2019/10/22 by Ruben Hühnerbein, Fabrizio Savarino, Hühnerbein, Ruben +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Medicine · #62H35 #62M45 #68T05 #68U10 #90C31 #91A22 #Algorithm #Applied mathematics #Artificial intelligence #Balanced flow #Cell Image Analysis Techniques #Computer Vision and Pattern Recognition (cs.CV) #Computer science #Discretization #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Inference #Inverse problem #Manifold (fluid mechanics) #Mathematical analysis #Mathematical optimization #Mathematics #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications #Optimization and Control (math.OC) #Regularization (linguistics) #cs.CV #math.DS #math.OC #msc:62H35 #msc:62M45 #msc:68T05 #msc:68U10 #msc:90C31 #msc:91A22
paper · pdf · doi:10.48550/arxiv.1910.09976
openalex publication_date 2019/10/22 · arxiv created 2020/06/25 · arxiv updated 2020/06/26 · openalex created_date 2022/07/28 · openalex updated_date 2026/08/06
We study the inverse problem of model parameter learning for pixelwise image labeling, using the linear assignment flow and training data with ground truth. This is accomplished by a Riemannian gradient flow on the manifold of parameters that determine the regularization properties of the assignment flow. Using the symplectic partitioned Runge--Kutta method for numerical integration, it is shown that deriving the sensitivity conditions of the parameter learning problem and its discretization commute. A convenient property of our approach is that learning is based on exact inference. Carefully designed experiments demonstrate the performance of our approach, the expressiveness of the mathematical model as well as its limitations, from the viewpoint of statistical learning and optimal control.