EDPHi: Equi-Depth Photon Histograms

Low-power 3D perception is useful in a wide range of computer-vision applications. Thanks to theincreasing availability of high-resolution single-photon avalanche diode (SPAD) arrays, single-photon LiDARs (SPLs) have emerged as a promising technology for 3D sensing. The conventional image formation model for an SPL involves capturing the time-varying light intensity—which we call the transient distribution—of a reflected laser pulse in the form of an equi-width (EW) histogram. Unfortunately, this approach leads to unmanageable data rates (∼gigabytes/second) with high-resolution arrays, severely limiting the applicability of SPLs in power- andbandwidth-constrained scenarios (e.g., mobile devices). We propose a radically different approach based onrace logic processing to construct equi-depth histograms with variable bin widths. This method avoids storinghigh-resolution histogram counts, thereby reducing the bandwidth requirement while maintaining similar ranging accuracy. We show simulation results with bandwidth reduction of over 100×.

Conventional methods rely on a coarsely binned equi-width (EW) histogram which suffers from strong quantization artifacts. In contrast, our method reliably captures scene distances with as few as 16 equi-depth (ED) histogram bins while achieving over 100× compression. The next figure explains the difference between EW and ED histograms.

This figures shows two types of histograms for student-age data from Dale et al.: (a) A 10-bin equi-width (EW) histogram has a single bin B3 near the peak. Many bins are close to zero and provide no useful information about the peak location. (b) A 10-bin equi-depth (ED) histogram with approximately 1000 students per bin reliably captures the shape of the peak. In this work we apply this intuition to single-photon camera data: ED histograms adaptively cluster around the transient-distribution peak providing accurate distance information with only a few bins.

(a) The binner circuit splits the incoming photon stream (SR) into an early stream (SE) and a late stream (SL) depending on transition point of a reference signal (RS) generated from a control value. (b) In this example, there are more photons in the early stream than the late stream, so the control value will decrease for the subsequent laser cycle, thus moving the transition point of RS earlier. The control value eventually settles close to the overall median.(c) An 8-bin ED histogram can be captured using a collection of 7 binners arranged in a 3-level binary tree. A binner at one stage feeds streams of early and late photon events to two binners at the next stage in the tree. (d) This example shows a transient distribution and the simulated results of an 8-bin EDH for low and high background levels. Notice that a majority of the bins cluster around the true peak location. The location of the narrowest bin provides a reliable estimate of scene distance.