Q-Seg: Quantum Annealing-Based Unsupervised Image Segmentation

TL;DR

Q-Seg addresses unsupervised image segmentation under limited labeled data by casting the task as a minimum-cut on a grid graph and solving the resulting QUBO with quantum annealing on a D-Wave device. The approach efficiently maps a binary cut problem to the hardware topology, yielding a scalable, hardware-friendly solution with a solution space of $2^n$ for $n$ pixels. Empirical results on synthetic data and earth-observation datasets (Forest Cover, Flood Mapping) show significant runtime advantages over a classical optimizer ($\text{Gurobi}$) while maintaining competitive segmentation quality, even under noisy ground truth; comparisons with SAM illustrate robustness in challenging real-world scenarios. The work demonstrates practical quantum-enabled segmentation for real tasks and discusses future directions, including multi-cut partitions and learning edge weights, to broaden applicability and performance on near-term quantum hardware.

Abstract

We present Q-Seg, a novel unsupervised image segmentation method based on quantum annealing, tailored for existing quantum hardware. We formulate the pixel-wise segmentation problem, which assimilates spectral and spatial information of the image, as a graph-cut optimization task. Our method efficiently leverages the interconnected qubit topology of the D-Wave Advantage device, offering superior scalability over existing quantum approaches and outperforming several tested state-of-the-art classical methods. Empirical evaluations on synthetic datasets have shown that Q-Seg has better runtime performance than the state-of-the-art classical optimizer Gurobi. The method has also been tested on earth observation image segmentation, a critical area with noisy and unreliable annotations. In the era of noisy intermediate-scale quantum, Q-Seg emerges as a reliable contender for real-world applications in comparison to advanced techniques like Segment Anything. Consequently, Q-Seg offers a promising solution using available quantum hardware, especially in situations constrained by limited labeled data and the need for efficient computational runtime.

Figures (9)

• Figure 1: The proposed Q-Seg for unsupervised image segmentation generates a graph representing the original image. The distinct semantic regions in the image are identified by finding the minimum cut in the graph, an NP-hard problem that can be formulated as Quadratic Unconstrained Binary Optimization (QUBO). The QUBO problem is subsequently encoded into the physical topology of the D-Wave quantum annealer. Leveraging quantum tunneling, the annealing process efficiently explores an exponentially large solution space to locate the global optimum, which can be decoded as the segmentation mask.
• Figure 2: Converting the pixel values into edge weights in the grid graph. The grid structure of the graph captures the spatial information (high-level information such as regions or objects) and the edge weight captures the spectral information (low-level information such as pixel values). The red-colored dotted curve passes through the set of edges that divide the vertices into two distinct sets, such that the sum of the edge weights is minimum.
• Figure 3: The figure illustrates the operational pipeline of D-Wave quantum annealer. It begins with reformulating the minimum cut problem as a QUBO, followed by authentication using a private token for remote access. The minorminer tool maps the logical qubits in QUBO to the physical qubits in hardware. The problem instance is sent over the internet to join the queue on the shared D-Wave device. The Quantum Processing Unit (QPU) performs the annealing process, producing a set of samples. The final step is extracting the optimal solution, identified by its lowest energy state that encodes the segmentation mask.
• Figure 4: Runtime comparison between D-Wave Advantage annealer and Gurobi for the synthetic data with $seed=333$. This graph illustrates the breakdown of annealer runtime, highlighting the components in Fig. \ref{['fig: annealer pipeline']}. Despite shared and remote access, the D-Wave Advantage demonstrates a consistently shorter total runtime compared to Gurobi's local execution.
• Figure 5: The plot illustrates the mean runtime (represented by a solid line), the range of runtimes (indicated by the broadly shaded area), and the standard deviation (denoted by the lightly shaded area) is aggregated over five sets of synthetic data for the minimum cut operation on graphs of square images of varying sizes. The results highlight the efficiency of Q-Seg, especially evident in processing larger images.