{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T15:23:45Z","timestamp":1743002625089,"version":"3.40.3"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319184609"},{"type":"electronic","value":"9783319184616"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-18461-6_3","type":"book-chapter","created":{"date-parts":[[2015,4,27]],"date-time":"2015-04-27T05:55:20Z","timestamp":1430114120000},"page":"28-39","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Morphological Equivalents of Relativistic and Alpha-Scale-Spaces"],"prefix":"10.1007","author":[{"given":"Martin","family":"Schmidt","sequence":"first","affiliation":[]},{"given":"Joachim","family":"Weickert","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,4,28]]},"reference":[{"key":"3_CR1","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/BF00375127","volume":"123","author":"L Alvarez","year":"1993","unstructured":"Alvarez, L., Guichard, F., Lions, P.-L., Morel, J.-M.: Axioms and fundamental equations in image processing. Archive for Rational Mechanics and Analysis 123, 199\u2013257 (1993)","journal-title":"Archive for Rational Mechanics and Analysis"},{"key":"3_CR2","doi-asserted-by":"crossref","unstructured":"Brockett, R.W., Maragos, P.: Evolution equations for continuous-scale morphology. In: Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 3, pp. 125\u2013128, San Francisco, CA (March 1992)","DOI":"10.1109\/ICASSP.1992.226260"},{"key":"3_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1007\/11577812_8","volume-title":"Deep Structure, Singularities, and Computer Vision","author":"B Burgeth","year":"2005","unstructured":"Burgeth, B., Didas, S., Weickert, J.: The Bessel Scale-Space. In: Fogh Olsen, O., Florack, L.M.J., Kuijper, A. (eds.) DSSCV 2005. LNCS, vol. 3753, pp. 84\u201395. Springer, Heidelberg (2005)"},{"key":"3_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/11408031_1","volume-title":"Scale Space and PDE Methods in Computer Vision","author":"B Burgeth","year":"2005","unstructured":"Burgeth, B., Didas, S., Weickert, J.: Relativistic scale-spaces. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 1\u201312. Springer, Heidelberg (2005)"},{"issue":"2\/3","key":"3_CR5","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/s11263-005-1841-z","volume":"64","author":"B Burgeth","year":"2005","unstructured":"Burgeth, B., Weickert, J.: An explanation for the logarithmic connection between linear and morphological system theory. International Journal of Computer Vision 64(2\/3), 157\u2013169 (2005)","journal-title":"International Journal of Computer Vision"},{"key":"3_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/11408031_2","volume-title":"Scale Space and PDE Methods in Computer Vision","author":"S Didas","year":"2005","unstructured":"Didas, S., Burgeth, B., Imiya, A., Weickert, J.: Regularity and scale-space properties of fractional high order linear filtering. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 13\u201325. Springer, Heidelberg (2005)"},{"key":"3_CR7","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0165-1684(94)90058-2","volume":"38","author":"L Dorst","year":"1994","unstructured":"Dorst, L., van den Boomgaard, R.: Morphological signal processing and the slope transform. Signal Processing 38, 79\u201398 (1994)","journal-title":"Signal Processing"},{"key":"3_CR8","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1023\/B:JMIV.0000024043.96722.aa","volume":"20","author":"R Duits","year":"2004","unstructured":"Duits, R., Florack, L., de Graaf, J., ter Haar Romeny, B.: On the axioms of scale space theory. Journal of Mathematical Imaging and Vision 20, 267\u2013298 (2004)","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"3_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/3-540-45404-7_17","volume-title":"Pattern Recognition","author":"M Felsberg","year":"2001","unstructured":"Felsberg, M., Sommer, G.: Scale adaptive filtering derived from the laplace equation. In: Radig, B., Florczyk, S. (eds.) DAGM 2001. LNCS, vol. 2191, pp. 124\u2013131. Springer, Heidelberg (2001)"},{"key":"3_CR10","doi-asserted-by":"crossref","unstructured":"Florack, L.: Image Structure. Computational Imaging and Vision, vol. 10. Kluwer, Dordrecht (1997)","DOI":"10.1007\/978-94-015-8845-4"},{"key":"3_CR11","first-page":"368","volume":"26","author":"T Iijima","year":"1962","unstructured":"Iijima, T.: Basic theory on normalization of pattern (in case of typical one-dimensional pattern). Bulletin of the Electrotechnical Laboratory 26, 368\u2013388 (1962). (In Japanese)","journal-title":"Bulletin of the Electrotechnical Laboratory"},{"key":"3_CR12","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/BF00336961","volume":"50","author":"JJ Koenderink","year":"1984","unstructured":"Koenderink, J.J.: The structure of images. Biological Cybernetics 50, 363\u2013370 (1984)","journal-title":"Biological Cybernetics"},{"key":"3_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6465-9","volume-title":"Scale-Space Theory in Computer Vision","author":"T Lindeberg","year":"1994","unstructured":"Lindeberg, T.: Scale-Space Theory in Computer Vision. Kluwer, Boston (1994)"},{"key":"3_CR14","volume-title":"Understanding Digital Signal Processing","author":"RG Lyons","year":"2004","unstructured":"Lyons, R.G.: Understanding Digital Signal Processing. Prentice Hall, Englewood Cliffs (2004)"},{"issue":"1","key":"3_CR15","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/0165-1684(94)90057-4","volume":"38","author":"P Maragos","year":"1994","unstructured":"Maragos, P.: Morphological systems: Slope transforms and max-min difference and differential equations. Signal Processing 38(1), 57\u201377 (1994)","journal-title":"Signal Processing"},{"key":"3_CR16","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"issue":"3","key":"3_CR17","first-page":"219","volume":"10","author":"R van den Boomgaard","year":"1992","unstructured":"van den Boomgaard, R.: The morphological equivalent of the Gauss convolution. Nieuw Archief Voor Wiskunde 10(3), 219\u2013236 (1992)","journal-title":"Nieuw Archief Voor Wiskunde"},{"key":"3_CR18","series-title":"Computational Imaging and Vision","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/978-94-015-8802-7_15","volume-title":"Gaussian Scale-Space Theory","author":"R van den Boomgaard","year":"1997","unstructured":"van den Boomgaard, R., Dorst, L.: The morphological equivalent of Gaussian scale-space. In: Sporring, J., Nielsen, M., Florack, L., Johansen, P. (eds.) Gaussian Scale-Space Theory. Computational Imaging and Vision, vol. 8, pp. 203\u2013220. Kluwer, Dordrecht (1997)"},{"key":"3_CR19","doi-asserted-by":"publisher","first-page":"1101","DOI":"10.1109\/34.334389","volume":"16","author":"R van den Boomgaard","year":"1994","unstructured":"van den Boomgaard, R., Smeulders, A.: The morphological structure of images: The differential equations of morphological scale-space. IEEE Transactions on Pattern Analysis and Machine Intelligence 16, 1101\u20131113 (1994)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"3","key":"3_CR20","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1023\/A:1008344623873","volume":"10","author":"J Weickert","year":"1999","unstructured":"Weickert, J., Ishikawa, S., Imiya, A.: Linear scale-space has first been proposed in Japan. Journal of Mathematical Imaging and Vision 10(3), 237\u2013252 (1999)","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"3_CR21","unstructured":"Witkin, A.P.: Scale-space filtering. In: Proc. Eighth International Joint Conference on Artificial Intelligence, vol. 2, pp. 945\u2013951, Karlsruhe, West Germany (August 1983)"}],"container-title":["Lecture Notes in Computer Science","Scale Space and Variational Methods in Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-18461-6_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T11:20:46Z","timestamp":1674904846000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-18461-6_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319184609","9783319184616"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-18461-6_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"28 April 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}