# Questions tagged [2d]

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### Fast/efficient way to decompose separable integer 2D filter coefficients

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. ...
1k views

### 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 ...
628 views

### 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 ...
4k views

### 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 ...
295 views

### 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 ...
1k views

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 ...
308 views

### 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 ...
1k views

### 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, ...
453 views

### 2D Convolution in MATLAB Causes Artifacts (Boundary Issues)

Im 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 ...
4k views

### How do you interpolate between points in an image (2D), e.g. using splines?

I can understand just fine how to use 1-dimensional interpolation on data points where one coordinate is a function of the other: y = f(x). However, when we have an ...
759 views

### 2D FFT of Vector

I have a bunch of 8x8 images which have been vectorized and formed into a 64xN matrix, X. I'd like to take the 2D-FFT of each of these images without reshaping each column of X into an 8x8 image and ...
1k views

### 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{...
788 views

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

This is my testing image,it is taken from this paper: I tried to transform it into its real cepstrum domain with this simple MATLAB code: ...
261 views

### Easy way to get rid of noise in a hand drawing

I would like to take a user's hand drawn input, and filter out "noise", aka small sketches or blobs, where the user might have screwed up and accidentally touched his hand to the drawing device, or ...
2k views

### Harmonics in 2-D FFT Signal

In case of 1-D FFT it is far more easier to find number of harmonics and their Respective frequencies and amplitudes. Lets say if i have 8 points signal the harmonics of it then would be 7 with one DC ...
8k views

### 2D Deconvolution in matlab

I am trying to solve the following equation for h (an [MxM matrix]): $$k[\tau_1,\tau_2]=\sum_{i_1=0}^M \sum_{i_2=0}^M h[i_1,i_2]x[\tau_1-i_1]x[\tau_2-i_2]$$ I have k, which is a 2D [MxM] symmetric ...
1k views

### Finding an Image's Orientation With DFT Frequency Amplitudes

I'm looking to get some general idea of an image's orientation so that I can then rotate it to the nearest 90 degree angle. My idea on how to do this is to take the DFT on the image, then do a "radar ...
418 views

### Understanding 2D FFT result of an image having a pattern

I have created Fast Fourier Transform (FFT 2D) of the following image (without pattern angle markers) using ejectamenta online tool. Input (Original image is here) Output I got is the following As ...
276 views

I've read there are two admissibility criteria for wavelets, both of which are designed to preserve total power of the signal (source: http://en.wikipedia.org/wiki/Wavelet#Mother_wavelet, as well as ...
4k views

### 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 ...
133 views

### Upsampling Methods for Computed-Tomography

I have two sets of data of given Field of view, one of them only covers a subset of the FOV of the other. I therefore want to upsample the one with the larger FOV to combine it with the other one. So ...
1k views

### How does MATLAB recover picture from magnitude spectrum alone?

This is the transformation I did. The code fft2() the Lena picture than ifft2() it back to the original. Add some ...
43 views

### Why does this plot correspond to this function?

I have a function: $$u_1(\mathbf{x})= \begin{cases} 1, & \text{if} \;\;|x_1|\le r_1, |x_2| \le r_2 \\ 0, & \text{otherwise} \end{cases} ,\mathbf{x}=[x_1,x_2]^T \in \mathbb{R}^2$$ And I'm ...
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### how to interpret the 2D FFT

I know how to compute the 1D FFT (and interpret values from 0 to Nyq). When computing the 2D FFT, do we compute the FFT of row then the FFT of row then the FFT of row up to the last row. ...
1k views

### MATLAB phase of 2D rectangular pulse's Fourier transform

I'm trying to plot the graph of the phase of the Fourier transform of a 2D rectangular pulse. I've been able to evaluate the FFT but I'm not sure if the phase is correct because there are some tilts I ...
356 views

### Linearity and shift-invariance of 2-D system on lattice

I know how to check a 1-D system for these conditions, but am confused about translating this to a 2-D system over a lattice. The system $H$ is define as: w[\mathbf x] = H\left\{u[\mathbf x]\right\}...
329 views

### Fast/efficient way to compute Laplacian edge enhancement filter

I would like to implement a somewhat smarter Laplacian edge enhancement convolution. Right now it is implemented as (generic 3x3 convolution): ...
3k views

### partial derivative of image

I have to find the partial derivative of an image with respect to its x dimension. I am using central difference method i.e $\partial_x F(x) = \frac{F(x+1,y)-F(x-1,y)}{2}$ Here $F(x,y)$ ...
178 views

### How do I implement the CDF wavelet inverse?

I understand and have implemented a 2D discrete wavelet transform that uses a Haar wavelet to process images. Now I would like to implement a 2D Cohen-Daubechies-Feauveau wavelet transform, but I am ...
96 views

### Two-dimensional wavelet analysis

Could you tell me why wavelets without scaling functions can't be used for two-dimensional analysis? What is the role of scaling function?
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### Require explanation for Matlab freqz2

Question I browsed the code of the Matlab freqz2 function (to find out how it is different to simple fft2.) First of all it ...