Table of Contents
What does the Laplacian matrix represent?
In chapter 5 of this article, Lovász covers the graph Laplacian. He explains the relation to random walks on graphs and also the link to the Colin de Vérdière graph invariant which sparked your interest (your link in the OP).
How do you calculate normalized Laplacian?
Definition 2 The normalized Laplacian matrix is 多 ≡ I − s . Notice that 多 = I − s = D−1/2(D − A)D−1/2 = D−1/2LGD−1/2, for LG the (unnor- malized) Laplacian. 1 = α1 ≥···≥ αn ≥ −1, 0 = λ1 ≤···≤ λn ≤ 2.
What is the degree of a directed graph?
The degree of a node in an undirected graph is the number of edges incident on it; for directed graphs the indegree of a node is the number of edges leading into that node and its outdegree, the number of edges leading away from it (see also Figures 6.1 and 6.2).
What is Laplacian energy?
The Laplacian energy of the graph G is defined as LE=LE(G)=n∑i=1∣∣∣μi−2mn∣∣∣ L E = L E ( G ) = ∑ i = 1 n | μ i − 2 m n | where μ1,μ2,…,μn−1,μn=0 μ 1 , μ 2 , … , μ n − 1 , μ n = 0 are the Laplacian eigenvalues of graph G .
What is the Laplacian of an image?
The Laplacian is a 2-D isotropic measure of the 2nd spatial derivative of an image. The Laplacian of an image highlights regions of rapid intensity change and is therefore often used for edge detection (see zero crossing edge detectors).
How do you find the Laplacian matrix of a graph?
The Laplacian matrix L = D − A, where D is the diagonal matrix of node degrees. We illustrate a simple example shown in Figure 6.5.
What is Indegree and Outdegree in tree?
A tree is a data structure that representation hierarchical relationship between data elements. Outdegree: Total number of leaving vertices is known as outdegree. Indegree: Total number of entering vertices is known as indegree. Branch node: All nodes except leaf node and root node are known as branch node.
What is Laplacian of Gaussian in image processing?
Laplacian of Gaussian is a popular edge detection algorithm. Edge detection is an important part of image processing and computer vision applications. It is used to detect objects, locate boundaries, and extract features.
What is Laplacian explain its derivation and show its application in image sharpening?
The Laplacian operator is an example of a second order or second derivative method of enhancement. It is particularly good at finding the fine detail in an image. The Laplacian operator is implemented in IDL as a convolution between an image and a kernel. The Convol function is used to perform the convolution.