Shape from Texture and Integrability

We describe a shape from texture method that constructs a maximum a posteriori estimate of surface coefficients using both the deformation of individual texture elements — as in local methods — and the overall distribution of elements — as in global methods. The method described applies to a much larger family of textures than any previous method, local or global. We demonstrate an analogy with shape from shading, and use this to produce a numerical method. Examples of reconstructions for synthetic images of surfaces are provided, and compared with ground truth. The method is defined for orthographic views, but can be generalised to perspective views simply.