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Automatic Determination of Plane of Symmetry

Abstract

Approximate plane symmetry is often encountered in medical imaging. Among various examples like the skeletal system, blood vessels, lungs, kidneys and many more, the human brain shows a high degree of symmetry within the mid-sagittal plane. Many medical decisions on this field are influenced by physicians taking the known symmetry into account. Using symmetry information for automatic classification therefore seems to be an intuitive and natural way. In order to ensure full-automatic classification, an automated determination of the symmetry plane is necessary. This can be achieved by the use of registration techniques: In image registration, a similarity measure between two fused medical images is calculated. The similarity measure is considered to have a maximum when the two images are aligned in an optimal way relative to each other. The same similarity measure can be used to find an optimal reflection plane. In our case, a new dataset which is the original dataset reflected with respect to an arbitrary plane, is created. It can be shown (1) that with the help of a subsequent translation and rotation, the image transformation is equal to a reflection with respect to any desired plane. In the case of a translation and rotation that maximizes the similarity measure (rigid registration) between reflected and original dataset the result is equal to a reflection with respect to the symmetry plane. We use the Mutual Information based on image intensities as similarity measure. The visual results seem to be accurate (Figure 1) and were confirmed by physicians, the technique can be applied to a variety of medical images (e.g. CT, SPECT, PET, MRI, ...).

 

Figure 1: Left: Mirrored dataset side-by-side to original dataset. Center: Registered datasets. Right: Based on the registriation information, the plane of symmetry was calculated (red line).

 

References:

  1. Tuzikov, Alexander V., Olivier Colliot, and Isabelle Bloch. "Evaluation of the symmetry plane in 3D MR brain images." Pattern Recognition Letters 24.14 (2003): 2219-2233.