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AxisQ: Depth-Adaptive Channel--Frequency Quantization for Camouflaged Object Detection

Chi Ruan, Tianqi Li, Xin He, Xue Geng, Ming-Ming Cheng, Yun Liu

arXiv:2610.36844v1cs.CV

TL;DR

Low-bit PTQ for COD must preserve weak foreground and boundary cues, but existing methods typically use one allocation domain across hierarchical backbones. AxisQ adapts allocation from channels in shallow features to local-frequency bands in deep features under a fixed per-layer average-bit budget. At W2A2, it reports higher mean weighted F-measure than the best competing results across four benchmarks for both evaluated models.

  • Problem

    COD depends on weak texture and boundary cues, while existing PTQ methods typically retain one precision-allocation domain throughout hierarchical backbones.

    Source: §1 · p. 1

  • Method

    AxisQ allocates precision across shallow-stage channels and deep-stage local-frequency bands under a fixed per-layer average-bit budget, using COD-aware sensitivity and boundary-aware reconstruction.

    Source: §1 · p. 2

  • Results

    At W2A2, AxisQ improves mean weighted F-measure over the best competing results by 6.6% on CFRN and 21.5% on CamoFormer-P across four benchmarks.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Experiments across COD models, benchmarks, and precision settings support the effectiveness of mixed-domain allocation for COD quantization.

    Source: §5 · p. 9

    The study evaluates low-bit COD quantization using publicly available benchmarks.

    Source: ETHICS STATEMENT · p. 10

Abstract

from arXiv · show

Camouflaged object detection (COD) depends on weak texture and boundary cues that can be destroyed by aggressive post-training quantization (PTQ). Existing PTQ methods mainly optimize quantizers or reconstruct network blocks, while using a single precision-allocation domain throughout hierarchical backbones. Instead, we introduce AxisQ, a depth-adaptive bit-allocation framework motivated by the observation that the useful allocation axis changes with feature depth. Under a fixed per-layer average activation-bit budget, AxisQ allocates precision in the channel domain for shallow features and in the local-frequency domain for deep features, using COD-aware sensitivity to better preserve subtle foreground regions and ambiguous boundaries. We also formulate a boundary-aware Hessian approximation for reconstruction by incorporating boundary-weighted gradient and error statistics. Experiments across multiple COD models and diverse benchmarks demonstrate improved accuracy over the strongest baselines at low bit widths, with relative weighted F-measure gains of 12.7% for CFRN and 33.3% for CamoFormer-P on CAMO under W2A2 quantization. These results support adapting the allocation domain to feature depth as a transferable quantization strategy for hierarchical COD models.

1 INTRODUCTION

Low-bit quantization can erase weak foreground and boundary cues that COD depends on, while prior PTQ methods typically retain one precision-allocation domain across model depth. AxisQ adapts that domain to feature depth and reports improved COD accuracy under W2A2.

1 INTRODUCTION

  • Prior PTQ methods typically use one precision-allocation domain throughout the model, leaving its suitability across shallow and deep features less explored.The question matters because low-bit calibration error can erase the cues distinguishing camouflaged foreground from background.Source: §1 · p. 1
  • Sensitivity is more concentrated across channels in shallow features and across local-frequency bands in deep features, motivating different allocation domains by depth.The selected-image analysis reports that 17 S2 bands and two S4 bands account for 80% of DCT sensitivity.Source: §1 · pp. 1–2, Figure 2 · p. 3
  • At W2A2, AxisQ improves mean weighted F-measure over the best competing results by 6.6% on CFRN and 21.5% on CamoFormer-P across four benchmarks.These are the introduction's reported cross-benchmark gains.Source: §1 · p. 2
  • AxisQ assigns activation precision across shallow-stage channels and deep-stage local-frequency bands under a fixed per-layer average-bit budget.Label-assisted empirical-Fisher costs guide channel sensitivity, and reverse water filling with exact budget correction assigns channel bits.Source: §1 · p. 2
  • For local-frequency allocation, AxisQ derives a positive-semidefinite COD-GGN cost that balances foreground and background while emphasizing multi-scale boundaries and uncertain pixels.The cost uses one first-order probe per layer and calibration batch.Source: §1 · p. 2

2 RELATED WORK

Related work spans COD methods for recovering concealed targets, PTQ methods for calibrating quantizers or reconstructing network outputs, and sensitivity-aware approaches that account for unequal quantization effects. AxisQ explores depth-dependent allocation domains for hierarchical features.

