The main objective of this paper is to modify the Grunwald-Letnikov (G-L) fractional derivative operator to enhance images much better than the usual G-L operator. This paper focuses on exploring the use of Grunwald-Letnikov fractional derivatives in digital image processing. The traditional Grunwald-Letnikov derivative has limitations when it comes to image processing. Therefore, this paper proposes a new improved version of the G-L fractional differential operator that outperforms the traditional operator in enhancing images. This modified G-L derivative is very flexible and shows improved values of derivatives in image processing and can be applied to medical images. Furthermore, some examples are presented that show the disorderliness of the usual G-L derivative in its application in image processing. The proposed research work also includes a comparative study of the operator using different values of parameters with experimental work.

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An Improved Grunwald-Letnikov Fractional Order Differential Operator for Image Enhancement

  • Nidhi Jain,
  • Nidhi H. Divecha

摘要

The main objective of this paper is to modify the Grunwald-Letnikov (G-L) fractional derivative operator to enhance images much better than the usual G-L operator. This paper focuses on exploring the use of Grunwald-Letnikov fractional derivatives in digital image processing. The traditional Grunwald-Letnikov derivative has limitations when it comes to image processing. Therefore, this paper proposes a new improved version of the G-L fractional differential operator that outperforms the traditional operator in enhancing images. This modified G-L derivative is very flexible and shows improved values of derivatives in image processing and can be applied to medical images. Furthermore, some examples are presented that show the disorderliness of the usual G-L derivative in its application in image processing. The proposed research work also includes a comparative study of the operator using different values of parameters with experimental work.