Numerical aspects of spectral segmentation on polygonal grids

Authors:
Anna Matsekh;Alexei Skurikhin;Lakshman Prasad;Edward Rosten
Affiliations:
Space and Remote Sensing Sciences Group, Los Alamos National Laboratory, Engineering Department, University of Cambridge, UK;Space and Remote Sensing Sciences Group, Los Alamos National Laboratory, Engineering Department, University of Cambridge, UK;Space and Remote Sensing Sciences Group, Los Alamos National Laboratory, Engineering Department, University of Cambridge, UK;Space and Remote Sensing Sciences Group, Los Alamos National Laboratory, Engineering Department, University of Cambridge, UK
Venue:
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
Year:
2010

Citing 9
Cited 0

Normalized Cuts and Image Segmentation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean Shift: A Robust Approach Toward Feature Space Analysis

IEEE Transactions on Pattern Analysis and Machine Intelligence
Contour and Texture Analysis for Image Segmentation

International Journal of Computer Vision
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1

Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Multiclass Spectral Clustering

ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Spectral Segmentation with Multiscale Graph Decomposition

CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Vectorized image segmentation via trixel agglomeration

Pattern Recognition
Weighted Graph Cuts without Eigenvectors A Multilevel Approach

IEEE Transactions on Pattern Analysis and Machine Intelligence
The Godunov-inverse iteration: A fast and accurate solution to the symmetric tridiagonal eigenvalue problem

Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present an implementation of the Normalized Cuts method for the solution of the image segmentation problem on polygonal grids. We show that in the presence of rounding errors the eigenvector corresponding to the k-th smallest eigenvalue of the generalized graph Laplacian is likely to contain more than k nodal domains. It follows that the Fiedler vector alone is not always suitable for graph partitioning, while the eigenvector subspace, corresponding to just a few of the lowest eigenvalues, contains sufficient information needed for obtaining meaningful segmentation. At the same time, the eigenvector corresponding to the trivial solution often carries nontrivial information about the nodal domains in the image and can be used as an initial guess for the Krylov subspace eigensolver. We show that proposed algorithm performs favorably when compared to the Multiscale Normalized Cuts and Segmentation by Weighted Aggregation.