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R.L. Stevenson, E.J. Delp, "Viewpoint Invariant Recovery of Visual Surfaces from Sparse Data," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 9, pp. 897909, September, 1992.  
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@article{ 10.1109/34.161349, author = {R.L. Stevenson and E.J. Delp}, title = {Viewpoint Invariant Recovery of Visual Surfaces from Sparse Data}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {14}, number = {9}, issn = {01628828}, year = {1992}, pages = {897909}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.161349}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Viewpoint Invariant Recovery of Visual Surfaces from Sparse Data IS  9 SN  01628828 SP897 EP909 EPD  897909 A1  R.L. Stevenson, A1  E.J. Delp, PY  1992 KW  viewpoint invariant recovery; picture processing; pattern recognition; visual surfaces; sparse data; 3D space; illposed inverse problem; invariant surface characteristics; finite element analysis; finite element analysis; pattern recognition; picture processing VL  14 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
An algorithm for the reconstruction of visual surfaces from sparse data is proposed. An important aspect of this algorithm is that the surface estimated from the sparse data is approximately invariant with respect to rigid transformation of the surface in 3D space. The algorithm is based on casting the problem as an illposed inverse problem that must be stabilized using a priori information related to the image and constraint formation. To form a surface estimate that is approximately invariant with respect to viewpoint, the stabilizing information is based on invariant surface characteristics. With appropriate approximations, this results in a convex functional to minimize, which is then solved using finite element analysis. The relationship of this algorithm to several previously proposed reconstruction algorithms is discussed, and several examples that demonstrate its effectiveness in reconstructing viewpointinvariant surface estimates are given.
[1] W. E. L. Grimson,From Images to Surfaces: A Computational Study of the Human Early visual System. Cambridge, MA: MIT Press, 1981.
[2] B. Julesz, "Binocular depth perception of computergenerated patterns,"Bell Syst. Techn. J., vol. 39, pp. 11251162, 1960.
[3] P. Allen,Object Recognition Using Vision and Touch. Philadelphia: Univ. of Pennsylvania, 1985.
[4] A. Blake and A. Zisserman,Visual Reconstruction. Cambridge, MA: MIT Press, 1987.
[5] T. E. Boult and J. R. Kender, "Visual surface reconstruction using sparse depth data," inProc. 1986 IEEE Comput. Vision Patt. Recogn. Conf. (Miami), June 2226, 1986, pp. 6876.
[6] J. R. Kender, D. Lee, and T. Boult, "Information based complexity applied to optimal recovery of the 2 1/2 D sketch," inProc. Third IEEE Workshop Comput. Vision: Representation Contr.(Bellaire, MI), Oct. 1316, 1985, pp. 157167.
[7] J. Mayhew, "The interpretation of stereo information: The computation of surface orientation and depth,"Perception, vol. 11, pp. 387403, 1982.
[8] S. S. Sinha and B. G. Schunck, "Discontinuitypreserving surface reconstruction in vision processing," inProc. Conf. Comput. Vision Patt. Recogn., 1989.
[9] D. Terzopoulos, "Multilevel computational processes for visual surface reconstruction,"Comput. Vision Graphics Image Processing, vol. 24, no. 1, pp. 5296, Oct. 1983.
[10] D. Terzopoulos, "Multilevel reconstruction of visual surfaces: Variational principles and finiteelement representations," inMultiresolution Image Processing and Analysis(A. Rosenfeld, Ed.). ___New York, NY: SpringerVerlag, 1984, pp. 237310.
[11] D. Terzopoulos, "Regularization of inverse visual problems involving discontinuities,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI8, no. 4, pp. 413424, July 1986.
[12] D. Terzopoulos, "The computation of visiblesurface representations,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI10, no. 4, pp. 417438, July 1988.
[13] R. Szeliski, "Fast surface interpolation using hierarchical basis functions," inProc. 1989 Conf. Comput. Vision Patt. Recogn. (San Diego, CA), June 48, 1989, pp. 222228.
[14] J. Marroquin, S. Mitter, and T. Poggio, "Probabilistic solution of illposed problems in computational vision,"J. Amer. Stat. Assoc., vol. 82, no. 397, pp. 7689, Mar. 1987.
[15] J. G. Harris, "A new approach to surface reconstruction: The coupled depth/slope model," inProc. First Int. Conf. Comput. Vision(London, England), June 811, 1987, pp. 277283.
[16] C. Chu and A. C. Bovik, "Visual surface reconstruction using minimax approximation,"Patt. Recogn., vol. 21, no. 4, pp. 303312, 1988.
[17] J. Y. Jou and A. C. Bovik, "Improving visiblesurface reconstruction," inProc. IEEE Conf. Computer vision and Pattern Recognition, June 1988, pp. 138143.
[18] J. Jou and A. C. Bovik, "Improved initial approximation and intensityguided discontinuity detection in visiblesurface reconstruction,"Comput. Vision Graphics Image Processing, vol. 47, no. 3, pp. 292325, Sept. 1989.
