Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [2d]

61 questions
22
votes
4 answers

Fast / Efficient Way to Decompose a Separable integer 2D Filter Coefficients without the SVD

I would like to be able to quickly determine whether a given 2D kernel of integer coefficients is separable into two 1D kernels with integer coefficients. E.g. 2 3 2 4 6 4 2 3 2 is separable into 2 3 2 and 1 2 1 The actual…
Paul R
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3 answers

Determining Type and Bandwidth of a filter

Given a filter, if it is given as an equation such as: $$f(x,y) = \left(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}\right) \exp\left(-\frac{x^2 + y^2}{\sigma^2}\right)$$ Or in a kernel such as: $$ \left[\begin{array}{rrr} 0 & 1…
Peter
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7
votes
2 answers

Standard Deviation in Gaussian Blur

I have a function that performs gaussian blur on image for some specific $\sigma$ (the standard deviation). It first computes kernel of size $\lceil 3\sigma \rceil$ and then performs convolution with that kernel. However, I would like to specify…
Libor
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6
votes
2 answers

How to separate the upwards-propagating from the downwards-propagating waves?

I've got a real 2D image of propagating waves in both directions. How can I separate this image into one with the upward-propagating waves and one with the downward-propagating ones? This example has one wave in each direction. The x-scale shows…
Andreas
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6
votes
2 answers

Laplacian Operator with and without Diagonal Direction Elements in the Kernel

This is a general question on the laplacian operator, which has two different versions. The first version is : \begin{matrix} 0 & 1 & 0 \\ 1 & -4 & 1 \\ 0 & 1 & 0 \end{matrix} The second version includes the diagonal: \begin{matrix} 1 & 1 &…
kuku
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6
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1 answer

Image 2D Real Cepstrum with DFT, Is `ifftshift` Needed?

This is my testing image, it is taken from the paper Image Restoration for Linear Local Motion-Blur Based on Cepstrum: I tried to transform it into its real cepstrum domain with this simple MATLAB…
fececagec812
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6
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1 answer

Data fusion using 2d discrete wavelet transform (DWT)

I am working on a project that employs a linear array sensor that provides data from the same object at two different energies. Collected in time, I end up with two images (16-bit sensor values, MxM image), call one HIGH the other LOW. My…
jjwebster
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5
votes
1 answer

Efficient implementation of 2-d circularly symmetric low-pass filter

How can a two-dimensional ideal circularly symmetric low-pass filter or its approximation be efficiently implemented on data sampled on a square grid? I'm referring to an ideal filter with a spatial frequency response that equals $1$ inside radius…
Olli Niemitalo
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5
votes
2 answers

Image Processing and applicability of 2D Fourier Transform

As a newbie in the world of signal processing, I am having a hard time in appreciating image 2-D fourier transforms. I am fully able to appreciate the concept of 1-D Fourier transform. Essentially, given a random causal signal, it can be decomposed…
Raj
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5
votes
1 answer

2D adaptive filters

Does anyone know about different adaptive filtering implementations (LMS, RLS ...) in 2D or even 3D ? I have sequences of 2D images and 3D volumes with repeating patterns but small differences. I was thinking of using one as my reference input and…
user1641496
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4
votes
1 answer

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 clamping to the edge its very confusing. I would…
Simon Balfe
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4
votes
1 answer

Show That a 2D Linear Transform $ T \left( \cdot \right) $ Is Homogeneous

By my understanding, a transform T is homogeneous if T[0] = 0. Then to prove that a linear transformation is homogeneous we say that: T[ax(n1, n2) + bx(n1, n2)] = aT[x(n1, n2)] + bT[x(n1, n2)] What I want to know is the difference between the…
CLDuser2.-
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4
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2 answers

Mathematical Approach to Detect If a 2D Signal Is Separable

In the Special 2-D Sequences page the following examples are demonstrated, 2D dirac 2D diagonals 2D unit step function Is there a more defined method or series of steps for determining if a function is separable or not? Other than: $$x(n_1, n_2)…
CLDuser2.-
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4
votes
1 answer

2D Convolution in MATLAB Causes Artifacts (Boundary Issues)

I`m trying to do a 2D fast convolution in Matlab of large matrices. If I use FFT version based on convolution theorem ( https://en.wikipedia.org/wiki/Convolution_theorem ), there are some artefacts in the image. Only imfilter produces correct…
Aleksander
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4
votes
1 answer

Calculate 1D Power Spectrum from 2D Images

Imagine satellite images, these are irregular sampled in X and Y direction and the shapes are of course are oddly off. We now want to estimate a 1D power spectrum from the whole image to estimate the atmospheric noise. What works is the 2D power…
n1nj4
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