{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:31:17Z","timestamp":1761597077071},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2008,4,8]],"date-time":"2008-04-08T00:00:00Z","timestamp":1207612800000},"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":[[2008,7]]},"DOI":"10.1007\/s10851-008-0080-7","type":"journal-article","created":{"date-parts":[[2008,4,7]],"date-time":"2008-04-07T15:10:34Z","timestamp":1207581034000},"page":"207-220","source":"Crossref","is-referenced-by-count":4,"title":["Second Order Structure of Scale-Space Measurements"],"prefix":"10.1007","volume":"31","author":[{"given":"Bo","family":"Markussen","sequence":"first","affiliation":[]},{"given":"Kim Steenstrup","family":"Pedersen","sequence":"additional","affiliation":[]},{"given":"Marco","family":"Loog","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,4,8]]},"reference":[{"key":"80_CR1","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1037\/h0054663","volume":"61","author":"F. Attneave","year":"1954","unstructured":"Attneave, F.: Some informational aspects of visual perception. Psychol. Rev. 61, 183\u2013193 (1954)","journal-title":"Psychol. Rev."},{"issue":"24","key":"80_CR2","doi-asserted-by":"crossref","first-page":"2527","DOI":"10.1016\/S0042-6989(03)00471-1","volume":"43","author":"R.M. Balboa","year":"2003","unstructured":"Balboa, R.M.: Power spectra and distribution of contrasts of natural images from different habitats. Vis. Res. 43(24), 2527\u20132537 (2003)","journal-title":"Vis. Res."},{"issue":"12","key":"80_CR3","doi-asserted-by":"crossref","first-page":"2379","DOI":"10.1364\/JOSAA.4.002379","volume":"4","author":"D.J. Field","year":"1987","unstructured":"Field, D.J.: Relations between the statistics of natural images and the response properties of cortical cells. J. Opt. Soc. Am. 4(12), 2379\u20132394 (1987)","journal-title":"J. Opt. Soc. Am."},{"key":"80_CR4","series-title":"Computational Imaging and Vision","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8845-4","volume-title":"Image Structure","author":"L.M.J. Florack","year":"1997","unstructured":"Florack, L.M.J.: Image Structure. Computational Imaging and Vision. Kluwer Academic, Dordrecht (1997)"},{"issue":"8","key":"80_CR5","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1109\/TPAMI.2007.1066","volume":"29","author":"L.D. Griffin","year":"2007","unstructured":"Griffin, L.D.: The second order local-image-structure solid. IEEE Trans. Pattern Anal. Mach. Intell. 29(8), 1355\u20131366 (2007)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"80_CR6","unstructured":"Iijima, T.: Basic theory of pattern observation. Technical report, Papers on technical group on automata and automatic control (1959), in Japanese"},{"key":"80_CR7","unstructured":"Iijima, T.: Theory of pattern recognition. Electron. Commun. Jpn. 123\u2013134 (1963)"},{"key":"80_CR8","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF00336961","volume":"50","author":"J.J. Koenderink","year":"1984","unstructured":"Koenderink, J.J.: The structure of images. Biol. Cybern. 50, 363\u2013370 (1984)","journal-title":"Biol. Cybern."},{"key":"80_CR9","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/BF00318371","volume":"55","author":"J.J. Koenderink","year":"1987","unstructured":"Koenderink, J.J., van Doorn, A.J.: Representation of local geometry in the visual system. Biol. Cybern. 55, 367\u2013375 (1987)","journal-title":"Biol. Cybern."},{"issue":"7","key":"80_CR10","first-page":"1165","volume":"E86-D","author":"J.J. Koenderink","year":"2003","unstructured":"Koenderink, J.J., van Doorn, A.J.: Local structure of Gaussian texture. J. Inst. Electron. Inf. Commun. Eng. Trans. Inf. Syst. E86-D(7), 1165\u20131171 (2003)","journal-title":"J. Inst. Electron. Inf. Commun. Eng. Trans. Inf. Syst."},{"issue":"966","key":"80_CR11","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1098\/rsta.1957.0002","volume":"249","author":"M.S. Longuet-Higgins","year":"1957","unstructured":"Longuet-Higgins, M.S.: The statistical analysis of a random, moving surface. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 249(966), 321\u2013387 (1957)","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci."},{"issue":"975","key":"80_CR12","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1098\/rsta.1957.0018","volume":"250","author":"M.S. Longuet-Higgins","year":"1957","unstructured":"Longuet-Higgins, M.S.: Statistical properties of an isotropic random surface. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 250(975), 157\u2013174 (1957)","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci."},{"key":"80_CR13","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/11577812_13","volume-title":"Deep Structure, Singularities and Computer Vision","author":"M. Loog","year":"2005","unstructured":"Loog, M., Pedersen, K.S., Markussen, B.: Maximum likely scale estimation. In: Olsen, F.O., Floruck, L.M.J. Kuipjer, A. (eds.) Deep Structure, Singularities and Computer Vision. LNCS, vol. 3753, pp. 146\u2013156. Springer, Berlin (2005)"},{"issue":"4","key":"80_CR14","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1137\/1010093","volume":"10","author":"B.B. Mandelbrot","year":"1968","unstructured":"Mandelbrot, B.B., van Ness, J.W.: Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10(4), 422\u2013437 (1968)","journal-title":"SIAM Rev."