Spectral Image Segmentation Using Image Decomposition and Inner Product-Based Metric

Abstract

Image segmentation is an indispensable tool in computer vision applications, such as recognition, detection and tracking. In this work, we introduce a novel user-assisted image segmentation technique which combines image decomposition, inner product-based similarity metric, and spectral graph theory into a concise and unified framework. First, we perform an image decomposition to split the image into texture and cartoon components. Then, an affinity graph is generated and the weights are assigned to its edges according to a gradient-based inner-product function. From the eigenstructure of the affinity graph, the image is partitioned through the spectral cut of the underlying graph. The computational effort of our framework is alleviated by an image coarsening process, which reduces the graph size considerably. Moreover, the image partitioning can be improved by interactively changing the graph weights by sketching. Finally, a coarse-to-fine interpolation is applied in order to assemble the partition back onto the original image. The efficiency of the proposed methodology is attested by comparisons with state-of-art spectral segmentation methods through a qualitative and quantitative analysis of the results.

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Acknowledgements

We would like to thank the anonymous reviewers for their useful comments to improve the quality of this work and Shawn Andrews for kindly providing us with the implementation of RWS-EP and RWS-EPP. This research has been funded by FAPESP-Brazil, INCT-MACC and CNPq-Brazil.

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Correspondence to Afonso Paiva.

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Casaca, W., Paiva, A., Gomez-Nieto, E. et al. Spectral Image Segmentation Using Image Decomposition and Inner Product-Based Metric. J Math Imaging Vis 45, 227–238 (2013). https://doi.org/10.1007/s10851-012-0359-6

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Keywords

  • Spectral cut
  • Image segmentation
  • Similarity graph
  • Cartoon-texture decomposition
  • Harmonic analysis