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Questions tagged [kernel]

A kernel is a function that acts as a parameter that is passed to some algorithm. For example, the two dimensional Gaussian kernel is often used as a parameter for low pass filtering in image processing.

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Having trouble calculating the correct Gaussian Kernel values from the Gaussian function formula

I'm having trouble calculating the same values for a Gaussian filter kernel as those derived in the Canny edge detector Wikipedia page It states: The equation for a Gaussian filter kernel of size (2k+...
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2nd derivative using gaussian filter (gnu scientific library) - offset?

I am working on an application where I use gaussian filtering (convolution) to smooth a signal and at the same time get the 1st and 2nd derivative in real time. The signal is an equidistant sampling ...
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Confusions regarding meaning of “kernel” in signal processing and image processing? [duplicate]

While studying filters in DSP and DIP, the term "kernel" is often encountered What is the meaning of "kernel" in context of filters??Please kindly explain in simple words with an example I have also ...
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Linear Kernel seems to be only Kernel to predict Class from Spectral Data in Support Vector Machine

I made a Support Vector Machine in Python using the sklearn library. The data I am using is Amplitude vs Frequency for 200-520 kHz with a 0.33 kHz step. My input data is the amplitude value for my n-...
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KCS - 3D profile representation

I was reading Character Recognition Systems book and in section 2-3-2-3 a new kind of filter is introduced (instead of normal Gaussian filter) to reduce mask size and to prevent data loss by the name ...
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Compute centered kernel value after zero-centering a kernel matrix

I am stuck trying to implement denoising with Kernel PCA. Most kernel is not supposed to be zero-mean. Say we have training inputs $[{\bf x}_1,\cdots, {\bf x}_n]$. The kernel (Gram) matrix is then $$ ...
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124 views

How to chose a kernel function for a FIR low pass filter in audio processing?

As the answer of a previous question, I was suggested to use a FIR filter to act as a low-pass filter to reconstruct the envelope of a sound wave (edited, emphasis mine): As I said in a comment, ...
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96 views

Problem implementing KL expansion with square-exponential kernel: output just looks like Gaussian

I am trying to implement the Karhunen Loeve expansion for a 1-D Gaussian random field with a square-exponential kernel. Specifically, I know that a Gaussian process has a KL expansion $\hat{U}=\sum_{...
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101 views

Why Are There Two Different Common $ 3 \times 3 $ Kernels for the Laplacian?

I find both of these 3x3 Laplacian kernels to be commonly used: 0 -1 0 -1 4 -1 0 -1 0 and: -1 -1 -1 -1 8 -1 -1 -1 -1 ...
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419 views

Why do convolution kernels such as Gaussian, Laplacian, LoG almost always seem to be expressed in integers?

I'm a total newb in search of some deeper understanding, but I'm not able to read the maths behind these on Wikipedia. If I understand correctly, you get the new value for each pixel by multiplying ...
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Difference in the meaning of kernel, filter, and dictionary atoms

While reading literature on wavelets, I have encountered keywords filters and dictionary atoms and their exact meaning is confusing for me. Basically, one can use them interchangeably and I won't see ...
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What is the betwwen [i,j] and [u,v] in explinations of correlation and convolution (picture attached)?

I don't know how to write 'summation' symbol here hence posting the picture. Can someone explain to me the difference between i,j and u,v in this explanation of correlation and convolution? I know ...
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Image Processing/ Computer Vision: How is separability of filters implemented?

I am trying to convince myself that a separable 2D filter can be implemented via two 1D filters. So, I took the example of following Sobel filter: $1/8\begin{bmatrix}-1&0&1\\-2&0&2\\-...
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153 views

What is the meaning of the sum of kernel components in digital image filtering?

When analyzing an image signal as a series of Dirac impulses in the continuous spatial domain, I applied continuous low pass filters (to reconstruct or smooth it) with area equal to 1 to preserve the ...
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What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix?

I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A ...
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What is a filter bank?

Suppose, I have 3 kernels: $$ \left[ \begin{array}{cc} a&b&c\\ d&e&f\\ g&h&i \end{array} \right] $$ $$ \left[ \begin{array}{cc} p&q&r\\ s&t&u\\ v&...
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Counting pixel connectivity groups

How many 4-connected and 8-connected components are present in the binary image below? Using definition of connectivities from the same textbook "A connected component is a group of pixels that are ...
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How to correct phase of Diagonal Volterra kernels obtained with exponential sweep sine?

I'm trying to model a non-linear system using non-linear convolution with Novak's (2010) synchronized exponential sine weep (SESS) that models them with a Generalized Hammerstein (Volterra diagonal). ...
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1k views

Volterra Kernel Convolution Method

Here I understand that the first term is a simple convolution of the input signal with first volterra kernel that I have acquired through farina sweep method, my question is if the second term is the ...
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1answer
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Why a Convolution Matrix Is Called a Kernel?

According to Wikipedia: In image processing, a kernel, convolution matrix, or mask is a small matrix. I am wondering, why the matrix is called a kernel? Does it has anything to do with kernel ...
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665 views

The Kernel of the Guided Image Filter

I am trying to understand how to calculate kernel matrix for guided image filter. Following is the formula for kernel calculation. where k is window withing pixels i and j belong i assumed that ...
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829 views

Using Convolution as Feature Extraction

I am now studying image processing in my spare time. My understanding of convolution is about 'response to a specific filter': When we have a raw image, or raw signal; and a filter, aka kernel; we ...
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Convolution of Two Kernels [OpenCV]

I've been completely stuck on a portion of my assignment for a few days now. After plenty of searching around, I have been unsuccessful in discovering information that leads me to the correct solution....
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583 views

Fourier Transform of Kernel Density Estimation - Convolution Theorem?

I am reading this paper about density estimation (Appendix A), where the authors apply a Fourier transform to the estimated probability density (the $X_j$ are a sample of $N$ data points drawn ...
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511 views

What is the benefit of using symmetric kernel in Fourier transform?

In image processing, a forward transform of an $M\times N\text{-}$pixel image $f$ from spatial domain coordinates $(x, y)$ to transform domain coordinates $(u, v)$ can be defined as [1, p.12]: $$T(u,...
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787 views

Convolution in the spatial domain vs frequency domain [closed]

Suppose, I have this kernel. -1, -1, -1, -1, 9, -1, -1, -1, -1 (1) Can this kernel be used in an FFT-based convolution? I am able to convolve an input-image ...
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91 views

What should be done if the mask-values are too small?

According to the research paper Multidirectional Scratch Detection and Restoration in Digitized Old Images, we have, $$H(u, v) = \frac{1}{1 + 0.414 {. \sqrt[{2n}]{\frac {u^*}{D_u}+\frac {v^*}{D_v}}}} ...
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2k views

Laplacian Operator with and without Diagonal Direction Elements in the Kernel

This is a general question on the laplacian operator, which has two different versions. The first version is : \begin{matrix} 0 & 1 & 0 \\ 1 & -4 & 1 \\ 0 & 1 & 0 \end{...
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When should the sum of all elements of a gaussian kernel be zero?

I found an approximation of a 5x5 2D convolution kernel like this : Here, the sum of the elements is zero and this one was used for Laplacian of Gaussian! Another one here : This one has all ...