Article

International Journal of Computer Vision

, Volume 89, Issue 2, pp 408-431

First online:

Learning Robust Similarity Measures for 3D Partial Shape Retrieval

  • Yi LiuAffiliated withKey Laboratory of Machine Perception (Ministry of Education), Peking UniversityChinese Academy of Sciences Key Laboratory of Molecular Developmental Biology, Center for Molecular Systems Biology, Institute of Genetics and Developmental Biology, Chinese Academy of Sciences Email author 
  • , Xu-Lei WangAffiliated withKey Laboratory of Machine Perception (Ministry of Education), Peking University
  • , Hua-Yan WangAffiliated withDepartment of Computer Science and Engineering, Hong Kong University of Science and Technology
  • , Hongbin ZhaAffiliated withKey Laboratory of Machine Perception (Ministry of Education), Peking University
  • , Hong QinAffiliated withDepartment of Computer Science, State University of New York at Stony Brook

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Abstract

In this paper, we propose a novel approach to learning robust ground distance functions of the Earth Mover’s distance to make it appropriate for quantifying the partial similarity between two feature-sets. First, we define the ground distance as a monotonic transformation of commonly used feature-to-feature base distance (or similarity) measures, so that in computing the Earth Mover’s distance, the algorithm could better turn its focus on the feature pairs that are correctly matched, while being less affected by irrelevant ones. As a result, the proposed method is especially suited for 3D partial shape retrieval where occlusion and clutter are serious problems. We prove that when the transformation satisfies certain conditions, the metric property of the base distance is sufficient to guarantee the ground distance is a metric (and so is the Earth Mover’s distance), which makes fast shape retrieval on large databases technically possible. Second, we propose a discriminative learning framework to optimize the transformation function based on the real Adaboost algorithm. The optimization is performed in the space of the piecewise constant approximations of the transformation without making any parametric assumption. Finally, extensive experiments on 3D partial shape retrieval convincingly demonstrate the effectiveness of the proposed techniques.

Keywords

Partial similarity measure 3D shape retrieval Earth mover’s distance Adaboost