A Bi-variant Variational Model for Diffeomorphic Image Registration with Relaxed Jacobian Determinant Constraints

• URL: http://arxiv.org/abs/2308.02393v2
• Date: Sun, 10 Mar 2024 06:17:08 GMT
• Title: A Bi-variant Variational Model for Diffeomorphic Image Registration with Relaxed Jacobian Determinant Constraints
• Authors: Yanyan Li, Ke Chen, Chong Chen, Jianping Zhang
• Abstract summary: We propose a new bi-variant diffeomorphic image registration model. A soft constraint on the Jacobian equation $det(nablabmvarphi(bmx)) = f(bmx) > 0$ allows local deformations to shrink and grow within a flexible range. A positive constraint is imposed on the optimization of the relaxation function $f(bmx)$, and a regularizer is used to ensure the smoothness of $f(bmx)$.
• Score: 17.93018427389816
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffeomorphic registration is a widely used technique for finding a smooth and invertible transformation between two coordinate systems, which are measured using template and reference images. The point-wise volume-preserving constraint $\det(\nabla\bm{\varphi}(\bm{x})) =1$ is effective in some cases, but may be too restrictive in others, especially when local deformations are relatively large. This can result in poor matching when enforcing large local deformations. In this paper, we propose a new bi-variant diffeomorphic image registration model that introduces a soft constraint on the Jacobian equation $\det(\nabla\bm{\varphi}(\bm{x})) = f(\bm{x}) > 0$. This allows local deformations to shrink and grow within a flexible range $0<\kappa_{m}<\det(\nabla\bm{\varphi}(\bm{x}))<\kappa_{M}$. The Jacobian determinant of transformation is explicitly controlled by optimizing the relaxation function $f(\bm{x})$. To prevent deformation folding and improve the smoothness of the transformation, a positive constraint is imposed on the optimization of the relaxation function $f(\bm{x})$, and a regularizer is used to ensure the smoothness of $f(\bm{x})$. Furthermore, the positivity constraint ensures that $f(\bm{x})$ is as close to one as possible, which helps to achieve a volume-preserving transformation on average. We also analyze the existence of the minimizer for the variational model and propose a penalty-splitting algorithm with a multilevel strategy to solve this model. Numerical experiments demonstrate the convergence of the proposed algorithm and show that the positivity constraint can effectively control the range of relative volume without compromising the accuracy of the registration. Moreover, the proposed model generates diffeomorphic maps for large local deformations and outperforms several existing registration models in terms of performance.

Related papers

• Probabilistic size-and-shape functional mixed models [6.424762079392286]
  We show that it is possible to recover the size-and-shape of a square-integrable $mu$ under a functional mixed model. A random object-level unitary transformation then captures size-and-shape emphpreserving deviations of $mu$ from an individual function.
  arXiv  Detail & Related papers  (2024-11-27T15:00:33Z)
• Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPs [56.237917407785545]
  We consider the problem of learning an $varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Key to our solution is a novel projection technique based on ideas from harmonic analysis. Our result bridges the gap between two popular but conflicting perspectives on continuous-space MDPs.
  arXiv  Detail & Related papers  (2024-05-10T09:58:47Z)
• Universal Online Learning with Gradient Variations: A Multi-layer Online Ensemble Approach [57.92727189589498]
  We propose an online convex optimization approach with two different levels of adaptivity. We obtain $mathcalO(log V_T)$, $mathcalO(d log V_T)$ and $hatmathcalO(sqrtV_T)$ regret bounds for strongly convex, exp-concave and convex loss functions.
  arXiv  Detail & Related papers  (2023-07-17T09:55:35Z)
• Conformalization of Sparse Generalized Linear Models [2.1485350418225244]
  Conformal prediction method estimates a confidence set for $y_n+1$ that is valid for any finite sample size. Although attractive, computing such a set is computationally infeasible in most regression problems. We show how our path-following algorithm accurately approximates conformal prediction sets.
  arXiv  Detail & Related papers  (2023-07-11T08:36:12Z)
• Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization [88.0031283949404]
  Many real-world problems have complicated non functional constraints and use a large number of data points. Our proposed method outperforms an existing method with the previously best-known result.
  arXiv  Detail & Related papers  (2022-12-19T14:48:54Z)
• Multi-block-Single-probe Variance Reduced Estimator for Coupled Compositional Optimization [49.58290066287418]
  We propose a novel method named Multi-block-probe Variance Reduced (MSVR) to alleviate the complexity of compositional problems. Our results improve upon prior ones in several aspects, including the order of sample complexities and dependence on strongity.
  arXiv  Detail & Related papers  (2022-07-18T12:03:26Z)
• Localization in 1D non-parametric latent space models from pairwise affinities [6.982738885923206]
  We consider the problem of estimating latent positions in a one-dimensional torus from pairwise affinities. We introduce an estimation procedure that provably localizes all the latent positions with a maximum error of the order of $sqrtlog(n)/n$, with high-probability.
  arXiv  Detail & Related papers  (2021-08-06T13:05:30Z)
• Hybrid Trilinear and Bilinear Programming for Aligning Partially Overlapping Point Sets [85.71360365315128]
  In many applications, we need algorithms which can align partially overlapping point sets are invariant to the corresponding corresponding RPM algorithm. We first show that the objective is a cubic bound function. We then utilize the convex envelopes of trilinear and bilinear monomial transformations to derive its lower bound. We next develop a branch-and-bound (BnB) algorithm which only branches over the transformation variables and runs efficiently.
  arXiv  Detail & Related papers  (2021-01-19T04:24:23Z)
• Ridge regression with adaptive additive rectangles and other piecewise functional templates [0.0]
  We propose an $L_2$-based penalization algorithm for functional linear regression models. We show how our algorithm alternates between approximating a suitable template and solving a convex ridge-like problem.
  arXiv  Detail & Related papers  (2020-11-02T15:28:54Z)
• MINA: Convex Mixed-Integer Programming for Non-Rigid Shape Alignment [77.38594866794429]
  convex mixed-integer programming formulation for non-rigid shape matching. We propose a novel shape deformation model based on an efficient low-dimensional discrete model.
  arXiv  Detail & Related papers  (2020-02-28T09:54:06Z)
• Efficient algorithms for multivariate shape-constrained convex regression problems [9.281671380673306]
  We prove that the least squares estimator is computable via solving a constrained convex programming (QP) problem with $(n+1)d$ variables and at least $n(n-1)$ linear inequality constraints. For solving the generally very large-scale convex QP, we design two efficient algorithms, one is the symmetric Gauss-Seidel based alternating direction method of multipliers (tt sGS-ADMM), and the other is the proximal augmented Lagrangian method (tt pALM) with the subproblems solved by the semismooth Newton method (t
  arXiv  Detail & Related papers  (2020-02-26T11:18:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.