{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T14:28:34Z","timestamp":1772116114209,"version":"3.50.1"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2003,8,1]],"date-time":"2003-08-01T00:00:00Z","timestamp":1059696000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2003,8,1]],"date-time":"2003-08-01T00:00:00Z","timestamp":1059696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Computer Vision"],"published-print":{"date-parts":[[2003,8]]},"DOI":"10.1023\/a:1023757417916","type":"journal-article","created":{"date-parts":[[2003,6,6]],"date-time":"2003-06-06T14:11:05Z","timestamp":1054908665000},"page":"105-115","source":"Crossref","is-referenced-by-count":18,"title":["Implicitization of Parametric Curves by Matrix Annihilation"],"prefix":"10.1007","volume":"54","author":[{"given":"Hulya","family":"Yalcin","sequence":"first","affiliation":[]},{"given":"Mustafa","family":"Unel","sequence":"additional","affiliation":[]},{"given":"William","family":"Wolovich","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"5125134_CR1","unstructured":"Bajaj, C., Garrity, T., and Warren, J. 1988. On the applications of multi-equational resultants. Technical report CSD-TR-826, Department of Computer Science, Purdue University."},{"key":"5125134_CR2","unstructured":"Bloomenthal, J. 1997. Introduction to Implicit Surfaces. Morgan Kaufmann Publishers, Inc."},{"key":"5125134_CR3","doi-asserted-by":"crossref","unstructured":"Buchberger, B. 1985. Groebner bases: An algorithmic method in polynomial ideal theory. In Multidimensional Systems Theory, N.K. Bose (Ed.), D. Reidel Publishing Company, pp. 184-232.","DOI":"10.1007\/978-94-009-5225-6_6"},{"key":"5125134_CR4","unstructured":"Buchberger, B. 1989. Applications of groebner bases in non-linear computational geometry. In Geometric Reasoning, D. Kapur and J. Mundy (Eds.), MIT Press, pp. 415-447."},{"issue":"2","key":"5125134_CR5","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1023\/A:1007992709392","volume":"26","author":"E. Calabi","year":"1998","unstructured":"Calabi, E., Olver, P.J., Shakiban, C., Tannenbaum, A., and Haker, S. 1998. Differential and numerically invariant signature curves applied to object recognition. IJCV, 26(2):107-135.","journal-title":"IJCV"},{"key":"5125134_CR6","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0747-7171(08)80012-0","volume":"9","author":"J.F. Canny","year":"1990","unstructured":"Canny, J.F. 1990. Generalized characteristic polynomials. Journal of Symbolic Computation, 9:241-250.","journal-title":"Journal of Symbolic Computation"},{"key":"5125134_CR7","unstructured":"Chionh, E.W. 1990. Base points, resultants, and the implicit representation of rational surfaces. Ph.D. Thesis, Department of Computer Sicence, University of Waterloo, Canada."},{"issue":"3","key":"5125134_CR8","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/BF01902137","volume":"8","author":"E.W. Chionh","year":"1992","unstructured":"Chionh, E.W. and Goldman, R.N. 1992. Using multivariate resultants to find the implicit equation of a rational surface. The Visual Computer, 8(3):171-180.","journal-title":"The Visual Computer"},{"key":"5125134_CR9","first-page":"49","volume":"7","author":"A.L. Dixon","year":"1908","unstructured":"Dixon, A.L. 1908. The eliminant of three quantics in two independent variables. Proc. London Mathematical Society, Series 2, 7:49-69.","journal-title":"Proc. London Mathematical Society"},{"key":"5125134_CR10","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1109\/TC.1972.5008926","volume":"21","author":"G.H. Granlund","year":"1972","unstructured":"Granlund, G.H. 1972. Fourier preprocessing for hand print character recognition. IEEE Trans. Computers, 21:195-201.","journal-title":"IEEE Trans. Computers"},{"key":"5125134_CR11","doi-asserted-by":"crossref","unstructured":"Hobby, J.D. 1991. Numerically stable implicitization of cubic curves. ACM Transactions on Graphics, 10(3).","DOI":"10.1145\/108541.108546"},{"key":"5125134_CR12","unstructured":"Hoffmann, C. 1989. