This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Nonlinear Multiresolution Techniques with Applications to Scientific Visualization in a Haptic Environment
January-March 2001 (vol. 7 no. 1)
pp. 76-93

Abstract—This paper develops nonlinear multiresolution techniques for scientific visualization utilizing haptic methods. The visualization of data is critical to many areas of scientific pursuit. Scientific visualization is generally accomplished through computer graphic techniques. Recent advances in haptic technologies allow visual techniques to be augmented with haptic methods. The kinesthetic feedback provided through haptic techniques provides a second modality for visualization and allows for active exploration. Moreover, haptic methods can be utilized by individuals with visual impairments. Haptic representations of large data sets, however, can be confusing to a user, especially if a visual representation is not available or cannot be used. Additionally, most haptic devices utilize point interactions, resulting in a low information bandwidth and further complicating data exploration. Multiresolution techniques can be utilized to address the issues of low information bandwidth and data complexity. Commonly used multiresolution techniques are based on the wavelet decomposition. Such linear techniques, however, tend to smooth important data features, such as discontinuities or edges. In contrast, nonlinear techniques can be utilized that preserve edge structures while removing fine data details. This paper develops a multiresolution data decomposition method based on the affine median filter. This results in a hybrid structure that can be tuned to yield a decomposition that varies from a linear wavelet decomposition to that produced by the median filter. The performance of this hybrid structure is analyzed utilizing deterministic signals and statistically in the frequency domain. This analysis and qualitative and quantitative implementation results show that the affine median decomposition has advantages over previously proposed methods. In addition to multiresolution decomposition development, analysis, and results, haptic implementation methods are presented.

