A Fully Quantum Algorithm for Image Edge Detection

TL;DR

This paper presents a fully quantum algorithm for image edge detection using NEQR encoding, quantum arithmetic, and novel techniques for improved efficiency and accuracy, demonstrating potential quantum advantage in image processing.

Contribution

It introduces a new quantum edge detection algorithm with in-place thresholding and direction-aware shifting, optimizing resource use and accuracy over prior quantum methods.

Findings

Achieves polynomial-time complexity improvements.

Reduces ancilla qubits compared to previous methods.

Demonstrates resource-efficient quantum edge detection.

Abstract

This work introduces a novel quantum algorithm for gradient-based edge detection that operates entirely within the quantum circuit model. Grayscale images are encoded using the Novel Enhanced Quantum Representation (NEQR), allowing exact arithmetic on pixel intensities. Directional gradients are computed by generating superpositions of neighboring pixels via cyclic shift operations and performing subtraction with an exact quantum arithmetic circuit. To refine accuracy, we introduce a direction-aware shifting mechanism that aligns edges with the darker side of intensity transitions. Our novel Quantum Partitioning Algorithm enables efficient in-place thresholding of edge candidates. This work exhibits polynomial-time improvements and optimizes the ancilla count compared to previous NEQR-based quantum edge detection algorithms. These results demonstrate a resource-efficient and fully quantum approach to edge detection, highlighting a practical quantum advantage in image processing.