{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T21:58:57Z","timestamp":1790891937587,"version":"4.1.0"},"reference-count":46,"publisher":"SPIE-Intl Soc Optical Eng","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Electron. Imag."],"published-print":{"date-parts":[[2005,4,1]]},"abstract":"<jats:p>In this paper, we discuss a unified theory for and performance evaluation of the ridge direction estimation through the minimization of the integral of the second directional derivative of the gray-level intensity function. The primary emphasis of this paper is on the ridge orientation estimation. The subsequent ridge detection can be performed using the traditional methods of using the zero crossing of the first directional derivative. The performance evaluation of the ridge orientation estimation is performed in terms of the mean orientation bias and orientation standard deviation given the true orientation and the same two measures given the noise standard deviation. We discuss two forms of our new ridge detector\u2014first (ISDDRO-CN) using the noise covariance matrix estimation procedure under colored noise assumption, and the second (ISDDRO-WN) using the white noise assumption. ISDDRO-CN performs better than the ISDDRO-WN in the presence of strong correlated noise. When the noise levels are moderate it performs as well as ISDDRO-WN. ISDDRO-CN has superior noise sensitivity characteristics. We also compare both forms of our algorithm with the algorithm, Maximum Level Set Extrinsic Curvature (MLSEC) designed by A. L\u00f3pez [IEEE Trans. Patter Anal. Mach. Intell. 21, 327\u2013335 (1999)].<\/jats:p>","DOI":"10.1117\/1.1901683","type":"journal-article","created":{"date-parts":[[2005,7,5]],"date-time":"2005-07-05T11:48:54Z","timestamp":1120564134000},"page":"1-12","source":"Crossref","is-referenced-by-count":0,"title":["Optimal ridge orientation estimator using integrated second directional derivative"],"prefix":"10.1117","volume":"14","author":[{"given":"Desikachari","family":"Nadadur","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert M.","family":"Haralick","sequence":"additional","affiliation":[{"name":"Univ. of Washington"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David E.","family":"Gustafson","sequence":"additional","affiliation":[{"name":"Siemens Medical Solutions USA, Inc."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"189","reference":[{"key":"10.1117\/1.1901683_r1","author":"Peuker","year":"1972"},{"key":"10.1117\/1.1901683_r2","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/0146-664X(75)90005-2","volume":"4","author":"Peuker","year":"1975","journal-title":"Comput. Graph. Image Process.","ISSN":"https:\/\/id.crossref.org\/issn\/0146-664X","issn-type":"print"},{"key":"10.1117\/1.1901683_r3","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1109\/TSMC.1975.5408443","volume":"5","author":"Johnston","year":"1975","journal-title":"IEEE Trans. Syst. Man Cybern.","ISSN":"https:\/\/id.crossref.org\/issn\/0018-9472","issn-type":"print"},{"key":"10.1117\/1.1901683_r4","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/0146-664X(75)90020-9","volume":"4","author":"Paton","year":"1975","journal-title":"Comput. Vis. Graph. Image Process.","ISSN":"https:\/\/id.crossref.org\/issn\/0146-664X","issn-type":"print"},{"key":"10.1117\/1.1901683_r5","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/0098-3004(76)90107-2","volume":"2","author":"Grender","year":"1976","journal-title":"Comput. Geosci.","ISSN":"https:\/\/id.crossref.org\/issn\/0098-3004","issn-type":"print"},{"key":"10.1117\/1.1901683_r6","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/S0146-664X(78)80012-4","volume":"7","author":"Toriwaki","year":"1978","journal-title":"Comput. Graph. Image Process.","ISSN":"https:\/\/id.crossref.org\/issn\/0146-664X","issn-type":"print"},{"key":"10.1117\/1.1901683_r7","unstructured":"S. Hsu, J. L. Mundy, and P. R. Beaudet, \u201cWeb representation of image data,\u201d in\n                      Proceedings of the Fourth International Conference on Pattern Recognition\n                      , pp. 675\u2013680 (1978)."},{"key":"10.1117\/1.1901683_r8","unstructured":"H. C. Lee and K. S. Fu, \u201cThe GLGS image representation and its application to preliminary segmentation,\u201d in\n                      Proceedings of the 1981 Conference on Pattern Recognition and Image Processing\n                      , New York, pp. 256\u2013261 (1981)."