Camouflaged object detection

  • COD approaches progressed from localization and search frameworks to methods combining multi-scale, frequency, or Transformer-based context and spatial detail.The cited examples include ZoomNet, FDCOD, HitNet, and CamoFormer.Source: §2 · p. 3

Post-training quantization

  • PTQ work addresses quantization through calibration, layer- or block-level reconstruction, and methods tailored to Vision Transformer attention and normalization.Examples include AdaRound, BRECQ, QDrop, PTQ4ViT, FQ-ViT, and RepQ-ViT.Source: §2 · p. 3

Sensitivity-aware quantization

  • Sensitivity-aware methods use curvature or information-importance measures for precision allocation and reconstruction, while COD-TDQ constrains token-group ranges to protect weak boundary cues.The passage describes Hessian-, Fisher-, least-squares-curvature-, and task-aware approaches.Source: §2 · p. 3

AxisQ overview

  • AxisQ distinguishes itself by using channel allocation in shallow stages and local-frequency allocation in deep stages of a hierarchical encoder.Its overview also depicts channel-wise and frequency-wise activation-bit assignments and an auxiliary boundary-aware Hessian approximation.Source: Figure 3 · p. 4, §2 · p. 4

3 METHOD

AxisQ adapts activation-bit allocation to feature depth, using channels in shallow stages and local-frequency bands in deep stages under a fixed per-layer average-bit budget. Task-aware costs guide allocation, followed by shared blockwise reconstruction with an optional boundary-aware extension.

3. METHOD

  • The method addresses low-bit suppression of weak foreground and boundary cues by changing the precision-allocation domain from channels in shallow features to local frequencies in deep features.The framework’s allocation branches are followed by a shared reconstruction stage.Source: §3.1 · p. 4, §3 · p. 4

3.1 DEPTH-ADAPTIVE MIXED-DOMAIN ALLOCATION

  • Stages 1–2 allocate bits across channels, while stages 3–4 allocate across block-DCT local-frequency bands, with the stage partition fixed before calibration.Frequency allocation takes precedence when both branches apply; assignments are frozen before shared blockwise reconstruction.Source: §3.1 · p. 4

3.2 TASK-SENSITIVE CHANNEL-BIT ALLOCATION

  • Label-assisted empirical-Fisher costs estimate channel sensitivity, and reverse water filling with exact budget correction gives sensitive channels more bits while meeting each layer’s target average precision.The channel score uses first derivatives and 64 ground-truth masks, retaining within-channel interactions but ignoring cross-channel interactions.Source: §3.2 · p. 5

3.3 COD-GGN TASK-AWARE FREQUENCY ALLOCATION

  • Deep-stage frequency allocation combines coefficient reconstruction error with COD-GGN sensitivity, penalizing errors more in COD-sensitive directions.The task metric balances foreground and background mass and emphasizes multi-scale boundaries and uncertain predictions; calibration costs are discarded after assignments are frozen.Source: §3.3 · p. 6

3.4 BOUNDARY-AWARE RECONSTRUCTION

  • The boundary-aware reconstruction extension reweights gradient and error statistics before Hessian fitting, giving greater weight to locally varying predictions while leaving AdaRound, QDrop, and final-logit BCE unchanged.The weights derive from teacher predictions, so this extension requires no additional segmentation labels.Source: §3.4 · p. 6

4 EXPERIMENTS

The experiments evaluate AxisQ on multiple COD models, benchmarks, and precision settings, then test its allocation choices and reconstruction components. Results favor AxisQ across low- and higher-precision comparisons, while ablations examine depth-specific allocation and boundary-focused reconstruction.

4.1 EXPERIMENTAL SETUP

  • Evaluation uses four standard COD test sets and compares quantized methods on both models, with additional precision settings evaluated on CFRN.Metrics include structural similarity, weighted F-measure, alignment, maximum F-measure, and MAE; higher is better except for MAE.Source: §4.1 · p. 7

