{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T01:55:53Z","timestamp":1755222953962,"version":"3.43.0"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1997,8,1]],"date-time":"1997-08-01T00:00:00Z","timestamp":870393600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1997,8,1]],"date-time":"1997-08-01T00:00:00Z","timestamp":870393600000},"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":[[1997,8]]},"DOI":"10.1023\/a:1007970107971","type":"journal-article","created":{"date-parts":[[2002,12,22]],"date-time":"2002-12-22T07:13:40Z","timestamp":1040541220000},"page":"37-55","source":"Crossref","is-referenced-by-count":16,"title":["Analyzing and Synthesizing Images by Evolving Curves with the Osher-Sethian Method"],"prefix":"10.1007","volume":"24","author":[{"given":"Ron","family":"Kimmel","sequence":"first","affiliation":[]},{"given":"Nahum","family":"Kiryati","sequence":"additional","affiliation":[]},{"given":"Alfred M.","family":"Bruckstein","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"138827_CR1","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1006\/jcph.1995.1098","volume":"118","author":"D. Adalsteinsson","year":"1995","unstructured":"Adalsteinsson, D. and Sethian, J. A. 1995. A fast level set method for propagating interfaces. J. of Comp. Phys., 118:269-277.","journal-title":"J. of Comp. Phys."},{"key":"138827_CR2","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1137\/0729052","volume":"29","author":"L. Alvarez","year":"1992","unstructured":"Alvarez, L., Lions, P. L., and Morel, J. M. 1992. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal., 29:845-866.","journal-title":"SIAM J. Numer. Anal."},{"key":"138827_CR3","doi-asserted-by":"crossref","unstructured":"Alvarez, L., Guichard, F., Lions, P. L., and Morel, J. M. 1993. Axioms and fundamental equations of image processing. Arch. Rational Mechanics, 123.","DOI":"10.1007\/BF00375127"},{"key":"138827_CR4","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0022-5193(73)90175-6","volume":"38","author":"H. Blum","year":"1973","unstructured":"Blum, H. 1973. Biological shape and visual science ( part I). J. Theor. Biol., 38:205-287.","journal-title":"J. Theor. Biol."},{"key":"138827_CR5","doi-asserted-by":"crossref","unstructured":"Brockett, R. W. and Maragos, P. 1992. Evolution equations for continuous-scale morphology. In Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing, San Francisco, California, pp. 1-4.","DOI":"10.1109\/ICASSP.1992.226260"},{"key":"138827_CR6","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/S0734-189X(88)80002-1","volume":"44","author":"A. M. Bruckstein","year":"1988","unstructured":"Bruckstein, A. M. 1988. On shape from shading. Comput. Vision Graphics Image Process., 44:139-154.","journal-title":"Comput. Vision Graphics Image Process."},{"key":"138827_CR7","first-page":"11","volume":"1","author":"A. M. Bruckstein","year":"1994","unstructured":"Bruckstein, A. M. 1994. Analyzing and synthesizing images by evolving curves. In Proceedings IEEE ICIP, Austin, Texas, vol. 1, pp. 11-15.","journal-title":"Proceedings IEEE ICIP"},{"key":"138827_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01385685","volume":"66","author":"V. Caselles","year":"1993","unstructured":"Caselles, V., Catte, F., Coll, T., and Dibos, F. 1993. A geometric model for active contours. Numerische Mathematik, 66:1-31.","journal-title":"Numerische Mathematik"},{"key":"138827_CR9","doi-asserted-by":"crossref","unstructured":"Caselles, V., Kimmel, R., and Sapiro, G. 1995a. Geodesic active contours. In Proceedings ICCVs'95, Boston, Massachusetts, pp. 694- 699.","DOI":"10.1109\/ICCV.1995.466871"},{"issue":"1","key":"138827_CR10","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1023\/A:1007979827043","volume":"22","author":"V. Caselles","year":"1997","unstructured":"Caselles, V., Kimmel, R., and Sapiro, G. 1997. Geodesic active contours. IJCV 