In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale. Despite the improved interpretability, accuracy and generalizability of these architectures, GCNNs have seen limited application in the context of perceptual quantities. Notably, the recent CEConv network uses a GCNN to achieve equivariance to hue transformations by convolving input images with a hue rotated RGB filter. However, this approach leads to invalid RGB values which break equivariance and degrade performance. We resolve these issues with a lifting layer that transforms the input image directly, thereby circumventing the issue of invalid RGB values and improving equivariance error by over three orders of magnitude. Moreover, we extend the notion of color equivariance to include equivariance to saturation and luminance shift. Our hue-, saturation-, luminance- and color-equivariant networks achieve strong generalization to out-of-distribution perceptual variations and improved sample efficiency over conventional architectures. We demonstrate the utility of our approach on synthetic and real world datasets where we consistently outperform competitive baselines.

翻译：本文提出了一种对颜色变化具有等变性的群卷积神经网络(GCNN)。GCNN最初是为处理各种几何变换而设计的，包括从二维和三维旋转群到尺度变换等半群结构。尽管这些架构在可解释性、准确性和泛化能力方面有所提升，但GCNN在感知量相关领域的应用仍较为有限。值得注意的是，近期提出的CEConv网络通过将输入图像与色调旋转的RGB滤波器进行卷积，实现了对色调变换的等变性。然而，这种方法会产生无效的RGB值，从而破坏等变性并降低性能。我们通过引入提升层直接转换输入图像来解决这些问题，既规避了无效RGB值的问题，又将等变误差降低了三个数量级以上。此外，我们将颜色等变的概念扩展到包括对饱和度和亮度变化的等变性。我们提出的色调、饱和度、亮度及颜色等变网络在分布外感知变化上展现出强大的泛化能力，并相比传统架构显著提升了样本效率。我们在合成数据集和真实数据集上验证了方法的有效性，实验结果表明我们的方法始终优于现有基线模型。