Implementation of a Single Photo Shape from Shading Method for the Automatic Dtm Generation

This research work is concerned with the implementation of a shape from shading (SFS) technique for automatically generating a digital terrain model (DTM) using a single digitized aerial photograph of a terrain area with low signal (information) content. The mathematical model for the SFS is established based on the fact that the pixel’s gray level variations in image space are proportional to the shading intensity variations of the terrain morphology. The terrain shades in its turn is the function of the illumination intensity and the direction of the incident light with respect to the local surface orientation as well as the incident light direction and the terrain albedo. In this project the Lambertian model is utilized for modeling the terrain reflectivity property. The implemented SFS algorithm is then tested with the simulated and the real data. The simulated data was generated using a predefined bilinear surface and for the real data, an aerial photograph of a smoothed hilly terrain with low information content was chosen. The rmse for the reconstructed surface for the simulated data and the real data were estimated to be equal to ± 3 cm and ± 4 m respectively. This means that the gray shade values are also significantly influenced by the other factors such as the non-uniform terrain albedo, atmosphere, etc., which have not been included into our SFS functional model. It should also be mentioned that our implemented SFS model for the real data was accompanied by a preprocessing stage by which the influential noise was significantly reduced. INTRODUCTION Digital image matching is a automatic method for the reconstruction of object surface information from the gray values of digital images. For the automatic derivation of object heights it is usually necessary to estimate the positions of conjugate points in all images. A necessary prerequisite to obtain a reliable solution when performing digital image matching is the presence of sufficient, non-periodic image texture. However, not all images fulfill this demand. Furthermore, if only a single image of the object is available, digital image matching can not be applied. It is necessary to investigate surface reconstruction method which allow for the estimation of object surface parameters from images with poor texture and from single images. Shape from shading(SFS) is one of these methods, that it directly relates image gray values to inclination of the corresponding surface patch relative to the direction of illumination and direction to the imaging sensor. Shape from shading has been investigate in different research area: Computer Vision, Photogrammetry and Astrogeology. In Computer Vision SFS has been developed for surface reconstruction in close range images(e.g. Zhang et al., 1999; Tsai and Shah, 1994; Lee and Kuo 1993)and in Photogrammetry, SFS has been studied for DTM reconstruction or refinement (Heipke et al. 2000 ). In the field of Asterogeology, SFS has been developed for the geometric reconstruction of planetary surfaces(Davis and Soderblom 1984). This paper is concerned with the implementation of a SFS technique for automatically generating a digital terrain model(DTM) using a single digitized aerial photograph of a terrain area with low signal(information) content.