Finlayson G D, Hordley S D
School of Information Systems, University of East Anglia, Norwich, United Kingdom.
J Opt Soc Am A Opt Image Sci Vis. 2001 Feb;18(2):253-64. doi: 10.1364/josaa.18.000253.
In computational terms we can solve the color constancy problem if device red, green, and blue sensor responses, or RGB's, for surfaces seen under an unknown illuminant can be mapped to corresponding RGB's under a known reference light. In recent years almost all authors have argued that this three-dimensional problem is too hard. It is argued that because a bright light striking a dark surface results in the same physical spectra as those of a dim light incident on a light surface, the magnitude of RGB's cannot be recovered. Consequently, modern color constancy algorithms attempt only to recover image chromaticities under the reference light: They solve a two-dimensional problem. While significant progress has been made toward achieving chromaticity constancy, recent work has shown that the most advanced algorithms are unable to render chromaticity stable enough so that it can be used as a cue for object recognition [B. V. Funt, K. Bernard, and L. Martin, in Proceedings of the Fifth European Conference on Computer Vision (European Vision Society, Springer-Verlag, Berlin, 1998), Vol. II, p. 445.] We take this reductionist approach a little further and look at the one-dimensional color constancy problem. We ask, Is there a single color coordinate, a function of image chromaticities, for which the color constancy problem can be solved? Our answer is an emphatic yes. We show that there exists a single invariant color coordinate, a function of R, G, and B, that depends only on surface reflectance. Two corollaries follow. First, given an RGB image of a scene viewed under any illuminant, we can trivially synthesize the same gray-scale image (we simply code the invariant coordinate as a gray scale). Second, this result implies that we can solve the one-dimensional color constancy problem at a pixel (in scenes with no color diversity whatsoever). We present experiments that show that invariant gray-scale histograms are a stable feature for object recognition. Indexing on invariant distributions supports almost perfect recognition for a dataset of 11 objects viewed under five colored lights. In contrast, object recognition based on chromaticity histograms (post-color constancy preprocessing) delivers much poorer recognition.
从计算角度而言，如果在未知光照下观察到的表面的设备红、绿、蓝传感器响应（即RGB值）能够被映射到已知参考光下对应的RGB值，那么我们就能解决颜色恒常性问题。近年来，几乎所有作者都认为这个三维问题太难了。有人认为，由于强光照射暗表面产生的物理光谱与弱光照射亮表面产生的物理光谱相同，因此无法恢复RGB值的大小。所以，现代颜色恒常性算法仅试图恢复参考光下的图像色度：它们解决的是一个二维问题。虽然在实现色度恒常性方面已经取得了显著进展，但最近的研究表明，最先进的算法仍无法使色度稳定到足以用作物体识别的线索[B. V. Funt、K. Bernard和L. Martin，《第五届欧洲计算机视觉会议论文集》（欧洲视觉协会，施普林格出版社，柏林，1998年），第二卷，第445页]。我们将这种简化方法进一步推进，研究一维颜色恒常性问题。我们要问，是否存在一个单一的颜色坐标，它是图像色度的函数，对于这个坐标颜色恒常性问题能够得到解决？我们的答案是肯定的。我们表明存在一个单一的不变颜色坐标，它是R、G和B的函数，并且仅取决于表面反射率。由此得出两个推论。第一，给定在任何光照下观察到的场景的RGB图像，我们可以轻松合成相同的灰度图像（我们只需将不变坐标编码为灰度）。第二，这个结果意味着我们可以在像素级别解决一维颜色恒常性问题（在没有任何颜色差异的场景中）。我们展示的实验表明，不变灰度直方图是用于物体识别的稳定特征。基于不变分布进行索引，对于在五种彩色光下观察到的11个物体的数据集，支持几乎完美的识别。相比之下，基于色度直方图（颜色恒常性预处理后）的物体识别效果要差得多。
