Abstract Non‐rigid iterative closest point (ICP) is a popular framework for shape alignment, typically formulated as alternating iteration of correspondence search and shape transformation. A common approach in the shape transformation stage is to solve a linear least squares problem to find a smoothness‐regularized transform that fits the target shape. However, completely solving the linear least squares problem to obtain a transform is wasteful because the correspondences used for constructing the problem are imperfect, especially at early iterations. In this work, we design a novel framework to compute a transform in single step without the exact linear solve. Our key idea is to use only a single step of an iterative linear system solver, conjugate gradient, at each shape transformation stage. For this single‐step scheme to be effective, appropriate preconditioning of the linear system is required. We design a novel adaptive Sobolev‐Jacobi preconditioning method for our single‐step transform to produce a large and regularized shape update suitable for correspondence search in the next iteration. We demonstrate that our preconditioned single‐step transform stably accelerates challenging 3D surface registration tasks.

Self-intersection repair in static 3D surface meshes presents unique challenges due to the absence of temporal motion and penetration depth information—two critical elements typically leveraged in physics-based approaches. We introduce a novel framework that transforms local contact handling into a global repair strategy through a combination of local signed tangent-point energies and their gradient diffusion. At the heart of our method is a key insight: rather than computing expensive global repulsive potentials, we can effectively approximate long-range interactions by diffusing energy gradients from local contacts throughout the mesh surface. In turn, resolving complex self-intersections reduces to simply propagating local repulsive energies through standard diffusion mechanics and iteratively solving tractable local optimizations. We further accelerate convergence through our momentum-based optimizer, which adaptively regulates momentum based on gradient statistics to prevent overshooting while maintaining rapid intersection repair. The resulting algorithm handles a variety of challenging scenarios, from shallow contacts to deep penetrations, while providing computational efficiency suitable for interactive applications.

Non-rigid registration of 3D shape collections using a template mesh is essential for constructing 3D datasets. Traditional non-rigid Iterative Closest Point (ICP) methods rely on manually selected template meshes, which can result in inconsistent registrations when applied to diverse shape collections. This inconsistency arises particularly when the template lacks common shape features with the input instances or when landmark annotations are sparse. To overcome this limitation, we propose a novel ICP framework that jointly optimizes a shared template shape and its instance-wise deformations. Our joint optimization framework assigns distinct roles to the shared template and instance-wise deformations: the template captures common shape features, while instance-wise deformations handle residual registration errors. We use stronger smoothness regularization on the instance-wise deformations in early iterations to prioritize the accumulation of common details on the template. Additionally, a distortion alignment energy minimizes interinstance map distortions, promoting consistent instance-wise deformations. On challenging 3D datasets with large shape variations, our method achieves state-of-the-art fitting accuracy and consistent results in shape averaging and deformation transfer. By removing the need for a carefully selected preset template, our method extends the capability of extrinsic non-rigid registration frameworks, offering a more robust and flexible solution for challenging registration scenarios.

Many surface reconstruction methods incorporate normal integration, which is a process to obtain a depth map from surface gradients. In this process, the input may represent a surface with discontinuities, e.g., due to self-occlusion. To reconstruct an accurate depth map from the input normal map, hidden surface gradients occurring from the jumps must be handled. To model these jumps correctly, we design a novel discretization scheme for the domain of normal integration. Our key idea is to introduce auxiliary edges, which bridge between piecewise-smooth patches in the domain so that the magnitude of hidden jumps can be explicitly expressed. Using the auxiliary edges, we design a novel algorithm to optimize the discontinuity and the depth map from the input normal map. Our method optimizes dis-continuities by using a combination of iterative re-weighted least squares and iterative filtering of the jump magnitudes on auxiliary edges to provide strong sparsity regularization. Compared to previous discontinuity-preserving normal integration methods, which model the magnitudes of jumps only implicitly, our method reconstructs subtle disconti-nuities accurately thanks to our explicit representation of jumps allowing for strong sparsity regularization.

We present a caricature generation framework based on shape and style manipulation using StyleGAN. Our framework, dubbed StyleCariGAN , automatically creates a realistic and detailed caricature from an input photo with optional controls on shape exaggeration degree and color stylization type. The key component of our method is shape exaggeration blocks that are used for modulating coarse layer feature maps of StyleGAN to produce desirable caricature shape exaggerations. We first build a layer-mixed StyleGAN for photo-to-caricature style conversion by swapping fine layers of the StyleGAN for photos to the corresponding layers of the StyleGAN trained to generate caricatures. Given an input photo, the layer-mixed model produces detailed color stylization for a caricature but without shape exaggerations. We then append shape exaggeration blocks to the coarse layers of the layer-mixed model and train the blocks to create shape exaggerations while preserving the characteristic appearances of the input. Experimental results show that our StyleCariGAN generates realistic and detailed caricatures compared to the current state-of-the-art methods. We demonstrate StyleCariGAN also supports other StyleGAN-based image manipulations, such as facial expression control.