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The Mixture Graph-A Data Structure for Compressing, Rendering, and Querying Segmentation Histograms
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 data structure allows us to compress, render, and query segmentation histograms. Such histograms arise when building a mipmap of a volume containing segmentation IDs. Each voxel in the histogram mipmap contains a convex combination (mixture) of segmentation IDs. Each mixture represents the distribution of IDs in the respective voxel's children. Our method factorizes these mixtures into a series of linear interpolations between exactly two segmentation IDs. The result is represented as a directed acyclic graph (DAG) whose nodes are topologically ordered. Pruning replicate nodes in the tree followed by compression allows us to store the resulting data structure efficiently. During rendering, transfer functions are propagated from sources (leafs) through the DAG to allow for efficient, pre-filtered rendering at interactive frame rates. Assembly of histogram contributions across the footprint of a given volume allows us to efficiently query partial histograms, achieving up to 178$\times$ speed-up over na$\mathrm{\"{i}}$ve parallelized range queries. Additionally, we apply the Mixture Graph to compute correctly pre-filtered volume lighting and to interactively explore segments based on shape, geometry, and orientation using multi-dimensional transfer functions.
Comment: To appear in IEEE Transacations on Visualization and Computer Graphics (IEEE Vis 2020)
- Hamad bin Khalifa University Qatar
- Khalifa University of Science and Technology United Arab Emirates
ACM Computing Classification System: ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION
Microsoft Academic Graph classification: Voxel computer.software_genre computer Artificial intelligence business.industry business Rendering (computer graphics) Mipmap Directed acyclic graph Frame rate Interpolation Segmentation Computer science Data structure Pattern recognition Histogram Convex combination
Computer Science - Graphics, Computer Science - Data Structures and Algorithms, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition, Signal Processing, Software, Graphics (cs.GR), Data Structures and Algorithms (cs.DS), FOS: Computer and information sciences
Computer Science - Graphics, Computer Science - Data Structures and Algorithms, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition, Signal Processing, Software, Graphics (cs.GR), Data Structures and Algorithms (cs.DS), FOS: Computer and information sciences
ACM Computing Classification System: ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION
Microsoft Academic Graph classification: Voxel computer.software_genre computer Artificial intelligence business.industry business Rendering (computer graphics) Mipmap Directed acyclic graph Frame rate Interpolation Segmentation Computer science Data structure Pattern recognition Histogram Convex combination
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- Hamad bin Khalifa University Qatar
- Khalifa University of Science and Technology United Arab Emirates
In this paper, we present a novel data structure, called the Mixture Graph. This data structure allows us to compress, render, and query segmentation histograms. Such histograms arise when building a mipmap of a volume containing segmentation IDs. Each voxel in the histogram mipmap contains a convex combination (mixture) of segmentation IDs. Each mixture represents the distribution of IDs in the respective voxel's children. Our method factorizes these mixtures into a series of linear interpolations between exactly two segmentation IDs. The result is represented as a directed acyclic graph (DAG) whose nodes are topologically ordered. Pruning replicate nodes in the tree followed by compression allows us to store the resulting data structure efficiently. During rendering, transfer functions are propagated from sources (leafs) through the DAG to allow for efficient, pre-filtered rendering at interactive frame rates. Assembly of histogram contributions across the footprint of a given volume allows us to efficiently query partial histograms, achieving up to 178$\times$ speed-up over na$\mathrm{\"{i}}$ve parallelized range queries. Additionally, we apply the Mixture Graph to compute correctly pre-filtered volume lighting and to interactively explore segments based on shape, geometry, and orientation using multi-dimensional transfer functions.
Comment: To appear in IEEE Transacations on Visualization and Computer Graphics (IEEE Vis 2020)