3,变分与泛函方法应用.pdfVIP

变分与泛函方法应用 Hongxin Zhang 2007-06-28 State Key Lab of CADCG, ZJU 主要内容 Shape from shading Kernel methods Shape from X Many cues can be used for inferring object shapes from images. Based on the number of images used, there are two categories of methods: methods using multiple images methods using a single image. A list of so called shape-from-X algorithms are shown in the following table. Shape from texture (a) image of a plane covered by a deterministic texture. (b) the same texture on a curved surface Shape from shading Shape can be recovered from a single image by human visual system based on the shading information To estimate the shape from a single image, some assumptions have to be made, e.g. constant albedo (surface color) This technique is very useful for reconstructing surfaces of planets from photographs acquired by spacecrafts two images of the same Lambertian surface seen 3D rendering of the surface from above but illuminated from different directions Shape from shading - Example Reflectance of a Lambertian surface The radiance at a 3D point is proportional to the cosine of the angle between the surface normal and the direction of the illuminant L (P) Rρ,i ρ iin ρis called the effective albedo(反照率）: the real albedo times the intensity of illuminant Illuminance 照度 Luminance 亮度 Intensity 强度，光强 Fundamental equation for shape from shading The pixel intensity at p =[x , y ]T is ⎛ ⎞2 d 4 E (P) L (P) ⎜ ⎟ cos α f ⎝ ⎠ Assumptions: If we neglect the constant term and if we assume the optical system has