},{"key":"80_CR15","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/11577812_2","volume-title":"Deep Structure, Singularities and Computer Vision","author":"B. Markussen","year":"2005","unstructured":"Markussen, B., Pedersen, K.S., Loog, M.: A scale invariant covariance structure on jet space. In: Olsen, F.O., Florack, L.M.J. Kuijper, A. (eds.) Deep Structure, Singularities and Computer Vision. LNCS, vol. 3753, pp. 12\u201323. Springer, Berlin (2005)"},{"key":"80_CR16","doi-asserted-by":"crossref","unstructured":"Markussen, B., Sporring, J., Erleben, K.: Guessing tangents in normal flows. J. Math. Imag. Vis. (2008, this issue)","DOI":"10.1007\/s10851-008-0082-5"},{"issue":"1","key":"80_CR17","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1109\/18.179371","volume":"39","author":"E. Masry","year":"1993","unstructured":"Masry, E.: The wavelet transform of stochastic processes with stationary increments and its application to fractional Brownian motion. IEEE Trans. Inf. Theory 39(1), 260\u2013264 (1993)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"80_CR18","series-title":"LNCS","first-page":"281","volume-title":"Proceeding of the 4th Scale-Space Conference","author":"K.S. Pedersen","year":"2003","unstructured":"Pedersen, K.S.: Properties of Brownian image models in scale-space. In: Griffin, L.D., Lillholm, M. (eds.) Proceeding of the 4th Scale-Space Conference. LNCS, vol. 2695, pp. 281\u2013296. Springer, Berlin (2003)"},{"issue":"2","key":"80_CR19","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1006\/jvci.1999.0443","volume":"11","author":"K.S. Pedersen","year":"2000","unstructured":"Pedersen, K.S., Nielsen, M.: The Hausdorff dimension and scale-space normalisation of natural images. J. Vis. Commun. Image Represent. 11(2), 266\u2013277 (2000)","journal-title":"J. Vis. Commun. Image Represent."},{"key":"80_CR20","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1007\/978-3-540-72823-8_31","volume-title":"1st International Conference on Scale Space and Variational Methods in Computer Vision","author":"K.S. Pedersen","year":"2007","unstructured":"Pedersen, K.S., Loog, M., Markussen, B.: Generic maximum likely scale selection. In: 1st International Conference on Scale Space and Variational Methods in Computer Vision. LNCS, vol.\u00a04485, pp. 362\u2013373. Springer, Berlin (2007)"},{"key":"80_CR21","unstructured":"Pedersen, K.S., Loog, M., van Dorst, P.: Salient point and scale detection by minimum likelihood. In: JMLR: Workshop and Conference Proceedings: Gaussian Processes in Practice, vol.\u00a01, pp.\u00a059\u201372 (2007)"},{"issue":"3","key":"80_CR22","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/S0165-1684(98)00240-0","volume":"75","author":"B. Pesquet-Popescu","year":"1999","unstructured":"Pesquet-Popescu, B.: Statistical properties of the wavelet decomposition of certain non-Gaussian self-similar processes. Sign. Process. 75(3), 303\u2013322 (1999)","journal-title":"Sign. Process."},{"issue":"5","key":"80_CR23","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1109\/18.412687","volume":"41","author":"I.S. Reed","year":"1995","unstructured":"Reed, I.S., Lee, P.C., Truong, T.K.: Spectral representation of fractional Brownian motion in n dimensions and its properties. IEEE Trans. Inf. Theory 41(5), 1439\u20131451 (1995)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"80_CR24","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1103\/PhysRevLett.73.814","volume":"73","author":"D.L. Ruderman","year":"1994","unstructured":"Ruderman, D.L., Bialek, W.: Statistics of natural images: scaling in the woods. Phys. Rev. Lett. 73(6), 814\u2013817 (1994)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"80_CR25","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1023\/A:1021889010444","volume":"18","author":"A. Srivastava","year":"2003","unstructured":"Srivastava, A., Lee, A.B., Simoncelli, E.P., Zhu, S.-C.: On advances in statistical modeling of natural images. J. Math. Imaging Vis. 18(1), 17\u201333 (2003)","journal-title":"J. Math. Imaging Vis."},{"key":"80_CR26","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1098\/rspb.1998.0303","volume":"265","author":"J.H. Hateren van","year":"1998","unstructured":"van Hateren, J.H., van der Schaaf, A.: Independent component filters of natural images compared with simple cells in primary visual cortex. Proc. R. Soc. Lond. Ser. B 265, 359\u2013366 (1998)","journal-title":"Proc. R. Soc. Lond. Ser. B"},{"key":"80_CR27","unstructured":"Witkin, A.P.: Scale space filtering. In: Proc. of the Eighth International Joint Conference on Artificial Intelligence, vol. 2, pp. 1019\u20131023. Karlsruhe, Germany (1983)"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-008-0080-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-008-0080-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-008-0080-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T02:31:09Z","timestamp":1559269869000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-008-0080-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,4,8]]},"references-count":27,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2008,7]]}},"alternative-id":["80"],"URL":"https:\/\/doi.org\/10.1007\/s10851-008-0080-7","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,4,8]]}}}