laplace tutorial

Mathematical path-python computing practice (20)-machine vision-Laplace operator convolution filtering and Laplace operatorTwo-dimensional convolution calculation by Laplace operator, linear sharpening Filtering #-*-Coding: UTF-8-*-# linear sharpening filtering-Laplace operator for two-dimensional convolution calculati

Original Address background: Why do you want to do smooth processing? 0 probability problem is that when calculating the probability of an instance, if a quantity X is not present in the Observation sample library (training set), the probability result of the whole instance is 0. In the text classification problem, when a word does not appear in the training sample, the word adjustment probability is 0, the use of a hyphen to calculate the probability of the text is also 0. This is unreasonabl

matrix). Again, the definition of eigenvectors and eigenvalues is reminded before continuing the derivation: If the numbers and non-zero vectors satisfy, then a eigenvector is the corresponding eigenvalue. Suppose =, at this moment, is the eigenvalue, which is the eigenvector. Both sides simultaneously left multiply, get =, and F ' f=n, where n is the sum of the number of vertices in the graph, so = n, because n is a fixed value, so to minimize, the equivalent is to minimize. So

The Laplace operator, like the Sobel operator, belongs to the spatial sharpening filter operation. The essence and the previous spatial filter operation is similar, the following is through the Laplace operator to introduce the spatial sharpening filter, and OPENCV provided in the Laplacian function for some explanation. Mathematical Principles Discrete function derivative The d

, from the step effect of the graph can be seen at the edge of the slope (first-order) the largest, so the first-order differential peak is the edge point, and the slope is increased first and then decreased, that is, the edge point of the second-order 0.(2) for the second case: the 0 point of the first order differential is the edge point, and the peak of the second derivative is the edge point. the difference between first-order guide and second derivative extraction edge The edges of the

features of signals, however, the frequency domain characteristics of signals are easily obtained through Fourier transformation.The simple and common understanding of Fourier transform is to combine seemingly chaotic signals into basic sine (Cosine) signals of a certain amplitude, phase, and frequency, the purpose of Fourier transformation is to find out the frequency corresponding to the large amplitude (High Energy) signals in these basic sine (Cosine) signals, so as to find out the main vib

When solving the optimization problem with constraints, the Laplace multiplier method and the kkt condition are two very important methods. For the optimization problem of equality constraints, the optimal value can be obtained using the Laplace multiplier method. If there is an inequality constraint, the kkt condition can be used to obtain the optimal value. Of course, the results obtained by these two met

1 LaplacePhysical Meaning of Operators The Laplace operator is defined as the gradient divergence. In the Cartesian coordinate system, it can also be expressed: Or, it is the trace of the Hessian matrix: Take the heat conduction equation as an example. Because the heat flow is proportional to the temperature gradient, the divergence of the temperature gradient is the loss rate of heat. It can be seen that the

Excerpt from 49300479and Https://en.wikipedia.org/wiki/Laplacian_matrixDefinedGiven a simple graph g of n vertices, its Laplace matrix is defined as:L = d-a, where D is the matrix of the G degree of the graph, and A is the adjacency matrix of Figure G. Because G is a simple graph, a contains only 0, 1, and its diagonal elements are all 0.The elements in L are given as:where deg (VI) represents the degree of vertex i.symmetric normalized

First, IntroductionThe effect of image sharpening is to enhance the grayscale contrast, so that the blurred image becomes clearer. The essence of image Blur is that the image is averaged or integral, so the image can be inverse, such as the differential operation can highlight the details of the image, so that the image becomes clearer. Because Laplace is a kind of differential operator, its application can enhance the region of gray mutation in the i

2. Laplace Pyramid FusionImage Pyramid Method principle is: to participate in the fusion of each image decomposition into a multi-scale pyramid image sequence, the low-resolution image in the upper layer, high-resolution image in the lower layer, the upper image size of the previous layer of image size of 1/4. The number of layers is 0,1,2 ... N. The pyramid of all images is fused with certain rules on the corresponding layer, then the synthetic pyram

Both the Sobel transform and the Laplace transform are high-pass filters. What is a Qualcomm filter? Is to retain the image's high-frequency components (the drastic changes), suppress the image's low-frequency components (the slow changes ). The sharp changes in the image often reflect the edge information of the image. In opencv, it is easy to call the Sobel function: Mat image = imread ("D:/picture/images/boldt.jpg", 0); If (! Image. data) Return-1;

would be a 2*2 matrix as followsThis operator is applied in the image to mean subtracting (x, y) the value of the pixel (x-1,y) from the value at (x, y) of the pixel value minus (x,y-1) and substituting the pixel value at (x, y). This represents a change in the image at (x, y), overlay The change with the original value (x, y), which can make the change more noticeable, that is, to magnify the change, thus achieving image sharpening.2. Image enhancement processing based on second-order differen

Original Address Laplace Matrix definition of Laplacian matrix Talking about the dimensionality reduction technology in machine learning, probably most of the friends who know a little about machine learning know PCA, and today we introduce a new dimensionality reduction Method-Laplace feature mapping The Laplace matrix (Laplacian matrix), also known as the Ki

Teaching objectives: 1. Understand General Dynamics equations. 2. Use the Laplace equation correctly to establish the moving differential equations of the point system. Highlights and difficulties of this chapter: Select generalized coordinates, and express the particle kinetic energy as a function of generalized coordinates and generalized velocity. Calculate the generalized force or represent the potential function of the conservative system as a

Original address Laplace matrix is a very ingenious thing, it is a kind of matrix of description graph, it is widely used in the field of machine learning such as dimensionality reduction, classification and clustering. what is a laplace matrix Laplace Matrix First of all, what is the Laplace matrix, the English name

The Gaussian pyramid has been studied in the past, but today it seems wrong that the upper and lower layers of the pyramid should be the relationship of sampling, not the relationship of scaling, and Sigma on different layers should also be different. The Laplace pyramid is applied in Image Fusion. The method is to first calculate the Laplace residual pyramid for the two images to be fused, and then use the

equalization Enhanced original image:Histogram equalization Enhanced effect:2. Image enhancement based on Laplace operatorThe use of a center 5 of the 8 neighborhood Laplace operator and image convolution can be achieved to sharpen the image enhancement, the Laplace operator as shown: the Laplace operator can enhance

, but it is not easy to use the direct method. Now, we can try another way. This is: the Laplace polynomial. 3. The structure of the Laplace polynomial, with four points as an Example Since the function goes through four points (x0, y0), (x1, Y1), (X2, Y2), (X3, Y3), you can set the function: F (x) = b0 (x) * y0 + B1 (x) * Y1 + B2 (x) * y2 + B3 (x) * Y3 Note: B0 (x),..., B3 (x) are all three polynomials

Returns the Extreme Value of the f (x, y, z) function under the condition (x, y, z) = 0 by using the "Laplace multiplier method,The method (STEP) is:1. Do the Laplace function L = f (x, y, z) + λ (x, y, z ).2. Evaluate the partial direction of X, Y, Z, and λ, obtain the equations, and obtain the p (x, y, z)If the maximum or minimum value of the actual problem exists, generally it is unique in the field, so