Superpixel-Based Image Segmentation Using Squared 2-Wasserstein Distances

TL;DR

This work addresses image segmentation under strong intensity inhomogeneity by introducing a two-level clustering framework that first builds superpixels and then greedily merges them using a squared $2$-Wasserstein distance between region histograms. The key idea is to unify clustering across scales within a distributional OT formulation, enabling robust region comparison without relying on ground-truth distributions. The proposed SP model leverages a region-adjacency graph, a memory-augmented merge cost, and OT-based dissimilarities to produce accurate, boundary-preserving segmentations at lower computational cost than pixel-based variational methods. Experimental results on challenging biomedical and synthetic datasets show that SP often outperforms variational, MST-based, and even some deep-learning approaches in accuracy while remaining computationally efficient. The approach is fully unsupervised and adaptable to marker-based guidance, offering a practical tool for robust segmentation in domains with strong illumination and inhomogeneity variations.

Abstract

We present an efficient method for image segmentation in the presence of strong inhomogeneities. The approach can be interpreted as a two-level clustering procedure: pixels are first grouped into superpixels via a linear least-squares assignment problem, which can be viewed as a special case of a discrete optimal transport (OT) problem, and these superpixels are subsequently greedily merged into object-level segments using the squared 2-Wasserstein distance between their empirical distributions. In contrast to conventional superpixel merging strategies based on mean-color distances, our framework employs a distributional OT distance, yielding a mathematically unified formulation across both clustering levels. Numerical experiments demonstrate that this perspective leads to improved segmentation accuracy on challenging images while retaining high computational efficiency.

Figures (11)

• Figure 1: Samples from Datasets 1–3. (a) First frame of the 74-frame video in Dataset 1 (1770 × 880) with a superimposed red mesh. (b,c) H&E-stained tissue images from Dataset 1 (1000 × 750; 950 × 730). (d,e) Cell images from Dataset 2 (600 × 600) with nuclei annotations. (f,g) Image from Dataset 3 (512 × 512) with annotation.
• Figure 2: Selection of the optimal number of regions. The LT curve (a) shows a general decrease with minor fluctuations, while the ROC--LT curve (b) remains essentially zero over $[1,\,162]$, suggesting an optimal region number below $162$. Zoomed views (c, d) reveal peaks at $115$ and $151$. Segmentations with 1835, 495, 425, 151, and 115 regions are shown in (e--i).
• Figure 3: Segmentation vs. Oversegmentation. (a) Noisy grayscale image containing 25 white objects. (b) Power-SLIC result with 300 superpixels, serving as input to our algorithm. (c–e) Intermediate and final steps of the algorithm, merging into 200, 100, and finally 25 regions, respectively. (f) Power-SLIC output with 25 superpixels.
• Figure 4: Comparison of OT-based segmentation and variance-based SMST. The first row (a–d) shows two images I1 and I2 from Dataset 1 partitioned into rectangular superpixels of sizes 40×40 (a), 30×30 (b), 80×80 (c), and 70×70 (d), respectively. The second row (e–h) shows SP results (times in seconds: 1.97, 0.28, 22.48, 16.12). The third row (i–l) shows SMST results (times in seconds: 0.35, 0.35, 0.37, 0.43).
• Figure 5: Selective segmentation seeds: (a,c) images with foreground (red) and background (blue) seeds, labeled ‘f’ and ‘b’ respectively (numbers indicate order); (b,d) corresponding zoomed-in views.

Theorems & Definitions (2)

• Proposition 1
• proof