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In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute…
We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…
Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…
We present a simple algorithm for differentiable rendering of surfaces represented by Signed Distance Fields (SDF), which makes it easy to integrate rendering into gradient-based optimization pipelines. To tackle visibility-related…
Switching between different levels of resolution is essential for multiscale modeling, but restoring details at higher resolution remains challenging. In our previous study we have introduced deepBackmap: a deep neural-network-based…
This paper presents a novel framework to recover detailed human body shapes from a single image. It is a challenging task due to factors such as variations in human shapes, body poses, and viewpoints. Prior methods typically attempt to…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
A differential geometric approach to singular perturbation theory is presented. It is shown that singular perturbation problems such as multiple-scale and boundary layer problems can be treated more easily on a differential geometric basis.…
Inspired by the seminal result that a graph and an associated rotation system uniquely determine the topology of a closed manifold, we propose a combinatorial method for reconstruction of surfaces from points. Our method constructs a…
In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique…
Reconstructing the shape and appearance of real-world objects using measured 2D images has been a long-standing problem in computer vision. In this paper, we introduce a new analysis-by-synthesis technique capable of producing high-quality…
Automated surface-anomaly detection using machine learning has become an interesting and promising area of research, with a very high and direct impact on the application domain of visual inspection. Deep-learning methods have become the…
This paper describes a framework for capturing geological structures in a 3D block model and improving its spatial fidelity given new mesh surfaces. Using surfaces that represent geological boundaries, the objectives are to identify areas…
The surface reconstruction problem from sets of planar parallel slices representing cross sections through 3D objects is presented. The final result of surface reconstruction is always based on the correct estimation of the structure of the…
Advancements in imaging technology have enabled hardware to support 10 to 16 bits per channel, facilitating precise manipulation in applications like image editing and video processing. While deep neural networks promise to recover high…
This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…
Smooth and curved microstructural topologies found in nature - from soap films to trabecular bone - have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far have been…
The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…