Combinatorial Optimization for Electrode Labeling of EEG Caps

An important issue in electroencephalographiy (EEG) experiments is to measure accurately the three dimensional (3D) positions of the electrodes. We propose a system where these positions are automatically estimated from several images using computer vision techniques. Yet, only a set of undifferentiated points are recovered this way and remains the problem of labeling them, i.e. of finding which electrode corresponds to each point. This paper proposes a fast and robust solution to this latter problem based on combinatorial optimization. We design a specific energy that we minimize with a modified version of the Loopy Belief Propagation algorithm. Experiments on real data show that, with our method, a manual labeling of two or three electrodes only is sufficient to get the complete labeling of a 64 electrodes cap in less than 10 seconds.

[1]  Alan L. Yuille,et al.  A Bayesian network framework for relational shape matching , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[2]  Bruce Hendrickson,et al.  Conditions for Unique Graph Realizations , 1992, SIAM J. Comput..

[3]  Vladimir Kolmogorov,et al.  What energy functions can be minimized via graph cuts? , 2002, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Hiroshi Ishikawa,et al.  Exact Optimization for Markov Random Fields with Convex Priors , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Michael I. Jordan,et al.  Loopy Belief Propagation for Approximate Inference: An Empirical Study , 1999, UAI.

[6]  Mads Nielsen,et al.  Computer Vision — ECCV 2002 , 2002, Lecture Notes in Computer Science.

[7]  James M. Coughlan,et al.  Finding Deformable Shapes Using Loopy Belief Propagation , 2002, ECCV.

[8]  Daniel P. Huttenlocher,et al.  Efficient Belief Propagation for Early Vision , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[9]  Zhengyou Zhang,et al.  Iterative point matching for registration of free-form curves and surfaces , 1994, International Journal of Computer Vision.

[10]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Vladimir Kolmogorov,et al.  Convergent Tree-Reweighted Message Passing for Energy Minimization , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  J. Besag Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[13]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[14]  William T. Freeman,et al.  On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs , 2001, IEEE Trans. Inf. Theory.

[15]  D. Greig,et al.  Exact Maximum A Posteriori Estimation for Binary Images , 1989 .

[16]  Ashish Raj,et al.  A graph cut algorithm for generalized image deconvolution , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[17]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Davi Geiger,et al.  Mapping image restoration to a graph problem , 1999, NSIP.

[19]  Anand Rangarajan,et al.  A new algorithm for non-rigid point matching , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[20]  Philip N. Klein,et al.  Alignment-Based Recognition of Shape Outlines , 2001, IWVF.

[21]  Olga Veksler,et al.  Markov random fields with efficient approximations , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[22]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Nikos Komodakis,et al.  Image Completion Using Global Optimization , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[24]  Gerald S. Russell,et al.  Geodesic photogrammetry for localizing sensor positions in dense-array EEG , 2005, Clinical Neurophysiology.

[25]  D. Kozinska,et al.  Automatic alignment of scalp electrode positions with head MRI volume and its evaluation , 1999, Proceedings of the First Joint BMES/EMBS Conference. 1999 IEEE Engineering in Medicine and Biology 21st Annual Conference and the 1999 Annual Fall Meeting of the Biomedical Engineering Society (Cat. N.

[26]  Zhengyou Zhang On Local Matching of Free-Form Curves , 1992 .

[27]  Olivier D. Faugeras,et al.  The geometry of multiple images - the laws that govern the formation of multiple images of a scene and some of their applications , 2001 .

[28]  F FelzenszwalbPedro,et al.  Efficient Belief Propagation for Early Vision , 2006 .

[29]  Pietro Perona,et al.  A Bayesian approach to unsupervised one-shot learning of object categories , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[30]  O. Faugeras,et al.  The Geometry of Multiple Images , 1999 .