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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

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Tensor scale: An analytic approach with efficient computation and applications.

Ziyue Xu¹, Punam K Saha², Soura Dasgupta¹

¹Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States.

Computer Vision and Image Understanding : CVIU

|August 4, 2015

Summary

This summary is machine-generated.

This study introduces an analytic definition for tensor scale in n-dimensional images, enabling unified analysis of local structure size, orientation, and anisotropy. Efficient computational methods and applications in image filtering and interpolation are presented.

Keywords:

Image filtering Image interpolation Local scale Morphometry Scale-space Tensor scale

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Area of Science:

Computer Vision
Image Analysis
Differential Geometry

Background:

Scale-space theory is fundamental for image analysis at multiple resolutions.
Previous tensor scale lacked an analytic definition and efficient 3D computation.
Existing methods struggle with unified representation of local image structure properties.

Purpose of the Study:

Formulate an analytic definition for tensor scale in n-dimensional images.
Develop efficient computational methods for tensor scale in 2D and 3D.
Explore and evaluate tensor scale applications in image filtering and interpolation.

Main Methods:

Derived an analytic definition for tensor scale in n-D images.
Developed novel differential geometric approaches for efficient 2D/3D computation.
Introduced a matrix representation for tensor scale operations like smoothing.

Main Results:

Presented an accurate and efficient tensor scale computation in 2D and 3D.
Demonstrated tensor scale's effectiveness in image filtering and n-linear interpolation.
Outperformed state-of-the-art methods in comparative evaluations.

Conclusions:

The analytic tensor scale provides a unified framework for image structure analysis.
Efficient computation and matrix representation enhance tensor scale's practical utility.
Tensor scale offers superior performance in image filtering and interpolation tasks.