Accurate compensation of brain deformation is critical for reliable image-guided neurosurgery. Surgical manipulation and tumor resection induce tissue motion, causing preoperative planning images to become misaligned with the intraoperative anatomy. In this review, we examine data-driven methods developed between 2020 and 2025 for brain deformation registration and modeling, with a particular focus on learning-based approaches. A comprehensive literature search was conducted in PubMed, IEEE Xplore, Scopus, and Web of Science using predefined inclusion and exclusion criteria for computational methods addressing brain deformation in neurosurgical imaging, resulting in 46 eligible studies. We provide a unified analysis of methodological strategies, including deep learning-based image registration, direct deformation field regression, synthesis-driven multimodal alignment, resection-aware architectures for handling missing correspondences, and hybrid models integrating biomechanical priors. We also examine dataset utilization, evaluation metrics, validation protocols, and the assessment of uncertainty and generalization across studies. While learning-based methods demonstrate promising accuracy and computational efficiency, current approaches remain limited by out-of-distribution robustness, standardized benchmarking, interpretability, and readiness for clinical deployment. Our review highlights these gaps and outlines future directions toward more robust, generalizable, and clinically translatable solutions for neurosurgical guidance. By organizing recent advances and critically assessing evaluation practices, this work provides a comprehensive reference for researchers and clinicians working on data-driven registration and modeling of brain deformation.

We propose a deep mixture of multimodal hierarchical variational auto-encoders called MMHVAE that synthesizes missing images from observed images in different modalities. MMHVAE's design focuses on tackling four challenges: (i) creating a complex latent representation of multimodal data to generate high-resolution images; (ii) encouraging the variational distributions to estimate the missing information needed for cross-modal image synthesis; (iii) learning to fuse multimodal information in the context of missing data; (iv) leveraging dataset-level information to handle incomplete data sets at training time. Extensive experiments are performed on the challenging problem of pre-operative brain multi-parametric magnetic resonance and intra-operative ultrasound imaging.

Intraoperative registration of real-time ultrasound (iUS) to preoperative Magnetic Resonance Imaging (MRI) remains an unsolved problem due to severe modality-specific differences in appearance, resolution, and field-of-view. To address this, we propose a novel 3D cross-modal keypoint descriptor for MRI-iUS matching and registration. Our approach employs a patient-specific matching-by-synthesis approach, generating synthetic iUS volumes from preoperative MRI. This enables supervised contrastive training to learn a shared descriptor space. A probabilistic keypoint detection strategy is then employed to identify anatomically salient and modality-consistent locations. During training, a curriculum-based triplet loss with dynamic hard negative mining is used to learn descriptors that are i) robust to iUS artifacts such as speckle noise and limited coverage, and ii) rotation-invariant. At inference, the method detects keypoints in MR and real iUS images and identifies sparse matches, which are then used to perform rigid registration. Our approach is evaluated using 3D MRI-iUS pairs from the ReMIND dataset. Experiments show that our approach outperforms state-of-the-art keypoint matching methods across 11 patients, with an average precision of ${69}.{8}\%$ . For image registration, our method achieves a competitive mean Target Registration Error of 2.39 mm on the ReMIND2Reg benchmark. Compared to existing iUS-MR registration approaches, our framework is interpretable, requires no manual initialization, and shows robustness to iUS field-of-view variation. Code, data and model weights are available at https://github.com/morozovdd/CrossKEY.

We introduce MHVAE, a deep hierarchical variational autoencoder (VAE) that synthesizes missing images from various modalities. Extending multi-modal VAEs with a hierarchical latent structure, we introduce a probabilistic formulation for fusing multi-modal images in a common latent representation while having the flexibility to handle incomplete image sets as input. Moreover, adversarial learning is employed to generate sharper images. Extensive experiments are performed on the challenging problem of joint intra-operative ultrasound (iUS) and Magnetic Resonance (MR) synthesis. Our model outperformed multi-modal VAEs, conditional GANs, and the current state-of-the-art unified method (ResViT) for synthesizing missing images, demonstrating the advantage of using a hierarchical latent representation and a principled probabilistic fusion operation. Our code is publicly available.

We present in this paper an efficient template-based method for 3D recovery of elastic shapes from a fixed monocular camera. By exploiting the objects elasticity, in contrast to isometric methods that use inextensibility constraints, a large range of deformations can be handled. Our method is expressed as a saddle point problem using Lagrangian multipliers resulting in a linear system which unifies both mechanical and optical constraints and integrates Dirichlet boundary conditions, whether they are fixed or free. We experimentally show that no prior knowledge on material properties is needed, which exhibit the generic usability of our method with elastic and inelastic objects with different kinds of materials. Comparisons with existing techniques are conducted on synthetic and real elastic objects with strains ranging from 25% to 130% resulting to low errors.

In this paper we introduce a method for semiautomatic registration of 3D deformable models using 2D shape outlines (silhouettes) extracted from a monocular camera view. Our framework is based on the combination of a biomechanical model of the organ with a set of projective constraints influencing the deformation of the model. To enforce convergence towards a global minimum for this ill-posed problem we interactively provide a rough (rigid) estimation of the pose. We show that our approach allows for the estimation of the non-rigid 3D pose while relying only on 2D information. The method is evaluated experimentally on a soft silicone gel model of a liver, as well as on real surgical data, providing augmented reality of the liver and the kidney using a monocular laparoscopic camera. Results show that the final elastic registration can be obtained in just a few seconds, thus remaining compatible with clinical constraints. We also evaluate the sensitivity of our approach according to both the initial alignment of the model and the silhouette length and shape.

