## Abstract

A new tool for image understanding is stated in this paper: the visual hull of an object. Many algorithms for identifying or reconstructing 3-D objects use the 2-D silhouette of the object. If a non-convex object S is considered, some features of the surface of S can be useless for identification based on silhouettes; the same features of S cannot be reconstructed by volume intersection algorithms using a set of silhouettes extracted from multiple views of the object. Broadly speaking, we define the visual hull of an object or set of objects S as the envelope of all the possible visual rays tangent to S. Only the features of the surface of S which lies also on the surface of the visual hull can be reconstructed or identified using silhouette-based algorithms. After a suitable general discussion, this paper presents an algorithm for computing the visual hull in 2-D. A precise statement of the visual hull concept appears to be new, as well as the problem of its computation.

## Keywords

Convex Hull Multiple View Tangency Point Fourier Descriptor Incidence Lattice## Preview

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## References

- [1]P.J. Besl and R.C. Jain, “Three-dimensional object recognition”, Computing Surveys, Vol. 17, pp. 75–145, 1985.CrossRefGoogle Scholar
- [2]C. Chien and J.K. Aggarwal, “Model reconstruction and shape recognition from occluding contours”, IEEE Trans. PAMI, Vol. 11, pp. 372–389, 1989.CrossRefGoogle Scholar
- [3]T.P. Wallace and P.A. Wintz, “An efficient three-dimensional aircraft recognition algorithm using normalized Fourier descriptors”, Comput. Graphics Image Processing, Vol 13, pp. 99–126, 1980.CrossRefGoogle Scholar
- [4]M. Hebert and T. Kanade, “The 3-D profile method for object recognition”, Proc. IEEE Comput. Soc. Conf. on Computer Vision and Pattern Recognition, pp.458-463, June 1985.Google Scholar
- [5]A.P. Reeves et al. “Three-dimensional shape analysis using moments and Fourier descriptors”, IEEE Trans. PAMI, Vol. 10, pp. 937–943, 1988.CrossRefGoogle Scholar
- [6]S.A. Dudani et al. “Aircraft identification by moment invariants”, IEEE Trans.Comput., Vol. 26, pp. 39–46, 1981.Google Scholar
- [7]Y.F. Wang, M.J. Magee and J.K. Aggarwal, “Matching three-dimensional objects using silhouettes”, IEEE Trans. PAMI, Vol. 6, pp. 513–518, 1984.CrossRefGoogle Scholar
- [8]W.N. Martin and J.K. Aggarwal, “Volumetric description of objects from multiple views”, IEEE Trans. PAMI, Vol. 5, pp. 150–158, 1983.CrossRefGoogle Scholar
- [9]P. Srinivasan et al., “Computational geometric methods in volumetric intersection for 3D reconstruction”, Pattern Recognition, Vol. 23, pp. 843–857, 1990.CrossRefGoogle Scholar
- [10]M. Potemesil, “Generating octree models of 3D objects from their silhouettes in a sequence of images”, Comput.Vision, Graphics and Image Process., Vol. 40, pp. 1–29, 1987.CrossRefGoogle Scholar
- [11]H. Noborio et al. “Construction of the octree approximating three-dimensional objects by using multiple views”, IEEE Trans.PAMI, Vol. 10, pp. 769–782, 1988.CrossRefGoogle Scholar
- [12]C.H. Chien and J.K. Aggarwal, “Volume/surface octrees for the representation of three-dimensional objects”, Comput. Vision, Graphics and Image Processing, Vol. 36, pp 100–113, 1986.CrossRefGoogle Scholar
- [13]V. Cappellini, et al. “From multiple views to object recognition”, IEEE Trans.Circuits Syst., Vol. 34, pp. 1344–1350, 1987.CrossRefGoogle Scholar
- [14]N. Ahuja and J. Veenstra, “Generating octrees from object silhouettes in orthographic views”, IEEE Trans PAMI, Vol. 11, pp. 137–149, 1989.CrossRefGoogle Scholar
- [15]T.H. Hong and M. Schneier, “Describing a robot’s workspace using a sequence of views from a moving camera”, IEEE Trans.PAMI, Vol. 7, pp. 721–726, 1985.CrossRefGoogle Scholar
- [16]H. Edelsbrunner, “Algorithms in combinatorial geometry”, Springer-Verlag, Berlin, Heidelberg, 1987.zbMATHCrossRefGoogle Scholar
- [17]B. Gruenbaum, “Convex polytopes”, Wiley-Interscience, New York, 1967.zbMATHGoogle Scholar
- [18]S. Baase, “Computer algorithms”, Addison-Wesley, New York, 1988.Google Scholar
- [19]F. Preparata and M. Shamos, “Computational geometry”, Springer-Verlag, New York, 1985.CrossRefGoogle Scholar
- [20]G. Salmon, “Analytic geometry of three dimensions”, Cambridge, England: Metcalfe, 1874.Google Scholar
- [21]Z. Gigus and J. Malik, “Computing the aspect graph for Une drawings of plyhedral objects”, IEEE Trans. PAMI, vol. 12, pp. 113–122, 1990.CrossRefGoogle Scholar
- [22]J. Stewman and K. Bowyer, “Constructing the perspective projection aspect graph of non-convex polyhedra”, IEEE Intern. Conf. on Comput. Vision, pp. 494-500, 1988.Google Scholar