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Fiber tract segmentation is a prerequisite for tract-based statistical analysis. Brain fiber streamlines obtained by diffusion magnetic resonance imaging and tractography technology are usually difficult to be leveraged directly, thus need to be segmented into fiber tracts. Previous research mainly consists of two steps: defining and computing the similarity features of fiber streamlines, then adopting machine learning algorithms for fiber clustering or classification. Defining the similarity feature is the basic premise and determines its potential reliability and application. In this study, we adopt geometric features for fiber tract segmentation and develop a novel descriptor (FiberGeoMap) for the corresponding representation, which can effectively depict fiber streamlines’ shapes and positions. FiberGeoMap can differentiate fiber tracts within the same subject, meanwhile preserving the shape and position consistency across subjects, thus can identify common fiber tracts across brains. We also proposed a Transformer-based encoder network called FiberGeoMap Learner, to perform segmentation based on the geometric features. Experimental results showed that the proposed method can differentiate the 103 various fiber tracts, which outperformed the existing methods in both the number of categories and segmentation accuracy. Furthermore, the proposed method identified some fiber tracts that were statistically different on fractional anisotropy (FA), mean diffusion (MD), and fiber number ration in autism.