Machine-based brain tumor segmentation can help doctors make better diagnoses. However, the complex structure of brain tumors and expensive pixel-level annotations present challenges for automatic tumor segmentation. In this paper, we propose a counterfactual generation framework that not only achieves exceptional brain tumor segmentation performance without the need for pixel-level annotations, but also provides explainability. Our framework effectively separates class-related features from class-unrelated features of the samples, and generate new samples that preserve identity features while altering class attributes by embedding different class-related features. We perform topological data analysis on the extracted class-related features and obtain a globally explainable manifold, and for each abnormal sample to be segmented, a meaningful normal sample could be effectively generated with the guidance of the rule-based paths designed within the manifold for comparison for identifying the tumor regions. We evaluate our proposed method on two datasets, which demonstrates superior performance of brain tumor segmentation. The code is available at https://github.com/xrt11/tumor-segmentation.
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