Specular Manifold Bisection Sampling for Caustics Rendering

We propose Specular Manifold Bisection Sampling (SMBS), an improved version of Specular Manifold Sampling (SMS) [ZGJ20]. SMBS is inspired by the small and large mutations in Metropolis Light Transport (MLT) [VG97]. While the Jacobian Matrix of the original SMS method performs well in local convergence (the small mutation), it might fail to find a valid manifold path when the ray deviates too much from the light or bounces from a complex surface. Our proposed SMBS method adds a large mutation step to avoid such a problematic convergence to the local minimum. The results show SMBS can find valid manifold paths in fewer iterations and also find more valid manifold paths. In scenes with complex reflective or refractive surfaces, our method achieves nearly twice or more improvement when measured in manifold walk success rate (SR) and root mean square error (RMSE).