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This paper introduces a probabilistic polygonal representation for plane curves using Gaussian Mixture Models, preserving local tangent, normal, and arc length while encoding uncertainty in the normal direction. The framework applies to various plane curves and supports uncertainty-aware geometric modeling for CAD, robotics, and trajectory planning.
This paper uses shape analysis tools to characterize how different data augmentation strategies reshape the geometry of neural network representations, finding that augmentation strength and type lead to distinct, well-behaved trajectories in shape space.