Development of 3D surface reconstruction by the images triad based on the Lambertian reflection model

A method for reconstructing the surface of an object using on a series of images based on the Lambertian model of light reflection is proposed. The original images are obtained by the method of photography under natural lighting. The model parameters are determined by changing the position of the light source using additional shading and the stable position of the receiver. The series contains a triad of images obtained from different directions of illumination and a shaded image of the surface of the reconstruction object. In the first stage, the derived surfaces of the reconstruction object are reconstructed. The next step is the accumulation of derivatives and determination of the surface height of the reconstruction object. To simplify the complexity of the practical implementation of the 3D-reconstruction a pyramid layout is chosen. The photography of the triad of images of the pyramid is done before noon, at noon and in the afternoon. The information about the triad and the shadowed image of the pyramid surface enters the processing system, where the directions of the photograph lighting are first determined. The parameters of the lighting directions are determined based on data on the height of the Sun at its upper culmination on the day and the time of the photo shoot. The procedure for determining the elevation of the Sun on a particular day of the year has been implemented. Calculated lighting direction data and image information using the Lambertian model of light reflection are reconstructed into horizontal and vertical derivatives. As a result of the discrete accumulation of derivatives, the pyramid surface is reconstructed.