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This paper presents a new kind of descriptors using spatial geometric constraints histogram descriptors (SGCHD) based on curvature mesh graph for automatic 3D pollen recognition. In order to reduce high dimensionality and noise disturbance arisen from the abnormal record approach under microscopy, the separated surface curvature voxels are extracted as the primitive features to represent the original 3D pollen particles. Due to the good invariance to pollen rotation and scaling transformation, the spatial geometric constraints vectors are calculated to describe the spatial position correlations of the curvature voxels on the 3D curvature mesh graph. For exact similarity evaluation purpose, the bidirectional histogram algorithm is applied to the spatial geometric constraints vectors to obtain the statistical histogram descriptors with fixed dimensionality, which is invariant to the number and the starting position of the voxels. Experimental results validate that the presented descriptors are invariant to different pollen particles geometric transformations, such as pose change and spatial rotation, and high recognition precision and speed can be obtained simultaneously.