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Histogram

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The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data represents (for instance, distance from your home to school). The vertical y-axis is labeled either frequency or relative frequency (or percent frequency or probability).
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An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, the cumulative percentages are added to the graph from left to right. An ogive graph plots cumulative frequency on the vertical y-axis and class boundaries along the horizontal x-axis. It’s very similar to a histogram; only instead of rectangles, an ogive displays a single point where the top right of the rectangle would be. Creating this...

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Updated: Dec 5, 2025

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data

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

Khaled Ai- Thelaya, Marco Agus, Jens Schneider

IEEE Transactions on Visualization and Computer Graphics

|October 15, 2020

Summary

This summary is machine-generated.

We introduce the Mixture Graph, a novel data structure for efficiently compressing, rendering, and querying segmentation histograms in volumetric data. This method accelerates visualization and analysis of complex datasets.

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Area of Science:

Computer Graphics
Data Structures
Scientific Visualization

Background:

Volume rendering often involves processing segmentation IDs within a mipmap.
Histograms of these IDs require efficient compression and querying for large datasets.
Existing methods struggle with interactive performance for complex volumetric data.

Purpose of the Study:

To present a novel data structure, the Mixture Graph, for handling segmentation histograms.
To enable efficient compression, rendering, and querying of volumetric segmentation data.
To improve interactive exploration and analysis of scientific visualizations.

Main Methods:

Developed the Mixture Graph data structure, representing mixtures as a topologically ordered directed acyclic graph (DAG).
Factorized mixtures into linear interpolations between two segmentation IDs.
Implemented efficient compression by pruning replicate nodes.
Propagated transfer functions through the DAG for pre-filtered rendering.
Assembled histogram contributions for accelerated partial histogram queries.

Main Results:

Achieved efficient compression and storage of segmentation histogram mipmaps.
Enabled pre-filtered volume rendering at interactive frame rates.
Demonstrated up to 178x speed-up in querying partial histograms compared to naive methods.
Enabled interactive exploration of segments based on shape, geometry, and orientation.

Conclusions:

The Mixture Graph provides an efficient solution for processing segmentation histograms in volumetric data.
This data structure significantly enhances interactive rendering and querying performance.
The method facilitates advanced analysis, including pre-filtered volume lighting and segment exploration.