OBJECT MODELLING: CALCULATION OF F-MATRIX USING VIDEO IMAGES

Year 2014, Volume: 16 Issue: 48, 9 - 20, 01.09.2014

Abdullah Erhan Akkaya Muhammed Fatih Talu

Abstract

Epipolar geometry, describes the geometric relationship between pairs of images that
belongs to an object or a scene taken from two different angles. To reveal the geometric
relationship, capturing of similar points in the two images, matching these points and
calculating fundamental matrix (F-matrix) that represents the epipolar geometry are required.
Calculation of the fundamental matrix has vital importance for the next stages like 3D
modelling, motion segmentation, stereo vision, camera calibration. In this study, effective Fmatrix
calculation methods of different concepts were examined on six image pairs and
comparisons were made according to the algorithms’ time and accuracy criteria. The obtained
numerical results are presented in tables.

Keywords

Fundamental matrix, Epipolar geometry, Hartley normalization, Sampson distance

NESNE MODELLEME: VIDEO İMGELERI KULLANILARAK F-MATRISININ HESAPLANMASI

Abstract

Epipolar geometri, bir nesneye veya sahneye ait farklı iki açıdan çekilmiş görüntü çiftleri
arasındaki geometrik ilişkiyi tanımlamaktadır. Geometrik ilişkiyi ortaya çıkarabilmek için iki
görüntüdeki benzer noktaların yakalanması, eşleştirilmesi ve epipolar geometriyi temsil eden
temel matrisin (F–fundamental matrix) hesaplanması gerekmektedir. Temel matrisin
hesaplanması, 3D modelleme, hareket segmentasyonu, stereo görme, kamera kalibrasyonu gibi
sonraki aşamalar için hayati derecede önem arz etmektedir. Bu çalışmada, farklı konseptlerdeki
etkin F-matrisi hesaplama yöntemleri altı görüntü çifti üzerinde incelenmiş, algoritmaların
zaman ve doğruluk kıstaslarına göre karşılaştırmaları yapılmıştır. Elde edilen sayısal sonuçlar
tablolar halinde sunulmuştur.

Keywords

Temel matris, Epipolar geometri, Hartley normalizasyonu, Sampson uzaklığı

References

• Armangué X., Salvi J. (2003): "Overall View Regarding Fundamental Matrix Estimation", Image and Vision Computing, Cilt 21, No. 2, s.205–220.
• Boufama B., Mohr R. (1995): "Epipole And Fundamental Matrix Estimation Using Virtual Parallax", Proceedings of IEEE Fifth International Conference on Computer Vision, s.1030–1036.
• Chojnacki W., Brooks M. J., Hengel A. V. D., Gawley D. (2002): "A New Approach to Constrained Parameter Estimation Applicable to Some Computer Vision Problems", Statistical Methods in Video Processing Workshop Held In Conjunction With ECCV, Cilt 2, s.1-2.
• Chojnacki W., Brooks M. J., Hengel A. V. D., Gawley D. (2004): "A New Constrained Parameter Estimator For Computer Vision Applications", Image and Vision Computing, Cilt 22, No. 2, s.85–91.
• Chojnacki W., Brooks M. J., Hengel, A. V. D., Gawley D. (2000): "On The Fitting Of Surfaces To Data With Covariances", IEEE Transactions on Pattern Analysis and Machine Intelligence, Cilt 22, No. 11, s.1294–1303.
• Hartley, R. I. (1995): "In Defence Of The 8-Point Algorithm", Fifth International Conference on Computer Vision, s.1064–1070.
• Hartley R., Zisserman A. (2003): "Multiple View Geometry In Computer Vision", Cambridge University Press.
• Li Y., Velipasalar S., Gürsoy M. C. (2013): "An Improved Evolutionary Algorithm For Fundamental Matrix Estimation", 10th IEEE International Conference on Advanced Video and Signal Based Surveillance (AVSS), s. 226–231
• Longuet-Higgins H. C. (1981): "A Computer Algorithm For Reconstructing A Scene From Two Projections", Nature, Cilt. 293, No. 5828, s.133–135.
• Lowe D. G. (2004): "Distinctive Image Features from Scale-Invariant Keypoints", International Journal of Computer Vision, Cilt 60, No. 2, s.91–110.
• Luong Q. T., Faugeras O. D. (1996): "The Fundamental Matrix: Theory, Algorithms, And Stability Analysis", International Journal of Computer Vision, Cilt 17, No. 1, s.43–75.
• Salvi J (1997): "An Approach To Coded Structured Light To Obtain Three Dimensional Information", Universitat de Girona, Departament d’Electrònica, Informàtica i Automàtica, PhD Thesis.
• Sampson P. D. (1982): "Fitting Conic Sections To “Very Scattered” Data: An Iterative Refinement Of The Bookstein Algorithm", Computer Graphics and Image Processing, Cilt 18, No. 1, s.97–108.
• Torr P. H. S. (2002): "Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Manifold Fitting", International Journal of Computer Vision, Cilt 50, No. 1, s.35- 61.
• Torr P. H. S., Murray D. W. (1997): "The Development And Comparison Of Robust Methods For Estimating The Fundamental Matrix", International Journal of Computer Vision, Cilt 24, s.271–300.
• Torr P. H. S., Zisserman A. (2000): "MLESAC: A New Robust Estimator with Application to Estimating Image Geometry", Computer Vision and Image Understanding, Cilt 78, No. 1, s.138–156. Vedaldi A. (2006): "SIFT for MATLAB", University of California. http://www.robots.ox.ac.uk/~vedaldi/code/sift.html, Erişim Tarihi: 15.03.2014
• Zhang Z. (1998): "Determining the Epipolar Geometry and its Uncertainty: A Review", International Journal of Computer Vision, Cilt 27, No.2, s.161–195.
• Zheng Y., Sugimoto S., Okutomi M. (2011): "A Branch And Contract Algorithm For Globally Optimal Fundamental Matrix Estimation", IEEE Conference on Computer Vision and Pattern Recognition (CVPR)", s.2953–2960.