Construction of 3D orthogonal cover of a digital object

  • Authors:

  • Nilanjana Karmakar;Arindam Biswas;Partha Bhowmick;Bhargab B. Bhattacharya

  • Affiliations:

  • Department of Information Technology, Bengal Engineering and Science University, Shibpur, Howrah, India;Department of Information Technology, Bengal Engineering and Science University, Shibpur, Howrah, India;Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India;Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India

  • Venue:
  • IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
  • Year:
  • 2011

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Abstract

The orthogonal cover of a 3D digital object is a minimum-volume 3D polytope having surfaces parallel to the coordinate planes, and containing the entire object so as to capture its approximate shape information. An efficient algorithm for construction of such an orthogonal cover imposed on a background grid is presented in this paper. A combinatorial technique is used to classify the grid faces constituting the polytope while traversing along the surface of the object in a breadthfirst manner. The eligible grid faces are stored in a doubly connected edge list, using which the faces are finally merged to derive the isothetic polygons parallel to the coordinate planes, thereby obtaining the orthogonal cover of the object. The complexity of the cover decreases with increasing grid size. The algorithm requires computations in integer domain only and runs in a time linear in the number of voxels constituting the object surface. Experimental results demonstrate the effectiveness of the algorithm.