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers Inc."},{"issue":"1","key":"5125134_CR13","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1109\/38.180121","volume":"13","author":"C. Hoffmann","year":"1993","unstructured":"Hoffmann, C. 1993. Implicit curves and surfaces in CAGD. IEEE Computer Graphics and Applications, 13(1):79-88.","journal-title":"IEEE Computer Graphics and Applications"},{"key":"5125134_CR14","doi-asserted-by":"crossref","unstructured":"Hong, H. 1995. Implicitization of curves parametrized by generalized trigonometric polynomials. In Proceedings of Applied Algebra, Algebraic Algorithms and Error Correcting Codes (AAECC-11), pp. 285-296.","DOI":"10.1007\/3-540-60114-7_21"},{"issue":"10","key":"5125134_CR15","doi-asserted-by":"crossref","first-page":"1473","DOI":"10.1109\/83.536895","volume":"5","author":"Z.H. Huang","year":"1996","unstructured":"Huang, Z.H. and Cohen, F.S. 1996. Affine invariant B-spline moments for curve matching. Image Processing, 5(10):1473- 1480.","journal-title":"Image Processing"},{"key":"5125134_CR16","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/34.273718","volume":"16","author":"D. Keren","year":"1994","unstructured":"Keren, D., Cooper, D., and Subrahmonia, J. 1994. Describing complicated objects by implicit polynomials. IEEE Trans. Pattern Analysis and Machine Intelligence, 16:38-53.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"5125134_CR17","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/0146-664X(82)90034-X","volume":"18","author":"F.P. Kuhl","year":"1982","unstructured":"Kuhl, F.P. and Giardina, C.R. 1982. Elliptic Fourier features of a closed contour. Computer Graphics and Image Processing, 18:236-258.","journal-title":"Computer Graphics and Image Processing"},{"key":"5125134_CR18","doi-asserted-by":"crossref","unstructured":"Lei, Z., Blane, M.M., and Cooper, D.B. 1996. 3L fitting of higher degree implicit polynomials. In Proceedings of Third IEEE Workshop on Applications of Computer Vision, Florida, pp. 148-153.","DOI":"10.1109\/ACV.1996.572044"},{"key":"5125134_CR19","doi-asserted-by":"crossref","unstructured":"Lestrel, P.E. 1997. Fourier Descriptors and Their Applications in Biology. Cambrigde Univ. Press.","DOI":"10.1017\/CBO9780511529870"},{"issue":"5","key":"5125134_CR20","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/0031-3203(87)90080-X","volume":"20","author":"C.S. Lin","year":"1987","unstructured":"Lin, C.S. and Hwang, C.L. 1987. Newforms of shape invariants from elliptic Fourier descriptors. Pattern Recognition, 20(5):535-545.","journal-title":"Pattern Recognition"},{"key":"5125134_CR21","doi-asserted-by":"crossref","unstructured":"Ma, S. 1993. De. Conics-based stereo, motion estimation and pose determination. IJCV, 10 (1).","DOI":"10.1007\/BF01440844"},{"key":"5125134_CR22","doi-asserted-by":"crossref","unstructured":"Macaulay, F.S. 1916. The Algebraic Theory of Modular Systems. Cambridge University Press.","DOI":"10.3792\/chmm\/1263317740"},{"key":"5125134_CR23","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/S0747-7171(10)80008-2","volume":"13","author":"D. Manocha","year":"1992","unstructured":"Manocha, D. and Canny, J.F. 1992a. The implicit representation of rational parametric surfaces. Journal of Symbolic Computation, 13:485-510.","journal-title":"Journal of Symbolic Computation"},{"key":"5125134_CR24","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0167-8396(92)90051-P","volume":"9","author":"D. Manocha","year":"1992","unstructured":"Manocha, D. and Canny, J.F. 1992b. Algorithms for implicitizing rational parametric surfaces. Journal of Computer-Aided Geometric Design, 9:25-50.","journal-title":"Journal of Computer-Aided Geometric Design"},{"issue":"2","key":"5125134_CR25","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1006\/cviu.1995.1014","volume":"61","author":"O. Monga","year":"1995","unstructured":"Monga, O. and Benayoun, S. 1995. Using partial derivatives of 3D images to extract typical surface features. Computer Vision and Image Understanding, 61(2):171-189.","journal-title":"Computer Vision and Image Understanding"},{"key":"5125134_CR26","unstructured":"Mundy, J.L. and Zisserman, A. (Eds.) 1992. Geometric Invariance in Computer Vision. MIT Press."