Abstract
In this paper we study some optimization problems resulting from image processing tasks in medical applications. These problems are solved using a coordinate-free approach which not only reduces the computational effort in finding the solutions and enhances conceptual clarity, but also leads to closed-form solutions.
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Arun, K.S., Huang, T.S., Blostein, S.D.: Least-Squares Fitting of Two 3-D Point Sets. IEEE Transactions on Pattern Analysis and Machine Intelligence 9(5), 698–700 (1987)
Costantini, G., Casali, D.: Detection of Symmetry Axis by a CNN-based Algorithm. In: Proc. 11th WSEAS Conf. Circuits, pp. 46–49. WSEAS Press, Agios Nikolaos (2007)
Faugeras, O.: Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press, Cambrige (1993)
Hartley, R.I., Zisserman, A.W.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2001)
Hüper, K., Helmke, U.: Jacobi-type Methods in Computer Vision: A Case Study. Zeitschrift für Angewandte Mathematik und Mechanik 78(suppl. 3), 945–948 (1998)
Kanatani, K.: Geometric Computation for Machine Vision. Oxford University Press, Oxford (1993)
Ma, Y., Soatto, S., Kosečkà, J., Sastry, S.S.: An Invitation to 3-D Vision. Springer, New York (2004)
Nowinski, W.L., Yang, G.L., Yeo, T.T.: Computer-Aided Stereotactic Functional Neurosurgery Enhanced by the Use of the Multiple Brain Atlas Database. IEEE Transactions on Medical Imaging 19(1), 62–69 (2000)
Olver, P.J., Tannenbaum, A. (eds.): Mathematical Methods in Computer Vision. Springer, New York (2003)
Picci, G., Gilliam, D.S. (eds.): Dynamical Systems, Control, Coding, Computer Vision. Birkhäuser, Basel, Boston, Berlin (1999)
Richter, D., La Torre, F., Egger, J., Straßmann, G.: Tetraoptical Camera System for Medical Navigation. In: Proc. 17th Biennial International Eurasip Conference Biosignal, Brno (2004)
Talairach, J., Tournoux, P.: Co-Planar Stereotaxic Atlas of the Human Brain. Thieme-Verlag, Stuttgart (1988)
Tsai, R.Y.: A Versatile Camera Calibration Technique for High Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses. IEEE Journal of Robotics and Automation RA-3(4), 323–344 (1987)
Umeyama, S.: Least-Squares Estimation of Transformation Parameters Between Two Point Patterns. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(4), 376–380 (1991)
van Huffel, S., Vandewalle, J.: The Total Least Squares Problem. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (PA) (1991)
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Spindler, K. (2008). A Unified Mathematical Treatment of Regression Problems in Image Processing. In: Perner, P., Salvetti, O. (eds) Advances in Mass Data Analysis of Images and Signals in Medicine, Biotechnology, Chemistry and Food Industry. MDA 2008. Lecture Notes in Computer Science(), vol 5108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70715-8_10
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DOI: https://doi.org/10.1007/978-3-540-70715-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70714-1
Online ISBN: 978-3-540-70715-8
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