Andreas Alpers

Jisui Huang, Andreas Alpers, Ke Chen et al.

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.

Andreas Alpers, Orkun Furat, Christian Jung et al.

This paper presents a comparative analysis of algorithmic strategies for fitting tessellation models to 3D image data of materials such as polycrystals and foams. In this steadily advancing field, we review and assess optimization-based methods -- including linear and nonlinear programming, stochastic optimization via the cross-entropy method, and gradient descent -- for generating Voronoi, Laguerre, and generalized balanced power diagrams (GBPDs) that approximate voxelbased grain structures. The quality of fit is evaluated on real-world datasets using discrepancy measures that quantify differences in grain volume, surface area, and topology. Our results highlight trade-offs between model complexity, the complexity of the optimization routines involved, and the quality of approximation, providing guidance for selecting appropriate methods based on data characteristics and application needs.

Maximilian Fiedler, Andreas Alpers

Superpixel algorithms grouping pixels with similar color and other low-level properties are increasingly used for pre-processing in image segmentation. In recent years, a focus has been placed on developing geometric superpixel methods that facilitate the extraction and analysis of geometric image features. Diagram-based superpixel methods are important among the geometric methods as they generate compact and sparsely representable superpixels. Introducing generalized balanced power diagrams to the field of superpixels, we propose a diagram method called Power-SLIC. Power-SLIC is the first geometric superpixel method to generate piecewise quadratic boundaries. Its speed, competitive with fast state-of-the-art methods, is unprecedented for diagram approaches. Extensive computational experiments show that Power-SLIC outperforms existing diagram approaches in boundary recall, under segmentation error, achievable segmentation accuracy, and compression quality. Moreover, Power-SLIC is robust to Gaussian noise.