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Section 6.5 Shape from Texture 187

FIGURE 6.18: From left to right and top to bottom: Camera JPEG output, Adobe
Camera Raw, DxO Optics Pro, and LSSC. Reprinted from “Non-local Sparse Models for
Image Restoration,” by J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman, Proc.
International Conference on Computer Vision, (2009). c 2009, IEEE.

6.5 SHAPE FROM TEXTURE
A patch of texture viewed frontally looks very different from the same patch viewed
at a glancing angle because foreshortening causes the texture elements (and the gaps
between them!) to shrink more in some directions than in others. This suggests
that we can recover some shape information from texture, at the cost of supplying
a texture model. This is a task at which humans excel (Figure 6.19). Remarkably,
quite general texture models appear to supply enough information to infer shape.

6.5.1 Shape from Texture for Planes
If we know we are viewing a plane, shape from texture boils down to determining
the configuration of the plane relative to the camera. Assume that we hypothesize
a configuration; we can then project the image texture back onto that plane. If
we have some model of the “uniformity” of the texture, then we can test that
property for the backprojected texture. We now obtain the plane with the “best”