计算机视觉课件(10)

*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,Course 10 Shading,Course 10 Shading,1.Basic Concepts:,Light Source:,Radiance:the light energy,radiated from a unit area of,light source(or surface)in,a unit solid angle.,Solid angle:,If light source is a point source,the“unit area is omitted in above definition.,Illumination,:,light energy radiated or received on a unit area of surface.,For a point light source,where is the radiance of light source in the direction ;is due to the foreshorten of effective area of the surface patch in the radiation direction.,Surface:,Bi-directional reflectance distribution function(BRDF),:,BRDF of a surface is the ratio of energy radiated from a surface patch in some direction to the energy arriving at the surface from some direction.,Where -incident angle;,-emitting angle,Radiance(reflectance),:,The is the brightness of an object surface that you look at.,Imaging,:,Assume that the irradiance at a point,(X,Y),of an image plane is equal to the radiance from a corresponding surface patch,i.e.,E(X,Y)=L(x,y,z),=,This indicates that the terms of brightness,intensity and gray-level will have the same meaning as irradiance for an image.,Note:,radiance -out-going energy,irradiance-in-going energy,2.Surface Reflectance,1),Lambertain surface(Diffuse surface),in micro:rough,in macro:smooth,Def.,Lambertain surface is a kind of surface that reflects incident light equally in all directions regardless the direction of incident light.A Lambertain surface is assumed not to absorb any incident illumination.,where,I,0,-illumination of incident light.,-incident angle to surface.,Remark:For a Lambertain surface,its brightness percieved by a viewer do not relate to the position of the viewer.But the brightness is strongly related to the direction from which the light is illuminated to the surface.,2),Specula surface(mirror),3)Combinational surface:,Surface with reflectance between Lambertain and specular surfaces:,Where -weigh factor,3.,Shape from shading(Horn,1970),Assumptions:,i),Lambertain surface,ii),Parallel light source from,known,direction,iii),Orthographic projection for image,Imaging:,given the condition of light source and object surface in 3D,the intensity of each pixel in image plane can be uniquely determined.,Question:,If an image is given,can we evaluate the structure of the 3D surface?i.e.,can we find the surface normal at each surface point?How is about the illumination of light source?,Surface Orientation,:,Let a 3D surface be,z=z,(,x,y,),then,Denote,p=,q=,Surface normal,Note:,p,and,q,are the functions of 3D point,(,x,y,z,),at a surface.Under the assumption of orthographic projection,p,and,q,are also the functions of,(,X,Y,),of image,i.e.,p=p,(,x,y,)=,p,(,X,Y,),q=q,(,x,y,)=,q,(,X,Y,),Question,:,How to determine the two functions from image clue?,1)Reflectance map,Assume:Lambertain surface,E,(,x,y,),=,When image intensity is normalized by,then,On another hand,for a 3D surface,let,be surface normal;Let be incident direction of light,then,Where is called reflectance map of a 3D surface.,To solve for,p,(,x,y,),and,q,(,x,y,),we can use variation to minimize,I,(,x,y,),R,(,p,q,),2,over image plane:,Note that this is an ill-conditional problem,to solve for functions,p,=,p,(,x,y,)and,q,=,q,(,x,y,),we enforce smoothness constraint:,Thus,the minimization becomes,In discrete images:,Let,We get,So,Since and are computed from the value of the neighbor pixels of,p,(,x,y,),iterative method should be used to solve for,p,(,x,y,)and,q,(,x,y,).,For a Lambertain surface,Remark:,1)assumed incident light direction is known.,2)the choice of initial values of,p,(,x,y,),and,q,(,x,y,),is,important to get a convergence at global minimum.,4.Photometric stereo,Assume,:,i),Fixed camera position,Light source located at 3 different positions to surface,at each position,One images is obtained.,Lambertain,surface,Orthographic projection for,three images.,Let incident direction be:,i=1,2,3,Surface normal:,unknown,Image:normalized image:,From reflectance map of Lambertain:,Write,Then we have .,This is a linear equation,which can be solved by,Further reading:,In estimation of surface orientation,we need to know the direction of the illumination from light source first!,How to estimate the direction of light source from an intensity image?,-Pentlands method,-,Lee&Rosenfelds method,-,Tsai and Shahs method,-,Zheng&Chellapas method,All assume that the 3D surface is a part of share in the stage of estimation of illumination direction of light source.,