Target-Background Contrast Metric

• The Target-Background Contrast (TBC) metric is a quantitative measure that evaluates local contrast by comparing mean intensities of target and background regions using Weber’s Law principles.
• It addresses limitations of traditional metrics like Entropy and Average Gradient by explicitly penalizing background noise, thereby aligning fusion quality assessment with human perception.
• Empirical evaluations on UAV datasets demonstrate TBC’s robustness and strong correlation with subjective scores, ensuring reliable performance in complex, high-noise imaging environments.

The Target-Background Contrast (TBC) metric is a specialized image quality measure developed to address the limitations of classical no-reference fusion metrics in complex, noise-prone environments, particularly in low-altitude UAV infrared and visible image fusion. TBC quantitatively assesses the perceptual saliency of small, high-value targets amid cluttered or noisy backgrounds by capturing the relative local contrast between target regions and their immediate surroundings. This approach is grounded in Weber’s Law, emphasizing perceptual relevance over global statistical measures and explicitly penalizing fusion outputs with high background noise, thereby aligning quality assessment more closely with human judgment (Xie, 17 Dec 2025).

1. Motivation and Limitations of Traditional Metrics

No-reference image fusion evaluation in low-light, high-noise settings is hindered by the inadequacy of widely used metrics such as Entropy (EN) and Average Gradient (AG). EN, defined as

$$\mathrm{EN}(F) = -\sum_{\ell=0}^{L-1} p_\ell \log_2 p_\ell$$

where $p_\ell$ is the intensity probability mass function, is insensitive to the distinction between structured detail and random noise; pure noise increases EN to its maximum.

AG, computed as

$$\mathrm{AG}(F) = \frac{1}{MN} \sum_{x, y} \sqrt{ \frac{ (\partial_x F(x, y))^2 + (\partial_y F(x, y))^2 }{2} }$$

treats any high-frequency content, including sensor-induced noise, as desirable detail. In scenarios such as UAV night surveillance where visible-band sensors are driven to extreme gains, both EN and AG are susceptible to the “Noise Trap,” assigning maximal scores to images with amplified background noise and failing to prioritize target saliency (Xie, 17 Dec 2025).

2. Formal Definition and Mathematical Properties

TBC is built to reflect Weber’s Law by evaluating the relative, rather than absolute, luminance differences between target and background:

• Target response:

$R_t = \mu_{\mathrm{obj}} - \mu_{\mathrm{bg}}$

• Background normalization:

$R_b = \mu_{\mathrm{bg}} + \epsilon$

where $\mu_{\mathrm{obj}}$ and $\mu_{\mathrm{bg}}$ are mean pixel values over the segmented target and background masks, respectively; $\epsilon > 0$ ensures numerical stability.

The TBC score is formulated as

$$\mathrm{TBC} = \frac{\mu_{\mathrm{obj}} - \mu_{\mathrm{bg}}}{\mu_{\mathrm{bg}} + \epsilon}$$

A high TBC indicates a salient, high-contrast target; if the target is lost ($\mu_{\mathrm{obj}} \approx \mu_{\mathrm{bg}}$), TBC approaches zero or negative values; strong background noise increases $\mu_{\mathrm{bg}}$, decreasing TBC (Xie, 17 Dec 2025).

3. Algorithmic Procedure and Implementation

The computational workflow for TBC is as follows:

1. Target Mask Generation:
   • Determine the $k$-th intensity percentile $T_{\mathrm{perc}}$ of the infrared image $I_{\mathrm{ir}}$.
   • Create a binary mask $M_{\mathrm{obj}}$ where $I_{\mathrm{ir}}(x, y) \geq T_{\mathrm{perc}}$.
2. Background Mask Construction:
   • Apply morphological dilation to $M_{\mathrm{obj}}$ with a structuring element $K$.
   • Define $$M_{\mathrm{bg}} = \mathrm{Dilate}(M_{\mathrm{obj}}, K) - M_{\mathrm{obj}}$$.
3. Regional Statistics:
   • Compute $\mu_{\mathrm{obj}}$ and $\mu_{\mathrm{bg}}$ as mean values of the fused image $F$ over $M_{\mathrm{obj}}$ and $M_{\mathrm{bg}}$.
4. Final Score:
   • Evaluate $$\mathrm{TBC} = (\mu_{\mathrm{obj}} - \mu_{\mathrm{bg}})/(\mu_{\mathrm{bg}} + \epsilon)$$ (Xie, 17 Dec 2025).

