Abstract
This paper proposes a robust estimation and validation framework for characterizing local structures in a positive multi-variate continuous function approximated by a Gaussian-based model. The new solution is robust against data with large deviations from the model and margin-truncations induced by neighboring structures. To this goal, it unifies robust statistical estimation for parametric model fitting and multi-scale analysis based on continuous scale-space theory. The unification is realized by formally extending the mean shift-based density analysis towards continuous signals whose local structure is characterized by an anisotropic fully-parameterized covariance matrix. A statistical validation method based on analyzing residual error of the chi-square fitting is also proposed to complement this estimation framework. The strength of our solution is the aforementioned robustness. Experiments with synthetic 1D and 2D data clearly demonstrate this advantage in comparison with the γ-normalized Laplacian approach [12] and the standard sample estimation approach [13, p.179]. The new framework is applied to 3D volumetric analysis of lung tumors. A 3D implementation is evaluated with high-resolution CT images of 14 patients with 77 tumors, including 6 part-solid or ground-glass opacity nodules that are highly non-Gaussian and clinically significant. Our system accurately estimated 3D anisotropic spread and orientation for 82% of the total tumors and also correctly rejected all the failures without any false rejection and false acceptance. This system processes each 32-voxel volume-of-interest by an average of two seconds with a 2.4GHz Intel CPU. Our framework is generic and can be applied for the analysis of blob-like structures in various other applications.
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Chen, Y., McInroy, J.: Estimating symmetric, positive definite matrices in robotic control. In: IEEE Int. Conf. Robotics and Automation, Washington D.C, pp. 4269–4274 (2002)
Comaniciu, D.: An algorithm for data-driven bandwidth selection. IEEE Trans. Pattern Anal. Machine Intell. 25(2), 281–288 (2003)
Comaniciu, D., Meer, P.: Mean shift: A robust approach toward feature space analysis. IEEE Trans. Pattern Anal. Machine Intell. 24(5), 603–619 (2002)
Fukunaga, K.: Statistical Pattern Recognition. Academic Press, San Diego (1990)
Golub, G., van Loan, C.: Matrix Computations. Johns Hopkins University Press, Baltimore (1996)
Henschke, C., Yankelevitz, D., Mirtcheva, R., McGuinness, G., McCauley, O., Miettinen, D.: CT screening for lung cancer: frequency and significance of partsolid and nonsolid nodules. AJR Am. J. Roentgenol. 178(5), 1053–1057 (2002)
Hu, H.: Positive definite constrained least-squares estimation of matrices. Linear Algebra and Its Applications 229, 167–174 (1995)
Kanazawa, Y., Kanatani, K.: Do we really have to consider covariance matrices for image features? In: Int. Conf. Computer Vision, Vancouver, pp. 586–591 (2001)
Koenderink, J.: The structure of images. Biol. Cybern. 50, 363–370 (1984)
Lee, Y., Hara, T., Fujita, H., Itoh, S., Ishigaki, T.: Automated detection of pulmonary nodules in helical CT images based on an improved template-matching technique. IEEE Trans. Medical Imaging 20(7), 595–604 (2001)
Lillholm, M., Nielsen, M., Griffin, L.: Feature-based image analysis. Int. J. Comput. Vision 52(2/3), 73–95 (2003)
Lindeberg, T.: Feature detection with automatic scale selection. Int. J. Comput. Vision 30(2), 79–116 (1998)
Matei, B.: Heteroscedastic Errors-In-Variables Models in Computer Vision. PhD thesis, Rutgers University (2001)
Nielsen, M., Florack, L., Deriche, R.: Regularization, scale space, and edge detection filters. J. Mathematical Imaging and Vision 7(4), 291–307 (1997)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell. 12(7), 629–639 (1990)
Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C. Cambridge University Press, Cambridge (1992)
Rousseeuw, P., Leroy, A.: Robust Regression and Outlier Detection. John Wiley, New York (1987)
Takizawa, H., Yamamoto, S., Matsumoto, T., Tateno, Y., Iinuma, T., Matsumoto, M.: Recognition of lung nodules from X-ray CT images using 3D markov random field models. In: Int. Conf. Pattern Recog., Quebec City (2002)
van Ginneken, B., ter Harr Romeny, B., Viergever, M.: Computer-aided diagnosis in chest radiography: A survey. IEEE Trans. Medical Imaging 20(12), 1228–1241 (2001)
van Huffel, S., Vandewalle, J.: The Total Least Squares Problem Computational Aspects and Analysis. SIAM, Philadelphia (1991)
Witkin, A.: Scale-space filtering. In: Int. Joint. Conf. Artificial Intell., Karlsruhe, pp. 1019–1021 (1983)
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Okada, K., Comaniciu, D., Dalal, N., Krishnan, A. (2004). A Robust Algorithm for Characterizing Anisotropic Local Structures. In: Pajdla, T., Matas, J. (eds) Computer Vision - ECCV 2004. ECCV 2004. Lecture Notes in Computer Science, vol 3021. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24670-1_42
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DOI: https://doi.org/10.1007/978-3-540-24670-1_42
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