[19] A. Blake and A. Zisserman, "Invariant surface reconstruction using weak continuity constraints," inProc. 1986 IEEE Comput. Vision Patt. Recogn. Conf.(Miami, FL), June 2226, 1986, pp. 6267.
[20] D. Lee and T. Pavlidis, "Onedimensional regularization with discontinuities,"IEEE Trans. Patt. Anal. Machine Intell., vol. 10, no. 6, pp. 822829, Nov. 1988.
[21] G. Wahba, "Three topics in illposed problems," inInverse and IllPosed Problems(H. W. Engl, C. W. Engl, and C. W. Groetsch, Eds.). Orlando, FL: Academic, 1987, pp. 3752, vol. 4.
[22] R. L. Stevenson and E. J. Delp, "Invariant recovery of curves inm dimensional space from sparse data,"J. Opt. Soc. Amer. A, Mar. 1990.
[23] R. L. Stevenson and E. J. Delp, "Invariant reconstruction of visual surfaces," inProc. IEEE Workshop Interpretation 3D Scenes(Austin, TX), Nov. 2729, 1989, pp. 131137.
[24] T. Poggio, V. Torre, and C. Koch, "Computational vision and regularization theory,"Nature, vol. 317, pp. 314319, 1985.
[25] A. N. Tikhonov and V. Y. Arsenin,Solutions of IllPosed Problems. Washington, DC: V. H. Winston, 1977.
[26] A. N. Tikhonov and A. V. Goncharsky, Eds.,IllPosed Problems in the Natural Sciences. Moscow: MIR, 1987.
[27] P. Besl and R. Jain, "Invariant surface characteristics for 3D object recognition in range images,"Comput. Vision Graphics Image Processing, 1986, pp. 3380, vol. 33.
[28] H. W. Guggenheimer,Differential Geometry. New York: Dover, 1977.
[29] M. M. Lipschutz,Differential Geometry. New York, NY: McGrawHill, 1969.
[30] P. T. Sander, "On reliably inferring differential structure from threedimensional images," Ph.D. thesis, Dept. of Elect. Eng., McGill Univ., Montreal, Canada, 1988.
[31] P. T. Sander and S. W. Zucker, "Inferring differential structure from threedimensional images: Smooth cross sections of fiber bundles,"IEEE Trans. Patt. Anal. Machine Intell., to be published.
[32] R. Courant and D. Hilbert,Methods of Mathematical Physics. New York: Interscience, 1953, vol. I.
[33] G. Bachman and L. Narici,Functional Analysis. New York: Academic, 1966.
[34] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing,"Sci., vol. 220, no. 4598, pp. 671680, May 13, 1983.
[35] L. Davis,Genetic Algorithms and Simulated Annealing. London: Pitman, 1987.
[36] A. Blake, "Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 1, pp. 212, Jan. 1989.
[37] J. Duchon, "Splines minimizing rotationinvariant seminorms in Sobolev spaces,"Constructive Theory of Functions of Several Variables, pp. 85100, 1976.
[38] J. Meinguet, "Multivariate interpolation at arbitrary points made simple,"J. Applied Math. Phys., vol. 30, pp. 292304, 1979.
[39] G. Wahba, "Spline bases, regularization and generalized cross validation for solving approximation problems with large quantities of noisy data,"Approximation Theory III(W. Cheney, Ed.). Academic, 1980, pp. 905912.
[40] G. Wahba, "Variational methods for multidimensional inverse problems,"Advances in Remote Sensing Retrieval Methods, pp. 385407, 1985.
[41] A. K. Cline and R. L. Renka, "A storageefficient method for construction of a Thiessen triangulation,"Rocky Mountain J. Math., vol. 14, no. 1, pp. 119139, Winter 1984.
[42] R. J. Renka, "A Storageefficient method for construction of a Thiessen triangulation," Tech. Rep. ORNL/CSD101, Oak Ridge Nat. Lab., 1982.
[43] F. Ferrie, J. Lagarde, and P. Whaite, "Darboux frames, snakes, and superquadrics: Geometry from the bottomup," inProc. Workshop Interpretation 3D Scenes, 1989, pp. 170176.
[44] P. J. Besl and R. C. Jain, "Segmentation through symbolic surface descriptions," inProc. 1986 Comput. Vision Patt. Recogn. Conf.(Miami, FL), June 2226, 1986, pp. 7785.
[45] T. J. Fan, G. Medioni, and R. Nevatia, "Description of surfaces from range data using curvature properties," inProc. 1986 IEEE Comput. Vision Patt. Recogn. Conf.(Miami, FL), June 2226, 1986, pp. 8691.
[46] I. Faux and M. Pratt,Computational Geometry for Design and Manufacture. Ellis Horwood, 1979.
[47] P. Parent and S. W. Zucker, "Curvature consistency and curve detection,"J. Opt. Soc. Amer. A, vol. 2, no. 13, pp. 5, 1985.