4. Theoretical Underpinnings and Relation to Contrast Energy Metrics

TBC is formally linked to the generalized contrast energy framework rooted in early vision science and receptive field models, primarily the difference-of-Gaussians (DoG) center-surround paradigm (Rodriguez et al., 2020). In this context, TBC can be viewed as the local output of a DoG filter tuned so that the “foreground” mask encompasses the target region and the “background” comprises its immediate spatial surround. The generalized contrast energy metric

$C(i) = \|J v\|_2 = \sqrt{v^T J^T J v}$

with $v$ as the image vector and $J$ defining the DoG filter bank, provides a unifying basis for various contrast metrics (including RMS-contrast as a special case). When the DoG kernel is localized to a target/background region—for instance, by Gaussian masks—the TBC represents the mean contrast energy between these regions. This approach is functionally homologous to the neurophysiological receptive field mechanisms underlying spatial contrast sensitivity (Rodriguez et al., 2020).

5. Experimental Assessment and Comparative Performance

Extensive empirical evaluation on the DroneVehicle dataset (8,980 samples) and MSRS (361 samples) demonstrates the unique monotonicity and noise-robustness of TBC:

Case	TBC (↑ better)	AG (↑)	EN (↑)
A: Ideal Fusion	2.1850	0.1217	6.6190
B: Target Lost	-0.0813	0.0894	6.4781
C: Noise Added	1.9742	0.4235	6.6148
D: Low Contrast	0.4557	0.0608	5.6201

Unlike AG, which is maximally sensitive to added noise (Case C > Case A), and EN, which fails to meaningfully distinguish target loss (A/B differ by only $0.141$), TBC preserves correct ordinal relationships: Ideal > Noisy > Low Contrast > Target Lost. Pearson’s correlation between TBC and subjective human scores is $r \approx 0.88$, significantly exceeding both AG ($r \approx 0.45$) and EN ($r \approx 0.32$) (Xie, 17 Dec 2025).

6. Practical Parameters, Limitations, and Extensions

• Default Parameters: $k = 98$ percentile, 5$\times$5 structuring element, $\epsilon = 1 \times 10^{-6}$. Parameter variations within reasonable bounds (e.g., $k \in [95, 99]$; 3$\times$3 to 7$\times$7 structuring elements) yield stable ranking performance ($<5\%$ accuracy change).
• Computational Complexity: $O(MN)$ for mask derivation, morphological operations $O(MN|K|^2)$, and two mean computations—real-time performance (≥30 fps for 512$\times$512 images) is attainable on commodity hardware.
• Limitations: TBC’s accuracy depends on the reliability of infrared target extraction. Fixed percentile thresholds might underperform for scenes with atypical target prevalence.
• Possible Extensions: Adaptive thresholding (Otsu/local adaptation), differentiable TBC variants for use as fusion network losses, and domain transfer to other “small target + noisy background” settings (e.g., medical or underwater imaging) are proposed for future work (Xie, 17 Dec 2025).

7. Broader Relevance in Contrast and Perceptual Quality Assessment

TBC is representative of a broader paradigm shift in image quality metrics toward localized, task-relevant, and perceptually motivated measures. Its incorporation of biological contrast principles through DoG-based or Gaussian-weighted masking directly addresses the confounding influence of global energy and high-frequency noise endemic to legacy metrics. This approach aligns with advances in computational neuroscience, psychophysics, and perceptually optimized computer vision algorithms. The explicit focus on the target-background relationship positions TBC as an archetype for assessment tools in environments where small, salient targets coexist with complex or degraded backgrounds (Xie, 17 Dec 2025, Rodriguez et al., 2020).