OPTIMIZATION OF 3D LOCAL ORIENTATION MAP CALCULATION IN THE MATLAB FRAMEWORK

Ranya Al Darwich

raldarwich@kis.p.lodz.pl
Lodz University of Technology, Institute of Applied Computer Science (Poland)

Laurent Babout


Lodz University of Technology, Institute of Applied Computer Science (Poland)

Abstract

This paper presents the development and evaluation of a new approach toward the optimization of 3D local orientation map calculation in the Matlab framework. This new approach can be detailed as: optimize eigenvector calculation for PCA analysis of X-ray micro tomography images of lamellar Titanium alloys image. We use two different methods to find the eigenvector of the largest eigenvalue and compare them with the Matlab built-in function (eigs). The results show a steep decrease of the calculation time using the authors' method compared to the Matlab built-in function.


Keywords:

local orientation, PCA analysis, eigenvalue, eigenvector, matrix of inertia

Babout L., Jopek L., Janaszewski M.: A New Directional Filter Bank for 3D Texture Segmentation: Application to Lamellar Microstructure in titanium Alloys, MVA2013 IAPR International Conference on Machine Vision Applications, May 20-23, 2013, Kyoto, JAPAN.
  Google Scholar

Eriksen E.: Principal Minors and the Hessian, BI Norwegian School of Management Department of Economics, October 01, 2010.
  Google Scholar

Wituła R., Słota D.: Cardano’s formula, square roots, Chebyshev polynomials and radicals, Journal of Mathematical Analysis and Applications, vol 363, Issue 2, 15 March 2010 , 639–647.
  Google Scholar

Jeulin D., Moreaud M.: Segmentation of 2D and 3D textures from estimates of the local orientation, Image Anal Stereol 27, 2008, 183-192.
  Google Scholar

Lanczos C.: An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators, Journal of Research of the National Bureau of Standard, vol 45, No. 4, October 1950.
  Google Scholar

Lehoucq R.B., Sorensen D.C.: Deflation Techniques for an Implicitly Re-Started Arnoldi Iteration, SIAMJ. Matrix Analysis and Applications, SIAM Journal on Matrix Analysis and Applications, Vol 17, Number 4, 1996, 789-821.
  Google Scholar

Schell J.S.U., Renggli M., van Lenthe G.H., Mu ̈ller R., Ermanni P.: Microcomputed tomography determination of glass fibre reinforced polymer mesostructure, Composites Science and Technologie,Vol66, Issue 13 October, 2006, 2016–2022.
  Google Scholar

Download


Published
2015-06-30

Cited by

Al Darwich, R., & Babout, L. . (2015). OPTIMIZATION OF 3D LOCAL ORIENTATION MAP CALCULATION IN THE MATLAB FRAMEWORK. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 5(2), 22–24. https://doi.org/10.5604/20830157.1159324

Authors

Ranya Al Darwich 
raldarwich@kis.p.lodz.pl
Lodz University of Technology, Institute of Applied Computer Science Poland

Authors

Laurent Babout 

Lodz University of Technology, Institute of Applied Computer Science Poland

Statistics

Abstract views: 171
PDF downloads: 47