## 3 Materials and Methods
### Adaptive Low-Light Enhancement  
Based on the retinex theory [43], we propose an adaptive brightness adjustment model to correct illumination degradation in night scenes and to enhance weak textures. The process is shown in Figure 3.  
Since HSV color space aligns better with human visual perception, we first convert the low-light image to HSV. Within this space, the scene's lighting components are extracted using a multi-scale mean function, defined as follows:  
Figure 3: Adaptive low light adjustment algorithm framework. Figure 2: The overall framework of the proposed VCAFusion. \[{L_{\rm s}}^{(i)}=\sum_{i=1}^{N}\left[\frac{1}{M}\sum_{(x,y)\in S_{\rm xy}}V(x,y) \right],i=1,2,\ldots,N \tag{1}\]  
where \(N\) is the number of scales, \(M\) is a mean filter window of size m \(\times\) n, \(S_{\rm xy}\) indicates that the center point is at (\(x\),\(y\)), and \(V(x\),\(y)\) is the brightness component of the original image. Subsequently, an adaptive brightness enhancement function can be formulated based on the localized average illumination components' distribution. This method dynamically modifies the enhancement function's parameters in accordance with the image's illumination components distribution, thereby enhancing the overall image quality in the presence of non-uniform illumination. The expression is presented as follows:  
\[g(\cdot)=1+C*\left(\left(\frac{1}{1+e^{\alpha(x-\beta)}}-\frac{1}{1+e^{\alpha( 1-\beta)}}\right)/\left(\frac{1}{1+e^{\alpha(0-\beta)}}-\frac{1}{1+e^{\alpha( 1-\beta)}}\right)\right) \tag{2}\]  
\[g(L_{\rm s})=\frac{L_{\rm s}^{(i)}g(\cdot)\ldots L_{\rm s}^{(N)}g(\cdot)}{N}, i=1,2,\ldots,N \tag{3}\]  
where \(\alpha\), \(\beta\), and \(C\) control the steepness, inflection point, and maximum gain of the brightness gain curve, respectively, while \(x\) represents the illumination. The adaptive low-light enhancement function is shown in Figure 4. The function dynamically adjusts brightness gains based on localized illumination components, with \(C\) directly influencing the upper bound of enhancement intensity. As demonstrated in the figure, when \(C\) is incrementally set to 2, 4, 6, 8, and 10, the brightness gain curve shifts upward, indicating heightened amplification for darker regions (lower input gray levels) while preserving brighter areas (higher input gray levels). This selective enhancement ensures a balanced luminance distribution, mitigating over-saturation in well-lit regions. The parameter \(\alpha\) governs the transition sharpness between enhanced and non-enhanced zones, while \(\beta\) determines the threshold at which maximal gain is applied. Such adaptability allows the function to address non-uniform illumination effectively, optimizing perceptual quality across diverse lighting conditions. The resultant brightness gain map, \(g(L_{\rm s})\), thus reflects spatially variant corrections tailored to the image's intrinsic illumination profile. Next, we use a side window guided filter (SWGF) [21; 29] to remove halo artifacts of the brightness gain map. Then, the corresponding mathematical operation is performed to obtain the final brightness gain map \(fg\) (\(L_{\rm s}\)), as follows:  
\[fg(L_{\rm s})=Min[L_{\rm s}*SWGF(L_{\rm s},g(L_{\rm s}),r,eps),1]/L_{\rm s} \tag{4}\]  
Figure 4: Local brightness adaptive adjustment curve. Next, the lighting component \(f_{S}\) (\(L_{s}\)) is independently processed for each of the \(R\), \(G\), and \(B\) channels to generate the final low-light-enhanced image, as follows:  
\[I_{a_{I,VIS}}=R*fg(L_{s})+G*fg(L_{s})+B*fg(L_{s}) \tag{5}\]  
In low-light images, weak edges are easily overlooked. According to [PERSON]'s law, a bright spot with luminance I + \(\Delta\)I is perceptible only if \(\Delta\)I exceeds a threshold, known as the just-noticeable difference (JND). As shown in Figure 5a, low illumination results in poor luminance discrimination, which improves as brightness increases.