Boolean operations for Boundary Representation (B-Rep) models are among the most commonly used functions in Computer Aided Design (CAD) systems. They are also one of the most delicate soft modules, with challenges arising from complex algorithmic flows and efficiency and accuracy issues, especially in extreme cases. Common issues encountered in processing complex models include low efficiency, missing results, and non-watertightness. In this paper, we propose a novel algorithm for efficient and accurate Boolean operations on B-Rep models. This is achieved by establishing a bijective mapping between B-Rep models and the corresponding triangle meshes with controllable approximation error, thus mapping B-Rep Boolean operations to mesh Boolean operations. By using conservative intersection detection on the mesh to locate all surface intersection curves and carefully handling degeneration and topology errors, we ensure that the results are consistently watertight and correct. We demonstrate the superior efficiency of the proposed method using the open-source geometry engine OCCT, the commercial engine ACIS, and the commercial software Rhino as benchmarks.

Cross-modality data translation has attracted great interest in medical image computing. Deep generative models show performance improvement in addressing related challenges. Nevertheless, as a fundamental challenge in image translation, the problem of zero-shot learning cross-modality image translation with fidelity remains unanswered. To bridge this gap, we propose a novel unsupervised zero-shot learning method called Mutual Information guided Diffusion Model, which learns to translate an unseen source image to the target modality by leveraging the inherent statistical consistency of Mutual Information between different modalities. To overcome the prohibitive high dimensional Mutual Information calculation, we propose a differentiable local-wise mutual information layer for conditioning the iterative denoising process. The Local-wise-Mutual-Information-Layer captures identical cross-modality features in the statistical domain, offering diffusion guidance without relying on direct mappings between the source and target domains. This advantage allows our method to adapt to changing source domains without the need for retraining, making it highly practical when sufficient labeled source domain data is not available. We demonstrate the superior performance of MIDiffusion in zero-shot cross-modality translation tasks through empirical comparisons with other generative models, including adversarial-based and diffusion-based models. Finally, we showcase the real-world application of MIDiffusion in 3D zero-shot learning-based cross-modality image segmentation tasks.