Identifying and analyzing power-law scaling in two-dimensional image datasets

Area of Science:

• Physics
• Materials Science
• Data Analysis

Background:

• Power-law distributions describe phenomena where large events are rare.
• Analyzing two-dimensional experimental data for power laws is difficult due to event interpretation and limited data.

Purpose of the Study:

• To develop and compare techniques for analyzing event distributions in two-dimensional images.
• To accurately extract scaling parameters from image-based datasets.

Main Methods:

• Tracking interface position in two-dimensional images.
• Comparing Hill, moments, and kernel estimators for scaling parameter analysis.
• Utilizing both experimental and synthetic image datasets.

Main Results:

• Interface tracking accurately extracts scaling parameters from two-dimensional image data.
• Developed techniques can differentiate between power-law and non-power-law behavior.
• Computational tools for power-law fitting in 2D datasets are presented.

Conclusions:

• Accurate extraction of scaling parameters is achievable for two-dimensional power-law analysis.
• The presented methods provide robust tools for analyzing complex image data.
• Reliable identification of scaling parameters is crucial for understanding natural phenomena.