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Predicting High-precision Depth on Low-Precision Devices Using 2D Hilbert Curves
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Represents high-dynamic-range depth/disparity as two low-dynamic-range components of a 2D Hilbert curve so that low-bit (W8A8) DSP outputs can be decoded on CPU into higher-precision depth, also reducing quantization error.
Problem
Low-bit (INT8) quantized dense depth networks cannot represent high-dynamic-range depth precisely, and hardware such as Qualcomm Hexagon DSP or Coral TPU cannot output higher bit-width or mixed precision, so on-device depth quality degrades regardless of quantization method.
Approach
Map the scalar normalized depth/disparity onto a 2D Hilbert space-filling curve and train the full-precision DNN to predict the two (x, y) components; the quantized model outputs these low-bit components and a lookup-table post-processing on CPU inverts the mapping, adding about log2(L) bits of precision and compressing quantization error by L when errors are independent.
Key results
- On DSP, h3DispNet W8A8 reaches Abs Rel 0.93% vs 2.03% for original DispNet W8A8 (FP32 CPU 1.01%), and S_C 0.81 vs 0.58.
- Quantization error reduction of up to 4.6 times on DSP for stereo matching (about 3.1 times on CPU).
- Modified DispNet in W8A8 beats original W8A16 on quality while cutting energy by 35% and latency by 30%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Represent disparity as h3 Hilbert components instead of direct depth output | DispNet · ScanNet v2 test, W8A8 DSP | Abs Rel, %: 2.03 -> 0.93 | Helped |
| Represent disparity as h3 Hilbert components instead of direct depth output | DispNet · ScanNet v2 test, W8A8 DSP | S_C: 0.58 -> 0.81 | Helped |
| Represent disparity as h2 Hilbert components instead of direct depth output | DPT · ScanNet v2 test, W8A8 DSP | Abs Rel, %: 4.18 -> 1.12 | Helped |
| Represent disparity as h2 Hilbert components instead of direct depth output | DPT · ScanNet v2 test, W8A8 DSP | S_C: 0.52 -> 0.62 | Helped |
| Use Hilbert components and W8A8 instead of direct output with W8A16 | DispNet · ScanNet v2 test | latency, ms: 18.7 -> 12.0 | Helped |
| Use Hilbert components and W8A8 instead of direct output with W8A16 | DPT · ScanNet v2 test | latency, ms: 46.2 -> 30.4 | Helped |
| Represent disparity as h2 Hilbert components instead of direct depth output | DispNet · KITTI 2012, W8A8 DSP | EPE, px: 1.63 -> 1.09 | Helped |
| Represent disparity as h2 Hilbert components instead of direct depth output | DispNet · KITTI 2012, W8A8 DSP | D1, %: 9.95 -> 5.36 | Helped |
| Use h3 rather than h1 Hilbert curve components (ablation) | DispNet · ScanNet v2 test, W8A8 DSP | Abs Rel, %: 1.50 -> 0.93 | Helped |
| Use h2 rather than h1 Hilbert curve components (ablation) | DPT · ScanNet v2 test, W8A8 DSP | Abs Rel, %: 1.48 -> 1.12 | Helped |
| Add a Gaussian noise layer before the Hilbert component heads (ablation) | Modified models quantized with SNPE · ScanNet v2 test | quantization quality | Helped |
| Use Hilbert heatmap representation instead of direct heatmap output | Human pose estimation heatmap model · MS COCO | quantization error: 2.69 times smaller | Helped |
Surprising findings
- Hilbert-curve-based models (h2DispNet) on KITTI 2012 outperform the original FP32 DispNet (EPE 1.07 vs 1.38 px), not just the quantized version.
- For direct keypoints regression, the quantization error stays unchanged, so only the bit-width increase is obtained.
Limitations
- Requires retraining the full-precision model.
- Requires quantization errors to be bounded so the one-to-one correspondence with the curve holds.
- Evaluated only on one-stage stereo models (DispNet, DPT); iterative refinement models not covered.
Experimental setup
Datasets: ScanNet v2 Virtual KITTI 2 KITTI 2012 MS COCO
Benchmarks: ScanNet v2 KITTI 2012 MS COCO
Metrics: Abs Rel RMSE EPE D1 S_C (DCT cosine similarity) scaled MAD quantization error AP50
Baselines: DispNet W8A8 DispNet W8A16 DPT W8A8 DPT W8A16 FP16 DispNet FP16 DPT
Builds on: DispNet DPT MobileViTv3 Hilbert curve SNPE
Closest papers by meaning
- QuartDepth: Post-Training Quantization for Real-Time Depth Estimation on the Edge (CVPR 2025 · similarity 0.86)
- Uncertainty-Aware CNNs for Depth Completion: Uncertainty from Beginning to End (CVPR 2020 · similarity 0.86)
- VA-DepthNet: A Variational Approach to Single Image Depth Prediction (ICLR 2023 · similarity 0.85)
- Non-Parametric Depth Distribution Modelling Based Depth Inference for Multi-View Stereo (CVPR 2022 · similarity 0.84)
- Generalized Binary Search Network for Highly-Efficient Multi-View Stereo (CVPR 2022 · similarity 0.84)
- Depth Pro: Sharp Monocular Metric Depth in Less Than a Second (ICLR 2025 · similarity 0.83)
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