Lifting-based variational multiclass segmentation algorithm: design, convergence analysis, and implementation with applications in medical imaging
This work addresses segmentation challenges in medical imaging, but it appears incremental as it builds on existing variational frameworks with theoretical extensions.
The authors tackled the problem of multiclass image segmentation by proposing a variational method that partitions images into regions with specific properties, achieving promising results in medical applications such as brain abscess and tumor growth classification.
We propose, analyze and realize a variational multiclass segmentation scheme that partitions a given image into multiple regions exhibiting specific properties. Our method determines multiple functions that encode the segmentation regions by minimizing an energy functional combining information from different channels. Multichannel image data can be obtained by lifting the image into a higher dimensional feature space using specific multichannel filtering or may already be provided by the imaging modality under consideration, such as an RGB image or multimodal medical data. Experimental results show that the proposed method performs well in various scenarios. In particular, promising results are presented for two medical applications involving classification of brain abscess and tumor growth, respectively. As main theoretical contributions, we prove the existence of global minimizers of the proposed energy functional and show its stability and convergence with respect to noisy inputs. In particular, these results also apply to the special case of binary segmentation, and these results are also novel in this particular situation.