The Mixture Graph-A Data Structure for Compressing, Rendering, and Querying Segmentation Histograms

In this paper, we present a novel data structure, called the Mixture Graph. This structure allows us to compress, render, and query segmentation histograms. Such histograms arise when building mipmap of volume containing IDs. Each voxel in histogram contains convex combination (mixture) mixture represents distribution IDs respective voxel's children. Our method factorizes these mixtures into series linear interpolations between exactly two The result is represented as directed acyclic graph (DAG) whose nodes are topologically ordered. Pruning replicate tree followed by compression store resulting efficiently. During rendering, transfer functions propagated from sources (leafs) through DAG allow for efficient, pre-filtered rendering at interactive frame rates. Assembly contributions across footprint given efficiently partial histograms, achieving up 178 x speed-up over naive parallelized range queries. Additionally, apply Graph compute correctly lighting interactively explore segments based on shape, geometry, orientation using multi-dimensional functions.