The Use of the Hough Transform in Shape-from-shading

Shape-from-shading is a challenging problem in the field of computer vision. The goal is to detect the three dimensional shape of an object when given an image of that object. The relationship between the shading information and the orientation of the object’s surface, known as the reflectance function, is used to perform this computation. The Hough transform is a statistical, probabilistic algorithm used to detect two-dimensional shapes that can be defined by algebraic functions. The parameters of these underlying functions are found from the image data. In previous work, the Hough transform has used edge points or other feature points as data, and is typically implemented by a discrete accumulator in the parameter space. The peak values in the accumulator correspond to the detected parameters of the underlying shapes. This work explores the application of the Hough transform to shape-fromshading problems. Previous work using the Hough transform has only detected two-dimensional shapes using feature points. In this work, the Hough transform is used together with the pixel intensity values to detect three-dimensional spheres from an image directly. As an example for possible applications, relighting of detected spheres is presented.