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Parametric Manifold of an Object under Different Viewing Directions

  • Xiaozheng Zhang
  • Yongsheng Gao
  • Terry Caelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7576)

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.

Keywords

pose manifold 3D object in-depth rotations viewing directions appearance prediction object rendering 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xiaozheng Zhang
    • 1
    • 2
  • Yongsheng Gao
    • 1
    • 2
  • Terry Caelli
    • 3
  1. 1.Biosecurity Group, Queensland Research LaboratoryNational ICT AustraliaAustralia
  2. 2.Computer Vision and Image Processing LabGriffith UniversityBrisbaneAustralia
  3. 3.Victoria Research LaboratoryNational ICT AustraliaAustralia

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