Information Theoretic Analysis of Multimodal Image Translation

Abstract:

This work presents a comprehensive information-theoretic framework for analyzing multimodal brain tumor image translation under an unpaired setting. Two heterogeneous datasets are considered, where Dataset A contains multiple tumor classes (glioma, meningioma, pituitary, and non-tumor) and Dataset B provides binary labels (tumor vs. non-tumor). The proposed approach quantifies cross-domain relationships using mutual information (MI) at class, distribution, and pixel levels to evaluate translatability between modalities. A translatability matrix is constructed using class-mean images to measure shared information content, while distribution-level MI captures global statistical dependency across randomly paired samples. Pixel-wise MI maps further reveal spatial regions contributing to cross-domain correlation, highlighting tissue-specific translation behavior. Two translation strategies are investigated: a fixed histogram matching (Type I) and an adaptive local mapping approach (Type II) that approximates deep learning-based translation. Their performance is evaluated using information gain and effectiveness metrics derived from entropy and MI principles. Additionally, a novel error prediction model based on MI is introduced to estimate translation uncertainty, showing strong correlation with actual reconstruction errors. An upper bound on achievable MI gain is also analyzed to assess theoretical limits of translation performance. Experimental results demonstrate that adaptive translation significantly improves shared information while reducing error, validating the effectiveness of the proposed framework. Overall, this study provides a rigorous and interpretable methodology for evaluating and optimizing multimodal medical image translation.

Index Terms  Multimodal image translation, Mutual Information (MI), Information theory, Brain tumor classification, Unpaired learning, Medical image analysis, Histogram matching, Adaptive mapping, Entropy, Pixel-level correlation, Translation error prediction, MRI image processing, Cross-domain learning, Image-to-image translation.