Parametric manifold of an object under different viewing directions

  • Authors:

  • Xiaozheng Zhang;Yongsheng Gao;Terry Caelli

  • Affiliations:

  • Biosecurity Group, Queensland Research Laboratory, National ICT Australia, Australia,Computer Vision and Image Processing Lab, Griffith University, Brisbane, Australia;Biosecurity Group, Queensland Research Laboratory, National ICT Australia, Australia,Computer Vision and Image Processing Lab, Griffith University, Brisbane, Australia;Victoria Research Laboratory, National ICT Australia, Australia

  • Venue:
  • ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
  • Year:
  • 2012

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Abstract

The appearance of a 3D object depends on both the viewing directions and illumination conditions. It is proven that all n-pixel images of a convex object with Lambertian surface under variable lighting from infinity form a convex polyhedral cone (called illumination cone) in n-dimensional space. This paper tries to answer the other half of the question: What is the set of images of an object under all viewing directions? A novel image representation is proposed, which transforms any n-pixel image of a 3D object to a vector in a 2n-dimensional pose space. In such a pose space, we prove that the transformed images of a 3D object under all viewing directions form a parametric manifold in a 6-dimensional linear subspace. With in-depth rotations along a single axis in particular, this manifold is an ellipse. Furthermore, we show that this parametric pose manifold of a convex object can be estimated from a few images in different poses and used to predict object's appearances under unseen viewing directions. These results immediately suggest a number of approaches to object recognition, scene detection, and 3D modelling. Experiments on both synthetic data and real images were reported, which demonstrates the validity of the proposed representation.