This paper analyzes a bilevel formulation for learning the regularization parameter of combined local-global (CLG) optical flow models. The lower-level problem computes the flow from a Lucas--Kanade data term and a quadratic or total variation (TV) regularizer, and the upper-level problem selects the parameter that minimizes the squared distance to a ground-truth flow. The setting is finite-dimensional, and a full-rank assumption makes the lower-level solution unique. For the quadratic model we derive sufficient conditions for the existence of an optimal parameter, for every optimal parameter to be positive, and for strict local optimality. For TV regularization an optimal parameter always exists, because the lower-level solution vanishes for large parameters, and we give a sufficient condition for positivity that accounts for the coupling of the two flow components through the local structure tensors. Synthetic examples illustrate the conditions, including cases in which they fail.
Haytham Ziani, El Mostafa Kalmoun, Zohaib Atif, Hyuk-Sang Kwon
原文摘要
Longitudinal rodent positron emission tomography (PET) studies of stroke and neuromodulation rely on accurate registration to a common atlas space to detect group-level effects. Prior work applying ultra-high frequency low-intensity magnetic stimulation (UHF-LiMS) to a rat model of chronic capsule infarct used affine normalization to a Sprague Dawley MRI template without evaluating that choice. We compare a two-stage (affine and nonlinear) pipeline against an affine- only one for rat PET-to-atlas alignment on the same dataset. Across 32 longitudinal [18F]-FDG PET scans (8 rats, 4 timepoints), the nonlinear stage gave a higher Dice similarity coefficient on every scan, and the gain was significant at the rat level. Jacobian determinants showed no folding on the sampling grid. Group-level linear mixed-effects maps of change from baseline (AFNI 3dLME), computed identically under both pipelines, differ in the size, number and location of their suprathreshold clusters. In this dataset, the registration pipeline is therefore a variable that can change the interpretation of downstream group-level analyses.