We address in this paper the ill-posed problem of initial alignment of pre-operative to intra-operative data for augmented reality during minimally invasive hepatic surgery. This problem consists of finding the rigid transformation that relates the scanning reference and the endoscopic camera pose, and the non-rigid transformation undergone by the liver w.r.t its scanned state. Most of the state-of-the-art methods assume a known initial registration. Here, we propose a method that permits to recover the deformation undergone by the liver while simultaneously finding the rotational and translational parts of the transformation. Our formulation considers the boundaries of the liver with its surrounding tissues as hard constraints directly encoded in an energy minimization process. We performed experiments on real in-vivo data of human hepatic surgery and synthetic data, and compared our method with related works.

This article presents a framework for fusing preoperative data and intra-operative data for surgery guidance. This framework is employed in the context of Minimally Invasive Surgery (MIS) of the liver. From stereoscopic images a three dimensional point cloud is reconstructed in real-time. This point cloud is then used to register a patient-specific biomechanical model derived from Computed Tomography images onto the laparoscopic view. In this way internal structures such as vessels and tumors can be visualized to help the surgeon during the procedure. This is particularly relevant since abdominal organs undergo large deformations in the course of the surgery, making it difficult for surgeons to correlate the laparoscopic view with the pre-operative images. Our method has the potential to reduce the duration of the operation as the biomechanical model makes it possible to estimate the in-depth position of tumors and vessels at any time of the surgery, which is essential to the surgical decision process. Results show that our method can be successfully applied during laparoscopic procedure without interfering with the surgical work flow.

Current methods dealing with non-rigid augmented reality only provide an augmented view when the topology of the tracked object is not modified, which is an important limitation. In this paper we solve this shortcoming by introducing a method for physics-based non-rigid augmented reality. Singularities caused by topological changes are detected by analyzing the displacement field of the underlying deformable model. These topological changes are then applied to the physics-based model to approximate the real cut. All these steps, from deformation to cutting simulation, are performed in real-time. This significantly improves the coherence between the actual view and the model, and provides added value.

This paper presents a method for real-time augmented reality of internal liver structures during minimally invasive hepatic surgery. Vessels and tumors computed from pre-operative CT scans can be overlaid onto the laparoscopic view for surgery guidance. Compared to current methods, our method is able to locate the in-depth positions of the tumors based on partial three-dimensional liver tissue motion using a real-time biomechanical model. This model 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. Experimentations conducted on phantom liver permits to measure the accuracy of the augmentation while real-time augmentation on in vivo human liver during real surgery shows the benefits of such an approach for minimally invasive surgery.

This paper focuses on the 3D shape recovery and augmented reality on elastic objects with self-occlusions handling, using only single view images. Shape recovery from a monocular video sequence is an underconstrained problem and many approaches have been proposed to enforce constraints and resolve the ambiguities. State-of-the art solutions enforce smoothness or geometric constraints, consider specific deformation properties such as inextensibility or resort to shading constraints. However, few of them can handle properly large elastic deformations. We propose in this paper a real-time method that uses a mechanical model and able to handle highly elastic objects. The problem is formulated as an energy minimization problem accounting for a non-linear elastic model constrained by external image points acquired from a monocular camera. This method prevents us from formulating restrictive assumptions and specific constraint terms in the minimization. In addition, we propose to handle self-occluded regions thanks to the ability of mechanical models to provide appropriate predictions of the shape. Our method is compared to existing techniques with experiments conducted on computer-generated and real data that show the effectiveness of recovering and augmenting 3D elastic objects. Additionally, experiments in the context of minimally invasive liver surgery are also provided and results on deformations with the presence of self-occlusions are exposed.

This article introduces a method for tracking the internal structures of the liver during robot-assisted procedures. Vascular network, tumors and cut planes, computed from pre-operative data, can be overlaid onto the laparoscopic view for image-guidance, even in the case of large motion or deformation of the organ. Compared to current methods, our method is able to precisely propagate surface motion to the internal structures. This is made possible by relying on a fast yet accurate biomechanical model of the liver combined with a robust visual tracking approach designed to properly constrain the model. Augmentation results are demonstrated on in-vivo sequences of a human liver during robotic surgery, while quantitative validation is performed on an ex-vivo porcine liver experimentation. Validation results show that our approach gives an accurate surface registration with an error of less than 6mm on the position of the tumor.

This paper proposes an efficient method to capture and augment highly elastic objects from a single view. 3D shape recovery from a monocular video sequence is an underconstrained problem and many approaches have been proposed to enforce constraints and resolve the ambiguities. State-of-the art solutions enforce smoothness or geometric constraints, consider specific deformation properties such as inextensibility or ressort to shading constraints. However, few of them can handle properly large elastic deformations. We propose in this paper a real-time method which makes use of a mechanical model and is able to handle highly elastic objects. Our method is formulated as a energy minimization problem accounting for a non-linear elastic model constrained by external image points acquired from a monocular camera. This method prevents us from formulating restrictive assumptions and specific constraint terms in the minimization. The only parameter involved in the method is the Young's modulus where we show in experiments that a rough estimate of its value is sufficient to obtain a good reconstruction. Our method is compared to existing techniques with experiments conducted on computer-generated and real data that show the effectiveness of our approach. Experiments in the context of minimally invasive liver surgery are also provided.

This paper presents a method for real-time augmentation of vascular 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. Compared 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 phantom data and illustrate the benefits of such an approach for minimally invasive surgery.