4.2 QUANTITATIVE RESULTS

  • At W2A2, AxisQ leads all 20 dataset–metric comparisons on CFRN and 19 on CamoFormer-P; CAMO weighted F-measure exceeds the best competing result by 0.082 and 0.125, respectively.The comparisons span both backbones and four COD benchmarks.Source: §4.2 · p. 7, Table 1 · p. 8
  • At W4A4, AxisQ is best in 33 of 40 dataset–metric comparisons and tied for best in the other seven, with smaller margins than at W2A2.Its strong position holds across both models and all four datasets.Source: §4.2 · pp. 7–8, Table 1 · p. 8
  • AxisQ raises mean weighted F-measure over the W2A2 LS-ViT baseline by approximately 0.104 on CamoFormer-P and 0.045 on CFRN, whose FP32 means are relatively close.CamoFormer-P has the larger drop under the W2A2 LS-ViT baseline.Source: §4.2 · p. 8
  • On CFRN, AxisQ improves 94 of 100 dataset–metric comparisons across precision settings, including all comparisons at W2A2, W3A3, and W4A4.The allocation hyperparameters are shared across settings; with weights fixed at two bits, mean weighted F-measure gains remain positive as activation precision rises from two to four bits.Source: §4.2 · p. 8, Table 2 · p. 9

4.3 ABLATION STUDIES AND ALLOCATION ANALYSIS

  • At W2A2, the mixed-domain no-GGN variant improves macro weighted F-measure by 0.025 over the stronger frequency-only control, exceeding that control’s 0.013 gain over baseline.The accompanying reduction in MAE supports an overall improvement in prediction quality.Source: §4.3 · p. 8, Table 3 · p. 9
  • CFRN’s W2A2 assignments mostly retain two bits for shallow channels, while deep frequency maps vary more, generally favoring lower frequencies and suppressing some high-frequency bands.Each displayed layer averages exactly two bits; S3 and S4 maps differ with layer-specific calibration costs.Source: Figure 4 · p. 9, §4.3 · p. 9
  • The full configuration improves structural agreement and prediction alignment while reducing pixel-wise error; boundary-weighted reconstruction shows a similar pattern on CFRN W2A4 on CHAMELEON.The improvements over no-GGN favor the complete design.Source: §4.3 · p. 9

5 CONCLUSION

AxisQ adapts activation-precision allocation to feature depth and uses COD-aware sensitivity with a boundary-aware Hessian approximation. Experiments across COD models, benchmarks, and precision settings demonstrate the mixed-domain allocation’s effectiveness.

5 CONCLUSION

  • Experiments across COD models, benchmarks, and precision settings demonstrate the effectiveness of AxisQ’s mixed-domain allocation.The framework allocates across shallow channels and deep local-frequency bands under a fixed per-layer average-bit budget.Source: §5 · p. 9
  • AxisQ combines Empirical-Fisher channel costs and COD-aware frequency costs with an auxiliary boundary-aware Hessian approximation for reconstruction.The approximation incorporates boundary-weighted gradient and error statistics.Source: §5 · p. 9
  • The work studies low-bit COD quantization using publicly available benchmarks and involves no human-subject studies or new personal data.The authors flag potential surveillance and military uses as warranting consideration.Source: ETHICS STATEMENT · p. 10
  • Implementation and configuration files document calibration data, precision settings, reconstruction, and evaluation commands for all four COD benchmarks.Source: REPRODUCIBILITY STATEMENT · p. 10

A EXPECTATION OF THE COD-GGN PROBE

The COD-GGN probe transfers teacher-derived output weights to layer activations through a random probe and first-order backpropagation. Its DCT-basis sensitivity estimate guides coefficient-error costs while omitting cross-coordinate curvature interactions.

A EXPECTATION OF THE COD-GGN PROBE

  • COD-GGN transfers teacher-derived output weights to layer activations using a random probe and a vector–Jacobian product via first-order backpropagation.This avoids explicitly forming the Jacobian or Hessian.Source: A EXPECTATION OF THE COD-GGN PROBE · p. 13
  • For a fixed calibration image, the probe holds the model and teacher weights fixed and takes expectation over independent Rademacher entries.Each entry is equally likely to be −1 or +1, with zero mean and identity covariance.Source: A EXPECTATION OF THE COD-GGN PROBE · p. 13
  • In the orthonormal block-DCT basis, squared probe components estimate diagonal curvature and weight coefficient-error costs, omitting cross-coordinate interactions.The expected matrix is positive semidefinite because the teacher weights are nonnegative.Source: A EXPECTATION OF THE COD-GGN PROBE · p. 13

B DETAILED GAINS OVER MATCHED BASELINES

Detailed matched-baseline comparisons show gains across most metric and dataset–precision comparisons, with the pattern varying by metric and precision setting.

B DETAILED GAINS OVER MATCHED BASELINES

C FIXED HYPERPARAMETERS AND QUANTIZATION SCOPE

The main mixed-domain runs use shared calibration, reconstruction, and allocation settings. Activation precision is an exact per-layer average over eligible units, while allocation and quantization scope varies by layer type and stage.

