Fractal feature analysis and classification in medical imaging

Area of Science:

• Medical Imaging
• Fractal Geometry
• Image Analysis

Background:

• Fractal theory, pioneered by B.B. Mandelbrot, provides a framework for analyzing complex natural phenomena.
• Fractional Brownian motion is a mathematical model used to describe fractal surfaces.
• Medical imaging generates complex data where fractal analysis can reveal underlying structures.

Purpose of the Study:

• To introduce an estimation concept for determining fractal dimension in medical images using fractional Brownian motion.
• To explore applications of this fractal dimension estimation in medical image classification and edge detection.

Main Methods:

• An estimation concept for fractal dimension based on fractional Brownian motion was developed.
• A normalized fractional Brownian motion feature vector was defined for classification, representing intensity differences across scales.
• A transformed image was generated by calculating the fractal dimension for each pixel using a 7x7 neighborhood.

Main Results:

• The proposed feature vector is invariant to linear intensity transformations and efficiently represents image surface characteristics.
• The fractal dimension calculation per pixel enabled effective edge enhancement and detection in medical images.

Conclusions:

• Fractal dimension estimation via fractional Brownian motion is a viable technique for medical image analysis.
• This method offers practical applications in both image classification and enhancing the detection of image features.