epsilon-Rotation Invariant Euclidean Spheres Packing in Slicer3D

Anonymous

Abstract: Sometimes SRS (Stereotactic Radio Surgery) requires using sphere packing on a Region of Interest (ROI) such as cancer to determine a treatment plan. We have developed a sphere packing algorithm which packs non-intersecting spheres inside the ROI. The region of interest in our case are those voxels which are identified as cancer tissues. In this paper, we analyze the rotational invariant properties of our sphere-packing algorithm which is based on distance transformations. Epsilon-Rotation invariant means the ability to arbitrary rotate the 3D ROI while keeping the volume properties remaining (almost) same within some limit of epsilon. The applied rotations produce spherical packing which remains highly correlated as we analyze the geometrically properties of sphere packing before and after the rotation of the volume data for the ROI. Our novel sphere packing algorithm has high degree of rotation invariance within the range of +/- epsilon. Our method used a shape descriptor derived from the values of the disjoint set of spheres form the distance-based sphere packing algorithm to extract the invariant descriptor from the ROI. We demonstrated by implementing these ideas using Slicer3D platform available for our research. The data is based on sing MRI Stereotactic images. We presented several performance results on different benchmarks data of over 30 patients in Slicer3D platform.

TL;DR: Packing region of Interest (ROI) such as cancerous regions identified in 3D Volume Data, Packing spheres inside the ROI, rotating the ROI , measures of difference in sphere packing before and after the rotation.

Keywords: Rotation Invariant, Slicer3D, Sphere Packing, Distance Transformation, Stereotactic Radiosurgery