On the Choice of Band-Pass Quadrature Filters

Band-pass quadrature filters are extensively used in computer vision to estimate information from images such as: phase, energy, frequency and orientation,1 possibly at different scales and utilise this in further processing-tasks. The estimation is intrinsically noisy and depends critically on the choice of the quadrature filters. In this paper, we first study the mathematical properties of the quadrature filter pairs most commonly seen in the literature and then consider some new pairs derived from the classical feature detection literature. In the case of feature detection, we present the first attempt to design a quadrature pair based on filters derived for optimal edge/line detection. A comparison of the filters is presented in terms of feature detection performance, wherever possible, in the sense of Canny and in terms of phase stability. We conclude with remarks on how our analysis can aid in the choice of a filter pair for a given image processing task.

[1]  Svetha Venkatesh,et al.  On the classification of image features , 1990, Pattern Recognit. Lett..

[2]  J. Alison Noble,et al.  2D+T Acoustic Boundary Detection in Echocardiography , 1998, MICCAI.

[3]  S Marcelja,et al.  Mathematical description of the responses of simple cortical cells. , 1980, Journal of the Optical Society of America.

[4]  Nicolai Petkov,et al.  Nonlinear operator for blob texture segmentation , 1999, NSIP.

[5]  Michael Felsberg,et al.  A New Extension of Linear Signal Processing for Estimating Local Properties and Detecting Features , 2000, DAGM-Symposium.

[6]  C. Ronse.  The Phase Congruence Model for Edge Detection in Two-dimensional Pictures: a Mathematical Study , 1995 .

[7]  David Casasent,et al.  Real, imaginary, and clutter Gabor filter fusion for detection with reduced false alarms , 1994 .

[8]  Nicolai Petkov,et al.  Computational models of visual neurons specialised in the detection of periodic and aperiodic oriented visual stimuli: bar and grating cells , 1997, Biological Cybernetics.

[9]  Daniel Reisfeld,et al.  The constrained phase congruency feature detector: simultaneous localization, classification and scale determination , 1996, Pattern Recognit. Lett..

[10]  Til Aach,et al.  On texture analysis: Local energy transforms versus quadrature filters , 1995, Signal Process..

[11]  Edward H. Adelson,et al.  Shiftable multiscale transforms , 1992, IEEE Trans. Inf. Theory.

[12]  Christian Ronse,et al.  On Idempotence and Related Requirements in Edge Detection , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Eero P. Simoncelli,et al.  Steerable wedge filters for local orientation analysis , 1996, IEEE Trans. Image Process..

[14]  Nicolai Petkov,et al.  Nonlinear operator for oriented texture , 1999, IEEE Trans. Image Process..

[15]  James J. Little.  Accurate Early Detection of Discontinuities , 1992 .

[16]  Rui J. P. de Figueiredo,et al.  Reply to "On the Localization Performance Measure and Optimal Edge Detection" , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Edwin R. Hancock,et al.  Resolving edge-line ambiguities using probabilistic relaxation , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[18]  D J Field,et al.  Relations between the statistics of natural images and the response properties of cortical cells. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[19]  Jun Shen,et al.  An optimal linear operator for step edge detection , 1992, CVGIP Graph. Model. Image Process..

[20]  Hans Knutsson,et al.  Signal processing for computer vision , 1994 .

[21]  Kim L. Boyer,et al.  "On the localization performance measure and optimal edge detection" , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Robyn A. Owens,et al.  2D feature detection via local energy , 1997, Image Vis. Comput..

[23]  C. D. Kuglin,et al.  The phase correlation image alignment method , 1975 .

[24]  J. Daugman.  Two-dimensional spectral analysis of cortical receptive field profiles , 1980, Vision Research.

[25]  Anil K. Jain,et al.  Unsupervised texture segmentation using Gabor filters , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[26]  Henry Horng-Shing Lu,et al.  A textural approach based on Gabor functions for texture edge detection in ultrasound images. , 2001, Ultrasound in medicine & biology.

[27]  M. A. Oldfield,et al.  Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[28]  Wilson S. Geisler,et al.  Multichannel Texture Analysis Using Localized Spatial Filters , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[29]  Tai Sing Lee,et al.  Image Representation Using 2D Gabor Wavelets , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[31]  Michael Elad,et al.  Optimal filters for gradient-based motion estimation , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[32]  David J. Fleet,et al.  Stability of Phase Information , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[34]  Djemel Ziou,et al.  Line detection using an optimal IIR filter , 1991, Pattern Recognit..

[35]  Kenji Okajima,et al.  Two-dimensional Gabor-type receptive field as derived by mutual information maximization , 1998, Neural Networks.

[36]  Dennis F. Dunn,et al.  Optimal Gabor filters for texture segmentation , 1995, IEEE Trans. Image Process..

