The Shape From Shading Problem Given a grayscale image And albedo And light source direction Reconstruct scene geometry Can be modeled by surface normals
The Shape From Shading Problem ▪ Given a grayscale image ➢And albedo ➢And light source direction ▪ Reconstruct scene geometry ➢Can be modeled by surface normals
Lambertian Surface Appears equally bright from all viewing directions Reflects all light without absorbing Matte surface, no" spots Brightness of the surface as seen from camera is linearly correlated to the amount of light falling on the surface Here we will discuss only Lambertian surfaces under point-source illumination
Lambertian Surface ▪ Appears equally bright from all viewing directions ▪ Reflects all light without absorbing ▪ Matte surface, no “shiny” spots ▪ Brightness of the surface as seen from camera is linearly correlated to the amount of light falling on the surface Here we will discuss only n Lambertian surfaces under point-source illumination
Some notations Surface Orientation A smooth surface has a tangent plane at every point az Mark p af ,gay Parametrize surface orientation by first partial derivatives of z q p Z ×y δX
Some Notations: Surface Orientation
Some notations Surface Orientation Surface normal Tx=(p,0,1),y=(0,q,1) n2=7x×7y=(P,q,-1) Normalize n= n1_(p.q,-1) p2+q2+1 az az ax, av goy po3 Z ×y δX
Some Notations: Surface Orientation
Reflectance Map Relationship between surface orientation and brightness Lambertian surface R(p,q)=n· 1+psp+ qs q 1+p2+q2√1+p32+qs2 Image irradiance(brightness)is proportional to r I(x,y)=r(p, g
Reflectance Map ▪