# Zero-TCE: Zero Reference Tri-Curve Enhancement for Low-Light Images
## 1 Introduction  
Low-light image enhancement attracts considerable attention in optical target detection applications across diverse fields, including autonomous driving, military reconnaissance, and public safety, owing to its pivotal role in improving the accuracy and reliability of detection systems under challenging lighting conditions. However, during actual shooting in special scenarios like nighttime, severe weather conditions, or enclosed environments, high-quality images are often unobtainable due to external natural factors and the limitations of shooting equipment [1]. The captured images frequently exhibit low contrast, blurred details, and color distortion [2], making it difficult to distinguish between targets and backgrounds. Furthermore, target edges and texture features are weakened, and noise interference is significantly increased, severely impacting the accuracy of optical target detection. Hence, the enhancement of low-light images is indispensable for ensuring optimal performance in various applications. The primary task of low-light image enhancement is to improve image visibility and contrast [3; 4], while simultaneously addressing complex degradation patterns such as noise, artifacts, and color distortion introduced by brightness enhancement. Researchers have introduced a multitude of algorithms for enhancing low-light images, which can be comprehensively categorized into three distinct groups: those grounded in traditional image processing theory, those built upon physical models, and those leveraging advanced deep learning techniques. Among them, algorithms grounded in traditional image theory focus on improving image quality by adjusting image grayscale values. They primarily encompass classic traditional image enhancement techniques such as histogram equalization [5; 6], gradient domain methods [7], homomorphic filtering [8], and image fusion [9]. Histogram equalization enhances contrast through the redistribution of pixels, with main approaches including standard histogram equalization (HE) [10], adaptive histogram equalization (AHE) [11], and contrast-limited adaptive histogram equalization (CLAHE) [12]. However, these methods largely ignore illumination factors, potentially leading to over-enhancement, artifacts, and unexpected local overexposure [13]. Gradient domain image enhancement algorithms are generally limited to the enhancement of single images or images captured in the same scene [14]. Meanwhile, homomorphic filtering algorithms enhance the high-frequency details of an image by attenuating its low-frequency components, but the cutoff frequency is not fixed and requires extensive experimentation based on specific images. Algorithms for enhancing low-light images based on physical models process these images by simulating the imaging principles of the human visual system. They primarily encompass the following two approaches: First, algorithms based on the Retinex theory [15], including Single-Scale Retinex (SSR) [16; 17], Multi-Scale Retinex (MSR) [18], and Multi-Scale Retinex with Color Restoration (MSRCR), are utilized [19]. These algorithms leverage human visual color constancy, simulating the human eye's perception mechanism of object colors, to separate color images into illumination and reflection components, thereby effectively enhancing the images. Such algorithms perform well in terms of illumination invariance, but if noise and other factors are not carefully considered, they may lead to unrealistic images or localized color distortions. To address this issue, [PERSON] et al. [20] transformed the approximate illumination problem into a quadratic programming problem to find an optimal solution, which improved the enhancement effect of low-light images to a certain extent. [PERSON] et al. [21] refined the Retinex algorithm by incorporating nonlocal bilateral filtering into the luminance component within the HIS color space. By subtracting the resultant image, via post-Laplacian filtering, from the original image, they achieved commendable enhancement results.