},{"key":"5125134_CR27","unstructured":"Rutter, J.W. 2000. Geometry of Curves Chapman & Hall\/CRC."},{"key":"5125134_CR28","first-page":"264","volume-title":"A Treatise on the Analytic Geometry of Three Dimensions","author":"G. Salmon","year":"1915","unstructured":"Salmon, G. 1915. A Treatise on the Analytic Geometry of Three Dimensions. Longmans, Green anc Co., London, 5th ed., p. 264.","edition":"5th ed."},{"key":"5125134_CR29","unstructured":"Sederberg, T.W. 1983. Implicit and parametric curves and surfaces for computer aided geometric design. Ph.D. Thesis, Dept. Mechanical Engineering, Purdue University."},{"issue":"1","key":"5125134_CR30","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/0734-189X(84)90140-3","volume":"28","author":"T.W. Sederberg","year":"1984","unstructured":"Sederberg, T.W. and Anderson, D.C. 1984. Implicit representation of parametric curves and surfaces. Comput. Vision & Graph. Image Process., 28(1):72-84.","journal-title":"Comput. Vision & Graph. Image Process."},{"key":"5125134_CR31","doi-asserted-by":"crossref","unstructured":"Sederberg, T. and Chen, F. 1995. Implicitization using moving curves and surfaces. In Proceedings of SIGGRAPH, pp. 301-308.","DOI":"10.1145\/218380.218460"},{"issue":"6","key":"5125134_CR32","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1109\/MCG.1986.276742","volume":"6","author":"T.W. Sederberg","year":"1986","unstructured":"Sederberg, T.W. and Goldman, R.N. 1986. Algebraic geometry for computer-aided geometric design. IEEE Comput. Graph. Appl., 6(6):52-59.","journal-title":"IEEE Comput. Graph. Appl."},{"issue":"2","key":"5125134_CR33","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/34.44401","volume":"12","author":"F. Solina","year":"1990","unstructured":"Solina, F. and Bajcsy, R. 1990. Recovery of parametric models from range images: The case for superquadrics with global deformations. IEEE Trans. on Pattern Anal. and Machine Intell., 12(2):131-147.","journal-title":"IEEE Trans. on Pattern Anal. and Machine Intell."},{"issue":"5","key":"5125134_CR34","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/34.494640","volume":"18","author":"J. Subrahmonia","year":"1996","unstructured":"Subrahmonia, J., Cooper, D.B., and Keren, D. 1996. Practical reliable bayesian recognition of 2D and 3D objects using implicit polynomials and algebraic invariants. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(5):505-519.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"3","key":"5125134_CR35","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1109\/83.826778","volume":"9","author":"T. T. Tasdizen","year":"2000","unstructured":"Tasdizen, T., Tarel, J.P., and Cooper, D.B. 2000. Improving the stability of algebraic curves for applications. IEEE Transactions in Image Processing, 9(3):405-416.","journal-title":"IEEE Transactions in Image Processing"},{"key":"5125134_CR36","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1109\/34.103273","volume":"13","author":"G. Taubin","year":"1991","unstructured":"Taubin, G. 1991. Estimation of planar curves, surfaces and nonplanar space curves defined by implicit equations, with applications to edge and range image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13:1115-1138.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"3","key":"5125134_CR37","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1109\/34.276128","volume":"16","author":"G. Taubin","year":"1994","unstructured":"Taubin, G., Cukierman, F., Sullivan, S., Ponce, J., and Kriegman, D.J. 1994. Parameterized families of polynomials for bounded algebraic curve and surface fitting. IEEE Trans. Pattern Analysis and Machine Intelligence, 16(3):287-303.