Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [image-processing]

This tag is for the mathematics involved in the field of image processing. Many such questions are also appropriate for Signal Processing Stack Exchange.

This tag is for mathematical questions about the field of image processing. Note: programming issues related to image processing belong on other Stack Exchange sites: Stack Overflow, Signal Processing or Computer Science.

673 questions
63
votes
2 answers

What do eigenvalues have to do with pictures?

I am trying to write a program that will perform OCR on a mobile phone, and I recently encountered this article : Can someone explain this to me ?
Patryk
  • 751
55
votes
2 answers

Mathematical explanation behind a picture posted (lifted from facebook)

In this image given below, there is an actor's (famous south Indian actor Rajinikanth) image which can be seen only if you shake your head ! I had lifted this from Facebook. I am just curious to know if there is any mathematical explanation for it.…
Rajesh D
  • 4,347
21
votes
3 answers

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 saying. What does it really mean and why is the…
water
  • 211
20
votes
2 answers

What is divergence in image processing?

What is the difference between gradient and divergence? I understood that gradient points in the direction of steepest ascent and divergence measures source strength. I couldn't relate this to the concept of divergence in image processing. What is…
Premnath D
  • 411
19
votes
2 answers

On Euler-Lagrange, gradient descent, heat equation and image denoising

For an image denoising problem, the author has a functional $E$ defined $$E(u) = \iint_\Omega F \;\mathrm d\Omega$$ which he wants to minimize. $F$ is defined as $$F = \|\nabla u \|^2 = u_x^2 + u_y^2$$ Then, the E-L equations are…
BBSysDyn
  • 16,513
15
votes
4 answers

Laplacian 2D kernel - is it separable?

I'm wondering if the 2D laplacian kernel 0 1 0 1 -4 1 0 1 0 is also a separable kernel. How can I find that out?
paulAl
  • 275
10
votes
1 answer

Algorithms to increase or decrease the contrast of an image

While tinkering with image editing, I thought I might implement a contrast algorithm; something that would take a range of values and, based on the value that the user provides (from 0 to 255; the range of a byte) the contrast will be decreased or…
kettlecrab
  • 445
10
votes
1 answer

How can I combine affine transformations into one matrix?

So from what I understand from this picture, the box is stretched to twice its width. And it is then flipped from the x-axis. And then it is rotated 30 degrees anticlockwise. So these three transformations are Scaling, then Reflection then…
Ogen
  • 2,295
  • 8
  • 34
  • 44
10
votes
1 answer

How to measure the irregularity of a hexagon?

I need to evaluate the quality of a list of machine parts, which roughly has one center point surrounded by 6 exterior points. If the quality is good, then the 6 exterior points will form a regular hexagon and the center point will locate in the…
Wei Feng
  • 173
10
votes
2 answers

What are the limitations /shortcomings of Fourier Transform and Fourier Series?

I am fond of Fourier series & Fourier transform. But every approach has some outcomes and some shortcomings. It's limitations lead to innovation of new approach. So, can anybody explain about The limitations/ shortcomings of the Fourier…
pandu
  • 375
9
votes
1 answer

How to mark rational points on a sphere

I found this picture on mathoverflow, which I find very intriguing and so I like to know how to draw such an image with a simple computer program. To calculate the rational point, I can draw a line from P_0(0,0,1) and P_1(u,v,0) and calculate the…
chhenning
  • 193
8
votes
1 answer

Euler-Lagrange, gradient descent, heat equation and image denoising

I have a question about Euler-lagrange equation which you can check this file, specifically equation $8$. There is a functional $F$ and we want to find a function $f$ which minimizes $F$. Then we attain the Euler-Lagrange function $E-L(f)$. And we…
Heather
  • 163
8
votes
1 answer

Homotopy and watershed

homotopy is a new word to me. Upon trying to understand this property, I immediately think of another well-known segmentation algorithm: watersheds. I see that watershed should exhibit some homotopic properties. In fact, I've also located a paper…
Gary Tsui
  • 195
8
votes
1 answer

A mathematical way to represent an 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) and save the result of the calculation in image…
user1095332
  • 321
8
votes
2 answers

Why is $8 \times 8$ matrix chosen for Discrete Cosine Transform?

In JPEG and MPEG, why is $8 \times 8$ matrix chosen for Discrete Cosine Transform? Why not any other, say $64 \times 64$?
user9476
1
2 3
…
44 45