Fig. 1 A classification of the applications of control variate techniques in rendering

Fig. 2 Equal-time comparison of different components of reference [11] direct illumination sampling method in a scene with over 5 000 lights and high occlusion ((a) Proportional; (b) Scalable; (c) ML (overfitting); (d) MAP for mean; (e) d + MAP for variance; (f) e + regression; (g) f + visibility model; (h) g + control variate)

Fig. 3 Comparison of diffuse hair-like fiber rendering ((a) With control variates; (b) Without control variates)[15]

Fig. 4 Results of using spherical harmonic control variate sampling in fur production rendering[15]

Fig. 5 Outgoing radiance produced by twotypes of light ((a) Polygon light; (b) Portal-masked environment)[20]

Fig. 6 Equal-sample comparison of trained light selection (Trained) and different combinations of defensive light selection techniques ((a) Uniform; (b) NoMax)[22]

Fig. 7 Equal-time comparison in many-light selection application ((a) Reference [23]; (b) Reference [11])

Fig. 8 Illustration of a progressive hierarchical solver based on path tracing[27]

Fig. 9 Reconstruction results of single-color-channel radiance estimates ((a) Stored in the directional grid; (b) Reconstructed using B-splines)[29]

Fig. 10 Flowchart of CRESPO et al.’s [32] method for a one-dimensional integration problem ((a) Original integrand and PDF; (b) Map integrand to primary space; (c) Select region with highest error; (d) Subdivide and update; (e) Final piecewise control variate; (f) Monte Carlo sample of the residual)

Fig. 11 Comparison flowchart of SALAüN et al.’s[33] method and the MC method for a one-dimensional integration problem ((a) Original integrand; (b) Sampling; (c) Constant function fitting; (d) Analytic integration; (e) Polynomial function fitting; (f) Summation)

Fig. 12 Figure from reference [35] ((a) Neural control variate; (b) Residual neural fitting; (c) Heuristic termination)

Fig. 13 Four processes after ray enters medium ((a) Absorption; (b) Out-scattering; (c) In-scattering; (d) Emission)

Fig. 14 Virtual medium particles alter the density but do not change the radiance or the direction of rays[41]

Fig. 15 Figure from reference [42] ((a) Original medium;(b) Homogeneous control component; (c) Heterogeneous residual component)

Fig. 16 The decomposed tracking method constructs partially free paths (yellow segments) in heterogeneous media without evaluating spatially varying collision parameters[42]

Fig. 17 Illustration of the application of control variates in reference[44] ((a) Original extinction coefficient; (b) Control extinction coefficient; (c) Residual extinction coefficient)

Fig. 18 Reference [47] estimate transmittance by truncating the power series (here with order N=3)

Fig. 19 Performance comparison of different methods in procedurally generated cloud scenes ((a) Reference [49]; (b) Reference [44]; (c) Reference [42]; (d) Reference [40])

Fig. 20 The online adaptive sampling framework designed by reference [51] (Including three modules: sample count estimation, control variate coefficient estimation, and estimation history update)

Fig. 21 Visualization of dynamic weight changes of recursive control variates during the optimization process[54]