A new perspective [on] shape-from-shading

Shape-from-shading (SFS) is a fundamental problem in computer vision. The vast majority of research in this field have assumed orthography as its projection model. This paper reexamines the basis of SFS, the image irradiance equation, under an assumption of perspective projection. The paper also shows that the perspective image irradiance equation depends merely on the natural logarithm of the depth function (and not on the depth function itself), and as such it is invariant to scale changes of the depth function. We then suggest a simple reconstruction algorithm based on the perspective formula, and compare it to existing orthographic SFS algorithms. This simple algorithm obtained lower error rates than legacy SFS algorithms, and equated with and sometimes surpassed state-of-the-art algorithms. These findings lend support to the assumption that transition to a more realistic set of assumptions improves reconstruction significantly.