Motion Comparison Method Combining Segmented Multi-Joint Line Graphs with the SIFT Matching Technique

2014 ◽  
Vol 599-601 ◽  
pp. 1566-1570
Author(s):  
Ming Zeng ◽  
Hong Lin Ren ◽  
Qing Hao Meng ◽  
Chang Wei Chen ◽  
Shu Gen Ma
Keyword(s):  
Feature Matching ◽  
Line Graph ◽  
Comparison Method ◽  
Joint Line ◽  
Line Graphs ◽  
3D Motion ◽  
Motion Data ◽  
Comparison Results ◽  
Matching Technique ◽  
Sift Features

In this paper, an effective motion comparison method based on segmented multi-joint line graphs combined with the SIFT feature matching method is proposed. Firstly, the multi-joint 3D motion data are captured using the Kinect. Secondly, 3D motion data are normalized and distortion data are removed. Therefore, a 2D line graph can be obtained. Next, SIFT features of the 2D motion line graph are extracted. Finally, the line graphs are divided into several regions and then the comparison results can be calculated based on SIFT matching ratios between the tutor’s local line graph and the trainee’s local line graph. The experimental results show that the proposed method not only can easily deal with the several challenge problems in motion analysis, e.g., the problem of different rhythm of motions, the problem of a large amount of data, but also can provide detailed error correction cues.

scholarly journals Topological invariants for the line graphs of some classes of graphs

2019 ◽  
Vol 17 (1) ◽  
pp. 1483-1490
Author(s):  
Xiaoqing Zhou ◽  
Mustafa Habib ◽  
Tariq Javeed Zia ◽  
Asim Naseem ◽  
Anila Hanif ◽  
...  
Keyword(s):  
Communication Theory ◽  
Chemical Reactivity ◽  
Line Graph ◽  
Chemical Properties ◽  
Topological Invariants ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Physical And Chemical ◽  
Ladder Graphs ◽  
And Chemical Properties

AbstractGraph theory plays important roles in the fields of electronic and electrical engineering. For example, it is critical in signal processing, networking, communication theory, and many other important topics. A topological index (TI) is a real number attached to graph networks and correlates the chemical networks with physical and chemical properties, as well as with chemical reactivity. In this paper, our aim is to compute degree-dependent TIs for the line graph of the Wheel and Ladder graphs. To perform these computations, we first computed M-polynomials and then from the M-polynomials we recovered nine degree-dependent TIs for the line graph of the Wheel and Ladder graphs.

The martingale comparison method for Markov processes

2021 ◽  
Vol 58 (1) ◽  
pp. 164-176
Author(s):  
Benedikt Köpfer ◽  
Ludger Rüschendorf
Keyword(s):  
Markov Processes ◽  
Martingale Problem ◽  
Function Class ◽  
Comparison Method ◽  
Stochastic Orders ◽  
Regularity Conditions ◽  
Evolution System ◽  
Basic Step ◽  
Theory Of Evolution ◽  
Comparison Results

AbstractComparison results for Markov processes with respect to function-class-induced (integral) stochastic orders have a long history. The most general results so far for this problem have been obtained based on the theory of evolution systems on Banach spaces. In this paper we transfer the martingale comparison method, known for the comparison of semimartingales to Markovian semimartingales, to general Markov processes. The basic step of this martingale approach is the derivation of the supermartingale property of the linking process, giving a link between the processes to be compared. This property is achieved using the characterization of Markov processes by the associated martingale problem in an essential way. As a result, the martingale comparison method gives a comparison result for Markov processes under a general alternative but related set of regularity conditions compared to the evolution system approach.

scholarly journals A Strengthening of Brooks' Theorem for Line Graphs

10.37236/632 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Landon Rabern
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Line Graph ◽  
Clique Number ◽  
Line Graphs ◽  
Delta G

We prove that if $G$ is the line graph of a multigraph, then the chromatic number $\chi(G)$ of $G$ is at most $\max\left\{\omega(G), \frac{7\Delta(G) + 10}{8}\right\}$ where $\omega(G)$ and $\Delta(G)$ are the clique number and the maximum degree of $G$, respectively. Thus Brooks' Theorem holds for line graphs of multigraphs in much stronger form. Using similar methods we then prove that if $G$ is the line graph of a multigraph with $\chi(G) \geq \Delta(G) \geq 9$, then $G$ contains a clique on $\Delta(G)$ vertices. Thus the Borodin-Kostochka Conjecture holds for line graphs of multigraphs.

