Quasi-Newton Solver for Robust Non-Rigid Registration

Imperfect data (noise, outliers and partial overlap) and high degrees of freedom make non-rigid registration a classical challenging problem in computer vision. Existing methods typically adopt the $\ell_{p}$ type robust estimator to regularize the fitting and smoothness, and the proximal operator is used to solve the resulting non-smooth problem. However, the slow convergence of these algorithms limits its wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust estimator for data fitting and regularization, which can handle outliers and partial overlaps. We apply the majorization-minimization algorithm to the problem, which reduces each iteration to solving a simple least-squares problem with L-BFGS. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlap, with quantitative evaluation showing that it outperforms state-of-the-art methods in terms of registration accuracy and computational speed. The source code is available at https://github.com/Juyong/Fast_RNRR.Comment: Accepted to CVPR2020. The source code is available at https://github.com/Juyong/Fast_RNR

Numerical methods for coupled reconstruction and registration in digital breast tomosynthesis.

Digital Breast Tomosynthesis (DBT) provides an insight into the fine details of normal fibroglandular tissues and abnormal lesions by reconstructing a pseudo-3D image of the breast. In this respect, DBT overcomes a major limitation of conventional X-ray mam- mography by reducing the confounding effects caused by the superposition of breast tissue. In a breast cancer screening or diagnostic context, a radiologist is interested in detecting change, which might be indicative of malignant disease. To help automate this task image registration is required to establish spatial correspondence between time points. Typically, images, such as MRI or CT, are first reconstructed and then registered. This approach can be effective if reconstructing using a complete set of data. However, for ill-posed, limited-angle problems such as DBT, estimating the deformation is com- plicated by the significant artefacts associated with the reconstruction, leading to severe inaccuracies in the registration. This paper presents a mathematical framework, which couples the two tasks and jointly estimates both image intensities and the parameters of a transformation. Under this framework, we compare an iterative method and a simultaneous method, both of which tackle the problem of comparing DBT data by combining reconstruction of a pair of temporal volumes with their registration. We evaluate our methods using various computational digital phantoms, uncom- pressed breast MR images, and in-vivo DBT simulations. Firstly, we compare both iter- ative and simultaneous methods to the conventional, sequential method using an affine transformation model. We show that jointly estimating image intensities and parametric transformations gives superior results with respect to reconstruction fidelity and regis- tration accuracy. Also, we incorporate a non-rigid B-spline transformation model into our simultaneous method. The results demonstrate a visually plausible recovery of the deformation with preservation of the reconstruction fidelity

Iterative PnP and its application in 3D-2D vascular image registration for robot navigation

This paper reports on a new real-time robot-centered 3D-2D vascular image alignment algorithm, which is robust to outliers and can align nonrigid shapes. Few works have managed to achieve both real-time and accurate performance for vascular intervention robots. This work bridges high-accuracy 3D-2D registration techniques and computational efficiency requirements in intervention robot applications. We categorize centerline-based vascular 3D-2D image registration problems as an iterative Perspective-n-Point (PnP) problem and propose to use the Levenberg-Marquardt solver on the Lie manifold. Then, the recently developed Reproducing Kernel Hilbert Space (RKHS) algorithm is introduced to overcome the ``big-to-small'' problem in typical robotic scenarios. Finally, an iterative reweighted least squares is applied to solve RKHS-based formulation efficiently. Experiments indicate that the proposed algorithm processes registration over 50 Hz (rigid) and 20 Hz (nonrigid) and obtains competing registration accuracy similar to other works. Results indicate that our Iterative PnP is suitable for future vascular intervention robot applications.Comment: Submitted to ICRA 202

Image-guided Simulation of Heterogeneous Tissue Deformation For Augmented Reality during Hepatic Surgery

International audienceThis paper presents a method for real-time augmentation of vas- cular network and tumors during minimally invasive liver surgery. Internal structures computed from pre-operative CT scans can be overlaid onto the laparoscopic view for surgery guidance. Com- pared to state-of-the-art methods, our method uses a real-time biomechanical model to compute a volumetric displacement field from partial three-dimensional liver surface motion. This permits to properly handle the motion of internal structures even in the case of anisotropic or heterogeneous tissues, as it is the case for the liver and many anatomical structures. Real-time augmentation results are presented on in vivo and ex vivo data and illustrate the benefits of such an approach for minimally invasive surgery

A Novel Diffeomorphic Model for Image Registration and Its Algorithm

In this work, we investigate image registration by mapping one image to another in a variational framework and focus on both model robustness and solver efficiency. We first propose a new variational model with a special regularizer, based on the quasi-conformal theory, which can guarantee that the registration map is diffeomorphic. It is well known that when the deformation is large, many variational models including the popular diffusion model cannot ensure diffeomorphism. One common observation is that the fidelity error appears small while the obtained transform is incorrect by way of mesh folding. However, direct reformulation from the Beltrami framework does not lead to effective models; our new regularizer is constructed based on this framework and added to the diffusion model to get a new model, which can achieve diffeomorphism. However, the idea is applicable to a wide class of models. We then propose an iterative method to solve the resulting nonlinear optimization problem and prove the convergence of the method. Numerical experiments can demonstrate that the new model can not only get a diffeomorphic registration even when the deformation is large, but also possess the accuracy in comparing with the currently best models

Image-guided Simulation of Heterogeneous Tissue Deformation For Augmented Reality during Hepatic Surgery

International audienceThis paper presents a method for real-time augmentation of vas- cular network and tumors during minimally invasive liver surgery. Internal structures computed from pre-operative CT scans can be overlaid onto the laparoscopic view for surgery guidance. Com- pared to state-of-the-art methods, our method uses a real-time biomechanical model to compute a volumetric displacement field from partial three-dimensional liver surface motion. This permits to properly handle the motion of internal structures even in the case of anisotropic or heterogeneous tissues, as it is the case for the liver and many anatomical structures. Real-time augmentation results are presented on in vivo and ex vivo data and illustrate the benefits of such an approach for minimally invasive surgery

Scalable Dense Monocular Surface Reconstruction

This paper reports on a novel template-free monocular non-rigid surface reconstruction approach. Existing techniques using motion and deformation cues rely on multiple prior assumptions, are often computationally expensive and do not perform equally well across the variety of data sets. In contrast, the proposed Scalable Monocular Surface Reconstruction (SMSR) combines strengths of several algorithms, i.e., it is scalable with the number of points, can handle sparse and dense settings as well as different types of motions and deformations. We estimate camera pose by singular value thresholding and proximal gradient. Our formulation adopts alternating direction method of multipliers which converges in linear time for large point track matrices. In the proposed SMSR, trajectory space constraints are integrated by smoothing of the measurement matrix. In the extensive experiments, SMSR is demonstrated to consistently achieve state-of-the-art accuracy on a wide variety of data sets.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October 201