MR Reconstruction And Soft Tissue Deformation Simulation Based On Euler's Elastica Minimization

Curvature is an important geometric quantity of curves and surfaces,and also is the basic geometric element of images,visual analysis,and computer graphics.As a curvature-based method,Euler's elastica regularization is applied to the field of image processing and computer vision earlier.In view of the exceptional ability of curvature in connecting missing edges and structures,we propose novel sparse reconstruction models via the Euler's elastica energy.Especially,we firstly extend the Euler's elastica regularity into the nonlocal formulation to fully take the advantages of the pattern redundancy and structural similarity in image data.Due to its non-convexity,non-smoothness and nonlinearity,we regard both local and nonlocal elastica functional as the weighted total variation for a good trade-off between the runtime complexity and performance.The splitting techniques and alternating direction method of multipliers(ADMM)are used to achieve efficient algorithms,the convergence of which is also discussed under certain assumptions.The weighting function occurred in our model can be well estimated according to the local approach.Numerical experiments demonstrate that our nonlocal elastica model achieves the state-of-the-art reconstruction results for different sampling patterns and sampling ratios,especially when the sampling rate is extremely low.Utilizing Euler's elastica,we propose a new mass spring model to simulate nonlinear and incompressible soft tissue deformation.We estimate the mean curvature within 1-ring neighborhood of the vertex,and use the Euler's elastica energy to describe the deformation of the spring in order to obtain the mass-spring model with nonlinear stress-strain relationship.Then,the explicit iterative scheme based on Verlet integral is designed to solve the proposed model.Compared with the traditional mass-spring model and the volume preserved mass-spring model,our model can not only effectively describe the nonlinear mechanical property of soft tissues,but also has higher computational efficiency.Therefore,the our improved mass-spring model is more suitable for real-time soft tissue simulation.