DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling

In recent years, there has been a growing interest in training Neural Networks to approximate Unsigned Distance Fields (UDFs) for representing open surfaces in the context of 3D reconstruction. However, UDFs are non-differentiable at the zero level set which leads to significant errors in distances and gradients, generally resulting in fragmented and discontinuous surfaces. In this paper, we propose to learn a hyperbolic scaling of the unsigned distance field, which defines a new Eikonal problem with distinct boundary conditions. This allows our formulation to integrate seamlessly with state-of-the-art continuously differentiable implicit neural representation networks, largely applied in the literature to represent signed distance fields. Our approach not only addresses the challenge of open surface representation but also demonstrates significant improvement in reconstruction quality and training performance. Moreover, the unlocked field's differentiability allows the accurate computation of essential topological properties such as normal directions and curvatures, pervasive in downstream tasks such as rendering. Through extensive experiments, we validate our approach across various data sets and against competitive baselines. The results demonstrate enhanced accuracy and up to an order of magnitude increase in speed compared to previous methods.

VesselVAE: Recursive Variational Autoencoders for 3D Blood Vessel Synthesis

We present a data-driven generative framework for synthesizing blood vessel 3D geometry. This is a challenging task due to the complexity of vascular systems, which are highly variating in shape, size, and structure. Existing model-based methods provide some degree of control and variation in the structures produced, but fail to capture the diversity of actual anatomical data. We developed VesselVAE, a recursive variational Neural Network that fully exploits the hierarchical organization of the vessel and learns a low-dimensional manifold encoding branch connectivity along with geometry features describing the target surface. After training, the VesselVAE latent space can be sampled to generate new vessel geometries. To the best of our knowledge, this work is the first to utilize this technique for synthesizing blood vessels. We achieve similarities of synthetic and real data for radius (.97), length (.95), and tortuosity (.96). By leveraging the power of deep neural networks, we generate 3D models of blood vessels that are both accurate and diverse, which is crucial for medical and surgical training, hemodynamic simulations, and many other purposes.