Using a Distance Sensor to Detect Deviations in a Planar Surface

TL;DR

This work tackles detecting deviations from a planar surface using only instantaneous, raw transient histograms from a low-cost SPAD-based time-of-flight sensor. The authors address the geometry–photometrics ambiguity by fitting a lightweight, multi-component Gaussian mixture model to a small dataset of deviation-free planar measurements after ambient-light removal and albedo normalization, and then computing a likelihood for new histograms to indicate planarity. Compared to baselines that rely on single-distance estimates, the histogram-based approach achieves higher AUROC in forward-facing and top-down obstacle detection, as well as cliff detection, demonstrating robust performance across distances and surfaces with minimal computation. The results support practical robotics applications, such as obstacle and cliff avoidance on resource-constrained platforms, while acknowledging remaining limitations from photometric–geometric ambiguity and fixed-pose assumptions, with future work aimed at broader surface modeling and pose-robustness.

Abstract

We investigate methods for determining if a planar surface contains geometric deviations (e.g., protrusions, objects, divots, or cliffs) using only an instantaneous measurement from a miniature optical time-of-flight sensor. The key to our method is to utilize the entirety of information encoded in raw time-of-flight data captured by off-the-shelf distance sensors. We provide an analysis of the problem in which we identify the key ambiguity between geometry and surface photometrics. To overcome this challenging ambiguity, we fit a Gaussian mixture model to a small dataset of planar surface measurements. This model implicitly captures the expected geometry and distribution of photometrics of the planar surface and is used to identify measurements that are likely to contain deviations. We characterize our method on a variety of surfaces and planar deviations across a range of scenarios. We find that our method utilizing raw time-of-flight data outperforms baselines which use only derived distance estimates. We build an example application in which our method enables mobile robot obstacle and cliff avoidance over a wide field-of-view.

Figures (7)

• Figure 1: Our method uses raw time-of-flight data to detect deviations from planar surfaces (e.g., objects, divots, cliffs, or walls). It is able to do so more accurately than methods that utilize on-sensor distance estimates.
• Figure 2: A low-cost distance sensor can distinguish between a flat surface and one with a small piece of heavyweight paper under controlled conditions. The effect of a change in surface photometrics caused by a change to a tile surface is much larger than the effect of a change in geometry caused by the presence of a small piece of paper on a background of the same material.
• Figure 3: Time-resolved distance sensors exhibit a fundamental ambiguity between geometry and albedo. While a geometric deviation from a flat plane does affect the histogram, a photometric deviation, in the form of a patch with a higher albedo, can affect the histogram in an identical way. This makes the detection of deviation an ill-posed problem aside from geometric variations that violate the space carving assumption. This space carving assumption is weaker at a steep angle of incidence with the plane.
• Figure 4: Surfaces (top) and obstacles (bottom) used in obstacle detection experiments.
• Figure 5: Our method outperforms baseline methods on AUROC on our forward-facing and top-down obstacle detection datasets.