Incorporating the Geometric Relationship of Adjacent Objects in Multi-Object Shape Analysis

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Modeling the shared boundary region between adjacent 3D objects can provide useful information regarding the geometric relationship of objects when performing multi-object shape analysis. Our analysis goes about modeling the shared boundary region of 3D objects with a 2D s-rep. An s rep is able to capture shape features like width, boundary locations, boundary normals, and object curvature. A 2D s-rep is fit to the shared boundary region of adjacent objects by mapping the shared boundary region onto the medial surface of an ellipsoid. Mapping onto a flat surface allows for the creation of the 2D s-rep, which we can map back to the curved shared boundary region. Incorporating the 2D s-rep of the shared boundary region along with the 3D s-reps of the adjacent objects allows for a more detailed multi-object representation to utilize for shape analysis. We conducted an experiment with computer-generated data of pairs of deformed ellipsoids that were either stretched, bent, or shifted and analyzed how well our representation is able to classify a deformed pair of ellipsoids from an undeformed pair. Our study found that a representation that included a 2D s-rep of the shared boundary region slightly increased the classification accuracy for classifying stretched, bent, and shifted ellipsoids.

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