An Automated Model for Fitting a Hemi-Ellipsoid and Calculating Eigenvalues Using Matrices
- 1 College of Engineering, University of South Florida, Tampa, USA;USF Health Morsani College of Medicine, University of South Florida, Tampa, USA
- 2 College of Engineering, University of South Florida, Tampa, USA;USF Health Morsani College of Medicine, University of South Florida, Tampa, USA
- 3 College of Engineering, University of South Florida, Tampa, USA
Abstract
Ellipsoid modeling is essential in a variety of fields, ranging from astronomy to medicine. Many response surfac es can be approximated by a hemi-ellipsoid, allowing estimation of shape, magnitude, and orientation via ortho gonal vectors. If the shape of the ellipsoid under investigation changes over time, serial estimates of the orthogonal vectors allow time-sequence mapping of these complex response surfaces. We have developed a quantitative, analytic method that evaluates the dynamic changes of a hemi-ellipsoid over time that takes data points from a surface and transforms the data using a kernel function to matrix form. A least square analysis minimizes the difference between actual and calculated values and constructs the corresponding eigenvectors. With this me thod , it is possible to quantify the shape of a dynamic hemi-ellipsoid over time. Potential applications include mo deling pressure surfaces in a variety of applications including medical.
- S. B. Pope, “Algorithms for Ellipsoids,” Cornell University Report FDA 08-01, 2008.
- D. A. Turner, I. J. Anderson, J. C. Mason and M. G. Cox, “An Algorithm for Fitting an Ellipsoid to Data,” 1999. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.2773
- E. S. Maini, “Enhanced Direct Least Square Fitting of Ellipses,” International Journal of Pattern Recognition and Artificial Intelligence, Vol. 20, No. 6, 2006, pp. 939-953. http://dx.doi.org/10.1142/S021800140600506X
- I. Markovsky, A. Kukush and S. Van Huffel, “Consistent Least Squares Fitting of Ellipsoids,” Numerische Mathematik, Vol. 98, No. 1, 2004, pp. 177-194. http://dx.doi.org/10.1007/s00211-004-0526-9
- S. J. Ahn, “Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space,” Ph.D. Dissertation, University of Stuttgard, Stuttgard, 2004.
- A. Gefen, “Reswick and Rogers Pressure-Time Curve for Pressure Ulcer Risk. Part 1,” Nursing Standard, Vol. 23, No. 45, 2009, pp. 64-74. http://dx.doi.org/10.7748/ns2009.07.23.45.64.c7115
- S. Portnoy, N. Vuillerme, Y. Payan and A. Gefen, “Clinically Oriented Real-Time Monitoring of the Individual’s Risk for Deep Tissue Injury,” Medical & Biological Engineering & Computing, Vol. 49, No. 4, 2011, pp. 473-483.
- L. Agam and A. Gefen, “Toward Real-Time Detection of Deep Tissue Injury Risk in Wheelchair Users Using Hertz Contact Theory,” Journal of Rehabilitation Research and Development, Vol. 45, No. 4, 2008, pp. 537-550. http://dx.doi.org/10.1682/JRRD.2007.07.0114
- A. Gefen, “Bioengineering Models of Deep Tissue Injury,” Advances in Skin and Woundcare, Vol. 21, No. 1, 2008, pp. 30-36. http://dx.doi.org/10.1097/01.ASW.0000305403.89737.6c
- E. L. Ganz, N. Shabshin, Y. Itzchak and A. Gefen, “Assessment of Mechanical Conditions in Sub-Dermal Tissues during Sitting: A Combined Experimental-MRI and Finite Element Approach,” Journal of Biomechanics, Vol. 40, No. 7, 2007, pp. 14431454. http://dx.doi.org/10.1016/j.jbiomech.2006.06.020
- “Matrices and Linear Algebra,” Reference Guide for Matrix.xla, 2006. http://digidownload.libero.it/foxes/matrix/MatrixTutorial1.pdf