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Recent works have demonstrated that natural language can be used to generate and edit 3D shapes. However, these methods generate shapes with limited fidelity and diversity. We introduce CLIP-Sculptor, a method to address these constraints…
We present a new manifold learning algorithm that takes a set of data points lying on or near a lower dimensional manifold as input, possibly with noise, and outputs a simplicial complex that fits the data and the manifold. We have…
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…
While previous studies have demonstrated successful 3D object shape completion with a sufficient number of points, they often fail in scenarios when a few points, e.g. tens of points, are observed. Surprisingly, via entropy analysis, we…
We construct worst-case examples for the standard reduction algorithm for computing persistent homology. Our constructions are similar to the worst-case examples introduced by Morozov, but we replace the single-triangle arrangement with a…
We introduce CRISP, a method that recovers simulatable human motion and scene geometry from monocular video. Prior work on joint human-scene reconstruction relies on data-driven priors and joint optimization with no physics in the loop, or…
For grasp network algorithms, generating grasp datasets for a large number of 3D objects is a crucial task. However, generating grasp datasets for hundreds of objects can be very slow and consume a lot of storage resources, which hinders…
We introduce families of decorations of a same topological space, as well as a family of sheaves over such decorated spaces. Making those families a directed system leads to the concept of emerald over a space. For the configuration space…
Point clouds are a set of data points in space to represent the 3D geometry of objects. A fundamental step in the processing is to identify a subset of points to represent the shape. While traditional sampling methods often ignore to…
A triangulation of a point configuration is regular if it can be given by a height function, that is every point gets lifted to a certain height and projecting the lower convex hull gives the triangulation. Checking regularity of a…
Vision-Language models like CLIP have been widely adopted for various tasks due to their impressive zero-shot capabilities. However, CLIP is not suitable for extracting 3D geometric features as it was trained on only images and text by…
Graph-based subspace clustering methods have exhibited promising performance. However, they still suffer some of these drawbacks: encounter the expensive time overhead, fail in exploring the explicit clusters, and cannot generalize to…
In this thesis we consider a way to construct a rich family of compact Riemann Surfaces in a combinatorial way. Given a 3-regualr graph with orientation, we construct a finite-area hyperbolic Riemann surface by gluing triangles according to…
In the paper a piecewise constant image approximations of sequential number of pixel clusters or segments are treated. A majorizing of optimal approximation sequence by hierarchical sequence of image approximations is studied. Transition…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
We propose a novel method for 3D object reconstruction from a sparse set of views captured from a 360-degree calibrated camera rig. We represent the object surface through a hybrid model that uses both an MLP-based neural representation and…
Many robotic tasks involving some form of 3D visual perception greatly benefit from a complete knowledge of the working environment. However, robots often have to tackle unstructured environments and their onboard visual sensors can only…
We introduce a linear dimensionality reduction technique preserving topological features via persistent homology. The method is designed to find linear projection $L$ which preserves the persistent diagram of a point cloud $\mathbb{X}$ via…
Fine-grained image recognition has been a hot research topic in computer vision due to its various applications. The-state-of-the-art is the part/region-based approaches that first localize discriminative parts/regions, and then learn their…
Many coupled problems in engineering and science can be described by elliptic partial differential equations on adjacent domains, where the coupling can be considered either as a thin equidimensional overlap between the model domains, or as…