Revisiting the Scale Loss Function and Gaussian-Shape Convolution for Infrared Small Target Detection

Hao Li; Man Fung Zhuo

cs.CVApr 11, 2026

Revisiting the Scale Loss Function and Gaussian-Shape Convolution for Infrared Small Target Detection

Authors: Hao Li, Man Fung Zhuo

Organizations: Department of Electrical and Computer Engineering, University of Arizona, Tucson, USA

Abstract

Infrared small target detection still faces two persistent challenges: training instability from non-monotonic scale loss functions, and inadequate spatial attention due to generic convolution kernels that ignore the physical imaging characteristics of small targets. In this paper, we revisit both aspects. For the loss side, we propose a diff-based scale loss that weights predictions according to the signed area difference between the predicted mask and the ground truth, yielding strictly monotonic gradients and stable convergence. We further analyze a family of four scale loss variants to understand how their geometric properties affect detection behavior. For the spatial side, we introduce Gaussian-shaped convolution with a learnable scale parameter to match the center-concentrated intensity profile of infrared small targets, and augment it with a rotated pinwheel mask that adaptively aligns the kernel with target orientation via a straight-through estimator. Extensive experiments on IRSTD-1k, NUDT-SIRST, and SIRST-UAVB demonstrate consistent improvements in $mIoU$ , $P_d$ , and $F_a$ over state-of-the-art methods. We release our anonymous code and pretrained models.

Figures & tables

Figure 1: Comparison between our monotonic diff-based scale loss and conventional non-monotonic scale losses. The proposed diff-based loss exhibits strict monotonicity with respect to scale deviation, stably penalizing mismatches between predicted and ground-truth target areas and naturally guiding optimization toward the optimal center, thus eliminating unstable gradients and ensuring stable convergence during training. In contrast, the var-based scale loss exhibits non-monotonic behavior, creating multiple local optima and erratic gradients that hinder stable convergence to the correct target scale.

Figure 2: Illustration of the Gaussian-like intensity distribution inherent to IRSTs. As shown, small targets exhibit a distinct center-concentrated, smoothly decaying grayscale pattern, which motivates the design of Gaussian-shaped spatial attention or convolution to align with this natural imaging characteristic, rather than using generic fully learned receptive fields.

Figure 3: Illustration of the directional morphological diversity of IRSTs. As shown, IRSTs exhibit varied directional structures (horizontal, vertical, or oblique point-like/elongated shapes), which motivates the use of learnable rotated pinwheel masks to adaptively align spatial attention with target orientation, complementing Gaussian-shaped convolution to better match the diverse directional properties of small targets.

Figure 4: Overview of the proposed framework. The U-Net encoder–decoder backbone applies channel attention and Gaussian-shaped spatial attention within each residual block. The $7\times 7$ spatial attention kernel is constructed by combining a Gaussian prior (learnable $\sigma$ ) with a learnable rotated pinwheel mask whose orientation $\theta$ is optimized via a straight-through estimator, as illustrated in the upper branch. The final prediction is supervised by the diff-based scale loss against the ground-truth mask.

Figure 5: Visualization of the four scale weighting functions. Each row corresponds to one variant (Diff-based, Var-based, Mobius, Var-denominator). Left : contour map over the $(A_{p},A_{t})$ plane. Middle : 3D surface. Right : anti-diagonal cross-section with $A_{p}+A_{t}=10$ , showing the weight value as $A_{p}$ varies. Only the Diff-based weight decays strictly and monotonically away from $A_{p}=A_{t}$ , while the Var-based weight is non-monotonic.

Methods	IRSTD-1k			NUDT-SIRST			SIRST-UAVB
Methods	mIoU $\uparrow$	$P_{d}\uparrow$	$F_{a}\downarrow$	mIoU $\uparrow$	$P_{d}\uparrow$	$F_{a}\downarrow$	mIoU $\uparrow$	$P_{d}\uparrow$	$F_{a}\downarrow$
ACM	57.03	93.27	65.28	64.40	93.12	55.22	18.46	69.24	11.08
DNANet	66.38	90.91	12.24	76.47	97.31	14.13	23.96	63.72	15.11
UIU-Net	66.66	93.98	22.07	78.09	96.77	12.54	26.84	66.57	7.38
MTU-Net	63.24	93.27	36.80	77.54	93.97	46.95	25.74	65.49	8.82
SCTransNet	68.15	93.27	10.74	80.69	95.71	16.52	27.33	74.34	8.87

