Patent ID: 6888960

Claim:
A method to calculate an element R(x,y) of a viewpoint-independent spatial covariance matrix of a given object in a database for infinitely dense sampling of illumination conditions, the method comprising: calculating E(u x ,u y ,c), an integral over all possible light directions, weighted by their respective intensities, according to the equation: E ( u x ,u y ,c )=âˆ« nÎµS 2 L ( n ) D ( n,p,q ) where nÎµS 2 is a particular direction on the unit sphere, S 2 , where L is the light intensity and n is a normal vector on the unit sphere S 2 , where u x and u y are the unit vectors of the special coordinate system defined by p and q, where p and q are vectors in which the x-axis is the bisector of the angle, 2Î¸, between them, where p=(c,+s,0) and q=(c,âˆ’s,0), where c=cos Î¸, s=sin Î¸, and (x,y) is the image point; solving for the viewpoint-independent spatial covariance matrix R(x,y) according to the equation: R ( x,y )=Î±( x )Î±( y ) E ( u x ,u y ,c ) where Î±(x) is the intrinsic reflectance at the image point x and Î±(y) is the intrinsic reflectance at the image point y; and tabulating and storing the result of said viewpoint-independent spatial covariance matrix R(x,y).