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<p>In this work, novel edge detectors based on the conformable derivatives of Khalil, Fractal, Atangana, and M-truncated are designed, and experimentally tested. To attenuate image noise, Gaussian filters based on these derivatives are also proposed. Our edge detectors were compared with conventional integer order methods highlighting the following aspects. According to an analysis based on the peak signal-to-noise ratio (PSNR) index applied to test images taken from three different well-known image databases, conformable filters exhibit greater robustness to noise compared to conventional integer-order methods. The image gradient is also generalized to an arbitrary order through the considered conformable derivatives so that the resulting edge operators have a high capability to preserve object contours and texture information. This is confirmed by a performance comparison based on the visual quality of the identified edges via the edge-strength similarity-based image quality metric (ESSIM). A further a priori analysis was performed, based on both metrics, to determine the conformable orders that provide the best performance. Finally, the edge detectors were applied to different types of images such as noisy images, medical images, images with rich texture, with shading patterns, among others. Taken together the findings obtained demonstrate the superiority of the proposed operators in terms of edge continuity, noise robustness, and preservation of texture details, obtaining brighter edges that allow better visual identification of the elements that make up the scene.</p>

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A Novel Approach for Edge Detection Algorithm Based on Conformable Derivatives for Image Processing

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • J.E. Lavín-Delgado,
  • R.M. Soto-Mendiola,
  • J. F. Gómez-Aguilar,
  • J. E. Solís-Pérez,
  • Z. Zamudio-Beltrán,
  • E. Hernández-Castillo

摘要

In this work, novel edge detectors based on the conformable derivatives of Khalil, Fractal, Atangana, and M-truncated are designed, and experimentally tested. To attenuate image noise, Gaussian filters based on these derivatives are also proposed. Our edge detectors were compared with conventional integer order methods highlighting the following aspects. According to an analysis based on the peak signal-to-noise ratio (PSNR) index applied to test images taken from three different well-known image databases, conformable filters exhibit greater robustness to noise compared to conventional integer-order methods. The image gradient is also generalized to an arbitrary order through the considered conformable derivatives so that the resulting edge operators have a high capability to preserve object contours and texture information. This is confirmed by a performance comparison based on the visual quality of the identified edges via the edge-strength similarity-based image quality metric (ESSIM). A further a priori analysis was performed, based on both metrics, to determine the conformable orders that provide the best performance. Finally, the edge detectors were applied to different types of images such as noisy images, medical images, images with rich texture, with shading patterns, among others. Taken together the findings obtained demonstrate the superiority of the proposed operators in terms of edge continuity, noise robustness, and preservation of texture details, obtaining brighter edges that allow better visual identification of the elements that make up the scene.