Ellipsoidal Path Connections for Time-gated Rendering

During the last decade, we have been witnessing the continued development of new time-of-flight imaging devices, and their increased use in numerous and varied applications. However, physics-based rendering techniques that can accurately simulate these devices are still lacking: while existing algorithms are adequate for certain tasks, such as simulating transient cameras, they are very inefficient for simulating time-gated cameras because of the large number of wasted path samples. We take steps towards addressing these deficiencies, by introducing a procedure for efficiently sampling paths with a predetermined length, and incorporating it within rendering frameworks tailored towards simulating time-gated imaging. We use our open-source implementation of the above to empirically demonstrate improved rendering performance in a variety of applications, including simulating proximity sensors, imaging through occlusions, depth-selective cameras, transient imaging in dynamic scenes, and non-line-of-sight imaging.

We broadly classify ToF rendering tasks into two categories. The first category includes tasks such as simulating continuous-wave time-of-flight cameras, which accumulate all photons with a weight that depends on their time of travel; as well as transient cameras, which aggregate all photons but separate them into a sequence of images, each recording contributions only from photons with a specific time of travel. Existing steady-state rendering algorithms remain efficient for simulation tasks in this category, as the majority of paths they generate will have a non-zero contribution, regardless of their path length. Tasks in this category have generally been the main focus of previous research on ToF rendering; for instance, Jarabo et al.~\cite{jarabo2014framework} improve rendering performance by introducing path-sampling schemes and reconstruction techniques tailored to the transient imaging setting.

The second type of ToF rendering tasks involves simulating images that accumulate contributions only from a small subset of photons, whose time of travel is within some narrow interval. These time-gated rendering tasks arise in a large number of practical situations; examples include time-gated sensors used as proximity detectors, gated laser ranging cameras, as well as situations where transient imaging is performed in dynamic scenes such as outdoors environments or tissue with blood flow. Unfortunately, existing rendering algorithms cannot be used for efficient time-gated rendering: the vast majority of the paths generated by these algorithms end up being rejected, for having length outside the narrow range accumulated by the simulated sensor.