Related papers: A fast and robust algorithm to count topologically…
We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying…
In this paper, we propose a new algorithm for point cloud denoising based on the tensor Tucker decomposition. We first represent the local surface patches of a noisy point cloud to be matrices by their distances to a reference point, and…
Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…
Persistence diagrams concisely represent the topology of a point cloud whilst having strong theoretical guarantees, but the question of how to best integrate this information into machine learning workflows remains open. In this paper we…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
Suppose that a polygon $P$ is given as an array containing the vertices in counterclockwise order. We analyze how many vertices (including the index of each of these vertices) we need to know before we can bound $P$, i.e., report a bounded…
We consider the problem of estimating a cloud of points from numerous noisy observations of that cloud after unknown rotations, and possibly reflections. This is an instance of the general problem of estimation under group action,…
We develop a new method to estimate the area, and more generally the intrinsic volumes, of a compact subset $X$ of $\mathbb{R}^d$ from a set $Y$ that is close in the Hausdorff distance. This estimator enjoys a linear rate of convergence as…
Recognition of occluded objects in unseen and unstructured indoor environments is a challenging problem for mobile robots. To address this challenge, we propose a new descriptor, TOPS, for point clouds generated from depth images and an…
Predicting how the world can evolve in the future is crucial for motion planning in autonomous systems. Classical methods are limited because they rely on costly human annotations in the form of semantic class labels, bounding boxes, and…
Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…
With the increased availability of 3D scanning technology, point clouds are moving into the focus of computer vision as a rich representation of everyday scenes. However, they are hard to handle for machine learning algorithms due to their…
Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
The rapid development of 3D acquisition technology has made it possible to obtain point clouds of real-world terrains. However, due to limitations in sensor acquisition technology or specific requirements, point clouds often contain defects…
Point cloud denoising aims to restore clean point clouds from raw observations corrupted by noise and outliers while preserving the fine-grained details. We present a novel deep learning-based denoising model, that incorporates normalizing…
Point clouds captured by scanning sensors are often perturbed by noise, which have a highly negative impact on downstream tasks (e.g. surface reconstruction and shape understanding). Previous works mostly focus on training neural networks…
The emergence of digital avatars has raised an exponential increase in the demand for human point clouds with realistic and intricate details. The compression of such data becomes challenging with overwhelming data amounts comprising…
We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of $n$ items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n…