Falcon: Fractional Alternating Cut with Overcoming Minima in Unsupervised Segmentation

Today's unsupervised image segmentation algorithms often segment suboptimally. Modern graph-cut based approaches rely on high-dimensional attention maps from Transformer-based foundation models, typically employing a relaxed Normalized Cut solved recursively via the Fiedler vector (the eigenvector of the second smallest eigenvalue). Consequently, they still lag behind supervised methods in both mask generation speed and segmentation accuracy. We present a regularized fractional alternating cut (Falcon), an optimization-based K-way Normalized Cut without relying on recursive eigenvector computations, achieving substantially improved speed and accuracy. Falcon operates in two stages: (1) a fast K-way Normalized Cut solved by extending into a fractional quadratic transformation, with an alternating iterative procedure and regularization to avoid local minima; and (2) refinement of the resulting masks using complementary low-level information, producing high-quality pixel-level segmentations. Experiments show that Falcon not only surpasses existing state-of-the-art methods by an average of 2.5% across six widely recognized benchmarks (reaching up to 4.3\% improvement on Cityscapes), but also reduces runtime by around 30% compared to prior graph-based approaches. These findings demonstrate that the semantic information within foundation-model attention can be effectively harnessed by a highly parallelizable graph cut framework. Consequently, Falcon can narrow the gap between unsupervised and supervised segmentation, enhancing scalability in real-world applications and paving the way for dense prediction-based vision pre-training in various downstream tasks. The code is released in https://github.com/KordingLab/Falcon.