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Histogram

Histogram

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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Local histograms and image occlusion models.

Melody L Massar¹, Ramamurthy Bhagavatula, Matthew Fickus

¹Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433, USA.

Applied and Computational Harmonic Analysis

|April 2, 2013

Summary

This summary is machine-generated.

Local histogram transforms analyze image textures by examining pixel value distributions within neighborhoods. This method is applied to digital microscopy histology images for tissue identification and segmentation.

Keywords:

classification local histogram occlusion segmentation texture

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Area of Science:

Digital image processing
Computational pathology
Computer vision

Background:

Local histogram transforms capture pixel value distributions in image neighborhoods.
These transforms are valuable for texture analysis in classification and segmentation tasks.
Histology images present complex textures requiring robust analysis methods.

Purpose of the Study:

To introduce a rigorous mathematical framework for using local histograms in histology image analysis.
To develop and validate probabilistic models for emulating histology textures.
To demonstrate a proof-of-concept algorithm for tissue segmentation and classification.

Main Methods:

Computing local histograms via systems of convolutions.
Developing probabilistic image models based on image occlusion principles.
Analyzing model-generated textures and their local histogram properties.

Main Results:

Local histograms of emulated textures are shown to be convex combinations of basic distributions under specific conditions.
Methods for creating models that generate realistic histology-like textures are presented.
The study establishes a theoretical basis for texture analysis via local histogram decomposition.

Conclusions:

Local histogram analysis provides a robust method for understanding histology image textures.
The developed mathematical formalism supports the application of local histograms in digital pathology.
The proof-of-concept algorithm demonstrates the practical utility of this approach for tissue segmentation and classification.