},{"key":"10.1117\/1.1901683_r9","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/0734-189X(83)90094-4","volume":"22","author":"Haralick","year":"1983","journal-title":"Comput. Vis. Graph. Image Process.","ISSN":"https:\/\/id.crossref.org\/issn\/0734-189X","issn-type":"print"},{"key":"10.1117\/1.1901683_r10","doi-asserted-by":"crossref","unstructured":"R. M. Haralick, \u201cCubic facet model edge detector and ridge-valley detector: Implementation details,\u201d in\n                      Pattern Recognition in Practice II\n                      , edited by E. S. Gelsema and L. N. Kanal, pp. 81\u201390, Elsevier Science (North-Holland), Netherlands (1986).","DOI":"10.1016\/B978-0-444-87877-9.50010-8"},{"key":"10.1117\/1.1901683_r11","doi-asserted-by":"crossref","unstructured":"S. Chinveeraphan, R. Takamatsu, and M. Sato, \u201cUnderstanding of ridge-valley lines on image-intensity surfaces in scale-space,\u201d in\n                      6th International Conference on Computer Analysis of Images and Patterns, CAIP\u201995\n                      , pp. 661\u2013667 (1995).","DOI":"10.1007\/3-540-60268-2_361"},{"key":"10.1117\/1.1901683_r12","doi-asserted-by":"crossref","unstructured":"T. Lindeberg, \u201cJunction detection with automatic selection of detection scales and localization scales,\u201d in\n                      International Conference on Image Processing\n                      , Vol. 1, pp. 924\u2013928 (1994).","DOI":"10.1109\/ICIP.1994.413244"},{"key":"10.1117\/1.1901683_r13","doi-asserted-by":"crossref","unstructured":"T. Lindeberg, \u201cEdge detection and ridge detection with automatic scale selection,\u201d in\n                      IEEE Computer Society Conference on Computer Vision and Pattern Recognition\n                      , pp. 465\u2013470 (1996).","DOI":"10.1109\/CVPR.1996.517113"},{"key":"10.1117\/1.1901683_r14","doi-asserted-by":"crossref","unstructured":"P. Sukanya, R. Takamatsu, and M. Sato, \u201cThe surface-shape operator based shading-tolerant method for multiscale image analysis,\u201d in\n                      International Conference on Image Processing\n                      , Vol. 1, pp. 221\u2013225 (1998).","DOI":"10.1109\/ICIP.1998.723461"},{"key":"10.1117\/1.1901683_r15","doi-asserted-by":"crossref","unstructured":"O. Monga, S. Benayoun, and O. D. Faugeras, \u201cFrom partial derivatives of 3D density images to ridge lines,\u201d in\n                      IEEE Computer Society Conference on Computer Vision and Pattern Recognition\n                      , pp. 354\u2013359 (1992).","DOI":"10.1109\/CVPR.1992.223165"},{"key":"10.1117\/1.1901683_r16","doi-asserted-by":"crossref","unstructured":"J. B. Subirana-Vilanova and K. K. Sung, \u201cRidge-detection for the perceptual organization without edges,\u201d in\n                      4th International Conference on Computer Vision\n                      , pp. 57\u201364 (1993).","DOI":"10.1109\/ICCV.1993.378235"},{"key":"10.1117\/1.1901683_r17","unstructured":"J. Hou and R. H. Bamberger, \u201cOrientation selective operators for ridge, valley, edge, and line detection in imagery,\u201d in\n                      IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP\u201994\n                      , pp. V\/25\u2013V\/28 (1994)."},{"key":"10.1117\/1.1901683_r18","doi-asserted-by":"crossref","unstructured":"P. Sukanya, R. Takamatsu, and M. Sato, \u201cA new operator for image structure analysis,\u201d in\n                      International Conference on Image Processing\n                      , Vol. 3, pp. 615\u2013618 (1996).","DOI":"10.1109\/ICIP.1996.560570"},{"key":"10.1117\/1.1901683_r19","doi-asserted-by":"crossref","unstructured":"P. Sukanya, H. Tanuma, R. Takamatsu, and M. Sato, \u201cA new operator for describing topograpical image structure,\u201d in\n                      13th International Conference on Pattern Recognition\n                      , pp. 50\u201354 (1996).","DOI":"10.1109\/ICPR.1996.545990"},{"key":"10.1117\/1.1901683_r20","unstructured":"P. G. Ducksbury, M. J. Varga, Z. Y. Xie, and J. M. Brady, \u201cImage content descriptors: The detection stage,\u201d in\n                      IEE Colloquium on Intelligent Image Databases\n                      , pp. 5\/1\u20135\/6 (1996)."