Blended Intrinsic Maps

Vladimir G. Kim, Yaron Lipman, Thomas Allen Funkhouser

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

This paper describes a fully automatic pipeline for finding an intrinsic map between two non-isometric, genus zero surfaces. Our approach is based on the observation that efficient methods exist to search for nearly isometric maps (e.g., Möbius Voting or Heat Kernel Maps), but no single solution found with these methods provides low-distortion everywhere for pairs of surfaces differing by large deformations. To address this problem, we suggest using a weighted combination of these maps to produce a “blended map.” This approach enables algorithms that leverage efficient search procedures, yet can provide the flexibility to handle large deformations. The main challenges of this approach lie in finding a set of candidate maps {mi} and their associated blending weights {bi(p)} for every point p on the surface. We address these challenges specifically for conformal maps by making the following contributions. First, we provide a way to blend maps, defining the image of p as the weighted geodesic centroid of mi(p). Second, we provide a definition for smooth blending weights at every point p that are proportional to the area preservation of miat p. Third, we solve a global optimization problem that selects candidate maps based both on their area preservation and consistency with other selected maps. During experiments with these methods, we find that our algorithm produces blended maps that align semantic features better than alternative approaches over a variety of data sets.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalACM Transactions on Graphics
Volume30
Issue number4
DOIs
StatePublished - Jul 1 2011

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design

Fingerprint Dive into the research topics of 'Blended Intrinsic Maps'. Together they form a unique fingerprint.

  • Cite this

    Kim, V. G., Lipman, Y., & Funkhouser, T. A. (2011). Blended Intrinsic Maps. ACM Transactions on Graphics, 30(4), 1-12. https://doi.org/10.1145/2010324.1964974