A shape deformation algorithm for constrained multidimensional scaling

Date

2015-12-01

Author

Sahillioğlu, Yusuf

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We present a new Euclidean embedding technique based on volumetric shape registration. Extrinsic representation of the intrinsic geometry of a shape is preferable in various computer graphics applications as it poses only a small degrees of freedom to deal with during processing. A popular Euclidean embedding approach to achieve such a representation is multidimensional scaling (MDS), which, however, distorts the original geometric details drastically. Our method introduces a constraint on the original MDS formulation in order, to preserve the initial geometric details while the input shape is pulled towards its MDS pose using the perfectly accurate bijection in between. The regularizer of this registration framework is chosen in such a way that the system supports large deformations yet remains fast. Consequently, we produce a detail-preserving MDS pose in 90 s for a 53 K-vertex high-resolution mesh on a modest computer. We can also add pairwise point constraints on the deforming shape without any additional cost. Detail-preserving MDS is superior for non-rigid shape retrieval and useful for shape segmentation, as demonstrated.

Subject Keywords

Detail-preserving MDS, High-resolution models, Canonical form, Sparse linear system, Retrieval, Segmentation

URI

https://hdl.handle.net/11511/34635

Journal

COMPUTERS & GRAPHICS-UK

DOI

https://doi.org/10.1016/j.cag.2015.10.003

Collections

Department of Computer Engineering, Article

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Citation Formats

Y. Sahillioğlu, “A shape deformation algorithm for constrained multidimensional scaling,” COMPUTERS & GRAPHICS-UK, pp. 156–165, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34635.