International Journal of Computer Vision

, Volume 115, Issue 1, pp 44–67

Theory and Practice of Hierarchical Data-driven Descent for Optimal Deformation Estimation


DOI: 10.1007/s11263-015-0838-5

Cite this article as:
Tian, Y. & Narasimhan, S.G. Int J Comput Vis (2015) 115: 44. doi:10.1007/s11263-015-0838-5


Real-world surfaces such as clothing, water and human body deform in complex ways. Estimating deformation parameters accurately and reliably is hard due to its high-dimensional and non-convex nature. Optimization-based approaches require good initialization while regression-based approaches need a large amount of training data. Recently, to achieve globally optimal estimation, data-driven descent (Tian and Narasimhan in Int J Comput Vis , 98:279–302, 2012) applies nearest neighbor estimators trained on a particular distribution of training samples to obtain a globally optimal and dense deformation field between a template and a distorted image. In this work, we develop a hierarchical structure that first applies nearest neighbor estimators on the entire image iteratively to obtain a rough estimation, and then applies estimators with local image support to refine the estimation. Compared to its non-hierarchical version, our approach has the theoretical guarantees with significantly fewer training samples, is faster by several orders, provides a better metric deciding whether a given image requires more (or fewer) samples, and can handle more complex scenes that include a mixture of global motion and local deformation. We demonstrate in both simulation and real experiments that the proposed algorithm successfully tracks a broad range of non-rigid scenes including water, clothing, and medical images, and compares favorably against several other deformation estimation and tracking approaches that do not provide optimality guarantees.


Deformation modeling Globally optimal solutions Non-rigid deformation Data-driven approach Non-linear optimization  Non-convex optimization Image deformation High-dimensional regression 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.The Robotics InstituteCarnegie Mellon UniversityPittsburghUSA

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