C FIXED HYPERPARAMETERS AND QUANTIZATION SCOPE

  • The main mixed-domain experiments share calibration, reconstruction, and allocation settings, with the reconstruction component study following a separate Appendix D protocol.Source: C FIXED HYPERPARAMETERS AND… · p. 14
  • Stated activation precision is an exact per-layer average over eligible channels or frequency bands, although individual units may receive different bit widths.Source: C FIXED HYPERPARAMETERS AND… · p. 14
  • Fisher allocation covers eligible non-frequency Conv/Linear paths including the decoder; DCT allocation covers frequency-eligible stage 3–4 Linear layers.Zero-bit bands are suppressed, patch-embedding activations remain A8, and unwrapped operations follow the reconstruction baseline.Source: C FIXED HYPERPARAMETERS AND… · p. 14

D BOUNDARY-RECONSTRUCTION COMPONENT PROTOCOL

The CFRN W2A4 reconstruction comparison isolates local boundary weighting while holding the calibration checkpoint and adaptive iteration counts fixed. The table reports results with and without those weights.

D BOUNDARY-RECONSTRUCTION COMPONENT PROTOCOL

  • Both CFRN W2A4 runs restore the same calibration checkpoint and use identical adaptive iteration counts across 35 blocks, totaling 153,800 iterations.The shared teacher BCE uses pixel weights 1 + 10| AvgPool9(p) −p|, normalized within each image.Source: D BOUNDARY-RECONSTRUCTION COMPONENT… · p. 14
  • Only the boundary-weighted variant adds local Hessian weighting, using αrec = 2 and kernels 7/5/3 for patch embedding and stages 1/2.The caption identifies the comparison as with versus without local boundary weights.Source: D BOUNDARY-RECONSTRUCTION COMPONENT… · p. 14, Table 6 · p. 14
  • With local boundary weights, the reported values change from .897/.841 to .901/.844.The table concerns historical CFRN W2A4 reconstruction on CHAMELEON; its caption lists Sα, F w β, Eϕ, F m β, and MAE as metrics.Source: D BOUNDARY-RECONSTRUCTION COMPONENT… · p. 14, Table 6 · p. 14

E W4A4 DEPLOYMENT PERFORMANCE

On CamoFormer-P, the fused W4A4 path reaches 88.6 FPS under CUDA Graph replay, with reported speedups over both the quantization simulation and FP32 reference. The packed-W4 prototype is slower but also exceeds the simulation speed, while both implementations retain comparable segmentation accuracy.

E W4A4 DEPLOYMENT PERFORMANCE

  • 88.6 FPS (11.28 ms) for fused W4A4 CamoFormer-P is 3.33× faster than the PyTorch quantization simulation and 1.52× faster than the FP32 reference.The reported latency reductions are 70.0% and 34.1%, respectively; the comparison is under CUDA Graph replay on an RTX 5090.Source: E W4A4 DEPLOYMENT PERFORMANCE · p. 15
  • The packed-W4 integer-GEMM prototype reaches 62.7 FPS, a 2.36× speedup over the quantization simulation.Both deployment paths reuse saved AxisQ bit assignments and quantization parameters without recalibration or reconstruction.Source: E W4A4 DEPLOYMENT PERFORMANCE · p. 15
  • On 250 CAMO test images, fused W4A4 achieves F w β = 0.8164 and Sα = 0.8670 versus 0.8179 and 0.8679 for the quantized reference.The packed-W4 prototype achieves F w β = 0.8191 and Sα = 0.8691; both implementations retain comparable segmentation accuracy.Source: E W4A4 DEPLOYMENT PERFORMANCE · p. 15
  • The fused path caches quantized weights, fuses Q/DQ, retains DCT/IDCT, and uses FP16 GEMM; packed W4 unpacks weights into INT8 registers for Tensor Core products with INT32 accumulation.The packed path covers 205 Linear layers and 76 pointwise convolutions, with FP16 outputs and remaining operators.Source: E W4A4 DEPLOYMENT PERFORMANCE · p. 15
  • Timing averages five rounds of 100 complete forwards after 30 warm-ups, using batch size 1 and 384 × 384 inputs on an RTX 5090.Measurements include channel gathering, padded computation, Q/DQ, DCT/IDCT, decoder, and prediction heads; I/O and preprocessing are excluded.Source: E W4A4 DEPLOYMENT PERFORMANCE · p. 15

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