RT-HDIST: Ray-Tracing Core-based Hausdorff Distance Computation

TL;DR

RT-HDIST tackles the computational bottleneck of the Hausdorff distance for large point clouds by reformulating the problem as a sequence of nearest-neighbor queries and introducing a quantized index space. The method leverages RT-cores to accelerate the broad-phase candidate search in index space, followed by a refinement step to guarantee exact results, achieving up to about $2$ orders of magnitude speedup over CPU-based state-of-the-art methods. The approach defines $H(A,B) = \max(h(A,B), h(B,A))$ with $h(A,B) = \max_{a \in A} \min_{b \in B} d(a,b)$ and bracketed radii to prune candidates, while carefully handling quantization and AABB-sphere discrepancies. Experiments across multiple GPU generations demonstrate strong performance gains with robust accuracy, enabling real-time and large-scale applications in graphics, vision, and robotics.

Abstract

The Hausdorff distance is a fundamental metric with widespread applications across various fields. However, its computation remains computationally expensive, especially for large-scale datasets. In this work, we present RT-HDIST, the first Hausdorff distance algorithm accelerated by ray-tracing cores (RT-cores). By reformulating the Hausdorff distance problem as a series of nearest-neighbor searches and introducing a novel quantized index space, RT-HDIST achieves significant reductions in computational overhead while maintaining exact results. Extensive benchmarks demonstrate up to a two-order-of-magnitude speedup over prior state-of-the-art methods, underscoring RT-HDIST's potential for real-time and large-scale applications.

Figures (6)

• Figure 1: Overview of RT-HDIST algorithm
• Figure 2: This figure illustrates the lower and upper bounds of $d(a_i, b_j)$, where $b_j$ is a target point affiliated with $b'_{xyz}$, and $a_i$ is a query point associated with $a'_i$, which was first identified at the $n$-th iteration.
• Figure 3: Processing time (log-scale) of each component of our method on RTX4080. For this analysis, we used the translation benchmark with a ratio of 0.5. The bold font in the bit count indicates the best performance case. Similar trends were observed for other benchmarks and GPUs.
• Figure 4: Results of the decimation benchmarks. The red mesh represents the original model, while the green mesh corresponds to the decimated version.
• Figure 5: Results of the translation benchmarks with a translation ratio of 0.5.