The method begins with an iterative Gaussian cloud soft clustering module, offering structured temporal point cloud representations.

Point Cloud Interpolation confronts challenges from point sparsity, complex spatiotemporal dynamics, and the difficulty of deriving complete 3D point clouds from sparse temporal information. This paper presents NeuroGauss4D-PCI, which excels at modeling complex non-rigid deformations across varied dynamic scenes. The method begins with an iterative Gaussian cloud soft clustering module, offering structured temporal point cloud representations. The proposed temporal radial basis function Gaussian residual utilizes Gaussian parameter interpolation over time, enabling smooth parameter transitions and capturing temporal residuals of Gaussian distributions. Additionally, a 4D Gaussian deformation field tracks the evolution of these parameters, creating continuous spatiotemporal deformation fields. A 4D neural field transforms low-dimensional spatiotemporal coordinates ($x,y,z,t$) into a high-dimensional latent space. Finally, we adaptively and efficiently fuse the latent features from neural fields and the geometric features from Gaussian deformation fields.NeuroGauss4D-PCI outperforms existing methods in point cloud frame interpolation, delivering leading performance on both object-level (DHB) and large-scale autonomous driving datasets (NL-Drive), with scalability to auto-labeling and point cloud densification tasks.

Modeling dynamic scenes is important for many applications such as virtual reality and telepresence. Despite achieving unprecedented fidelity for novel view synthesis in dynamic scenes, existing methods based on Neural Radiance Fields (NeRF) suffer from slow convergence (i.e., model training time measured in days). In this paper, we present DeVRF, a novel representation to accelerate learning dynamic radiance fields. The core of DeVRF is to model both the 3D canonical space and 4D deformation field of a dynamic, non-rigid scene with explicit and discrete voxel-based representations. However, it is quite challenging to train such a representation which has a large number of model parameters, often resulting in overfitting issues. To overcome this challenge, we devise a novel static-to-dynamic learning paradigm together with a new data capture setup that is convenient to deploy in practice. This paradigm unlocks efficient learning of deformable radiance fields via utilizing the 3D volumetric canonical space learnt from multi-view static images to ease the learning of 4D voxel deformation field with only few-view dynamic sequences. To further improve the efficiency of our DeVRF and its synthesized novel view's quality, we conduct thorough explorations and identify a set of strategies. We evaluate DeVRF on both synthetic and real-world dynamic scenes with different types of deformation.

In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a general-purpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through state-of-the-art results across multiple deformable shape matching benchmarks.

Image-to-image translation models have achieved notable success in converting images across visual domains and are increasingly used for medical tasks such as predicting post-operative outcomes and modeling disease progression. However, most existing methods primarily aim to match the target distribution and often neglect spatial correspondences between the source and translated images. This limitation can lead to structural inconsistencies and hallucinations, undermining the reliability and interpretability of the predictions. These challenges are accentuated in clinical applications by the stringent requirement for anatomical accuracy. In this work, we present TraceTrans, a novel deformable image translation model designed for post-operative prediction that generates images aligned with the target distribution while explicitly revealing spatial correspondences with the pre-operative input. The framework employs an encoder for feature extraction and dual decoders for predicting spatial deformations and synthesizing the translated image. The predicted deformation field imposes spatial constraints on the generated output, ensuring anatomical consistency with the source. Extensive experiments on medical cosmetology and brain MRI datasets demonstrate that TraceTrans delivers accurate and interpretable post-operative predictions, highlighting its potential for reliable clinical deployment.

Alzheimer's disease (AD), a degenerative brain condition, can benefit from early prediction to slow its progression. As the disease progresses, patients typically undergo brain atrophy. Current prediction methods for Alzheimers disease largely involve analyzing morphological changes in brain images through manual feature extraction. This paper proposes a novel method, the Deformation-Aware Temporal Generative Network (DATGN), to automate the learning of morphological changes in brain images about disease progression for early prediction. Given the common occurrence of missing data in the temporal sequences of MRI images, DATGN initially interpolates incomplete sequences. Subsequently, a bidirectional temporal deformation-aware module guides the network in generating future MRI images that adhere to the disease's progression, facilitating early prediction of Alzheimer's disease. DATGN was tested for the generation of temporal sequences of future MRI images using the ADNI dataset, and the experimental results are competitive in terms of PSNR and MMSE image quality metrics. Furthermore, when DATGN-generated synthetic data was integrated into the SVM vs. CNN vs. 3DCNN-based classification methods, significant improvements were achieved from 6. 21\% to 16\% in AD vs. NC classification accuracy and from 7. 34\% to 21. 25\% in AD vs. MCI vs. NC classification accuracy. The qualitative visualization results indicate that DATGN produces MRI images consistent with the brain atrophy trend in Alzheimer's disease, enabling early disease prediction.