What's In A Patch, I: Tensors, Differential Geometry and Statistical Shading Analysis
This work addresses illumination invariance in computer vision for shape reconstruction, but appears incremental as it builds on existing shape-from-shading methods.
The paper tackles the shape-from-shading problem by developing a linear algebraic framework using tensors and differential geometry, and shows that matching image gradients instead of intensities leads to more accurate reconstructions when illumination is incorrectly estimated, with computational validation under a Lambertian model.
We develop a linear algebraic framework for the shape-from-shading problem, because tensors arise when scalar (e.g. image) and vector (e.g. surface normal) fields are differentiated multiple times. The work is in two parts. In this first part we investigate when image derivatives exhibit invariance to changing illumination by calculating the statistics of image derivatives under general distributions on the light source. We computationally validate the hypothesis that image orientations (derivatives) provide increased invariance to illumination by showing (for a Lambertian model) that a shape-from-shading algorithm matching gradients instead of intensities provides more accurate reconstructions when illumination is incorrectly estimated under a flatness prior.