Variational 3D Shape Segmentation for Bounding Volume Computation

We propose a variational approach to computing an optimal segmentation of a 3D shape for computing a union of tight bounding volumes. Based on an affine invariant measure of e‐tightness, the resemblance to ellipsoid, a novel functional is formulated that governs an optimization process to obtain a partition with multiple components. Refinement of segmentation is driven by application‐specific error measures, so that the final bounding volume meets pre‐specified user requirement. We present examples to demonstrate the effectiveness of our method and show that it works well for computing ellipsoidal bounding volumes as well as oriented bounding boxes.

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