Photomotion

Shape from shading uses a single light source, i.e., one image as input, to recover the shape information [4, 10, Traditional shape from shading techniques, using a single image, do not reconstruct accurate surfaces and have difficulty 17]. It has the advantage that it requires the least amount with shadow areas. Traditional shape from photometric stereo of input; however, this also introduces disadvantages. One techniques have the disadvantage that they need all of the input disadvantage is that since it has less image information images together at once to minimize the total cost, and this available, it is less accurate. At each pixel, intensity proprocess must be restarted if new images become available. To vides only one constraint; however, the description of surovercome the shortcomings of the above two techniques, we face shape (surface gradient, or surface normal) requires introduce a new technique called shape from photomotion. two parameters. Therefore, many shape from shading techShape from photomotion uses a series of 2-D Lambertian input niques introduce additional constraints, such as smoothimages, generated by moving a light source around a scene, to ness of surface, and use optimization methods to estimate recover the depth map. In each of the input images, the object shape. Another disadvantage is that since it employs only in the scene remains at a fixed position and the only variable is the light source direction. The movement of the light source a single image, shape from shading will not be able to causes a change in the intensity of any given point in the provide a complete description of a scene with shadow image. The change in intensity is what enables us to recover areas. Some methods also have problems when the scene the unknown parameter, the depth map, since it remains conis illuminated from the side. stant in each of the input images. This configuration is suitable To overcome some of the above problems, shape from for iterative refinement through the use of the extended Kalman photometric stereo was introduced [2, 3, 6–8, 13, 15, 16, filter. Our novel method for computing shape is a continuous 18]. The main idea behind photometric stereo is to take form of the photometric stereo technique. It significantly differs multiple images of a scene with different light source direcfrom photometric stereo in the sense that the shape estimate tions for each image, while keeping the viewing direction will not only be computed for each light source orientation, constant. Each image of the scene provides one constraint but also gradually be refined by photomotion. Since the camera on the surface shape. Hence, multiple images of the same is fixed, the mapping between the depths at various light source scene create an overconstrained system, which is solved locations is known; therefore, this method has an advantage over those which move the camera (egomotion) and keep the for the surface shape. Shape from photometric stereo comlight source fixed. Results of this method are presented for bines all of the input information together in order to sequences of synthetic and real images.  1996 Academic Press, Inc. minimize total cost. This method can only be used to compute shape of the areas which receive light from all of the light sources.