This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Design and Implementation of Multisteerable Matched Filters
February 2012 (vol. 34 no. 2)
pp. 279-291
M. Muehlich, CanControls, Aachen, Germany
D. Friedrich, Inst. of Imaging & Comput. Vision, RWTH Aachen Univ., Aachen, Germany
T. Aach, Inst. of Imaging & Comput. Vision, RWTH Aachen Univ., Aachen, Germany
Image analysis problems such as feature tracking, edge detection, image enhancement, or texture analysis require the detection of multi-oriented patterns which can appear at arbitrary orientations. Direct rotated matched filtering for feature detection is computationally expensive, but can be sped up with steerable filters. So far, steerable filter approaches were limited to only one direction. Many important low-level image features are, however, characterized by more than a single orientation. We therefore present here a framework for efficiently detecting specific multi-oriented patterns with arbitrary orientations in grayscale images. The core idea is to construct multisteerable filters by appropriate combinations of single-steerable filters. We exploit that steerable filters are closed under addition and multiplication. This allows to derive a design guide for multisteerable filters by means of multivariate polynomials. Furthermore, we describe an efficient implementation scheme and discuss the use of weighting functions to reduce angular oscillations. Applications in camera calibration, junction analysis of images from plant roots, and the discrimination of L, T, and X-junctions demonstrate the potential of this approach.

[1] Z. Zhang, "A Flexible New Technique for Camera Calibration," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 11, pp. 1330-1334, Nov. 2000.
[2] J. Bouguet, "Visual Methods for Three-Dimensional Modeling," PhD dissertation, California Inst. of Tech nology, 1999.
[3] J. Kannala and S.S. Brandt, "A Generic Camera Model and Calibration Method for Conventional, Wide-Angle, and Fish-Eye Lenses," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 8, pp. 1335-1340, Aug. 2006.
[4] M. Jacob and M. Unser, "Design of Steerable Filters for Feature Detection Using Canny-Like Criteria," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 8, pp. 1007-1019, Aug. 2004.
[5] W. Freeman and E. Adelson, "The Design and Use of Steerable Filters," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 9, pp. 891-906, Sept. 1991.
[6] J. Bigün and G.H. Granlund, "Optimal Orientation Detection of Linear Symmetry," Proc. IEEE First Int'l Conf. Computer Vision, pp. 433-438, June 1987.
[7] J. Bigün, G.H. Granlund, and J. Wiklund, "Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 8, pp. 775-790, Aug. 1991.
[8] M. Kass and A. Witkin, "Analyzing Oriented Patterns," Computer Vision, Graphics, and Image Processing, vol. 37, pp. 362-385, 1987.
[9] S. Di Zenzo, "A Note on the Gradient of a Multi-Image," Computer Vision, Graphics, and Image Processing, vol. 33, pp. 116-125, 1986.
[10] M. Shizawa and K. Mase, "Simultaneous Multiple Optical Flow Estimation," Proc. Int'l Conf. Pattern Recognition, pp. 274-278, 1990.
[11] M. Shizawa and K. Mase, "A Unified Computational Theory for Motion Transparency and Motion Boundaries Based on Eigenenergy Analysis," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 289-295, 1991.
[12] T. Iso and M. Shizawa, "Detecting L-, T-, and X-Junctions from Low-Order Image Derivatives," Proc. Visual Comm. and Image Processing, pp. 1185-1197, Nov. 1993.
[13] T. Aach, C. Mota, I. Stuke, M. Mühlich, and E. Barth, "Analysis of Superimposed Oriented Patterns," IEEE Trans. Image Processing, vol. 15, no. 12, pp. 3690-3700, Dec. 2006.
[14] M. Mühlich and T. Aach, "A Theory for Multiple Orientation Estimation," Proc. European Conf. Computer Vision, H. Bischof and A. Leonardis, eds., pp. 69-82, 2006.
[15] M. Mühlich and T. Aach, "Analysis of Multiple Orientations," IEEE Trans. Image Processing, vol. 18, no. 7, pp. 1424-1437, July 2009.
[16] W. Yu, K. Daniilidis, and G. Sommer, "Rotated Wedge Averaging Method for Junction Characterization," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 390-395, June 1998.
