Technical Advances

Pattern Analysis and Applications

, Volume 13, Issue 4, pp 451-468

3D object recognition using invariants of 2D projection curves

  • Mustafa UnelAffiliated withFaculty of Engineering and Natural Sciences, Sabanci University Email author 
  • , Octavian SoldeaAffiliated withFaculty of Engineering and Natural Sciences, Sabanci University
  • , Erol OzgurAffiliated withFaculty of Engineering and Natural Sciences, Sabanci University
  • , Alp BassaAffiliated withFaculty of Engineering and Natural Sciences, Sabanci University

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Abstract

This paper presents a new method for recognizing 3D objects based on the comparison of invariants of their 2D projection curves. We show that Euclidean equivalent 3D surfaces imply affine equivalent 2D projection curves that are obtained from the projection of cross-section curves of the surfaces onto the coordinate planes. Planes used to extract cross-section curves are chosen to be orthogonal to the principal axes of the defining surfaces. Projection curves are represented using implicit polynomial equations. Affine algebraic and geometric invariants of projection curves are constructed and compared under a variety of distance measures. Results are verified by several experiments with objects from different classes and within the same class.

Keywords

Recognition Algebraic surfaces Implicit polynomials Invariants Principal axes