Single-view Perspective Shape-from-Texture with Focal Length Estimation: A Piecewise Affine Approach

We present a new formulation to the well known problem of shape-from-texture from a single image by casting the task as a multi-plane based camera pose estimation problem. Our first contribution is methodological: we show that by using a piecewise affine model, instead of a perspective one, we can avoid the numerical instabilities in the estimation of the surface pose compared with the full-perspective model, yet retaining high accuracy. Our second contribution is to show that the information provided by a smooth textured surface makes it possible to perform shape-fromtexture and camera focal length calibration jointly. This advances state-of-the-art where a calibrated camera is nearly always assumed in order to compute 3D shape from a single image. We validate both these contributions on simulated and real image data.