Rate-Distortion-Classification Model In Lossy Image Compression

Rate-distortion (RD) theory is a fundamental theory for lossy image compression that treats compressing the original images to a specified bitrate with minimal signal distortion, which is an essential metric in practical application. Moreover, with the development of visual analysis applications (such as classification, detection, segmentation, etc.), the semantic distortion in compressed images are also an important dimension in the theoretical analysis of lossy image compression. In this paper, we model the rate-distortion-classification (RDC) trade-off in lossy image compression based on the previous RD model. Specifically, the classification task is used as a representative image vision analysis task to calculate the semantic distortion. For the joint optimization modeling of RDC, the optimization objective function is the code rate expressed by the mutual information $I(\cdot,\ \cdot)$ with the constraints of MSE loss $\mathrm{E}[\triangle(\cdot,\ \cdot)]$ and the classification task error rate $\varepsilon$, where $\varepsilon$ is defined by Equation (2). Define the binary classifier as: