p-IC and p-SC: fractional convolution-based morphology for grayscale images

Abstract Morphological image processing is a cornerstone of feature extraction and image analysis, but conventional dilation and erosion operations tend to be inflexible for complex tasks. In this paper, we present a new method of applying these operations called fractional infimal and supremal convolution through fractional convolutions, which offers very high customization and flexibility. By using convolution in a different manner, our approach enables greater control over morphological transformations, which is an essential limitation of traditional techniques. This breakthrough represents a significant step in the field of image morphology and enhancement, leading to the construction of new classes of neural networks, morphological networks, and adaptive image processing devices. The applications are numerous, ranging from medical imaging to remote sensing and automated flaw detection, where the proper preservation of complex features is essential for accurate analysis. The experimental results of this study apply two new basic fractional morphological operations (p-IC, p-SC) on which other new operations were extracted, such as pq-OP, pq-CLO and the new metric (CUST₏ₐ C U S T pq) on general-purpose and medical images, showing good calculation of object features such as area and length.