System and method for rendering images using a Russian roulette methodology for evaluating global illumination

摘要

A computer graphics system generate a pixel value for a pixel in an image to simulate global illumination represented by an evaluation of an unknown function f of the form $f\left(x\right)=g\left(x\right)+{\int }_0^{1}K\left(x,y\right)f\left(y\right)dy,$ g(x) and K(x,y) known functions, with K(x,y) a "kernel" including a function associated with at least two colors. An estimator generator module generates "N" estimators f⁽ⁿ⁾_lds,RR(x) as ${\stackrel{\_}{f}}_{\mathrm{lds},\mathrm{RR}}^{\left(n\right)}\left(x\right)=g\left(x\right)+K\left(x,{\mathrm{xi}}_1^{\left(n\right)}\right)S_1^{\left(n\right)}+K\left(x,{\mathrm{xi}}_2^{\left(n\right)}\right)S_2^{\left(n\right)}+K\left(x,{\mathrm{xi}}_3^{\left(n\right)}\right)S_3^{\left(n\right)}+\cdots ,\mathrm{or}$ $f_{\mathrm{lds},\mathrm{RR}}^{\left(n\right)}\left(x\right)=g\left(x\right)+T_1^{\left(n\right)}\left(x\right)g\left({\mathrm{xi}}_1^{\left(n\right)}\right)+T_2^{\left(n\right)}\left(x\right)g\left({\mathrm{xi}}_2^{\left(n\right)}\right)+T_3^{\left(n\right)}\left(x\right)g\left({\mathrm{xi}}_3^{\left(n\right)}\right)+\cdots ,\mathrm{where}$ $S_1^{\left(n\right)}:=g\left({\mathrm{xi}}_1^{\left(n\right)}\right),S_{j+1}^{\left(n\right)}:=\frac{\mathrm{Theta}\left(M_{K\left({\mathrm{xi}}_{j+1}^n,{\mathrm{xi}}_j^{\left(n\right)}\right),S_j^{\left(n\right)}}-{\mathrm{xi}}_j^{\text{'}\left(n\right)}\right)}{M_{K\left({\mathrm{xi}}_{j+1}^n,{\mathrm{xi}}_j^n\right),S_j^{\left(n\right)}}}K\left({\mathrm{xi}}_{j+1}^n,{\mathrm{xi}}_j^n\right)S_j^{\left(n\right)},\mathrm{and}$