{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T11:54:34Z","timestamp":1775217274903,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2008,5,17]],"date-time":"2008-05-17T00:00:00Z","timestamp":1210982400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2008,10]]},"DOI":"10.1007\/s10851-008-0096-z","type":"journal-article","created":{"date-parts":[[2008,5,16]],"date-time":"2008-05-16T16:32:34Z","timestamp":1210955554000},"page":"161-179","source":"Crossref","is-referenced-by-count":59,"title":["Multidimensional Size Functions for Shape Comparison"],"prefix":"10.1007","volume":"32","author":[{"given":"S.","family":"Biasotti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Cerri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Frosini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"Giorgi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Landi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,5,17]]},"reference":[{"key":"96_CR1","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1007\/BF01459088","volume":"99","author":"W. Ackermann","year":"1928","unstructured":"Ackermann, W.: Zum Hilbertschen Aufbau der reellen Zahlen. Math. Ann. 99, 118\u2013133 (1928)","journal-title":"Math. Ann."},{"key":"96_CR2","first-page":"27","volume":"4","author":"M. Allili","year":"2004","unstructured":"Allili, M., Corriveau, D., Ziou, D.: Morse homology descriptor for shape characterization. ICPR\u201904 4, 27\u201330 (2004)","journal-title":"ICPR\u201904"},{"key":"96_CR3","doi-asserted-by":"crossref","unstructured":"Biasotti, S., De Floriani, L., Falcidieno, B., Frosini, P., Giorgi, D., Landi, C., Papaleo, L., Spagnuolo, M.: Describing shapes by geometrical\u2013topological properties of real functions, ACM Comput. Surv. (2008, to appear)","DOI":"10.1145\/1391729.1391731"},{"key":"96_CR4","first-page":"362","volume-title":"Models for the Perception of Speech and Visual Form","author":"H. Blum","year":"1967","unstructured":"Blum, H.: A transformation for extracting new descriptors of shape. In: Wathen-Dunn, W. (ed.) Models for the Perception of Speech and Visual Form, Boston, November 1964, pp. 362\u2013380. The MIT Press, Cambridge (1967)"},{"key":"96_CR5","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1023\/A:1011923819754","volume":"67","author":"F. Cagliari","year":"2001","unstructured":"Cagliari, F., Ferri, M., Pozzi, P.: Size functions from a categorical viewpoint. Acta Appl. Math. 67, 225\u2013235 (2001)","journal-title":"Acta Appl. Math."},{"key":"96_CR6","doi-asserted-by":"crossref","unstructured":"Carlsson, G., Zomorodian, A.: The theory of multidimensional persistence. In: Proc. of SCG\u201907, Gyeongju, South Korea, 6\u20138 June 2007","DOI":"10.1145\/1247069.1247105"},{"key":"96_CR7","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.gmod.2006.07.001","volume":"68","author":"A. Cerri","year":"2006","unstructured":"Cerri, A., Ferri, M., Giorgi, D.: Retrieval of trademark images by means of size functions. Graph. Models 68, 451\u2013471 (2006)","journal-title":"Graph. Models"},{"key":"96_CR8","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.endm.2006.08.004","volume":"26","author":"A. Cerri","year":"2006","unstructured":"Cerri, A., Frosini, P., Landi, C.: A global reduction method for multidimensional size graphs. Electron. Not. Discrete Math. 26, 21\u201328 (2006)","journal-title":"Electron. Not. Discrete Math."},{"key":"96_CR9","first-page":"410","volume-title":"Springer Lecture Notes in Computer Science","author":"A. Cerri","year":"2006","unstructured":"Cerri, A., Giorgi, D., Muse, P., Sur, F., Tomassini, F.: Shape recognition via an a contrario model for size functions. In: Springer Lecture Notes in Computer Science, vol. 4141, pp. 410\u2013421. Springer, Berlin (2006)"},{"key":"96_CR10","doi-asserted-by":"crossref","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. In: Proc. 21st Symp. Comput. Geom., pp.