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Photon counting lidar has become an invaluable tool for 3D depth imaging dueto the fine-precision it can achieve over long ranges. However, high framerate, high resolution lidar devices produce an enormous amount oftime-of-flight (ToF) data which can cause a severe data processing bottleneckhindering the deployment of real-time systems. In this paper, an efficientphoton counting approach is proposed that exploits the simplicity of piecewisepolynomial splines to form a hardware-friendly compressed statistic, or aso-called spline sketch, of the ToF data without sacrificing the quality of therecovered image. As each piecewise polynomial spline is a simple function withlimited support over the timing depth window, the spline sketch can be computedefficiently on-chip with minimal computational overhead. We show that apiecewise linear or quadratic spline sketch, requiring minimal on-chiparithmetic computation per photon detection, can reconstruct real-world depthimages with negligible loss of resolution whilst achieving $95\%$ compressioncompared to the full ToF data, as well as offering multi-peak detectionperformance. These contrast with previously proposed coarse binning histogramsthat suffer from a highly nonuniform accuracy across depth and can failcatastrophically when associated with bright reflectors. Further, by buildingrange-walk correction into the proposed estimation algorithms, it isdemonstrated that the spline sketches can be made robust to photon pile-upeffects. The computational complexity of both the reconstruction and range walkcorrection algorithms scale only with the size of the spline sketch which isindependent to both the photon count and temporal resolution of the lidardevice.

Spline Sketches: An Efficient Approach for Photon Counting Lidar