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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How would I modify a squared-exponential covariance kernel to be periodic?

I want to create a Gaussian process that resembles one generated by an exponential kernel (smooth and with a lot of variance) with a single caveat: I need the final value to be the same as the initial ...
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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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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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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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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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784 views

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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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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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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The Kernel in 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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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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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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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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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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80 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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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 ...