Abstract
Stereotactic Radiosurgery (SRS) treatment and surgical planning could involve approximating the affected region with spheres of unequal size. This quickly turns into an optimization problem of finding minimum number of unequal size spheres to cover a bounded region. Since this optimization problem is NP-Hard, search for approximate algorithms is of immense important specially to support such SRS treatment. Our goal is to provide fast computational tools using well known Distance Transformations (DTs) and rarely used Dynamic Logic (DL). These two techniques are on the opposite ends of solving the approximate sphere packing problem: DT is bottoms up and DL in top down. Our research is significant in the sense that DL has not been previously used towards developing a sphere packing algorithm. We plan to implement both techniques in 3D on volume data sets in future.
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Acknowledgments
We want to acknowledge the role Slicer3D Community has played in our research directions. Although we have implemented the code using Processing Language, we want to implement the DL and Distance Transformations algorithms using 3D Slicer platform in future. The first author of this paper is also grateful to Dr. Arcady Godin who introduced Dr. Leonid Perlovsky, and Dr. Perlovsky’s work on Dynamic Logic to the first author during conversations in Summer of 2016 when Dr. Godin was visiting Colorado.
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Semwal, S.K., Janzen, M., Promersbeger, J., Perlovsky, L. (2020). Towards Approximate Sphere Packing Solutions Using Distance Transformations and Dynamic Logic. In: Arai, K., Kapoor, S. (eds) Advances in Computer Vision. CVC 2019. Advances in Intelligent Systems and Computing, vol 944. Springer, Cham. https://doi.org/10.1007/978-3-030-17798-0_31
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