\u00a0263\u2013271 (2005)","DOI":"10.1145\/1064092.1064133"},{"key":"96_CR11","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s00454-006-1276-5","volume":"37","author":"D. Cohen-Steiner","year":"2007","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. Discrete Comput. Geom. 37, 103\u2013120 (2007)","journal-title":"Discrete Comput. Geom."},{"key":"96_CR12","doi-asserted-by":"crossref","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Morozov, D.: Vines and vineyards by updating persistence in linear time. In: SCG\u201906, Sedona, Arizona, USA, 5\u20137 June 2006","DOI":"10.1145\/1137856.1137877"},{"key":"96_CR13","unstructured":"d\u2019Amico, M.: A new optimal algorithm for computing size function of shapes. In: Proc. CVPRIP Algorithms III, International Conference on Computer Vision, Pattern Recognition and Image Processing, pp. 107\u2013110 (2000)"},{"key":"96_CR14","unstructured":"d\u2019Amico, M., Frosini, P., Landi, C.: Natural pseudo-distance and optimal matching between reduced size functions. Tech. Rep. 66, DISMI, Univ. degli Studi di Modena e Reggio Emilia, Italy (2005), see also arXiv:0804.3500v1"},{"issue":"5","key":"96_CR15","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1002\/ima.20076","volume":"16","author":"M. d\u2019Amico","year":"2006","unstructured":"d\u2019Amico, M., Frosini, P., Landi, C.: Using matching distance in size theory: a survey. Int. J. Imaging Syst. Technol. 16(5), 154\u2013161 (2006)","journal-title":"Int. J. Imaging Syst. Technol."},{"issue":"2","key":"96_CR16","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1023\/B:JMIV.0000035177.68567.3b","volume":"21","author":"F. Dibos","year":"2004","unstructured":"Dibos, F., Frosini, P., Pasquignon, D.: The use of size functions for comparison of shapes through differential invariants. J. Math. Imaging Vis. 21(2), 107\u2013118 (2004)","journal-title":"J. Math. Imaging Vis."},{"issue":"5","key":"96_CR17","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1515\/form.2004.032","volume":"16","author":"P. Donatini","year":"2004","unstructured":"Donatini, P., Frosini, P.: Natural pseudodistances between closed manifolds. Forum Math. 16(5), 695\u2013715 (2004)","journal-title":"Forum Math."},{"issue":"1","key":"96_CR18","first-page":"1","volume":"2","author":"P. Donatini","year":"2004","unstructured":"Donatini, P., Frosini, P.: Lower bounds for natural pseudodistances via size functions. Arch. Inequal. Appl. 2(1), 1\u201312 (2004)","journal-title":"Arch. Inequal. Appl."},{"key":"96_CR19","doi-asserted-by":"crossref","first-page":"231","DOI":"10.4171\/jems\/82","volume":"9","author":"P. Donatini","year":"2007","unstructured":"Donatini, P., Frosini, P.: Natural pseudodistances between closed surfaces. J. Eur. Math. Society 9, 231\u2013253 (2007)","journal-title":"J. Eur. Math. Society"},{"key":"96_CR20","doi-asserted-by":"crossref","unstructured":"Donatini, P., Frosini, P.: Natural pseudodistances between closed curves, Forum Math. (2008, to appear)","DOI":"10.4171\/JEMS\/82"},{"key":"96_CR21","first-page":"44","volume-title":"Proceedings Second International Workshop EMMCVPR\u201999. Lecture Notes in Computer Science","author":"P. Donatini","year":"1999","unstructured":"Donatini, P., Frosini, P., Landi, C.: Deformation energy for size functions. In: Hancock, E.R., Pelillo, M. (eds.) Proceedings Second International Workshop EMMCVPR\u201999. Lecture Notes in Computer Science, vol. 1654, pp. 44\u201353. Springer, Berlin (1999)"},{"key":"96_CR22","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/S1077-3142(03)00062-6","volume":"90","author":"U. Eckhardt","year":"2003","unstructured":"Eckhardt, U., Latecki, L.J.: Topologies for the digital spaces \u21242 and \u21243. Comput. Vis. Image Underst. 90, 295\u2013312 (2003)","journal-title":"Comput. Vis. Image Underst."