# 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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### 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 ...
376 views

### 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? ...
154 views

### 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 '...
1 vote
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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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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&... 0 votes 1 answer 881 views ### 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 ... 4 votes 3 answers 439 views ### 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). ... 4 votes 3 answers 2k 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 ... 6 votes 1 answer 2k views ### 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 ... 4 votes 1 answer 1k 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 ... 5 votes 2 answers 997 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 ... 6 votes 1 answer 2k views ### 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.... 2 votes 1 answer 853 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 ... 2 votes 2 answers 944 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,... 1k views

### 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? ... 124 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}}}} ... 