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Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…
Vessel segmentation and centerline extraction are two crucial preliminary tasks for many computer-aided diagnosis tools dealing with vascular diseases. Recently, deep-learning based methods have been widely applied to these tasks. However,…
Object skeletons are useful for object representation and object detection. They are complementary to the object contour, and provide extra information, such as how object scale (thickness) varies among object parts. But object skeleton…
DBSCAN is a fundamental spatial clustering algorithm with numerous practical applications. However, a bottleneck of the algorithm is in the worst case, the run time complexity is $O(n^2)$. To address this limitation, we propose a new…
Multiscale shape skeletonization on pixel adjacency graphs is an advanced intriguing research subject in the field of image processing, computer vision and data mining. The previous works in this area almost focused on the graph vertices.…
Morphological methods play a crucial role in remote sensing image processing, due to their ability to capture and preserve small structural details. However, most of the existing deep learning models for semantic segmentation are based on…
Deep Learning for Geometric Shape Understating has organized a challenge for extracting different kinds of skeletons from the images of different objects. This competition is organized in association with CVPR 2019. There are three…
This paper focuses on the challenging task of learning 3D object surface reconstructions from single RGB images. Existing methods achieve varying degrees of success by using different geometric representations. However, they all have their…
Collision-free motion planning in complex outdoor environments relies heavily on perceiving the surroundings through exteroceptive sensors. A widely used approach represents the environment as a voxelized Euclidean distance field, where…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…
The skeleton formalism aims at extracting and quantifying the filamentary structure of the universe is generalized to 3D density fields; a numerical method for computating a local approximation of the skeleton is presented and validated…
Object skeleton is a useful cue for object detection, complementary to the object contour, as it provides a structural representation to describe the relationship among object parts. While object skeleton extraction in natural images is a…
We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…
Let $A$ be a $n$ by $n$ matrix. A skeleton decomposition is any factorization of the form $CUR$ where $C$ comprises columns of $A$, and $R$ comprises rows of $A$. In this paper, we consider uniformly sampling $\l\simeq k \log n$ rows and…
The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…
The Hamilton-Jacobi skeleton, also known as the medial axis, is a powerful shape descriptor that represents binary objects in terms of the centres of maximal inscribed discs. Despite its broad applicability, the medial axis suffers from…
Thinning of character images is a big challenge. Removal of strokes or deformities in thinning is a difficult problem. In this paper, we have proposed a medial axis based thinning strategy used for performing skeletonization of printed and…
We propose a novel algorithm for the task of supervised discriminative distance learning by nonlinearly embedding vectors into a low dimensional Euclidean space. We work in the challenging setting where supervision is with constraints on…
We discuss the skeleton as a probe of the filamentary structures of a 2D random field. It can be defined for a smooth field as the ensemble of pairs of field lines departing from saddle points, initially aligned with the major axis of local…
In many data science applications, the objective is to extract appropriately-ordered smooth low-dimensional data patterns from high-dimensional data sets. This is challenging since common sorting algorithms are primarily aiming at finding…