},{"key":"10.1117\/1.1901683_r21","doi-asserted-by":"crossref","unstructured":"P. G. Ducksbury and M. J. Varga, \u201cRegion based image content descriptors and representation,\u201d in\n                      6th International Conference on Image Processing and Its Applications\n                      , Vol. 2, pp. 561\u2013565 (1997).","DOI":"10.1049\/cp:19970964"},{"key":"10.1117\/1.1901683_r22","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1109\/34.761263","volume":"21","author":"Lo\u0301pez","year":"1999","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell.","ISSN":"https:\/\/id.crossref.org\/issn\/0162-8828","issn-type":"print"},{"key":"10.1117\/1.1901683_r23","doi-asserted-by":"crossref","unstructured":"A. G. Bors, E. R. Hancock, and R. C. Wilson, \u201cTerrain feature identification by modeling radar image statistics,\u201d in\n                      International Conference on Image Processing\n                      , Vol. 1, pp. 721\u2013724 (2000).","DOI":"10.1109\/ICIP.2000.901060"},{"key":"10.1117\/1.1901683_r24","doi-asserted-by":"crossref","unstructured":"A. G. Bors, E. R. Hancock, and R. C. Wilson, \u201c3-D terrain from synthetic aperture radar,\u201d in\n                      IEEE Workshop on Computer Vision Beyond the Visible Spectrum: Methods and Applications\n                      , Vol. 1, pp. 63\u201372 (2000).","DOI":"10.1109\/CVBVS.2000.855251"},{"key":"10.1117\/1.1901683_r25","first-page":"293","volume":"30","author":"Tao","year":"2001","journal-title":"Journal of the Institute of Image Electronics Engineers of Japan"},{"key":"10.1117\/1.1901683_r26","doi-asserted-by":"crossref","unstructured":"A. G. Bors, E. R. Hancock, and R. C. Wilson, \u201cA Bayesian framework for radar shape-from-shading,\u201d in\n                      IEEE Conference on Computer Vision and Pattern Recognition\n                      , Vol. 1, pp. 262\u2013268 (2000).","DOI":"10.1109\/CVPR.2000.855828"},{"key":"10.1117\/1.1901683_r27","doi-asserted-by":"crossref","unstructured":"J. Stoeckel, F. M. Vos, P. H. Vos, and A. M. Vossepoel, \u201cAn evaluation of ridge extraction methods for portal imaging,\u201d in\n                      15th International Conference on Pattern Recognition\n                      , Vol. 3, pp. 429\u2013432 (2000).","DOI":"10.1109\/ICPR.2000.903576"},{"key":"10.1117\/1.1901683_r28","unstructured":"G. Subsol, J. Ph. Thirion, and N. Ayache, \u201cNonrigid registration for building 3D anatomical atlases,\u201d in\n                      12th IAPR International Conference on Pattern Recognition, Conference A: Computer Vision and Image Processing\n                      , Vol. 1, pp. 576\u2013578 (1994)."},{"key":"10.1117\/1.1901683_r29","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1109\/34.491617","volume":"18","author":"Maintz","year":"1996","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell.","ISSN":"https:\/\/id.crossref.org\/issn\/0162-8828","issn-type":"print"},{"key":"10.1117\/1.1901683_r30","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1117\/1.482674","volume":"8","author":"Lloret","year":"1999","journal-title":"J. Electron. Imaging","ISSN":"https:\/\/id.crossref.org\/issn\/1017-9909","issn-type":"print"},{"key":"10.1117\/1.1901683_r31","first-page":"100","volume":"45","author":"Hoshino","year":"1992","journal-title":"NEC Technical Journal"},{"key":"10.1117\/1.1901683_r32","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/34.566808","volume":"19","author":"Maio","year":"1997","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell.","ISSN":"https:\/\/id.crossref.org\/issn\/0162-8828","issn-type":"print"},{"key":"10.1117\/1.1901683_r33","unstructured":"I. G. Bae, B. H. Cho, J. S. Kim, J. H. Bae, and K. Y. Yoo, \u201cOnline fingerprint verification system using direct minutiae extraction,\u201d in\n                      ISCA 13th International Conference on Computer Applications in Industry and Engineering\n                      , pp. 120\u2013123 (2000)."