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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 $s = 0.5$ (...
wcochran's user avatar
  • 243
5 votes
3 answers
133 views

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 ...
hasanghaforian's user avatar
5 votes
2 answers
11k 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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4 votes
1 answer
1k views

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
  • 143
4 votes
1 answer
225 views

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
3 votes
0 answers
5k views

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
2 votes
1 answer
340 views

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 ...
user avatar
2 votes
1 answer
899 views

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
  • 143
1 vote
2 answers
2k views

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
  • 189
1 vote
1 answer
247 views

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
  • 111
1 vote
1 answer
1k views

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
1 vote
1 answer
257 views

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 ...
Jokerp's user avatar
  • 189
1 vote
0 answers
65 views

Best large gaussian filter for current SIMD instruction sets?

I'd like to make a faster version of the Gaussian blur for Inkscape. Here's what I found various open source projects use: librsvg: 3 box blurs when stdev > 2. Else, separable FIR filter. Krita:  ...
Yale Zhang's user avatar
1 vote
0 answers
298 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
0 votes
1 answer
25 views

Comparing two sequences of events for similarity

Suppose I have two sequences of unequal lengths whose elements are timestamps of discrete events in milliseconds: $S_1 = \{150, 200, 700, 1300, 2500\}$, $S_2 = \{300, 670, 900, 1300\}$. These ...
Gaslight Deceive Subvert's user avatar
0 votes
0 answers
18 views

GMSK Modulator Large sample Buffer size and high Bandwidth

I found good answers to my queries here Gaussian Pulse shaping filter and suggestion for NCO based GMSK modulator seems to be undersstandable. Thanks to Dan Boschen , but when moving ahead to design ...
user3696623's user avatar
0 votes
1 answer
93 views

Gaussian Pulse shaping filter

I need expert advice on implementation of Gaussian Pulse Shaping filter for generating GMSK signal in further steps. I have implemented as follows, Can anyone confirm that the Pulse would be shaped as ...
user3696623's user avatar
0 votes
0 answers
23 views

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 ...
CfourPiO's user avatar
  • 107
0 votes
1 answer
39 views

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
0 votes
0 answers
83 views

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 ...
Mário Fernandes's user avatar
0 votes
0 answers
468 views

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 ...
faine10's user avatar
0 votes
0 answers
2k views

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
  • 101
0 votes
0 answers
218 views

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
  • 101
0 votes
0 answers
142 views

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 \...
Nirmal's user avatar
  • 101