Reconstruction of 3D objects Based on images is useful in many applications. One of the methods Based on multi-image data is the Photometric Stereo technique relying on several photographs of the observed object from the same point of view, each one taken under a different illumination condition. The common approach is to estimate the gradient field of the surface by minimizing a functional, integrating the distance from the camera and thereby obtaining the geometry of the observed object. We propose an alternative method that consists of a novel differential approach for multi-image Photometric Stereo and permits a direct solution of a novel PDE Based model without going through the gradient field while naturally dealing with shadowed regions. The mathematical well-posed ness of the problem in terms of numerical stability yields a fast algorithm that efficiently converges, even for pictures of sizes in the order of several mega pixels affected by noise.