22(1):61-79.","journal-title":"IJCV"},{"issue":"1","key":"138827_CR11","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1006\/jcph.1993.1092","volume":"106","author":"D. L. Chopp","year":"1993","unstructured":"Chopp, D. L. 1993. Computing minimal surfaces via level set curvature flow. J. of Computational Physics, 106(1):77-91.","journal-title":"J. of Computational Physics"},{"issue":"1","key":"138827_CR12","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1023\/A:1007922224810","volume":"24","author":"L. D. Cohen","year":"1997","unstructured":"Cohen, L. D. and Kimmel, R. 1997. Global minimum for active contour models: A minimal path approach. IJCV 24(1):57- 78.","journal-title":"IJCV"},{"key":"138827_CR13","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/BF01448839","volume":"100","author":"R. Courant","year":"1928","unstructured":"Courant, R., Friedrichs, K. O., and Lewy, H. 1928. Uber die partiellen differenzengliechungen der mathematisches Physik. Math. Ann., 100:32-74.","journal-title":"Math. Ann."},{"key":"138827_CR14","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1147\/rd.112.0215","volume":"11","author":"R. Courant","year":"1967","unstructured":"Courant, R., Friedrichs, K. O., and Lewy, H. 1967. On the partial difference equations of mathematical physics. IBM Journal, 11:215- 235.","journal-title":"IBM Journal"},{"key":"138827_CR15","volume-title":"Wave Motion: Theory, Modeling, and Computation","author":"C. L. Epstein","year":"1987","unstructured":"Epstein, C. L. and Gage, M. 1987. The curve shortening flow. In Wave Motion: Theory, Modeling, and Computation. A. Chorin and A. Majda (Eds.), Springer-Verlag: New York."},{"key":"138827_CR16","volume-title":"The Feynman Lectures on Physics","author":"R. P. Feynman","year":"1964","unstructured":"Feynman, R. P., Leighton, R. B., and Sands, M. 1964. The Feynman Lectures on Physics. Addison Wesley: Massachusetts."},{"key":"138827_CR17","doi-asserted-by":"crossref","unstructured":"Gage, M. and Hamilton, R. S. 1986. The heat equation shrinking convex plane curves. J. Diff. Geom., 23.","DOI":"10.4310\/jdg\/1214439902"},{"key":"138827_CR18","doi-asserted-by":"crossref","unstructured":"Grayson, M. 1987. The heat equation shrinks embedded plane curves to round points. J. Diff. Geom., 26.","DOI":"10.4310\/jdg\/1214441371"},{"key":"138827_CR19","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1002\/cpa.3160290305","volume":"29","author":"A. Harten","year":"1976","unstructured":"Harten, A., Hyman, J. M., and Lax, P. D. 1976. On finite-difference approximations and entropy conditions for shocks. Comm. Pure Appl. Math., 29:297.","journal-title":"Comm. Pure Appl. Math."},{"key":"138827_CR20","unstructured":"Kimmel, R. 1992. Shape from shading via level sets. M. Sc. Thesis (in Hebrew), Technion-Israel Institute of Technology."},{"key":"138827_CR21","unstructured":"Kimmel, R. 1995. Curve Evolution on Surfaces. D. Sc. Thesis, Technion-Israel Institute of Technology."},{"issue":"5","key":"138827_CR22","first-page":"154","volume":"25","author":"R. Kimmel","year":"1993","unstructured":"Kimmel, R. and Bruckstein, A. M. 1993. Shape offsets via level sets. CAD, 25(5):154-162.","journal-title":"CAD"},{"key":"138827_CR23","doi-asserted-by":"crossref","unstructured":"Kimmel, R., Kiryati, N., and Bruckstein, A. M. 1994. Using multilayer distance maps in finding shortest paths between moving obstacles. In Proceedings of ICPR, International Conference of Pattern Recognition, Jerusalem, Israel, pp. 367-372.","DOI":"10.1109\/ICPR.1994.576300"},{"issue":"3","key":"138827_CR24","first-page":"360","volume":"62","author":"R. Kimmel","year":"1995","unstructured":"Kimmel, R. and Bruckstein, A. M. 1995a. Global shape from shading. CVIU, 62(3):360-369.","journal-title":"CVIU"},{"issue":"2","key":"138827_CR25","first-page":"47","volume":"62","author":"R. Kimmel","year":"1995","unstructured":"Kimmel, R. and Bruckstein, A. M. 1995b. Tracking level sets by level sets: Amethod for solving the shape from shading problem. CVIU, 