Adaptive fuzzy c-shells clustering and detection of ellipses

Area of Science:

• Computer Vision
• Pattern Recognition
• Machine Learning

Background:

• The fuzzy c-shells (FCS) algorithm is used for detecting hyperellipsoidal shell clusters.
• Previous adaptive fuzzy c-shells (AFCS) algorithms exhibit convergence issues with partial shapes.

Purpose of the Study:

• To present and evaluate new generalizations of the FCS algorithm for improved hyperellipsoidal shell detection.
• To address the global convergence problems of existing AFCS algorithms, particularly for partial shapes.

Main Methods:

• Introduced the adaptive fuzzy c-shells unconstrained (AFCS-U) algorithm with an unconstrained norm-inducing matrix.
• Developed a formulation based on the second-order quadrics equation for shape detection.
• Compared AFCS-U and quadrics-based methods against Hough transform (HT)-based ellipse detection techniques.

Main Results:

• The AFCS-U algorithm demonstrates superior performance for detecting partial shapes compared to earlier AFCS methods.
• AFCS algorithms require less memory and are significantly faster (over an order of magnitude) than HT-based methods for ellipse detection.
• The proposed methods effectively detect ellipses and circles in 2D data.

Conclusions:

• The novel AFCS-U algorithm offers a more robust and efficient solution for hyperellipsoidal shell cluster detection, especially in cases of partial shapes.
• These generalized fuzzy c-shells algorithms present a competitive alternative to traditional Hough transform methods in terms of speed and memory usage.