Using the variogram for vector outlier screening: application to feature-based image registration



Matching points that are derived from features or landmarks in image data is a key step in some medical imaging applications. Since most robust point matching algorithms claim to be able to deal with outliers, users may place high confidence in the matching result and use it without further examination. However, for tasks such as feature-based registration in image-guided neurosurgery, even a few mismatches, in the form of invalid displacement vectors, could cause serious consequences. As a result, having an effective tool by which operators can manually screen all matches for outliers could substantially benefit the outcome of those applications.


We introduce a novel variogram-based outlier screening method for vectors. The variogram is a powerful geostatistical tool for characterizing the spatial dependence of stochastic processes. Since the spatial correlation of invalid displacement vectors, which are considered as vector outliers, tends to behave differently than normal displacement vectors, they can be efficiently identified on the variogram.


We validate the proposed method on 9 sets of clinically acquired ultrasound data. In the experiment, potential outliers are flagged on the variogram by one operator and further evaluated by 8 experienced medical imaging researchers. The matching quality of those potential outliers is approximately 1.5 lower, on a scale from 1 (bad) to 5 (good), than valid displacement vectors.


The variogram is a simple yet informative tool. While being used extensively in geostatistical analysis, it has not received enough attention in the medical imaging field. We believe there is a good deal of potential for clinically applying the proposed outlier screening method. By way of this paper, we also expect researchers to find variogram useful in other medical applications that involve motion vectors analyses.

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This work was supported by National Institute of Health Grants P41-EB015898-09 and P41-EB015902. This work was also supported by the International Research Center for Neurointelligence (WPI-IRCN) at the University of Tokyo Institute for Advanced Study.

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Correspondence to Jie Luo.

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All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Declaration of Helsinki and its later amendments or comparable ethical standards.

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Luo, J., Frisken, S., Machado, I. et al. Using the variogram for vector outlier screening: application to feature-based image registration. Int J CARS 13, 1871–1880 (2018).

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  • Vector outlier screening
  • Variogram
  • Feature-based registration
  • Neurosurgery