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"5125134_CR38","doi-asserted-by":"crossref","unstructured":"Unel, M. and Wolovich, W.A. 1998. Pose estimation and object identification using complex algebraic representations. Pattern Analysis and Applications Journal, 1 (3).","DOI":"10.1007\/BF01259367"},{"key":"5125134_CR39","doi-asserted-by":"crossref","unstructured":"Unel, M. and Wolovich, W.A. 1999. A new representation for quartic curves and complete sets of geometric invariants. Int. Jour. of Pattern Recognition and Artificial Intelligence, 13(8).","DOI":"10.1142\/S0218001499000641"},{"key":"5125134_CR40","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1006\/aama.1999.0679","volume":"24","author":"M. Unel","year":"2000","unstructured":"Unel, M. and Wolovich, W.A. 2000. On the construction of complete sets of geometric invariants for algebraic curves. Advances in Applied Mathematics, 24:65-87.","journal-title":"Advances in Applied Mathematics"},{"key":"5125134_CR41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/cviu.2000.0881","volume":"81","author":"C. Unsalan","year":"2001","unstructured":"Unsalan, C. and Ercil, A. 2001. Conversions between parametric and implicit forms using polar\/spherical coordinate representations. Computer Vision and Image Understanding, 81:1-25.","journal-title":"Computer Vision and Image Understanding"},{"issue":"6","key":"5125134_CR42","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1109\/TPAMI.1980.6447707","volume":"2","author":"T.P. Wallace","year":"1980","unstructured":"Wallace, T.P. and Mitchell, O.R. 1980. Analysis of three-dimensional movement using fourier descriptors. IEEE Trans. Pattern Analysis and Machine Intelligence, 2(6):583-588.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"5125134_CR43","doi-asserted-by":"crossref","unstructured":"Wolovich, W., Albakri, H., and Yalcin, H. 2002. The precise modeling and measurement of free-form surfaces. Journal of Manufacturing Science and Engineering.","DOI":"10.1115\/1.1430677"},{"issue":"10","key":"5125134_CR44","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1109\/34.722620","volume":"20","author":"W.A. Wolovich","year":"1998","unstructured":"Wolovich, W.A. and Unel, M. 1998. The determination of implicit polynomial canonical curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(10):1080-1090.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"8","key":"5125134_CR45","first-page":"583","volume":"20","author":"M.F. Wu","year":"1998","unstructured":"Wu, M.F. and Sheu, H.T. 1998. Representation of 3D surfaces by two-variable Fourier descriptors. IEEE Trans. Pattern Analysis and Machine Intelligence, 20(8):583-588.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"issue":"3","key":"5125134_CR46","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TC.1972.5008949","volume":"21","author":"C.T. Zahn","year":"1972","unstructured":"Zahn, C.T. and Roskies, R.Z. 1972. Fourier descriptors for plane closed curves. IEEE Trans. Computers, 21(3):269-281.","journal-title":"IEEE Trans. Computers"}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1023757417916.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1023757417916\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1023757417916.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T09:37:28Z","timestamp":1754905048000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1023757417916"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,8]]},"references-count":46,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2003,8]]}},"alternative-id":["5125134"],"URL":"https:\/\/doi.org\/10.1023\/a:1023757417916","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,8]]}}}