Table 1: Comparison on IRSTD-1k, NUDT-SIRST, and SIRST-UAVB. IoU and

P_{d}

are reported in percentage (%), and

F_{a}

is reported in

\times 10^{-6}

. Higher is better for IoU and

P_{d}

, while lower is better for

F_{a}

Figure 6: Qualitative segmentation comparison. Each row shows one test scene. Zoomed insets highlight the target region. Green pixels indicate true positives, red pixels indicate false positives, and yellow pixels indicate false negatives. L1-GP-Rotated consistently produces clean segmentation masks with fewer false alarms and missed detections compared to competing methods.

Figure 7: 3D prediction heatmap comparison. Each bar represents a detected blob: green bars are true detections at the correct location, red bars are false alarms. L1-GP-Rotated yields a single clean green bar aligned with the ground-truth target, demonstrating significantly better false alarm suppression.

Conv Module	YOLOv8n Detection							RetinaNet Detection
	IRSTD-1K			SIRST-UAVB			Params	IRSTD-1K			SIRST-UAVB
	$P$	$R$	mAP50	$P$	$R$	mAP50	Params	$P$	$R$	mAP50	$P$	$R$	mAP50
Conv	88.0	80.6	85.9	83.9	79.9	83.6	3.048	8.2	21.8	31.3	12.6	23.9	46.7
DySConv	87.9	79.4	85.8	87.7	83.7	88.1	3.117	23.5	35.3	66.7	36.2	48.2	84.4
DWConv	81.2	74.4	77.6	78.5	51.1	59.6	2.660	23.4	34.5	69.2	36.8	48.0	86.4
DSConv	79.8	75.7	80.6	90.6	92.3	94.3	2.796	23.4	35.0	70.1	37.1	48.1	86.5

Table 2: Plug-and-play comparison of convolution modules on YOLOv8n and RetinaNet across IRSTD-1K and SIRST-UAVB.

P

: precision (%),

R

: recall (%), mAP50 (%), Params: total parameters (M).

Methods	IRSTD-1k			NUDT-SIRST
Methods	mIoU $\uparrow$	$P_{d}\uparrow$	$F_{a}\downarrow$	mIoU $\uparrow$	$P_{d}\uparrow$	$F_{a}\downarrow$
MSHNet (LLOSS-ONLY-GP)	60.94	90.48	12.22	77.13	92.16	23.59
MSHNet (L1-ONLY-GP)	64.87	92.52	20.42	81.38	95.75	16.24
MSHNet (L1-GP)	68.98	93.20	9.95	82.55	97.42	16.16
MSHNet (L1-GP-Rotated)	69.19	94.22	7.67	82.86	97.40	20.89

Table 3: Effect of location loss on

F_{a}

. mIoU and

P_{d}

in %;

F_{a}

\times 10^{-6}

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Infrared small target detection (IRSTD) remains challenging due to tiny target size, low signal-to-noise ratio, severe foreground-background imbalance, and blurred boundaries in complex scenes. Existing methods usually rely on post-activation probability-domain supervision for discrimination, where weak targets and strong clutter may produce saturated and close probabilities, limiting weak-target discrimination. Meanwhile, blurred boundaries and halo-like predictions mainly stem from thermal diffusion, tiny target scale, boundary uncertainty, and insufficient explicit contour constraints. To address these issues, we propose Adaptive-Contrastive SLSIoU (AC-SLSIoU), a plug-and-play discriminative and shape-aware loss for IRSTD. Specifically, a Logit-Domain Margin Constraint (LDMC) is introduced to enlarge the response gap between targets and informative hard negatives in the logit space, thereby enhancing weak-target discrimination. Adaptive Boundary Suppression (ABS) applies scale-aware annular penalties to refine target contours and suppress halo-like overflow responses. In addition, False-Alarm Focal Loss assigns larger weights to high-probability negative samples, further penalizing persistent high-confidence false alarms. Without introducing extra inference overhead, the proposed method can be seamlessly integrated into existing detectors and consistently improves both detection accuracy and shape quality. Extensive experiments and cross-backbone evaluations demonstrate the effectiveness, robustness, and generalization ability of the proposed method for infrared small target detection.

Abstract

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