[37]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[38]  Marc Acheroy,et al.  Texture classification using Gabor filters , 2002, Pattern Recognit. Lett..

[39]  Rachid Deriche,et al.  Fast algorithms for low-level vision , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[40]  H. Tagare,et al.  On the localization performance measure and optimal edge detection , 1989, Sixth Multidimensional Signal Processing Workshop,.

[41]  Alan L. Yuille,et al.  A regularized solution to edge detection , 1985, J. Complex..

[42]  Amir A. Amini,et al.  Quantitative coronary angiography with deformable spline models , 1997, IEEE Transactions on Medical Imaging.

[43]  Thomas S. Huang,et al.  Image processing , 1971 .

[44]  Robyn A. Owens,et al.  Feature detection from local energy , 1987, Pattern Recognit. Lett..

[45]  Michael Felsberg,et al.  Scale Adaptive Filtering Derived from the Laplace Equation , 2001, DAGM-Symposium.

[46]  J. Canny.  Finding Edges and Lines in Images , 1983 .

[47]  Michael Felsberg,et al.  The Multidimensional Isotropic Generalization of Quadrature Filters in Geometric Algebra , 2000, AFPAC.

[48]  Steven W. Zucker,et al.  Local Scale Control for Edge Detection and Blur Estimation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[49]  David J. Fleet,et al.  Performance of optical flow techniques , 1994, International Journal of Computer Vision.

[50]  Edward H. Adelson,et al.  The Design and Use of Steerable Filters , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[51]  J. Alison Noble,et al.  2D+T acoustic boundary detection in echocardiography , 2000, Medical Image Anal..

[52]  Djemel Ziou,et al.  Edge Detection Techniques-An Overview , 1998 .

[53]  William E. Higgins,et al.  An algorithm for designing multiple Gabor filters for segmenting multi-textured images , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[54]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[55]  Cordelia Schmid,et al.  Indexing Based on Scale Invariant Interest Points , 2001, ICCV.

[56]  Thomas Bülow,et al.  Hypercomplex spectral signal representations for the processing and analysis of images , 1999 .

[57]  Manuel Servin,et al.  Robust quadrature filters , 1997 .

[58]  Kenji Okajima,et al.  The Gabor function extracts the maximum information from input local signals , 1998, Neural Networks.

[59]  David G. Lowe,et al.  Object recognition from local scale-invariant features , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[60]  Kim L. Boyer,et al.  On Optimal Infinite Impulse Response Edge Detection Filters , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[61]  William E. Higgins,et al.  Gabor filter design for multiple texture segmentation , 1996 .

[62]  Mitra Basu,et al.  A Gaussian Derivative Operator for Authentic Edge Detection and Accurate Edge Localization , 1999, Int. J. Pattern Recognit. Artif. Intell..

[63]  Olaf Kübler,et al.  Simulation of neural contour mechanisms: from simple to end-stopped cells , 1992, Vision Research.

[64]  Laurenz Wiskott,et al.  Segmentation from motion: combining Gabor- and Mallat-wavelets to overcome the aperture and correspondence problems , 1999, Pattern Recognit..

[65]  Chung-Lin Huang,et al.  Motion estimation method using a 3D steerable filter , 1995, Image Vis. Comput..

[66]  A.D. Jepson,et al.  The fast computation of disparity from phase differences , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[67]  Michael Felsberg,et al.  The monogenic signal , 2001, IEEE Trans. Signal Process..

[68]  M. Concetta Morrone,et al.  An adaptive approach to scale selection for line and edge detection , 1995, Pattern Recognit. Lett..

[69]  Nicolai Petkov,et al.  Comparison of texture features based on Gabor filters , 1999, Proceedings 10th International Conference on Image Analysis and Processing.

[70]  David J. Fleet,et al.  Computation of component image velocity from local phase information , 1990, International Journal of Computer Vision.

[71]  S. Klein,et al.  Hyperacuity thresholds of 1 sec: theoretical predictions and empirical validation. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[72]  Jun S. Huang,et al.  A transformation invariant matching algorithm for handwritten chinese character recognition , 1990, Pattern Recognit..

[73]  Rama Chellappa,et al.  A General Motion Model and Spatio-Temporal Filters for Computing Optical Flow , 1994, International Journal of Computer Vision.

[74]  Chuan Yi Tang,et al.  A 2.|E|-Bit Distributed Algorithm for the Directed Euler Trail Problem , 1993, Inf. Process. Lett..

[75]  Michael Brady,et al.  Mammographic Image Analysis , 1999, Computational Imaging and Vision.

[76]  Eero P. Simoncelli.  Design of multi-dimensional derivative filters , 1994, Proceedings of 1st International Conference on Image Processing.