10,686 research outputs found
A Sparse Graph Formulation for Efficient Spectral Image Segmentation
Spectral Clustering is one of the most traditional methods to solve
segmentation problems. Based on Normalized Cuts, it aims at partitioning an
image using an objective function defined by a graph. Despite their
mathematical attractiveness, spectral approaches are traditionally neglected by
the scientific community due to their practical issues and underperformance. In
this paper, we adopt a sparse graph formulation based on the inclusion of extra
nodes to a simple grid graph. While the grid encodes the pixel spatial
disposition, the extra nodes account for the pixel color data. Applying the
original Normalized Cuts algorithm to this graph leads to a simple and scalable
method for spectral image segmentation, with an interpretable solution. Our
experiments also demonstrate that our proposed methodology over performs
traditional spectral algorithms for segmentation
Tight Continuous Relaxation of the Balanced -Cut Problem
Spectral Clustering as a relaxation of the normalized/ratio cut has become
one of the standard graph-based clustering methods. Existing methods for the
computation of multiple clusters, corresponding to a balanced -cut of the
graph, are either based on greedy techniques or heuristics which have weak
connection to the original motivation of minimizing the normalized cut. In this
paper we propose a new tight continuous relaxation for any balanced -cut
problem and show that a related recently proposed relaxation is in most cases
loose leading to poor performance in practice. For the optimization of our
tight continuous relaxation we propose a new algorithm for the difficult
sum-of-ratios minimization problem which achieves monotonic descent. Extensive
comparisons show that our method outperforms all existing approaches for ratio
cut and other balanced -cut criteria.Comment: Long version of paper accepted at NIPS 201
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