Morphing is a long-standing problem in vision and computer graphics, requir- ing a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit neural representations (INRs) for modeling such deformations, due to their meshlessness and differentiability; however, extracting coherent and accurate morphings from standard MLPs typically relies on costly regularizations, which often lead to unstable training and prevent effective feature alignment. To overcome these limitations, we propose FLOWING (FLOW morphING), a framework that recasts warping as the construction of a differential vector flow, naturally ensuring continuity, invertibility, and temporal coherence by encoding structural flow prop- erties directly into the network architectures. This flow-centric approach yields principled and stable transformations, enabling accurate and structure-preserving morphing of both 2D images and 3D shapes. Extensive experiments across a range of applications—including face and image morphing, as well as Gaussian Splatting morphing—show that FLOWING achieves state-of-the-art morphing quality with faster convergence. Code and pretrained models are available in https://schardong.github.io/flowing.

Covariance matrices outperform first-order features in many tasks, attracting considerable attention from the computer vision research community. Covariance matrices encode second-order statistics between features, at the same time it is robust to noise. Based on this, we propose representing images by covariance matrices and defining a loss function that measures the distance between them through the Riemannian distance. Motivated by the robustness and invariance properties of the affine invariant Riemannian metric the proposed method was validated in printer-proof data transmission, which is a challenging task due to the trade-off between image quality and message recovery capabilities after printing and digitization procedures. The effectiveness of this approach was systematically assessed using MS COCO and IMM Face datasets. The results demon-strated that the proposed approach outperforms conventional methods that use Euclidean distance, generating encoded images with better quality and achieving higher recovery accuracy in printed images. Additionally, a broader application of the proposed loss was successfully tested in image generation tasks, using generative adversarial networks (GANs).

Face morphing is a problem in computer graphics with numerous artistic and forensic applications. It is challenging due to variations in pose, lighting, gender, and ethnicity. This task consists of a warping for feature alignment and a blending for a seamless transition between the warped images. We propose to leverage coord-based neural networks to represent such warpings and blendings of face images. During training, we exploit the smoothness and flexibility of such networks by combining energy functionals employed in classical approaches without discretizations. Additionally, our method is time-dependent, allowing a continuous warping/blending of the images. During morphing inference, we need both direct and inverse transformations of the time-dependent warping. The first (second) is responsible for warping the target (source) image into the source (target) image. Our neural warping stores those maps in a single network dismissing the need for inverting them. The results of our experiments indicate that our method is competitive with both classical and generative models under the lens of image quality and face-morphing detectors. Aesthetically, the resulting images present a seamless blending of diverse faces not yet usual in the literature.

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time ℝ3× ℝ, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions.The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually ℝ3× {0}. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.