Linear shape from shading

Simple example illustrating the linear shading approximation:

(with Edward Adelson, MIT)

Range image (left), rendered with Lambertian shading (right):

Linear, quadratic, and higher order shading components:

Linear shape from shading, applied to Lambertian image (left) and linearly shaded image (right):

We see that the effect of the linear component of shading often dominates the reconstructed shape. The resulting shape from shading algorithm is very simple: one essentially applies the linear inverse filter to the linear shading derivative filter.

Linear shape from shading, using steerable pyramid:

The steerable pyramid offers a simple, biologically plausible method to compute the shape of an input image, assuming linear shading. Decompose the input image into a steerable pyramid. Steer the coefficients, according to the assumed light direction. Reconstruct the pyramid, replacing coefficient values perpendicular to the light direction with the steerable Hilbert transformed coefficients.

References