A Non-local Topology-Preserving Segmentation-Guided Registration Model

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

“…So for almost every t ∈]0,T [, ψ k (t) strongly converges toψ(t) in W 1,4 (Ω, R 2 ) and det ∇ψ k (t) → k→+∞ det ∇ψ(t) in L 2 (Ω). From what was done in the stationary case [15], for almost every t ∈]0,T [,…”

“…holds, these three elements combined allowing to handle the fidelity term. In order to deal with the nonlinearity in ∇ϕ, we propose introducing an auxiliary variable V i simulating the Jacobian deformation with a quadratic penalty method as in [15]. The decoupled problem becomes :…”

“…We then use an alternating minimization scheme to solve the problem. We refer the reader to [15,Section 4.3. ] for an exhaustive description of the algorithm relying on the derivation of Euler-Lagrange equations solved by an L 2 gradient flow algorithm and an implicit/semi-implicit Euler time stepping scheme.…”

“…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.…”

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.…”