62(2):47-58.","journal-title":"CVIU"},{"issue":"3","key":"138827_CR26","first-page":"49","volume":"29","author":"R. Kimmel","year":"1995","unstructured":"Kimmel, R. and Sapiro, G. 1995. Shortening three dimensional curves via two dimensional flows. International Journal: Computers & Mathematics with Applications, 29(3):49-62.","journal-title":"International Journal: Computers & Mathematics with Applications"},{"issue":"3","key":"138827_CR27","first-page":"382","volume":"62","author":"R. Kimmel","year":"1995","unstructured":"Kimmel, R., Shaked, D., Kiryati, N., and Bruckstein, A. M. 1995a. Skeletonization via distance maps and level sets. CVIU, 62(3): 382-391.","journal-title":"CVIU"},{"key":"138827_CR28","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF01539551","volume":"16","author":"R. Kimmel","year":"1995","unstructured":"Kimmel, R., Siddiqi, K., Kimia, B. B., and Bruckstein, A. M. 1995b. Shape from shading: Level set propagation and viscosity solutions. International Journal of Computer Vision, 16:107-133.","journal-title":"International Journal of Computer Vision"},{"issue":"6","key":"138827_CR29","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1109\/34.387512","volume":"17","author":"R. Kimmel","year":"1995","unstructured":"Kimmel, R., Amir, A., and Bruckstein, A. M. 1995c. Finding shortest paths on surfaces using level sets propagation. IEEE Trans. on PAMI, 17(6):635-640.","journal-title":"IEEE Trans. on PAMI"},{"key":"138827_CR30","doi-asserted-by":"crossref","unstructured":"Kimmel, R., Kiryati, N., and Bruckstein, A. M. 1996. Sub-pixel distance maps and weighted distance transforms. Journal of Mathematical Imaging and Vision, Special Issue on Topology and Geometry in Computer Vision (to appear).","DOI":"10.1007\/BF00119840"},{"issue":"11","key":"138827_CR31","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1016\/0031-3203(93)90018-R","volume":"26","author":"N. Kiryati","year":"1993","unstructured":"Kiryati, N. and Sz\u00e9kely, G. 1993. Estimating shortest paths and minimal distances on digitized three dimensional surfaces. Pattern Recognition, 26(11):1623-1637.","journal-title":"Pattern Recognition"},{"key":"138827_CR32","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/0041-5553(76)90046-X","volume":"16","author":"N. N. Kuznetsov","year":"1976","unstructured":"Kuznetsov, N. N. 1976. Accuracy of some approximate methods for computing the weak solutions of first-order quasi-linear equation. USSR Comp. Math. and Math Phys., 16:105-119.","journal-title":"USSR Comp. Math. and Math Phys."},{"key":"138827_CR33","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970562","volume-title":"Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves","author":"P. D. Lax","year":"1973","unstructured":"Lax, P. D. 1973. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves. Society for Industrial and Applied Mathematics: Philadelphia, Pennsylvania."},{"key":"138827_CR34","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8629-1","volume-title":"Numerical Methods for Conservation Laws","author":"R. J. LeVeque","year":"1992","unstructured":"LeVeque, R. J. 1992. Numerical Methods for Conservation Laws. Lectures in Mathematics. Birkhauser Verlag, Basel."},{"key":"138827_CR35","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1109\/34.368173","volume":"17","author":"R. Malladi","year":"1995","unstructured":"Malladi, R., Sethian, J. A., and Vemuri, B. C. 1995. Shape modeling with front propagation: A level set approach. IEEE Trans. on PAMI, 17:158-175.","journal-title":"IEEE Trans. on PAMI"},{"key":"138827_CR36","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S. J. Osher","year":"1988","unstructured":"Osher, S. J. and Sethian, J. A. 1988. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. of Comp. Phys., 79:12-49.","journal-title":"J. of Comp. Phys."},{"issue":"4","key":"138827_CR37","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1137\/0728049","volume":"28","author":"S. Osher","year":"1991","unstructured":"Osher, S. and Shu, C. W. 1991. High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Analy., 28(4):907-922.","journal-title":"SIAM J. Numer. Analy."