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For an oriented surface $S$, the singular set of a fold map $f:S\rightarrow \mathbb{R}^2$ is a collection of smooth curves, also known as fold singularities. We construct a sharp lower bound on the number of self-intersections of such fold…
Despite the success of deep functional maps in non-rigid 3D shape matching, there exists no learning framework that models both self-symmetry and shape matching simultaneously. This is despite the fact that errors due to symmetry mismatch…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is…
In this paper, we propose a object detection method expressed as rotated bounding box to solve grasping challenge in the scenes where rigid objects and soft objects are mixed together. Compared with traditional detection methods, this…
The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favor as shape gave way to…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so…
In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…
We develop a cylindrical shape decomposition (CSD) algorithm to decompose an object, a union of several tubular structures, into its semantic components. We decompose the object using its curve skeleton and restricted translational sweeps.…
3D scan geometry and CAD models often contain complementary information towards understanding environments, which could be leveraged through establishing a mapping between the two domains. However, this is a challenging task due to strong,…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Achieving tight bounding boxes of a shape while guaranteeing complete boundness is an essential task for efficient geometric operations and unsupervised semantic part detection. But previous methods fail to achieve both full coverage and…
Simulating stiff materials in applications where deformations are either not significant or can safely be ignored is a pivotal task across fields. Rigid body modeling has thus long remained a fundamental tool and is, by far, the most…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
A fundamental problem in computer vision is boundary estimation, where the goal is to delineate the boundary of objects in an image. In this paper, we propose a method which jointly incorporates geometric and topological information within…
Changes in the extent of local concavity along with changes in surface roughness of binding sites of proteins have long been considered as useful markers to identify functional sites of proteins. However, an algorithm that describes the…
Seam carving is a computational method capable of resizing images for both reduction and expansion based on its content, instead of the image geometry. Although the technique is mostly employed to deal with redundant information, i.e.,…
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…