A Joint Segmentation/Registration Model Based on a Nonlocal Characterization of Weighted Total Variation and Nonlocal Shape Descriptors

A variational joint segmentation and registration framework for multimodal images

“…The is just a small numerical constant to prevent extra considerations such as 00 0log0 00 . Furthermore, we are using homogeneous Neumann boundary conditions approximated by one side differences u l ðx i;1 Þ ¼ u l ðx i;2 Þ; u l ðx 1;j Þ ¼ u l ðx 2;j Þ; u l ðx i;NÀ1 Þ ¼ u l ðx i;N Þ; u l ðx NÀ1;j Þ ¼ u l ðx N;j Þ; l ¼ 1; 2: Minimizing equation (19) brings a system of nonlinear equation with unknown U:…”

“…for dU and update U U þ sdU with s as the Armijo line search parameter. 26 H and G are the Hessian and gradient matrix for the functional J in equation (19) with respect to the displacement vector U. The algorithm for the proposed regmentation model based on MI is given in Algorithm 1 where the multilevel approach is adapted for fast computation of the model.…”

“…This model is not designed for general image deformation as the model applies rigid image transformation. Recently, a joint segmentation and registration model has been proposed by Debroux and Le Guyader, 19 which is formulated based on the combination of nonlocal total variation and nonlocal shape descriptors. The fitting term of this model uses a weighted sum of squared difference distance measure, similar to 7 and the model depends on the many parameters such as window size, patch size, number of neighbors pixels, etc.…”

A Variational Model Dedicated to Joint Segmentation, Registration, and Atlas Generation for Shape Analysis

“…In recent years, joint image processing models have experienced increasing attention, including combined segmentation/registration models [30,34] (joint phase field approximation and registration), [45] (model based on metric structure comparison), [26,61] (level set formulation that merges the piecewise constant Mumford-Shah model with registration principles), [33] (grounded in the expectation maximisation algorithm), [25] (based on a nonlocal characterisation of weighted-total variation and nonlocal shape descriptors), or [1,43,52,55,63,68]; joint image reconstruction and motion estimation [9,14,19,51,57,62,13,46,6]; joint reconstruction and registration for post-acquisition motion correction [22] with the goal to reconstruct a single motion-free corrected image and retrieve the physiological dynamics through the deformation maps, joint optical flow estimation with phase field segmentation of the flow field [12], or joint segmentation/optimal transport models [10] (to determine the velocity of blood flow in vascular structures). This can be attributed to several factors: (i) the will to limit error propagation.…”

A Time-Dependent Joint Segmentation and Registration Model: Application to Longitudinal Registration of Hepatic DCE-MRI Sequences

“…Sharing representation between tasks and carefully intertwining them allows to reduce error propagation, to create synergies, to compensate for some possible flaws such as image quality impairment, while increasing the accuracy of the outcomes and bridging the gap towards generalization. Joint segmentation and registration models such as [16], [18] (joint phase field approximation and registration), [21] (model based on metric structure comparison), [15], [25] (level set formulation that merges the piecewise constant Mumford-Shah model with registration principles), [17] (grounded in the expectation maximization algorithm), [14] (based on a nonlocal characterization of weighted-total variation and nonlocal shape descriptors), or [1], [20], [23], [24], [27], fall within this framework.…”