Edge detection method for color images based on $F^1$-transform and hierarchical fuzzy inference system

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, University of Tabriz, Tabriz, Iran.

Abstract

This study presents a novel RGB image edge detection algorithm using
a first-degree polynomial fuzzy transform ($F^1$-transform) and a
hierarchical fuzzy inference system (HFIS). The $F^1$-transform
generates adaptable convolution kernels that enable adjustable image
smoothing and create directional derivatives in four orientations,
producing an optimized gradient matrix. These derivatives help
connect and refine edges into smooth, continuous contours. For
computational efficiency, we implement a multi-layer HFIS structure
with two-input single-output fuzzy systems at each layer. This
hierarchy progressively refines fuzzified gradient inputs, enhancing
edge extraction while reducing noise. The method shows improved
performance with additional layers due to flexible rules and diverse
membership functions. Comparisons with traditional (e.g., Canny) and
modern techniques demonstrate its effectiveness.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 14 September 2025

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History

  • Receive Date: 15 July 2025
  • Revise Date: 08 September 2025
  • Accept Date: 10 September 2025

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