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We propose, analyze and realize a variational multiclass segmentation schemethat partitions a given image into multiple regions exhibiting specificproperties. Our method determines multiple functions that encode thesegmentation regions by minimizing an energy functional combining informationfrom different channels. Multichannel image data can be obtained by lifting theimage into a higher dimensional feature space using specific multichannelfiltering or may already be provided by the imaging modality underconsideration, such as an RGB image or multimodal medical data. Experimentalresults show that the proposed method performs well in various scenarios. Inparticular, promising results are presented for two medical applicationsinvolving classification of brain abscess and tumor growth, respectively. Asmain theoretical contributions, we prove the existence of global minimizers ofthe proposed energy functional and show its stability and convergence withrespect to noisy inputs. In particular, these results also apply to the specialcase of binary segmentation, and these results are also novel in thisparticular situation.

Lifting-based variational multiclass segmentation algorithm: design, convergence analysis, and implementation with applications in medical imaging