Vision is one of the essential sources through which humans acquire information. In this paper, we establish a novel framework for measuring image information content to evaluate the variation in information content during image transformations. Within this framework, we design a nonlinear function to calculate the neighboring information content of pixels at different distances, and then use this information to measure the overall information content of the image. Hence, we define a function to represent the variation in information content during image transformations. Additionally, we utilize this framework to prove the conclusion that swapping the positions of any two pixels reduces the image's information content. Furthermore, based on the aforementioned framework, we propose a novel image encryption algorithm called Random Vortex Transformation. This algorithm encrypts the image using random functions while preserving the neighboring information of the pixels. The encrypted images are difficult for the human eye to distinguish, yet they allow for direct training of the encrypted images using machine learning methods. Experimental verification demonstrates that training on the encrypted dataset using ResNet and Vision Transformers only results in a decrease in accuracy ranging from 0.3\% to 6.5\% compared to the original data, while ensuring the security of the data. Furthermore, there is a positive correlation between the rate of information loss in the images and the rate of accuracy loss, further supporting the validity of the proposed image information content measurement framework.

翻译：视觉是人类获取信息的重要来源之一。本文建立了一种新颖的图像信息量测量框架，用于评估图像变换过程中信息量的变化。在此框架下，我们设计了一种非线性函数来计算像素在不同距离下的邻域信息量，进而利用该信息衡量图像的整体信息量。由此，我们定义了一个函数来表示图像变换过程中信息量的变化。此外，我们利用该框架证明了任意两个像素位置互换会降低图像信息量的结论。进一步地，基于上述框架，我们提出了一种名为随机涡旋变换的新型图像加密算法。该算法通过随机函数对图像进行加密，同时保持像素的邻域信息。加密后的图像人眼难以辨识，却能够直接使用机器学习方法对加密图像进行训练。实验验证表明，使用ResNet和Vision Transformers在加密数据集上进行训练，相较于原始数据仅导致0.3%至6.5%的准确率下降，同时确保了数据的安全性。此外，图像信息丢失率与准确率损失率呈正相关，进一步支持了所提图像信息量测量框架的有效性。