Related papers: Reconstructing Curves from Points and Tangents
In this paper, we study a 2D tomography problem for point source models with random unknown view angles. Rather than recovering the projection angles, we reconstruct the model through a set of rotation-invariant features that are estimated…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
We study the problem of reconstructing an image from information stored at contour locations. We show that high-quality reconstructions with high fidelity to the source image can be obtained from sparse input, e.g., comprising less than…
This paper presents a simple yet powerful method for 3D human mesh reconstruction from a single RGB image. Most recently, the non-local interactions of the whole mesh vertices have been effectively estimated in the transformer while the…
In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…
We construct invariants for any closed semipositive symplectic manifold which count rational curves satisfying tangency constraints to a local divisor. More generally, we introduce invariants involving multibranched local tangency…
In the film and gaming industries, achieving a realistic hair appearance typically involves the use of strands originating from the scalp. However, reconstructing these strands from observed surface images of hair presents significant…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…
While self-similar sets have no tangents at any single point, self-affine curves can be smooth. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the curve…
3D reconstruction from images is a core problem in computer vision. With recent advances in deep learning, it has become possible to recover plausible 3D shapes even from single RGB images for the first time. However, obtaining detailed…
Computer-Aided Design is ubiquitous in todays world, as almost every manufactured object begins as a digital model across industries. At the same time, advances in 3D sensing have made point clouds a dominant form of raw 3D data. Recovering…
Reconstructing a 3D shape based on a single sketch image is challenging due to the large domain gap between a sparse, irregular sketch and a regular, dense 3D shape. Existing works try to employ the global feature extracted from sketch to…
Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise. A key development is the reformulation of the reverse sampling process as a deterministic probability flow…
We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its…
Controlled ordinary differential equations driven by continuous bounded variation curves can be considered a continuous time analogue of recurrent neural networks for the construction of expressive features of the input curves. We ask up to…
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…
Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the…
The well-known trace reconstruction problem is the problem of inferring an unknown source string $x \in \{0,1\}^n$ from independent "traces", i.e. copies of $x$ that have been corrupted by a $\delta$-deletion channel which independently…
We introduce a variational approach for extracting curves between a list of possible endpoints, based on the discretization of an energy and Smirnov's decomposition theorem for vector fields. It is used to design a bi-level minimization…