Questions tagged [gaussian-kernel]

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Confusion with Complex Gaussian process with Auto-covariance

I have a complex sequence $z(t)$ in time which I know to be a Gaussian process. I read that the complex Gaussian process is not only characterized by the covariance, but also the pseudo-covariance ...
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The Effect of the Finite Radius of Gaussian Kernel

Page 168 of Digital Image Processing, Global Edition says: we know that the values of a Gaussian function at a distance larger than 3𝜎 from the mean are small enough that they can be ignored. If we ...
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Inverting the normalized Gaussian to get a kernel window radius

I am seeking to compute a kernel radius to use with my gaussian convolution filter, and inspired by https://stackoverflow.com/a/68050503/, I came up with: $$r=\sqrt{-2\sigma^2\ln\left( \epsilon\sigma\...
multiscale's user avatar
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Rolling sum of dataframe with custom function gets really slow on large averaging windows. Can I fix with convolve?

I am using the following function to estimate the Gaussian window rolling average of my timeseries. Though it works great from small size averaging windows, it crushes (or gets extremely slow) for ...
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Rolling average in pandas using a Gaussian window

I want to estimate the rolling average of a time series B using a Gaussian window. The equation to do this would correspond to $$\tilde{B_{s}}(t_{n}) = \frac{1}{A_{s}} \sum_{t_{m}= t_{n}-3s}^{t_{n}+3s}...
Jokerp's user avatar
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1 answer
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How to upscale an image using a Gaussian filter in R?

I want to resample a raster from 15m to 460m using a Gaussian filter. The goal I am having a coarse image which I want to downscale. I also have a fine resolution band to assist the downscaling. The ...
Nikos's user avatar
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What is the outcome of applying a derivative on X and Y for an image? and Other Gaussian Questions

I've been diving into smoothing kernels and I came up with a lot of questions that I haven't been able to find in the internet. If you can I'd appreciate the help :) (Capitals and bold were used for ...
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Fast computation of a convolution integral with Gaussian kernel

Given a convolution integral with gaussian kernel $$ g(y) =\int_a^b\varphi(y-x)f(x)dx=\int_{-\infty}^{+\infty}\varphi(y-x)f(x)\mathbb{I}_{[a,b]}(x)dx $$ where $\varphi(x)= \frac{1}{\sqrt{2\pi}}\exp{\...
NN2's user avatar
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6 votes
1 answer
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Appropriate Gaussian filter parameters when resizing image

When scaling an image down it is common to first convolve the image with a Gaussian filter. Given a scale factor $0 < s < 1,$ what is an appropriate $\sigma$ to use? For example, if $s = 0.5$ (...
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How to enhance thermogram image in grayscale?

I'm trying to do some image processing to improve the image below but I'm having some trouble. I already tried to do histogram equalization followed by laplace sharpening, I tried to implement a ...
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Choose the right Sigma for Gaussian filter

I have the following problem: I have a time series with counted data. I now want to smooth it using a Gaussian low-pass filter. Is there a method to determine the sigma value? The window should have a ...
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1 answer
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Is Unsharp Mask (USM) Equivalent to Applying Laplacian of Gaussian Filter Directly on the Image?

There are some educational materials, like Alex Pan - CS 194-26: Image Manipulation and Computational Photography - Fun With Frequencies and Gradients, which demonstrate the unsharp masking technique ...
today's user avatar
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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+...
Nevermore's user avatar
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Generating Kawase Blur Kernels to Approximate a Gaussian Blur on an Image

Is there an algorithm to generate the Kawase Blur Kernels to approximate the actual Gaussian Blur (of a specific kernel size, and if possible, a sigma)?
Shukant Pal's user avatar
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temporal smoothing: FWHM of Gaussian kernel vs. window length of moving average

Suppose in one case I convolve Gaussian kernel with FWHM=10 samples. I would like to compare the result with moving average. My question: should I take the moving average window also 10 samples? In ...
student's user avatar
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Gaussian kernel notation

In this paper on content-aware seam carving, they have given an equation: $$ w^{s}(k)=\frac{1}{n^{k}} \sum_{i=1}^{N}\left[\mathcal{N}\left( \|z_{i}-o| |_{2} \; | \; 0, \sigma^{2}\right) \cdot \...
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PYTHON Calculating Laplacian of Gaussian Kernel Matrix

I've been trying to create a LoG kernel for various sigma values. But the problem is that I always get float value matrix and I need integer value matrix as it is published on every document. I haven'...
Fatih M.'s user avatar
1 vote
0 answers
269 views

What are the differences between Gaussian down-sampling and bicubic down-sampling in Matlab? Which is more accurate for simulating low resolution?

I see in some of the technical papers, good practice for downsampling is to first pass the image through a Gaussian Filter and then take sampling to avoid problems like aliasing and so on. However, ...
ackbar03's user avatar
5 votes
2 answers
10k views

How to approximate gaussian kernel for image blur

From wiki, a $3 \times3$ gaussian kernel is approximated as: $$\frac{1}{16}\begin{bmatrix}1&2&1\\2&4&2\\1&2&1 \end{bmatrix}.$$ Applying this kernel in an image equals to ...
Finley's user avatar
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What Are Different Approaches to Realize a Gaussian Blur (Smoothing) Step on an Image? [closed]

Could some review some methods to apply Gaussian Filter (Blur) on an image besides the direct one using Truncated FIR (classic convolution with Truncated Kernel) approximation?
user36526's user avatar