},{"key":"138827_CR38","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/BF01901584","volume":"10","author":"Y. Pnueli","year":"1994","unstructured":"Pnueli, Y. and Bruckstein, A. M. 1994. DigiDurer-a digital engraving system. The Visual Computer, 10:277-292.","journal-title":"The Visual Computer"},{"issue":"1","key":"138827_CR39","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1006\/gmip.1996.0003","volume":"58","author":"Y. Pnueli","year":"1996","unstructured":"Pnueli, Y. and Bruckstein, A. M. 1996. Gridless halftoning. Graphic Models and Image Processing, 58(1):38-64.","journal-title":"Graphic Models and Image Processing"},{"issue":"1","key":"138827_CR40","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/BF01420591","volume":"11","author":"G. Sapiro","year":"1993","unstructured":"Sapiro, G. and Tannenbaum, A. 1993. Affine invariant scalespace. International Journal of Computer Vision, 11(1):25- 44.","journal-title":"International Journal of Computer Vision"},{"issue":"9","key":"138827_CR41","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1016\/0031-3203(93)90142-J","volume":"26","author":"G. Sapiro","year":"1993","unstructured":"Sapiro, G., Kimmel, R., Shaked, D., Kimia, B., and Bruckstein, A. M. 1993. Implementing continuous-scale morphology via curve evolution. Pattern Recognition, 26(9):1363-1372.","journal-title":"Pattern Recognition"},{"key":"138827_CR42","doi-asserted-by":"crossref","unstructured":"Sapiro, G. and Tannenbaum, A. 1995. Area and length preserving geometric invariant scale-spaces. IEEE Trans. on PAMI, 17(1).","DOI":"10.1109\/34.368150"},{"issue":"1","key":"138827_CR43","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/BF03023504","volume":"5","author":"Schroeder","year":"1983","unstructured":"Schroeder 1983. The eikonal equation. The Mathematical Intelligencer, 5(1):36-37.","journal-title":"The Mathematical Intelligencer"},{"key":"138827_CR44","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1007\/BF01210742","volume":"101","author":"J. A. Sethian","year":"1985","unstructured":"Sethian, J. A. 1985. Curvature and the evolution of fronts. Commun. in Math. Phys., 101:487-499.","journal-title":"Commun. in Math. Phys."},{"key":"138827_CR45","first-page":"131","volume":"33","author":"J. A. Sethian","year":"1989","unstructured":"Sethian, J. A. 1989. A review of recent numerical algorithms for hypersurfaces moving with curvature dependent speed. J. of Diff. Geom., 33:131-161.","journal-title":"J. of Diff. Geom."},{"key":"138827_CR46","unstructured":"Shaked, D. and Bruckstein, A. M. 1995. The curve axis. CGIU (to appear)."},{"key":"138827_CR47","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0152-3","volume-title":"Shock Waves and Reaction-Diffusion Equations","author":"J. Smoller","year":"1983","unstructured":"Smoller, J. 1983. Shock Waves and Reaction-Diffusion Equations. Springer-Verlag: New York."},{"key":"138827_CR48","unstructured":"Sod, G. A. Numerical Methods in Fluid Dynamics. Cambridge Univ. Press."},{"key":"138827_CR49","unstructured":"Weickert, J., Anisotropic diffusion in image processing. Ph. D. Thesis. Kaiserslautern Univ. Germany, Nov. 1995."}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1007970107971.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1007970107971\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1007970107971.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T09:26:27Z","timestamp":1754904387000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1007970107971"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,8]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1997,8]]}},"alternative-id":["138827"],"URL":"https:\/\/doi.org\/10.1023\/a:1007970107971","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"type":"print","value":"0920-5691"},{"type":"electronic","value":"1573-1405"}],"subject":[],"published":{"date-parts":[[1997,8]]}}}