A Line Feature Matching Technique Based on an Eigenvector Approach

2000 ◽  
Vol 77 (3) ◽  
pp. 263-283 ◽  
Author(s):  
Sang Ho Park ◽  
Kyoung Mu Lee ◽  
Sang Uk Lee
Keyword(s):  
Feature Matching ◽  
Line Feature ◽  
Matching Technique

On Spanning and Dominating Circuits in Graphs

1977 ◽  
Vol 20 (2) ◽  
pp. 215-220 ◽  
Author(s):  
L. Lesniak-Foster ◽  
James E. Williamson
Keyword(s):  
Line Graph ◽  
Dominating Set ◽  
Line Graphs ◽  
Sufficient Condition ◽  
Vertex Set ◽  
On Line ◽  
One To One

AbstractA set E of edges of a graph G is said to be a dominating set of edges if every edge of G either belongs to E or is adjacent to an edge of E. If the subgraph 〈E〉 induced by E is a trail T, then T is called a dominating trail of G. Dominating circuits are defined analogously. A sufficient condition is given for a graph to possess a spanning (and thus dominating) circuit and a sufficient condition is given for a graph to possess a spanning (and thus dominating) trail between each pair of distinct vertices. The line graph L(G) of a graph G is defined to be that graph whose vertex set can be put in one-to-one correspondence with the edge set of G in such a way that two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. The existence of dominating trails and circuits is employed to present results on line graphs and second iterated line graphs, respectively.

scholarly journals Efficient Algorithm for Generating Maximal L-Reflexive Trees

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 809
Author(s):  
Milica Anđelić ◽  
Dejan Živković
Keyword(s):  
Efficient Algorithm ◽  
Line Graph ◽  
Common Vertex ◽  
Line Graphs ◽  
Algebraic Numbers ◽  
Pisot Numbers ◽  
Full Characterization ◽  
Vertex Set ◽  
Second Largest Eigenvalue

The line graph of a graph G is another graph of which the vertex set corresponds to the edge set of G, and two vertices of the line graph of G are adjacent if the corresponding edges in G share a common vertex. A graph is reflexive if the second-largest eigenvalue of its adjacency matrix is no greater than 2. Reflexive graphs give combinatorial ground to generate two classes of algebraic numbers, Salem and Pisot numbers. The difficult question of identifying those graphs whose line graphs are reflexive (called L-reflexive graphs) is naturally attacked by first answering this question for trees. Even then, however, an elegant full characterization of reflexive line graphs of trees has proved to be quite formidable. In this paper, we present an efficient algorithm for the exhaustive generation of maximal L-reflexive trees.

An Image Mosaic Method Based on SIFT Feature Matching

2012 ◽  
Vol 433-440 ◽  
pp. 5420-5424 ◽  
Author(s):  
Li Jing Cao ◽  
Ming Lv
Keyword(s):  
Image Matching ◽  
Feature Matching ◽  
Image Mosaic ◽  
Sift Feature ◽  
Mosaic Image ◽  
Blending Method ◽  
Orientation Scale ◽  
Sift Features ◽  
Human Eyes ◽  
Arbitrary Matching

This paper concerns the problem of image mosaic. An image matching method based on SIFT features and an image blending method of improved Hat function are proposed in the paper. SIFT feature is local feature and keeps invariant to scale zoom, rotation and illumination. It is also insensitive to noise, view point changing and so on. Because of this our method is insensitive to orientation, scale and illumination of input images, so it’s possible to accomplish image mosaic between arbitrary matching images and the Hat function blending algorithm with global intensity revise makes the mosaic image accepted by human eyes.

Reference Point-Based SIFT Feature Matching

2014 ◽  
Vol 543-547 ◽  
pp. 2670-2673
Author(s):  
Lei Cao ◽  
Di Liao ◽  
Bin Dang Xue
Keyword(s):  
Reference Point ◽  
Image Matching ◽  
Euclidean Distance ◽  
Feature Matching ◽  
Experimental Results ◽  
Feature Descriptor ◽  
Matching Algorithm ◽  
Sift Feature ◽  
Sift Features ◽  
Suitable Reference

Aiming to solve the high computational and time consuming problem in SIFT feature matching, this paper presents an improved SIFT feature matching algorithm based on reference point. The algorithm starts from selecting a suitable reference point in the feature descriptor space when SIFT features are extracted. In the feature matching stage, this paper uses the Euclidean distance between descriptor vectors of the feature point to be matched and the reference point to make a fast filtration which removes most of the features that could not be matched. For the remaining SIFT features, Best-bin-first (BBF) algrithm is utilized to obtain precise matches. Experimental results demonstrate that the proposed matching algorithm achieves good effectiveness in image matching, and takes only about 60 percent of the time that the traditional matching algorithm takes.

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