数学与统计学院知识库

人类视觉系统在不同光照强度下对同一物体感知到的色彩是相同的。 Retinex理论解释了色彩感知只与物体的内在反射属性有关，与光照强度无关。Retinex要解决的问题是从一定光照强度下得到的图像中获得物体的反射属性，以获得物体的真色彩。Retinex在图像增强，阴影消除，遥感图像纠正和目标跟踪等领域有着广泛地应用。对Retinex问题的解决，已有多种有效方法。变分方法是解决Retinex问题的一种重要方法，它利用在一定曝光强度下得到的单幅图像恢复了物体的反射值，但当曝光过度或不足时， 恢复的反射图像在饱和或过暗区域会丢失部分细节。本文在深入地研究Retinex理论的基础上，结合变分方法的思想，利用同一场景不同曝光强度下得到的多幅图像，构建了多曝光变分模型，并证明了该模型解的存在性和唯一性。然后，我们利用交替迭代算法求解了提出的模型，并进行了收敛性分析。数值实验结果表明，当使用同一场景不同曝光强度下得到的图像时，多幅图像恢复的反射图像比单幅图像恢复的反射图像具有更好的视觉质量， 我们提出的多曝光变分方法对于恢复反射图像非常有效。

Human visual system can identify the same colors of a given object under varying illumination conditions. Retinex theory explains color sensations correlate with the intrinsic reflectance of objects and are independent of the illumination conditions. The goal of Retinex is to decompose the reflectance from the given images and thereby obtaining the real color of the objects. The Retinex theory is widely applied in image enhancement, shadow removal, remote sensing, image correction, target tracking and so on. There have been many efficient methods for Retinex problem. The variational methods are important to solve Retinex problem, only single image with a fixed exposure is used to restore the reflectance of the image, but certain parts of image details may be lost in the saturated or over-dark regions due to the different exposure times. In this paper, deeply inspired by Retinex theory and the variational methods for Retinex, we propose a multi-exposure variational method for Retinex by utilizing several images of a same scene with different exposures, and give some theoretical analysis to show the existence and the uniqueness of the solutions of the model. Then, we utilize an alternating iterative algorithm to solve the proposed problem, and discuss the convergence of the algorithm. Numerical experiments show that when we use several images of a same scene with different exposures, the reflectance recovered by multiple images is better than that recovered by a single image in term of the visual quality, then the proposed multi-exposure variational method is useful for recovering the reflectance.