K T Aakash Ajit supervised by Prof. Narayanan P J received  his doctorate in  Computer Science and Engineering (CSE). Here’s a  summary of his research work on Efficient Physically Based Rendering with Analytic and Neural Approximations:

Path tracing is ubiquitous for photorealistic rendering of various real-world appearances. It follows the principles of light transport adapted from physics, which describe light propagation as a set of integral equations. These equations are stochastically evaluated by tracing light rays in virtual scenes. Such stochastic evaluations with ray-tracing form the bulk of the path tracing algorithm, which is widely used in the industry.

Stochastic evaluations in path tracing converge to the correct answer in time that is proportional to the inverse square root of the number of iterations. This coupled with the fact that the underlying integrals are often complex and high dimensional results in large compute complexity. Research efforts have thus largely focused on accelerating path tracing by improving the stochastic sampling processes. However, it is interesting to look at efficient analytic approximations by making reasonable assumptions on the nature of these light transport integrals. Such analytic methods have the potential to achieve zero variance at the outset. Practically, they are often used in conjunction with stochastic methods thereby achieving lower variance than the fully stochastic counterparts.

 The primary focus of this thesis is to develop new (semi-)analytic methods and improve existing ones to accelerate direct lighting computations in path tracing. Specifically, we base our research on Linearly Transformed Cosines (LTC) which is a well-known semi-analytic method for real-time direct lighting. LTCs produce plausible renderings by building on the principles of light transport from the ground up and have proved useful for tasks other than real-time rendering as well. We make the following three contributions that either build on LTCs or improve it.

We first explore fully-analytic direct lighting for arbitrarily shaped area lights, built on LTCs at the core. Due to assumptions of the LTC method, it can only handle polygonal area lights. Furthermore, rendering shadows with LTCs require stochastic evaluations- our contribution here relaxes these assumptions, enabling fully-analytic direct lighting with shadows from an arbitrary shaped area light. We show that our method achieves plausible and noise-free renderings compared to semi-analytic LTCs and ground truth ray-tracing, given equal compute budget.

Our second contribution improves the LTC formulation by relaxing an assumption that restricts their usage to isotropic GGX reflection functions. Isotropic GGX restricts the kind of reflectance that can be modeled, ultimately restricting the visual fidelity of rendering with LTCs. We identify the core issues that prevent the use of anisotropic GGX, and propose solutions for each. Our contribution not only benefits (semi-)analytic rendering with LTCs but also other related methods that use LTCs at their core.

In our third contribution, we extend the theory of Linearly Transformed Spherical Distributions (LTSDs), which are a superset of and core to LTCs, to work with phase functions. This enables us to analytically compute in-scattered radiance, which we build on to semi-analytically render single scattering. Like the original LTC method, we ground our derivations and formulations on the Volume Rendering Equation (VRE) which paves the way for plausible photorealistic renderings despite the biased nature of our method. In effect, our work enables semi-analytic volumetric rendering with area lights.

 Another focus of this thesis is to accelerate path tracing computations with neural approximations. Path tracing poses a challenge for (semi-)analytic methods as the underlying integrals become increasingly more complex and high-dimensional. In this setting, it is beneficial to use a neural network to approximate parts of these complex integrals for improved efficiency. Previous works have demonstrated the usage of neural networks in this manner, however their main focus was on scenes with relatively shorter light paths. We instead focus on scenes where longer paths are required for accurate rendering. More specifically, we tackle the problem of accelerating multiple scattering computations in hair using neural networks.

The contributions of this thesis range from exploring analytic and semi-analytic methods to neural approximations for physically based rendering. Moreover, our contributions advance the state of the art, in terms of efficiency, fidelity and capability. We believe our work can inspire further research in computer graphics and adjacent fields.

July 2025