Estimation of Non-Cartesian Local Structure Tensor Fields

  • Björn Svensson
  • Anders Brun
  • Mats Andersson
  • Hans Knutsson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4522)


In medical imaging, signals acquired in non-Cartesian coordinate systems are common. For instance, CT and MRI often produce significantly higher resolution within scan planes, compared to the distance between two adjacent planes. Even oblique sampling occurs, by the use of gantry tilt. In ultrasound imaging, samples are acquired in a polar coordinate system, which implies a spatially varying metric.

In order to produce a geometrically correct image, signals are generally resampled to a Cartesian coordinate system. This paper concerns estimation of local structure tensors directly from the non-Cartesian coordinate system, thus avoiding deteriorated signal and noise characteristics caused by resampling. In many cases processing directly in the warped coordinate system is also less time-consuming.

A geometrically correct tensor must obey certain transformation rules originating from fundamental differential geometry. Subsequently, this fact also affects the tensor estimation. As the local structure tensor is estimated using filters, a change of coordinate system also change the shape of the spatial support of these filters. Implications and limitations brought on by sampling require the filter design criteria to be adapted to the coordinate system.


Cartesian Coordinate System Order Tensor Simple Signal Orientation Tensor Covariant Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Björn Svensson
    • 1
  • Anders Brun
    • 1
  • Mats Andersson
    • 1
  • Hans Knutsson
    • 1
  1. 1.Department of Biomedical Engineering, Medical Informatics, Center for Medical Image Science and Visualization, Linköping UniversitySweden

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