussian smoothing, rst order derivatives, and non-linear pointwise combinations of these. The same scale-selection method can be used for multi-scale blob detection without any tuning parameters or thresholding. The resulting texture description can be combined with various assumptions about surface texture in order to estimate local surface orientation. Two speci c 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.