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

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

cs.CVOct 27, 2026

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

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

Organizations: SpinEntropy · Nankai University · Tianjin University of Technology · I2R, A*STAR

Abstract

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.

Figures & tables

Figure 1: Qualitative comparison of quantization methods on two COD models at W2A2. Model A is CFRN, and Model B is CamoFormer-P. Each pair of rows corresponds to one model, with IoU reported for each prediction against the ground-truth mask. The compared methods show incomplete foreground regions and false detections in the background. In these examples, AxisQ recovers more complete object shapes and clearer boundaries while reducing background false positives.

Figure 2: Depth-dependent sensitivity on a selected COD image. (a) shows the input and ground-truth mask, and (b) shows independently normalized S2 and S4 feature responses. In (c), 17 bands in S2 and two in S4 account for 80% of DCT sensitivity. (d) plots cumulative sensitivity above uniform versus the percentage of top-ranked channels or frequency bands, with separate vertical scales. Sensitivity is more concentrated across channels in S2 and across frequency bands in S4, supporting channel-wise allocation in shallow stages and local-frequency allocation in deep stages.

Figure 3: Overview of AxisQ for a four-stage hierarchical encoder. Channel-domain allocation is used in shallow and eligible non-frequency paths, while deep encoder features use local-frequency allocation. The strip and grid visualize channel-wise and frequency-wise activation-bit assignments at W2A2; darker orange indicates higher precision, and gray denotes zero-bit bands. (d) sketches the auxiliary boundary-aware Hessian approximation using teacher-derived boundary weights and weighted gradient statistics.

CFRN
	CAMO					CHAMELEON					COD10K					NC4K
Method	$S_{\alpha}$ $\uparrow$	$F_{\beta}^{w}$ $\uparrow$	$E_{\phi}$ $\uparrow$	$F_{\beta}^{m}$ $\uparrow$	MAE $\downarrow$	$S_{\alpha}$ $\uparrow$	$F_{\beta}^{w}$ $\uparrow$	$E_{\phi}$ $\uparrow$	$F_{\beta}^{m}$ $\uparrow$	MAE $\downarrow$	$S_{\alpha}$ $\uparrow$	$F_{\beta}^{w}$ $\uparrow$	$E_{\phi}$ $\uparrow$	$F_{\beta}^{m}$ $\uparrow$	MAE $\downarrow$	$S_{\alpha}$ $\uparrow$	$F_{\beta}^{w}$ $\uparrow$	$E_{\phi}$ $\uparrow$	$F_{\beta}^{m}$ $\uparrow$	MAE $\downarrow$
FP32	.876	.843	.932	.877	.042	.912	.874	.959	.898	.020	.870	.794	.937	.835	.022	.888	.849	.939	.880	.030
W4A4
RepQ-ViT	.676	.608	.750	.656	.099	.701	.622	.774	.672	.067	.676	.549	.779	.599	.062	.718	.651	.783	.691	.072
COD-TDQ	.813	.723	.864	.795	.070	.861	.759	.906	.825	.040	.802	.650	.864	.737	.038	.836	.746	.883	.816	.052

Table 1: Quantitative comparison on CFRN and CamoFormer-P across four COD benchmarks at W4A4 and W2A2. FP32 denotes the full-precision reference. Bold indicates the best quantized results within each model and precision setting.

Table 5

Figure 4: Actual CFRN W2A2 bit assignments in the first attention-output projection of each encoder stage. Channels retain their original order; frequency maps use DCT coordinates. Every shown layer averages two bits. Gray indicates suppressed, zero-bit bands.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	Dataset	$\Delta S_{\alpha}$	$\Delta F_{\beta}^{w}$	$\Delta E_{\phi}$	$\Delta F_{\beta}^{m}$	$\Delta$ MAE
W2A2	CAMO	+.052	+.082	+.067	+.062	-.017
	CHAMELEON	+.025	+.044	+.051	+.023	-.009
	COD10K	+.011	+.030	+.026	+.020	-.003
	NC4K	+.010	+.025	+.023	+.016	-.005
W2A3	CAMO	+.017	+.026	+.019	+.024	-.005
	CHAMELEON	+.001	+.001	+.006	.000	.000

Appendix

Table 4: Per-dataset metric changes of AxisQ relative to the precision-matched baseline, rounded to three decimal places.

Item	Value
Input resolution	$384\times 384$
Calibration / reconstruction images	128 / 1,024
Fisher image–mask pairs / frequency images	64 / 16
Reconstruction iterations	20,000 per block
Reconstruction method	Least-squares Hessian + AdaRound + QDrop
QDrop probability / temperature	0.5 / 20

Appendix

Table 5: Configuration used for the main mixed-domain runs.

Table 9

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When W4A4 Breaks Camouflaged Object Detection: Token-Group Dual-Constraint Activation Quantization

Tianqi Li, Wenyu Fang, Xin He, Xue Geng+2

VCIP, College of Computer Science, Nankai University · School of Computer Science and Engineering, Tianjin University of Technology · Institute for Infocomm Research, A*STAR+2

4-Bit Quantization Activation Quantization Post-Training Quantization Camouflaged Object Detection

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Camouflaged object detection (COD) segments objects that intentionally blend with the background, so predictions depend on subtle texture and boundary cues. COD is often needed under tight on-device memory and latency budgets, making low-bit inference highly desirable. However, COD is unusually hard to quantize aggressively. We study post-training W4A4 quantization of Transformer-based COD and find a task-specific cliff: heavy-tailed background tokens dominate a shared activation range, inflating the step size and pushing weak-but-structured boundary cues into the zero bin. This exposes a token-local bottleneck -- remove cross-token range domination and bound the zero-bin mass under 4-bit activations. To address this, we introduce COD-TDQ, a COD-aware Token-group Dual-constraint activation Quantization method. COD-TDQ addresses this token-local bottleneck with two coupled steps: Direct-Sum Token-Group (DSTG) assigns token-group scales to suppress cross-token range domination, and Dual-Constraint Range Projection (DCRP) projects each token-group clip range to keep the step-to-dispersion ratio and the zero-bin mass bounded. Across four COD benchmarks and two baseline models (CFRN and ESCNet), COD-TDQ consistently achieves an

S_α

score more than 0.12 higher than that of the state-of-the-art quantization method without retraining. The code is available at https://github.com/MCG-NKU/nku-model-compre.

Abstract

Post-Training Quantization

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