},{"key":"10.1117\/1.1901683_r34","doi-asserted-by":"crossref","first-page":"1907","DOI":"10.1016\/S0031-3203(00)00133-3","volume":"34","author":"Chang","year":"2001","journal-title":"Pattern Recogn.","ISSN":"https:\/\/id.crossref.org\/issn\/0031-3203","issn-type":"print"},{"key":"10.1117\/1.1901683_r35","doi-asserted-by":"crossref","first-page":"2027","DOI":"10.1109\/83.887971","volume":"9","author":"Almansa","year":"2000","journal-title":"IEEE Trans. Image Process.","ISSN":"https:\/\/id.crossref.org\/issn\/1057-7149","issn-type":"print"},{"key":"10.1117\/1.1901683_r36","unstructured":"E. Salari, \u201cA method for medial line transformation,\u201d in\n                      IEEE International Conference on Systems, Man and Cybernetics\n                      , Vol. 1, pp. 815\u2013817 (1986)."},{"key":"10.1117\/1.1901683_r37","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/0010-4809(86)90038-8","volume":"19","author":"Nguyen","year":"1986","journal-title":"Journal of Computers and Biomedical Research"},{"key":"10.1117\/1.1901683_r38","doi-asserted-by":"crossref","unstructured":"Y. Kawata, N. Niki, H. Ohmatsu, R. Kakinuma, K. Eguchi, M. Kaneko, and N. Moriyama, \u201cClassification of pulmonary nodules in thin-section CT images based on shape characterization,\u201d in\n                      IEEE Computer Society International Conference on Image Processing\n                      , Vol. 3, pp. 528\u2013530 (1997).","DOI":"10.1109\/ICIP.1997.632174"},{"key":"10.1117\/1.1901683_r39","unstructured":"A. M. Lo\u0301pez, W. Niessen, J. Serrat, K. Nicolay, B. Ter Haar Romeny, J. Villanueva, and M. Viergever, \u201cNew improvements in the multiscale analysis of trabecular bone patterns,\u201d in\n                      Pattern Recognition and Applications (Frontiers in Artificial Intelligence and Applications)\n                      , Vol. 56, pp. 251\u2013260 (2000)."},{"key":"10.1117\/1.1901683_r40","unstructured":"R. M. Haralick and L. G. Shapiro,\n                      Computer and Robot Vision\n                      , Vol. 1, Addison-Wesley, Reading (1992)."},{"key":"10.1117\/1.1901683_r41","unstructured":"D. Nadadur, \u201cNoise covariance estimation in low-level computer vision,\u201d Ph.D. thesis, Box 352500, Department of Electrical Engineering, University of Washington, Seattle, Washington (2001)."},{"key":"10.1117\/1.1901683_r42","doi-asserted-by":"crossref","unstructured":"D. Nadadur, R. M. Haralick, and D. E. Gustafson, \u201cA Bayesian framework for noise covariance estimation using the facet model,\u201d\n                      IEEE Transactions on Image Processing\n                      (submitted).","DOI":"10.1109\/TIP.2005.854480"},{"key":"10.1117\/1.1901683_r43","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1137\/0105007","volume":"5","author":"Forsythe","year":"1957","journal-title":"Journal of the Society for Industrial Applied Mathematics"},{"key":"10.1117\/1.1901683_r44","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1109\/TSMC.1987.4309068","volume":"SMC-17","author":"Zuniga","year":"1987","journal-title":"IEEE Trans. Syst. Man Cybern.","ISSN":"https:\/\/id.crossref.org\/issn\/0018-9472","issn-type":"print"},{"key":"10.1117\/1.1901683_r45","unstructured":"W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,\n                      Numerical Recipes in C: The Art of Scientific Computing\n                      , 2nd ed., Cambridge University Press (1992)."},{"key":"10.1117\/1.1901683_r46","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1109\/83.841511","volume":"9","author":"Nadadur","year":"2000","journal-title":"IEEE Trans. Image Process.","ISSN":"https:\/\/id.crossref.org\/issn\/1057-7149","issn-type":"print"}],"container-title":["Journal of Electronic Imaging"],"original-title":[],"link":[{"URL":"https:\/\/www.spiedigitallibrary.org\/journals\/journal-of-electronic-imaging\/volume-14\/issue-02\/023012\/Optimal-ridge-orientation-estimator-using-integrated-second-directional-derivative\/10.1117\/1.1901683.full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T21:31:28Z","timestamp":1790890288000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.spiedigitallibrary.org\/journals\/journal-of-electronic-imaging\/volume-14\/issue-02\/023012\/Optimal-ridge-orientation-estimator-using-integrated-second-directional-derivative\/10.1117\/1.1901683.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,4,1]]},"references-count":46,"journal-issue":{"issue":"02"},"URL":"https:\/\/doi.org\/10.1117\/1.1901683","relation":{},"ISSN":["1017-9909","1560-229X"],"issn-type":[{"value":"1017-9909","type":"print"},{"value":"1560-229X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,4,1]]}}}