US 6,529,193 B1Granted

System and method for generating pixel values for pixels in an image using strictly deterministic methodologies for generating sample points

AssigneeMental Images GmbH

InventorsRolf Herken, Martin Grabenstein

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Abstract

A computer graphics system and a method for generating pixel values in an image of objects using strictly-deterministic low-discrepancy sequences as sample points for evaluating integrals which are used to simulate a number of computer graphic techniques including soft shadows, simulation of depth of field, motion blur, jittering, and global illumination. Unlike the random numbers used in connection with the Monte Carlo technique, the low discrepancy sequences ensure that the sample points are evenly distributed over a respective region or time interval, thereby reducing clumping of such sample points. The invention facilitates the generation of images of improved quality when using the same number of sample points at the same computational cost as in the Monte Carlo technique.

Claims10

Dependent claims

A computer graphics system for generating a pixel value for a pixel in an image, the pixel being representative of a point {right arrow over (x)} in a scene, the computer graphics system generating the pixel value to simulate global illumination that is represented by an evaluation of a function f(x) over a sphere centered at the point in the scene, the function f(x) having the form f(x)=g(x)+∫K(x,y)f(y)dy, where f(x) (and similarly f(y)) is an unknown function, and g(x) and K(x,y) are known functions, with K(x,y) serving as a “kernel” of the integral, the computer graphics system comprising:

A. an estimator generator for generating a selected number “N” of estimators f(n)RR(x) as
fRR(n)=g(x)+Θ(K(x,ξ1(n))−ξ′1(n))g(ξ1(n))+Θ(K(x,ξ1(n))−ξ′1(n))Θ(K(ξ1(n),ξ2(n))−ξ′2(n))g(ξ2(n))+Θ(K(x,ξ1(n))−ξ′1(n))Θ(K(ξ1(n),ξ2(n))−ξ′2(n))Θ(K(ξ2(n),ξ3(n))−ξ′3(n))g(ξ3(n))+ . . .
where Θ(x) represents the Heaviside function, and ξ1(n), ξ′1(n), ξ2(n), ξ′2(n), . . . , ξL(n), ξ′L(n), represent components of a predetermined multi-dimensional strictly deterministic low-discrepancy sequence and where “n” denotes a sequence index, the estimator generator generating successive terms for each estimator f(n)RR(x) until it generates a term having the value zero;
B. a luminance value generator for generating a luminance value for the point in the scene as the average of said estimator values generated by said estimator generator;
and
C. a pixel value generator for using the luminance value generated for the point in the scene in generating the pixel value.

3 more elements

A computer graphics method for generating a pixel value for a pixel in an image, the pixel being representative of a point {right arrow over (x)} in a scene, the pixel value being generated so as to simulate global illumilnation that is represented by an evaluation of an integral over a sphere centered at the point in the scene, the integral having the form f(x)=g(x)+∫K(x,y)f(y)dy, where f(x) (and similarly f(y)) is an unknown function, and g(x) and K(x,y) are known functions, with K(x,y) serving as a “kernel” of the integral, the computer graphics system comprising:

A. generating a selected number “N” of estimators f(n)RR(x) as
fRR(n)=g(x)+Θ(K(x,ξ1(n))−ξ′1(n))g(ξ1(n))+Θ(K(x,ξ1(n))−ξ′1(n))Θ(K(ξ1(n),ξ2(n))−ξ′2(n))g(ξ2(n))+Θ(K(x,ξ1(n))−ξ′1(n))Θ(K(ξ1(n),ξ2(n))−ξ′2(n))Θ(K(ξ2(n),ξ3(n))−ξ′3(n))g(ξ3(n))+ . . .
where Θ(x) represents the Heaviside function, and ξ1(n), ξ′1(n), ξ2(n), ξ′2(n), . . . , ξL(n), ξ′L(n), represent components of a predetermined multi-dimensional strictly deterministic low-discrepancy sequence and where “n” denotes a sequence index, the estimator generator generating successive terms for each estimator f(n)RR(x) until it generates a term having the value zero;
B. generating a luminance value for the point in the scene as the average of said estimator values;
and
C. using the luminance value generated for the point in the scene in generating the pixel value.

3 more elements

Dependencies are inferred from the claim text.