[1] K.J. Kokjer, “The Information Capacity of the Human Fingertip,” IEEE Trans. Systems, Man, and Cybernetics, vol. 17, no. 1, 1987.
[2] T.L. Brooks, “Telerobotic Response Requirements,” Proc. IEEE Int'l Conf. Systems, Man, and Cybernetics, pp. 113-120, 1990, also Report No. STX/ROB/90-03, STX Corp., Lanham, Md.
[3] J.C. Craig, “Vibrotactile Pattern Perception: Extraordinary Observers,” Science, vol. 196, 1977.
[4] G. Burdea, J. Zhuang, E. Roskos, D. Silver, and N. Langrana, “A Portable Dextrous Master with Force Feedback,” Presence—Teleoperators and Virtual Environments, vol. 1, no. 1, pp. 18-27, Mar. 1992.
[5] G. Burdea, Force and Touch Feedback for Virtual Reality, John Wiley and Sons, New York, 1996.
[6] H. Iwata, “Pen-Based Haptic Virtual Environment,” Proc. IEEE Virtual Reality Ann. Int'l Symp., pp. 287-292, 1993.
[7] B. Jackson and L. Rosenberg, “Force Feedback and Medical Simulation,” Interactive Technology and the New Paradigm for Healthcare, K. Morgan, R. Satava, H. Sieburg, R. Mattheus, and J. Christensen, eds., chapter 24, pp. 147-151, Amsterdam: IOS Press, Jan. 1995.
[8] EXOS, Co., “Sensing and Force Reflecting Exoskeleton (SAFiRE) Specifications,” company brochure, Woburn, Mass., year?
[9] T. Massie and J.K. Salisbury, “The PHANToM Haptic Interface: A Device for Probing Virtual Objects,” Proc. ASME Winter Ann. Meeting, Symp. Haptic Interfaces for Virtual Environment and Teleoperator Systems, 1994.
[10] A. Mor, S. Gibson, and J.T. Samosky, “Interacting with 3-Dimensional Medical Data Haptic Feedback for Surgical Simulation,” Proc. First PHANToM Users Group Workshop, J.K. Salisbury and M.A. Srinivasan, eds., MIT Research Lab for Electronics Technical Report No. 612 and MIT Artificial Intelligence Laboratory Technical Report AITR-1596, Cambridge, Mass., Dec. 1996.
[11] W.R. Mark, S.C. Randolph, M. Finch, and J.M. Van Verth, “UNC-CH Force-Feedback Library,” Internal Technical Report TR94-056, Revision C, Univ. of North Carolina at Chapel Hill, Apr. 1996.
[12] W.R. Mark, S.C. Randolph, M. Finch, J.M. Van Verth, and R.M. Taylor II, “Adding Force Feedback to Graphics Systems: Issues and Solutions,” Computer Graphics: Proc. SIGGRAPH '96, Aug. 1996.
[13] L.B. Rosenberg, “Feelit Mouse: Adding a Realistic Sense of Feel to the Computing Experience,” technical report, Immersion Corp., San Jose, Calif., 1997.
[14] Haptic Tech nologies, “Mouse CAT,” technical report, Montreal, Quebec, Canada, 1998, http:/www.haptech.com.
[15] T.P. Way and K.E. Barner, “Automatic Visual to Tactile Translation, Part I: Human Factors, Access Methods and Image Manipulation,” IEEE Trans. Rehabilitation Eng., vol. 5, pp. 81-94, Mar. 1997.
[16] T.P. Way and K.E. Barner, “Automatic Visual to Tactile Translation, Part II: Evaluation of the Tactile Image Creation System,” IEEE Trans. Rehabilitation Eng., vol. 5, pp. 95-105, Mar. 1997.
[17] D. Griffith, “Computer Access for Person Who Are Blind or Visually Impaired: Human Factors Issues,” Human Factors, vol. 68, no. 2, 1990.
[18] A. Ciampalini, P. Cignoni, C. Montani, and R. Scopigno, “Multiresolution Decimation Based on Global Error,” The Visual Computer, vol. 13, pp. 228-246, June 1997.
[19] P. Cignoni, C. Montani, and R. Scopigno, “A Comparison of Mesh Simplification Alogrithms,” Computers and Graphics, vol. 22, 1998.
[20] R.J. Moorhead and Z. Zhu, “Signal Processing Aspects of Scientific Visualization,” IEEE Signal Processing Magazine, pp. 20-41, Sept. 1995.
[21] A. Rosenfel, Multiresolution Image Processing. Springer-Verlag, 1984.
[22] P.S. Heckbert and M. Garland, “Survey of Polygonal Surface Simplification Alogorithms,” technical report, Carnegie Mellon Univ., 1997.
[23] J.M. Lounsbery, “Multiresolution Analysis for Surfaces of Arbitrary Topological Type,” PhD thesis, Univ. of Washington, Sept. 1994.
[24] M. Ech, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle, "Multiresolution Analysis of Arbitrary Meshes," Computer Graphics Proc. Ann. Conf. Series (Proc. Siggraph '95), pp. 173-182, 1995.
[25] H. Hoppe, “Efficient Implementation of Progressive Meshes,” Computer Graphics, SIGGRAPH '97 Proc., vol. 22, no. 1, pp. 27-36, 1998.
[26] P. Cignoni, E. Puppo, and R. Scopigno, “Representation and Visualization of Terrain Surfaces at Variable Resolution,” Proc. Scientific Visualization '95, pp. 50-68, 1995.
[27] S.G. Mallat,“A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, 1989.
[28] G.R. Arce, N.C. Gallagher Jr., and T.A. Nodes, “Median Filters: Theory and Applications,” Advances in Computer Vision and Image Processing, T.S. Huang, ed., vol. 2, JAI Press, 1986.
[29] K.E. Barner and G.R. Arce, “Order-Statistic Filtering and Smoothing of Time Series: Part 2,” Order Statistics and Their Applications, C.R. Rao and N. Balakrishnan, eds., vol. 16 of Handbook of Statistics, Amsterdam, The Netherlands: Elsevier Science, 1998.
[30] A. Flaig, G.R. Arce, and K.E. Barner, “Affine Order Statistic Filters: A Data-Adaptive Filtering Framework for Nonstationary Signals,” IEEE Trans. Signal Processing, vol. 46, pp. 2101-2112, Aug. 1998.
[31] J.P. Fritz and K.E. Barner, “Design of a Haptic Data Visualization System for People with Visual Impairments,” IEEE Trans. Rehabilitation Eng., vol. 7, Sept. 1999.
[32] C.B. Zilles and J.K. Salisbury, A Constraint-Based God-Object Method for Haptic Display Proc. Int'l Conf. Intelligent Robots and Systems, pp. 3146-3152, 1995.
[33] I. Biederman, “Human Image Understanding: Recent Research and Theory,” Computer Vision, Graphics, and Image Processing, vol. 32, 1985.
[34] I. Daubechies,“Ten lectures on wavelets,” SIAM CBMS-61, 1992.
[35] G. Strang and T.Q. Nguyen, Wavelets and Filter Banks. Wellesley-Cambridge Press, 1996.
[36] K. Anandakumar and S.A. Kassam, “Nonlinear Multiresolution Decomposition with Application in Image Restoration,” J. Electronic Imaging, Special Ed. Signal Precessing, vol. 5, pp. 367-378, July 1997.
[37] P. Ghandi and S.A. Kassam, “Design and Performance of Combination Filters,” IEEE Trans. Signal Processing, vol. 39, July 1991.
[38] R.C. Hardie and C.G. Boncelet Jr., “LUM Filters: A Class Rank Order Based Filters for Smoothing and sharpening,” IEEE Trans. Signal Processing, vol. 41, pp. 1061-1076, Mar. 1993.
[39] I. Pitas and A.N. Venetsanopoulos, Non-Linear Filters. Kluwer, 1989.
[40] N.C. Gallagher Jr. and G.L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 29, pp. 1136-1141, Dec. 1981.
[41] K.E. Barner, A. Flaig, and G.R. Arce, “Fuzzy Time-Rank Relations and Order Statistics,” IEEE Signal Processing Letters, vol. 5, pp. 252-255, Oct. 1988.
[42] F. Palmieri and C.G. Boncelet, Jr., “Ll-Filters—A New Class of Order Statistic Filters,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 37, May 1989.
[43] M.W. Asghar, “Nonlinear Multiresolution Techniques with Applications to Scientific Visualization in a Haptic Environment,” master's thesis, Univ. of Delaware, May 1999.

Index Terms:
Visualization, haptics, multiresolution, wavelets, nonlinear filtering, blindness.
Citation:
Mohammad Waqas Asghar, Kenneth E. Barner, "Nonlinear Multiresolution Techniques with Applications to Scientific Visualization in a Haptic Environment," IEEE Transactions on Visualization and Computer Graphics, vol. 7, no. 1, pp. 76-93, Jan.-March 2001, doi:10.1109/2945.910825
Usage of this product signifies your acceptance of the Terms of Use.