Implicit Encoding and Simplification/Reduction of nGmaps

This paper aims to present a new method of translating labeled 3D scans of biological tissues into Generalized Maps (nGmaps). Creating such nGmaps from labeled images is a solved problem in 2D and 3D using incremental algorithms. We present a new approach that works in arbitrary dimensions. To achieve this in an effective manner, we perform the necessary operations implicitly using theory rather than explicitly in memory. First we define implicit nGmaps. We then present a scheme to construct said nGmap representing an nD pixel/voxel-grid implicitly. Thirdly we give a description of the process needed to reduce such implicit nGmap. We demonstrate that our implicit approach is able to reduce nGmaps in a fraction of otherwise necessary memory.