0
votes
0answers
25 views

What does an image of Fourier Transformation of an image tell us?

First time studying image processing... I just don't understand what does fourier transformed image of an image describe? For example consider given following pictures, The first one is the image, and ...
0
votes
0answers
17 views

Convolution of an image with a kernel that is a product of two functions

Suppose that $G(i,j)$ is a Gaussian decay function on the distance between points $i$ and $j$ of an image. In addition, $D(i,j)$ is the difference between the VALUES of the image at those points. ...
0
votes
1answer
39 views

Omitting part of Frequency domain, Fourier Transform, Image Processing

In my Image and Signal Processing lecture, the Professor said that if every other column of the frequency domain of an image is zeroed out, then the reconstructed image is aliased. (along the x-axis) ...
0
votes
1answer
79 views

How to interpret the results of 2D Fourier Transform on an image?

I have a class where we're studying signals processing (mostly filtering of sounds and images) and while I kind of understand the results of a Fourier Transform for sounds I don't really get the ...
1
vote
1answer
88 views

FFT of a matrix and its square.

I am doing something computationally intensive that requires that I compute the fast fourier transform of a matrix, let's say $A$, and also compute the FFT of its square, $A^2$. I am wondering if ...
0
votes
0answers
31 views

Best transform for detecting frequencies of sinusoidal signals.

Between Discrete Fourier Transform (DFT) and Discrete Cosine Tranform (DCT) could we say that one of them is better than the other in detecting frequencies of sinusoidal signals?
2
votes
1answer
98 views

Unclear on relationship between different dimensionalities of Fourier transform

This is probably a silly question, but it's one that's directly relevant to a project of mine and I figured this was the place to go. I have some objects that contain a 1d and a 2d array of double ...
7
votes
1answer
205 views

A Mathematical way to represent a image kernel?

How to represent the calculation in this image mathematically? For example: With the discrete convolution and Fourier Transform. It tries to do a calculation on the original image (image A/input) ...
2
votes
0answers
94 views

2-D DFT of a matrix PxP and 1-D DFT of a vector of size P^2?

What is the difference between the following two things: make a 2-D Discrete Fourier Transform of a certain matrix A[p,p], first reshape this matrix into a 1-D vector a[p^2,1], and compute the 1-D ...
0
votes
1answer
36 views

Quantization Uniform

Let the output of image sensor take values between 0 to 10. If the samples are quantized uniformly to 256 levels, show that transition and reconstruction levels are $$t_k=\dfrac{10(k-1)}{256},\, ...
1
vote
0answers
178 views

Projection Slice theorem getting rid of artifacts?

I have employed the fourier(projection) slice theorem in matlab. I have a 3D image, P(x,y,z) defines their pixel intensities at a given location int he image volume, it is discrete and uniform. I ...
4
votes
5answers
649 views

The mathematics behind Fourier Transform for Image Processing

I am following http://homepages.inf.ed.ac.uk/rbf/HIPR2/fourier.htm . I understand the application of Fourier Transform behind Image Processing, but right now, I am curious about the mathematics behind ...
0
votes
2answers
2k views

DFT and DWT difference?

what is the basic difference between the Discrete Fourier Transform and the Wavelet Transform ? and why does JPEG2000 preferred DWT over DCT or DFT ?
9
votes
3answers
10k views

What does the Fourier Transform mean in the context of images?

This is clearly a very important equation with tonnes of properties that I see come up a lot in image processing literature, but I don't understand why this equation is important, and what it is ...
3
votes
2answers
108 views

How can I measure the properties of a Point Spread Function?

What quantity or property can I use that describes by how much a point spread function distorts/blurs an image?
5
votes
2answers
3k views

Why is 8x8 matrix chosen for Discrete Cosine Transform?

In JPEG and MPEG, why is 8x8 matrix chosen for Discrete Cosine Transform? Why not any other, say 64x64?