},{"key":"96_CR23","doi-asserted-by":"crossref","unstructured":"Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. In: Proc. 41st Ann. IEEE Symp. Found. Comput. Sci., pp. 454\u2013463 (2000)","DOI":"10.1109\/SFCS.2000.892133"},{"key":"96_CR24","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1007\/s00454-002-2885-2","volume":"28","author":"H. Edelsbrunner","year":"2002","unstructured":"Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete Comput. Geom. 28, 511\u2013533 (2002)","journal-title":"Discrete Comput. Geom."},{"key":"96_CR25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0016-0032(67)90568-6","volume":"248","author":"H. Freeman","year":"1967","unstructured":"Freeman, H., Morse, S.P.: On searching a contour map for a given terrain profile. J. Frankl. Inst. 248, 1\u201325 (1967)","journal-title":"J. Frankl. Inst."},{"issue":"3","key":"96_CR26","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1017\/S0004972700028574","volume":"42","author":"P. Frosini","year":"1990","unstructured":"Frosini, P.: A distance for similarity classes of submanifolds of a Euclidean space. Bull. Aust. Math. Soc. 42(3), 407\u2013416 (1990)","journal-title":"Bull. Aust. Math. Soc."},{"key":"96_CR27","doi-asserted-by":"crossref","unstructured":"Frosini, P.: Measuring shapes by size functions. In: Intelligent Robots and Computer Vision X: Algorithms and Techniques, Boston, MA. Proc. of SPIE, vol. 1607, pp. 122\u2013133 (1991)","DOI":"10.1117\/12.57059"},{"key":"96_CR28","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1002\/(SICI)1099-1476(19960510)19:7<555::AID-MMA787>3.0.CO;2-X","volume":"19","author":"P. Frosini","year":"1996","unstructured":"Frosini, P.: Connections between size functions and critical points. Math. Methods Appl. Sci. 19, 555\u2013569 (1996)","journal-title":"Math. Methods Appl. Sci."},{"key":"96_CR29","first-page":"596","volume":"9","author":"P. Frosini","year":"1999","unstructured":"Frosini, P., Landi, C.: Size theory as a topological tool for computer vision. Pattern Recognit. Image Anal. 9, 596\u2013603 (1999)","journal-title":"Pattern Recognit. Image Anal."},{"key":"96_CR30","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s002000100078","volume":"12","author":"P. Frosini","year":"2001","unstructured":"Frosini, P., Landi, C.: Size functions and formal series. Appl. Algebra Eng. Commun. Comput. 12, 327\u2013349 (2001)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"96_CR31","doi-asserted-by":"crossref","first-page":"455","DOI":"10.36045\/bbms\/1103065863","volume":"6","author":"P. Frosini","year":"1999","unstructured":"Frosini, P., Mulazzani, M.: Size homotopy groups for computation of natural size distances. Bull. Belg. Math. Soc. 6, 455\u2013464 (1999)","journal-title":"Bull. Belg. Math. Soc."},{"key":"96_CR32","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1080\/00207169908804771","volume":"70","author":"P. Frosini","year":"1999","unstructured":"Frosini, P., Pittore, M.: New methods for reducing size graphs. Int. J. Comput. Math. 70, 505\u2013517 (1999)","journal-title":"Int. J. Comput. Math."},{"key":"96_CR33","unstructured":"Handouyaya, M., Ziou, D., Wang, S.: Sign language recognition using moment-based size functions. In: Proc. of Vision Interface 99, Trois-Rivi\u00e8res, Canada, 19\u201321 May 1999, pp. 210\u2013216 (1999)"},{"key":"96_CR34","doi-asserted-by":"crossref","DOI":"10.1007\/b97315","volume-title":"Computational Homology, Applied Mathematical Sciences","author":"T. Kaczynski","year":"2004","unstructured":"Kaczynski, T., Mischaikow, K., Mrozek, M.: Computational Homology, Applied Mathematical Sciences, vol. 157. Springer, New York (2004)"},{"key":"96_CR35","doi-asserted-by":"crossref","unstructured":"Landi, C., Frosini, P.: New pseudodistances for the size function space. In: Melter, R.A., Wu, A.Y., Latecki, L.J. (eds.) Vision Geometry VI. Proc. SPIE, vol. 3168, pp. 52\u201360 (1997)","DOI":"10.1117\/12.279674"},{"key":"96_CR36","doi-asserted-by":"crossref","unstructured":"Landi, C., Frosini, P.: Size functions as complete invariants for image recognition, In: Latecki, L.J., Mount, D.M., Wu, A.Y. (eds.) Vision Geometry XI. Proc. SPIE, vol. 4794, pp. 101\u2013109 (2002)","DOI":"10.1117\/12.453596"},{"key":"96_CR37","first-page":"562","volume":"21","author":"T. Motzkin","year":"1935","unstructured":"Motzkin, T.: Sur quelques propri\u00e9t\u00e9s caract\u00e9ristiques des ensembles convexes. Atti R. Accad. Naz. Lince. Ser. Rend. Classe Sci. Fis. Mat. Nat. 21, 562\u2013567 (1935)","journal-title":"Atti R. Accad. Naz. Lince. Ser. Rend. Classe Sci. Fis. Mat. Nat."},{"key":"96_CR38","first-page":"773","volume":"21","author":"T. Motzkin","year":"1935","unstructured":"Motzkin, T.: Sur quelques propri\u00e9t\u00e9s caract\u00e9ristiques des ensembles born\u00e9s non convexes. Atti R. Accad. Naz. Linc. Ser. Rend. Classe Sci. Fis. Mat. Nat. 21, 773\u2013779 (1935)","journal-title":"Atti R. Accad. Naz. Linc. Ser. Rend. Classe Sci. Fis. Mat. Nat."},{"key":"96_CR39","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.gmod.2006.09.004","volume":"692","author":"G. Patan\u00e8","year":"2007","unstructured":"Patan\u00e8, G., Spagnuolo, M., Falcidieno, B.: Families of cut-graphs for bordered meshes with arbitrary genus. Graph. Models 692, 119\u2013138 (2007)","journal-title":"Graph. Models"},{"key":"96_CR40","first-page":"4577","volume":"25","author":"I. Stanganelli","year":"2005","unstructured":"Stanganelli, I., Brucale, A., Calori, L., Gori, R., Lovato, A., Magi, S., Kopf, B., Bacchilega, R., Rapisarda, V., Testori, A., Ascierto, P.A., Simeone, E., Ferri, M.: Computer-aided diagnosis of melanocytic lesions. Anticancer Res. 25, 4577\u20134582 (2005)","journal-title":"Anticancer Res."},{"issue":"2","key":"96_CR41","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1023\/A:1007910913691","volume":"23","author":"C. Uras","year":"1997","unstructured":"Uras, C., Verri, A.: Computing size functions from edge maps. Internat. J. Comput. Vis. 23(2), 169\u2013183 (1997)","journal-title":"Internat. J. Comput. Vis."},{"key":"96_CR42","first-page":"215","volume-title":"Applications of Invariance in Computer Vision. Lecture Notes in Comput. Sci.","author":"A. Verri","year":"1993","unstructured":"Verri, A., Uras, C.: Invariant size functions. In: Applications of Invariance in Computer Vision. Lecture Notes in Comput. Sci., vol.\u00a0825, pp. 215\u2013234. Springer, Berlin (1993)"},{"key":"96_CR43","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0262-8856(95)01056-4","volume":"14","author":"A. Verri","year":"1996","unstructured":"Verri, A., Uras, C.: Metric-topological approach to shape representation and recognition. Image Vis. Comput. 14, 189\u2013207 (1996)","journal-title":"Image Vis. Comput."},{"key":"96_CR44","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF00200823","volume":"70","author":"A. Verri","year":"1993","unstructured":"Verri, A., Uras, C., Frosini, P., Ferri, M.: On the use of size functions for shape analysis. Biol. Cybern. 70, 99\u2013107 (1993)","journal-title":"Biol. Cybern."},{"key":"96_CR45","volume-title":"General Topology","author":"S. Willard","year":"1970","unstructured":"Willard, S.: General Topology. Addison-Wesley, Reading (1970)"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-008-0096-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-008-0096-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-008-0096-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T09:35:11Z","timestamp":1738229711000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-008-0096-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5,17]]},"references-count":45,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,10]]}},"alternative-id":["96"],"URL":"https:\/\/doi.org\/10.1007\/s10851-008-0096-z","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5,17]]}}}