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The exact shape of intracranial aneurysms is critical in medical diagnosis and surgical planning. While voxel-based deep learning frameworks have been proposed for this segmentation task, their performance remains limited. In this study, we offer a two-step surface-based deep learning pipeline that achieves significantly higher performance. Our proposed model takes a surface model of entire principal brain arteries containing aneurysms as input and returns aneurysms surfaces as output. A user first generates a surface model by manually specifying multiple thresholds for time-of-flight magnetic resonance angiography images. The system then samples small surface fragments from the entire brain arteries and classifies the surface fragments according to whether aneurysms are present using a point-based deep learning network (PointNet++). Finally, the system applies surface segmentation (SO-Net) to surface fragments containing aneurysms. We conduct a direct comparison of segmentation performance by counting voxels between the proposed surface-based framework and the existing voxel-based method, in which our framework achieves a much higher dice similarity coefficient score (72%) than the prior approach (46%).