EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Steerable Snake


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

3-D Shape Estimation of DNA Molecules from Stereo Cryo-Electron Micro-Graphs Using a Projection-Steerable Snake

M. Jacob, T. Blu, C. Vaillant, J.H. Maddocks, M. Unser

IEEE Transactions on Image Processing, vol. 15, no. 1, pp. 214-227, January 2006.



We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; we choose the global model as a 3-D filament with a B-spline skeleton and a specified radial profile. The active contour algorithm iteratively updates the B-spline coefficients, which requires us to evaluate the projections and match them with the micrographs at every iteration. Since the evaluation of the projections of the global model is computationally expensive, we propose a fast algorithm based on locally approximating it by elongated blob-like templates. We introduce the concept of projection-steerability and derive a projection-steerable elongated template. Since the two-dimensional projections of such a blob at any 3-D orientation can be expressed as a linear combination of a few basis functions, matching the projections of such a 3-D template involves evaluating a weighted sum of inner products between the basis functions and the micrographs. The weights are simple functions of the 3-D orientation and the inner-products are evaluated efficiently by separable filtering. We choose an internal energy term that penalizes the average curvature magnitude. Since the exact length of the DNA molecule is known a priori, we introduce a constraint energy term that forces the curve to have this specified length. The sum of these energies along with the image energy derived from the matching process is minimized using the conjugate gradients algorithm. We validate the algorithm using real, as well as simulated, data and show that it performs well.


@ARTICLE(http://bigwww.epfl.ch/publications/jacob0601.html,
AUTHOR="Jacob, M. and Blu, T. and Vaillant, C. and Maddocks, J.H. and
        Unser, M.",
TITLE="\mbox{3-D} Shape Estimation of {DNA} Molecules from Stereo
        Cryo-Electron Micro-Graphs Using a Projection-Steerable Snake",
JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="2006",
volume="15",
number="1",
pages="214--227",
month="January",
note="")

© 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.