Integration of Digital Image Matching and Multi Image Shape from Shading

Classical shape from shading (SFS) is based on the analysis of the intensity values of a single digital image in order to derive three dimensional information of the depicted scene. It involves the orthographic projection for the transformation from object to image space and has been successfully applied to weakly textured images. In general the illumination conditions must be known, Lambertian reflection and constant albedo must be assumed for the object surface, and only surface slopes can be determined. Digital image matching for photogrammetric processing on the other hand needs at least two images of the same scene taken from different view points and the images must be well textured. Therefore, the two methods are complementary to each other, and a combined model should yield better results than any of the two separate ones. In this paper a new global approach is presented integrating digital image matching and multi image SFS in object space. In a least squares adjustment the unknowns (geometric and radiometric parameters of the object surface) are estimated from the pixel intensity values and control information. The perspective projection is used for the transformation from object to image space. The approach is investigated using synthetic images. The main results of this study are the following: Heights of a digital terrain model (DTM) or a digital surface model (DSM) instead of surface slopes can be calculated directly using multi image SFS alone or the combined approach (in this paper the term "DTM" den~tes a classical DTM as well as a DSM). There is no need for conjugate points in the multi image SFS approach. This is especially important, 832 since in weakly textured images the correspondence problem is extremely hard to solve due to the lack of large image intensity gradients. If variable albedo is present in parts of the object surface only the combined approach yields correct results. Multi image SFS and digital image matching alone fail in this case.