Related papers: Reconstructing Curves from Points and Tangents
The gradients used to train neural networks are typically computed using backpropagation. While an efficient way to obtain exact gradients, backpropagation is computationally expensive, hinders parallelization, and is biologically…
Extracting shape information from object bound- aries is a well studied problem in vision, and has found tremen- dous use in applications like object recognition. Conversely, studying the space of shapes represented by curves satisfying…
Traditionally, training neural networks to perform semantic segmentation required expensive human-made annotations. But more recently, advances in the field of unsupervised learning have made significant progress on this issue and towards…
This paper explores the challenge of teaching a machine how to reverse-engineer the grid-marked surfaces used to represent data in 3D surface plots of two-variable functions. These are common in scientific and economic publications; and…
Extracting high-level structural information from 3D point clouds is challenging but essential for tasks like urban planning or autonomous driving requiring an advanced understanding of the scene at hand. Existing approaches are still not…
This paper considers the approximate reconstruction of points, x \in R^D, which are close to a given compact d-dimensional submanifold, M, of R^D using a small number of linear measurements of x. In particular, it is shown that a number of…
Reassembling 3D broken objects is a challenging task. A robust solution that generalizes well must deal with diverse patterns associated with different types of broken objects. We propose a method that tackles the pairwise assembly of 3D…
We propose a novel method that reconstructs hair strands directly from colorless 3D scans by leveraging multi-modal hair orientation extraction. Hair strand reconstruction is a fundamental problem in computer vision and graphics, essential…
Quantitative tissue information, like the light scattering properties, is considered as a key player in the detection of cancerous cells in medical diagnosis. A promising method to obtain these data is optical coherence tomography (OCT). In…
In this paper, we revisit the long-standing problem of automatic reconstruction of 3D objects from single line drawings. Previous optimization-based methods can generate compact and accurate 3D models, but their success rates depend heavily…
Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…
3D object reconstruction from a single image is a highly under-determined problem, requiring strong prior knowledge of plausible 3D shapes. This introduces challenges for learning-based approaches, as 3D object annotations are scarce in…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
Charts are an excellent way to convey patterns and trends in data, but they do not facilitate further modeling of the data or close inspection of individual data points. We present a fully automated system for extracting the numerical…
Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…
Neural networks excel at discovering statistical patterns in high-dimensional data sets. In practice, higher-order cumulants, which quantify the non-Gaussian correlations between three or more variables, are particularly important for the…
Let $P$ be a polygonal curve in $\mathbb{R}^d$ of length $n$, and $S$ be a point-set of size $k$. The Curve/Point Set Matching problem consists of finding a polygonal curve $Q$ on $S$ such that the Fr\'echet distance from $P$ is less than a…
Fast and robust three-dimensional reconstruction of facial geometric structure from a single image is a challenging task with numerous applications. Here, we introduce a learning-based approach for reconstructing a three-dimensional face…
The problem of estimating the accuracy of signal reconstruction from threshold-based sampling, by only taking the sampling output into account, is addressed. The approach is based on re-sampling the reconstructed signal and the application…
Let K be a field and let L/K be a finite extension. Let X/K be a scheme of finite type. A point of X(L) is said to be new if it does not belong to the union of X(F), when F runs over all proper subextensions of L. Fix now an integer g>0 and…