A photorealistic and controllable 3D caricaturization framework for faces is introduced. We start with an intrinsic Gaussian curvature-based surface exaggeration technique, which, when coupled with texture, tends to produce oversmoothed renders. To address this, we resort to 3D Gaussian Splatting (3DGS), which has recently been shown to produce realistic free-viewpoint avatars. Given a multiview sequence, we extract a FLAME mesh, solve a curvatureweighted Poisson equation, and obtain its exaggerated form. However, directly deforming the Gaussians yields poor results, necessitating the synthesis of pseudo–groundtruth caricature images by warping each frame to its exaggerated 2D representation using local affine transformations. We then devise a training scheme that alternates real and synthesized supervision, enabling a single Gaussian collection to represent both natural and exaggerated avatars. This scheme improves fidelity, supports local edits, and allows continuous control over the intensity of the caricature. In order to achieve real-time deformations, an efficient interpolation between the original and exaggerated surfaces is introduced. We further analyze and show that it has a bounded deviation from closed-form solutions. In both quantitative and qualitative evaluations, our results outperform prior work, delivering photorealistic, geometry-controlled caricature avatars. Project page: https://c4ricaturegs.github.io

When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of whether distances measured between pairs of surface points should influence the matching process. The approach we propose treats surfaces as manifolds equipped with geodesic distances, and addresses the partial shape matching challenge by introducing a novel criterion to meticulously search for consistent distances between pairs of points. The new criterion explores the relation between intrinsic geodesic distances between the points, geodesic distances between the points and surface boundaries, and extrinsic distances between boundary points measured in the embedding space. It is shown to be less restrictive compared to previous measures and achieves state-of-the-art results when used as a loss function in training networks for partial shape matching.

Reconstruction of geometric structures from images using supervised learning suffers from limited available amount of accurate data. One type of such data is accurate real-world RGB-D images. A major challenge in acquiring such ground truth data is the accurate alignment between RGB images and the point cloud measured by a depth scanner. To overcome this difficulty, we consider a differential optimization method that aligns a colored point cloud with a given color image through iterative geometric and color matching. In the proposed framework, the optimization minimizes the photometric difference between the colors of the point cloud and the corresponding colors of the image pixels. Unlike other methods that try to reduce this photometric error, we analyze the computation of the gradient on the image plane and propose a different direct scheme. We assume that the colors produced by the geometric scanner camera and the color camera sensor are different and therefore characterized by different chromatic acquisition properties. Under these multimodal conditions, we find the transformation between the camera image and the point cloud colors. We alternately optimize for aligning the position of the point cloud and matching the different color spaces. The alignments produced by the proposed method are demonstrated on both synthetic data with quantitative evaluation and real scenes with qualitative results.