Euclidean Skeleton Research Articles

Early gesture detection in untrimmed streams: A controlled CTC approach for reliable decision-making

This paper focuses on the problem of online action detection for interactive systems, with a special emphasis on earliness. Online Action Detection (OAD) refers to the challenging task of recognizing gestures in untrimmed, streaming videos where the actions occur in unpredictable orders and durations. To address these challenges, we present a skeleton-based system for OAD incorporating a decision mechanism to accurately detect ongoing gestures. This allows us to provide instance-level output, achieving a high level of stream understanding. This mechanism relies on a novel Connectionist Temporal Classification (CTC) loss design that restricts the path possibilities according to the action boundaries. We also present a mechanism to tune the trade-off between accuracy and earliness according to the needs of the interactive system using a weighted label prior. This system includes a 3D CNN network, referred to as DOLT-C3D, exploiting the spatial–temporal information provided by the euclidean skeleton representation. We extensively evaluate our approach on eight publicly available datasets, demonstrating its superior performance compared to state-of-the-art methods in terms of both accuracy and earliness. We also successfully applied our approach to early 2D gestures detection. Furthermore, our system shows real-time performance, making it a suitable choice for interactive systems.

The isothermal evolution of nanoporous gold from the ring perspective - an application of graph theory

The ring structures of five isothermally annealed nanoporous gold (npg) samples were analyzed explicitly by applying results and algorithms from graph theory to skeletonized 3D reconstructions from focused ion beam (FIB) tomography data. Simplified skeletons of the reconstructions were utilized, in which the real ligaments are reduced to straight edges between the branching points of the npg microstructure. So-called minimum weight cycle bases of each skeleton graph’s cycle vector space were calculated, assigning different weight functions to these straight edges: equal weights, Euclidean lengths, and the real ligament lengths from backmapping the Euclidean skeleton edges to the skeletonized real ligament sections. These cycle bases contain the maximum number of linearly independent rings that cannot be generated by smaller rings via the ring sum specified in the cycle vector space. Such a decomposition of the npg network structures into the fundamental ring building blocks served to provide a new perspective of the isothermal evolution of npg, since the coarsening of the npg network structure could be examined from analyzing the local ring topologies and the classification of the ring topological classes. Our results suggest an increasing relative dominance of ligament pinch-off events over ring collapse events, manifesting in a broadening of the distribution of topological classes, and leading to a small but steady increase of the average number of ring edges. Furthermore, self-similar evolution of the investigated sample series cannot be stated. The implications on the topological evolution of npg as a function of the solid volume fraction are discussed.

Discrete bisector function and Euclidean skeleton in 2D and 3D

We propose a new definition and an algorithm for the discrete bisector function, which is an important tool for analyzing and filtering Euclidean skeletons. We also introduce a new thinning algorithm which produces homotopic discrete Euclidean skeletons. These algorithms, which are valid both in 2D and 3D, are integrated in a skeletonization method which is based on exact transformations, allows the filtering of skeletons, and is computationally efficient.

Extraction of the Euclidean skeleton based on a connectivity criterion

The skeleton is essential for general shape representation. The commonly required properties of a skeletonization algorithm are that the extracted skeleton should be accurate; robust to noise, position and rotation; able to reconstruct the original object; and able to produce a connected skeleton in order to preserve its topological and hierarchical properties. However, the use of a discrete image presents a lot of problems that may influence the extraction of the skeleton. Moreover, most of the methods are memory-intensive and computationally intensive, and require a complex data structure.In this paper, we propose a fast, efficient and accurate skeletonization method for the extraction of a well-connected Euclidean skeleton based on a signed sequential Euclidean distance map. A connectivity criterion is proposed, which can be used to determine whether a given pixel is a skeleton point independently. The criterion is based on a set of point pairs along the object boundary, which are the nearest contour points to the pixel under consideration and its 8 neighbors. Our proposed method generates a connected Euclidean skeleton with a single pixel width without requiring a linking algorithm or iteration process. Experiments show that the runtime of our algorithm is faster than the distance transformation and is linearly proportional to the number of pixels of an image.

Skeleton-based three-dimensional geometric morphing

In this paper, we describe a method for generating geometric morphs between general 3D solid models. The method is based on the Euclidean skeleton and is capable of generating morphs between shapes that possess different feature sets and different topology. The essential concept that enables the morphing method is utilization of the trimmed skeleton of the symmetric difference as an intermediate shape. The intermediate shape is a valid solid model whose boundary does not self-intersect and is everywhere equidistant from the boundaries of the source shapes. We apply the skeleton-based intermediate shape generation procedure recursively to produce a sequence of shapes, referred to as a morph history, that gradually transform between the initial and target shapes. The method is sufficiently robust to handle significant changes in geometry and topology, such as the creation and annihilation of protrusions, indentations, internal holes and handles, and produces intuitive morph histories. The skeleton also establishes a correspondence between points on the boundaries of the source and target objects. Interpolation between corresponding points is performed to enable fast generation of a morph history consisting of a sequence of valid solid models. For source and target models that are sufficiently close, this interpolative morphing scheme generates results comparable to those obtained by the recursive skeletonization procedure, but with improved computational efficiency. The boundary point correspondence generated by the skeleton enables morphing with surface attributes (e.g., color, texture, surface roughness, and transparency). The skeleton-based procedure also allows for morphing between open curves or surfaces. A modification of the basic procedure allows the user to control the morph by specifying corresponding feature sets on the initial and final objects. Examples are presented to demonstrate the capabilities of the methods described.

An efficient voxel‐based visualization system from an implicit skeletal surface characterization

This paper presents a new algorithm of volume rendering based on a dual representation of data. The algorithm improves both the image generation speed and its quality. Two shape descriptors are used to characterize the object: a Euclidean distance transform (EDT) and a digital Euclidean skeleton. The EDT is used at one point in time to accelerate the image generation and compute the skeleton of the shape, whilst the skeleton is used as an initialization of the processing of the implicit surface. The goal is to build an interactive system of visualization for the analysis of volumetric data, either in the setting of a qualitative exploration or as a guide for qualitative measurements. The speed of treatment together with good visualization should give the feasibility to achieve a 3D survey of a natural object in an interactive manner. The method has been successfully applied to both synthetic and real data. Copyright © 2000 John Wiley & Sons, Ltd.

Continuous skeleton computation by Voronoi diagram

The skeleton of a continuous shape can be approximated from the Voronoi diagram of points sampled along the shape boundary. To bound the error of this approximation, one must relate the spatial complexity of the shape to the boundary sampling density. The regular set model of mathematical morphology provides a practical basis to establish such a relationship. Given a binary image shape, we exhibit a corresponding continuous, regular shape such that the sequence of points describing its boundary constitutes a sufficiently dense sampling for an accurate skeleton approximation. Additionally, we bound the regeneration error from the sampling density and the regularity parameter. This approach opens significant new possibilities for shape analysis by the exact, Euclidean skeleton. As a simple example, we describe how the skeleton can be refined by pruning, without introducing significant error in the regenerated image.

Isthmus critical points for solving jigsaw puzzles in computer vision

A computer vision system that can assemble canonical jigsaw puzzles is described. The most novel aspect of this system is that the methodology derives a new set of critical points that define a feature that can be used in matching partial boundaries (or contours) of planar regions. This global feature, called an isthmus, can be efficiently and reliably computed from the Euclidean skeleton or medial axis transformation of an object. A heuristic matching technique using isthmus critical points is applied to the partial boundary matching problem of jigsaw puzzle fitting. The isthmus may also be a useful feature in any application in which the point of narrowest necking of a planar region needs to be located. >