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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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### Using the Dirichlet kernel as a lowpass filter

I have a question about using the Dirichlet kernel as a filter. Let us suppose that I have samples of a continuous function sampled with frequency $F_s=10 \,\texttt{Hz}$. The function is band-limited ...
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### Why do people use signs in columns/rows of several kernels reversed?

I have observed that different citations/codes use signs in different (reversed) columns/rows for many kernels. Here is an example for Prewitt (but same for Sobel, Scharr, etc); in some cases is ...
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### Why to use Sobel/Scharr kernels for image gradient computation?

I'm confused about image gradient computation mechanism in Python. I try to find gradient magnitude and orientation of a pixel. Here is my example image: ...
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### The Second Derivative of an Image Using the Sobel Filter

For computing the Harris corner detector, I want to calculate $I_{xy}$ and $I_{xy}$. Obtaining $I_x$ and $I_y$ are clear for me. But what about the second order derivatives? This and this and this one ...
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### Laplacian Filter kernel size meaning

I'm using laplacian filter in opencv. I usually use laplacian filter with kernel size 3 which is default setting in opencv. I'm just curious what happen(intuitively) when I choose bigger size kernel? ...
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### Optimize FIR filter kernel in Matlab

I am currently using the firls function in Matlab to create my FIR filter kernel. This works well but I typically have to play with the filter order to get the gain to 1 and the shape to be somewhat ...
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### How to Find the Kernel of the Convolution for Linear Interpolation?

I'm trying to solve the following exercise: Image A was doubled by linear interpolation. The magnification was performed in two stages. In the first stage, add about zero pixel to the image between ...
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### Applying a 2D Convolution Using 2D FFT

So I was following the article Victor Podlozhnyuk (nVidia) - FFT Based 2D Convolution (Page 7). I have expanded the kernel to the correct way they have done it. However when it comes to the part on ...
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### Is there any complex-valued function used to smooth signals?

To obtain a smoother signal, we usually convolve the original signal with a real-valued kernel function, such as Gaussian and Top-hat. Is there any complex-valued kernel function to smooth signals?
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### Is there an adjective describing a filter with kernel that has zero mean?

A linear filter with a kernel that has zero mean could be thought of as a "DC-rejecting" filter. Is there a better or more commonly used adjective for such a filter?
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### kernel to calculate second order partial derivative of digital image

I'm working on image stacks, and I need to calculate second order partial derivatives of it. I already know how to calculate derivative on x and y axis, using Finite Cameron Taylor - Difference ...
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### Is the Laplacian Filter an High Pass Filter (HPF)?

Is this kernel name as mean difference kernel or Laplacian filter? Is mean difference just a method?
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### Finding the equivalent filter H(u,v) in the frequency domain of a 3x3 spatial mask

I'm trying to find the equivalent frequency domain filter, $H(u,v)$, of a 3x3 spatial mask that averages all neighbours of a point $(x,y)$ in said 3x3 neighbourhood excluding the point itself. So far, ...
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### Applying 2D Image Convolution in Frequency Domain with Replicate Border Conditions in MATLAB

I have created a function that filters an image (250x250) with a gaussian blur kernel (5x5) using FFT and IFFT. I am trying to get my filtered image to equal exactly the filtered image created by the '...
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### Mean shift algorithm formula

I am watching a lecture on mean shift clustering. In the video, the mean shift vector is first defined and then it's relation to the gradient of a kernel density estimate is shown. The mean shift ...
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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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### 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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### 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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### 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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### 2D Convolution in the Spatial Domain vs Frequency Domain [closed]

Suppose, I have this kernel. -1, -1, -1, -1, 9, -1, -1, -1, -1 Can this kernel be used in a FFT based convolution? How? What could be the reason of my failure? ...
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### 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}}}} ...