This study presents a novel quantum-based edge detection algorithm integrated with clustering techniques, specifically designed for medical imaging applications. The methodology employs Flexible Representation of Quantum Images (FRQI) and Quantum Hadamard Edge Detection (QHED), enhanced with K-means clustering, to improve precision and robustness against noise. Experimental evaluations, using metrics such as F1-score, accuracy, and precision, demonstrate that the quantum approach achieves an F1-score consistently above 80% under noisy conditions, compared to 70–75% for classical methods like Sobel and LoG. Quantum edge detection also demonstrated higher image density at 106.72 compared to 85% (Sobel) and 83% (LoG). While the quantum model’s processing time (0.176898 s) is longer than classical methods (e.g., Canny at 0.098943 s), auxiliary quantum processes such as clustering and density detection compensate with near-real-time efficiency. These results highlight the quantum algorithm’s superior performance in noisy conditions, making it particularly suited for high-dimensional medical imaging tasks.