# Scene reconstruction from ray tracing simulation

## Context

In optics, acoustics, or telecommunications, there are many methods to estimate the power of a received signal, depending on the position of the transmitter, that of the receiver, and the geometry of the scene. Among these methods, ray tracing has gained a particular interest in recent years, especially thanks to advances in terms of computing power.

Ray tracing is quite simple to understand: from an emitting source (e.g., a light source, a speaker or a radio antenna), one traces a very large number of rays going in all directions. Each time we encounter an obstacle, we apply a specular reflection1, and we continue until we reach the receiver. If a ray has not reached the target after a fixed number of bounces, it is abandoned. The method described here is similar to ray launching, one of the many ray tracing variants.

## Problem

As one may notice, the number of rays that arrive to the receiver is much lower than the number of rays sent. Our question is the following: can we infer some parameters of the scene just by looking at the rays that we receive?

Of course, the answer to this question depends on the parameters you know apriori, and those you need to infer. The next section will detail the objectives we thought about.

## Objectives

For this Master thesis, we propose the following steps2:

1. From a known 2D scene, a fixed number of reflections, and a known antenna pattern3, show how you can determine the emitter’s location from the set of rays received at the receiver (what are the necessary conditions in this setting for this to work?);
2. Study the sparsity / scaristy of the number of rays received, depending on the emitter’s position, or the antenna pattern (i.e., very directive vs omnidirectionnal);
3. Do the same as (1), but the unkown is now the reflection coefficient of some wall(s) in the scene;
4. Study how uncertainty on some parameter (e.g., you know the position of the receiver with a precision of 1cm) impacts your estimation of unknown parameters;
5. Can you infer more information about the emitter (e.g., its radiation pattern) from the knowledge of the scene’s response to a set of known emitter configurations?
• Ray Tracing Gems from Nvidia (url)
• Book chapter about sound propagation (url)
• Fast and simple algorithm to detect object shadowing (url)

## References

• [1] Chandak, A., Antani, L., Taylor, M., & Manocha, D. (2011). Fast and Accurate Geometric Sound Propagation Using Visibility Computations. Building Acoustics, 18(1–2), 123–144. (doi)
• [2] Geok, T. K., Hossain, F., & Chiat, A. T. W. (2018). A Novel 3D Ray Launching Technique for Radio Propagation Prediction in Indoor Environments. PLOS ONE, 13(8), e0201905. (doi)
• [3] Liu, S., & Manocha, D. (2022). Sound Propagation. In S. Liu & D. Manocha (Eds.), Sound Synthesis, Propagation, and Rendering (pp. 29–43). Cham: Springer International Publishing. (doi)
• [4] Marrs, A., Shirley, P., & Wald, I. (Eds.). (2021). Ray Tracing Gems II: Next Generation Real-Time Rendering with DXR, Vulkan, and OptiX. Berkeley, CA: Apress. (doi)

1. We could also account for refraction, diffraction, and so on. ↩︎

2. Note that this is not fixed, and you are welcome to propose modifications in the proposal. ↩︎

3. That is, how the rays are emitted. The simplest one is omnidirectionnal (same power regardless of the angle of departure). ↩︎