[17] P. Perona, "Steerable-Scalable Kernels for Edge Detection and Junction Analysis," Image and Vision Computing, vol. 10, no. 10, pp. 663-672, 1992.
[18] M. Michaelis and G. Sommer, "Junction Classification by Multiple Orientation Detection," Proc. Third European Conf. Computer Vision, pp. 101-108, May 1994.
[19] E. Simoncelli and H. Farid, "Steerable Wedge Filters," Proc. Fifth IEEE Int'l Conf. Computer Vision, pp. 189-195, June 1995.
[20] E. Simoncelli and H. Farid, "Steerable Wedge Filters for Local Orientation Analysis," IEEE Trans. Image Processing, vol. 5, no. 9, pp. 1377-1382, Sept. 1996.
[21] M. Mühlich, T. Dahmen, and T. Aach, "Design of Multi-Steerable Filters and Their Application for the Detection of Corners and Junctions," Proc. IEEE Int'l Conf. Image Processing, Sept. 2007.
[22] M. Mülich, T. Dahmen, and T. Aach, "Doubly-Rotated Matched Filtering," Proc. 15th European Signal Processing Conf., Sept. 2007.
[23] M. Mühlich and T. Aach, "High Accuracy Feature Detection for Camera Calibration: A Multi-Steerable Approach," DAGM '07: Proc. 29th Ann. Symp. German Assoc. for Pattern Recognition, pp. 284-293, Sept. 2007.
[24] A. Oppenheim and R. Schafer, Discrete-Time Signal Processing. Prentice-Hall, 1999.
[25] W. Yu, K. Daniilidis, and G. Sommer, "Approximate Orientation Steerability Based on Angular Gaussians," IEEE Trans. Image Processing, vol. 10, no. 2, pp. 193-205, Feb. 2001.
[26] Y. Katznelson, An Introduction to Harmonic Analysis. Dover Publisher, 1976.
[27] M. Michaelis and G. Sommer, "A Lie Group Approach to Steerable Filters," Pattern Recognition Letters, vol. 16, no. 11, pp. 1165-1174, 1995.
[28] Y. Hel-Or and P.C. Teo, "Canonical Decomposition of Steerable Functions," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 809-816, 1996.
[29] Y. Hel-Or and P.C. Teo, "A Common Framework for Steerability, Motion Estimation and Invariant Feature Detection," Proc. IEEE Int'l Symp. Circuits and Systems, vol. 5, pp. 337-340, May/June 1998.
[30] C.G. Harris and M.J. Stevens, "A Combined Corner and Edge Detector," Proc. Fourth Alvey Vision Conf., pp. 147-151, 1988.
[31] M. Mühlich, D. Truhn, K. Nagel, A. Walter, H. Scharr, and T. Aach, "Measuring Plant Root Growth," Proc. 30th DAGM Symp. Pattern Recognition, G. Rigoll, ed., pp. 497-506, 2008.
[32] K.A. Nagel, B. Kastenholz, S. Jahnke, D. van Dusschoten, T. Aach, M. Mühlich, D. Truhn, H. Scharr, S. Terjung, A. Walter, and U. Schurr, "Temperature Response of Roots: Impact on Growth, Root System Architecture and Implications for Phenotyping," Functional Plant Biology, vol. 36, pp. 947-959, 2009.

Index Terms:
matched filters,filtering theory,image processing,junction analysis,multisteerable matched filters,image analysis,feature tracking,edge detection,image enhancement,texture analysis,multioriented pattern detection,rotated matched filtering,feature detection,steerable filter,multivariate polynomials,angular oscillations,camera calibration,Polynomials,Junctions,Approximation methods,Feature extraction,Correlation,Fourier series,Image edge detection,camera calibration.,Steerable filters,feature detection,junction analysis,orientation estimation,rotated matched filtering,multi-oriented patterns,template equation,trigonometric polynomials,multivariate polynomials
Citation:
M. Muehlich, D. Friedrich, T. Aach, "Design and Implementation of Multisteerable Matched Filters," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 2, pp. 279-291, Feb. 2012, doi:10.1109/TPAMI.2011.143
Usage of this product signifies your acceptance of the Terms of Use.