Skip to main content

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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
27 views

Hough transformation: get line function from Hough parameters (rho, theta)

I have two an input image (256px x 256px) with a line and Hough space image (256px x 256px) with a mark where the corresponding ...
Schelmuffsky's user avatar
0 votes
0 answers
24 views

Finite Difference For a Fourth Order PDE With Neumann Boundary Conditions.

I'm trying to implement a method I found for image decomposition that boils down to solving a PDE of fourth order. The equation in question is $$ u_t = -\frac{1}{2\lambda}\Delta\left(\text{div}\left(\...
Choripán Con Pebre's user avatar
1 vote
0 answers
23 views

Compressed image using SVD draws a clear line between part that's blank and part with a drawing. Why? [closed]

I'm trying to compress grayscale images using SVD. This is the original image: Yes, there's a lot of blank space. I then choose the x% largest singular values, perform the transformed matrices ...
Elizabeth Middleford's user avatar
1 vote
1 answer
84 views

Determining the Center of Rotation in a Video: A Mathematical Approach

I have a video where the camera rotates, causing the images to rotate around a specific point. I need to determine the coordinates of this rotation center. Here's my plan: I use a function to measure ...
Peter Jackson's user avatar
0 votes
2 answers
52 views

Solution of $V'(t)=AV(t)+V(t)A^T+\sigma^2I_m$, where $A$ is the discretized Neumann-Laplacian

I'm considering a PDE involving the Laplacian on $[0,1)^2$. I'm discretizing the problem using the finite difference approach. The resolution discretized Laplcian opertor $A$ with Neumann boundary ...
0xbadf00d's user avatar
  • 13.9k
0 votes
1 answer
29 views

Algorithm to calculate visual similarity of two point trajectories

I have a program where I let a user draw an image and record the strokes by saving the coordinates. I save the coordinates on every "onMove" event so it is highly detailed, with one point ...
Sarah Multitasker's user avatar
0 votes
0 answers
24 views

Doubling the numbers within an image matrix

I have an image Matrix tag that looks like this ...
MarkyMark's user avatar
0 votes
0 answers
14 views

How this variational derivative is calculated?

In this paper https://arxiv.org/pdf/1907.09605.pdf \ let $\Omega \subset \mathbb{R}^n$ with $n \geq 1$ be a bounded Lipschitz domain with boundary $\partial \Omega$, $f: \Omega \rightarrow \mathbb{R}$ ...
Mohamed's user avatar
1 vote
1 answer
118 views

Is it possible to extract the translation of an affine transformation matrix independent of rotation center and angle?

I have $2$ images rotated by $60^\circ$ to each other with different center of rotation. The here presented matrices are affine transformation matrices derived from OpenCV: https://docs.opencv.org/4.x/...
TMul's user avatar
  • 13
1 vote
0 answers
36 views

Deriving the DCT-II from the DFT

Recently, I was looking into the theory behind the discrete Fourier transform (DFT) when I frequently encountered the discrete cosine transform (DCT-II). Due to the similarities between the DFT and ...
Fynn Zentner's user avatar
0 votes
0 answers
13 views

Book Recommendation on Edge or Boundary Detection

I have recently being interested in the estimation of discontinuities or jumps from noisy signals or densities and spend some time reading "Image Processing and Jump Regression Analysis" by ...
BabaUtah's user avatar
0 votes
1 answer
68 views

How can we calculate the Euler-lagrange equations?

In this paper https://arxiv.org/pdf/1907.09605.pdf \ let $\Omega \subset \mathbb{R}^n$ with $n \geq 1$ be a bounded Lipschitz domain with boundary $\partial \Omega$, $f: \Omega \rightarrow \mathbb{R}$ ...
Mohamed's user avatar
0 votes
0 answers
33 views

Numerical solution of Perona-Malik equation: How to handle the boundary properly?

In the paper Perona-Malik equation and its numerical properties, the following PDE is considered: The $u_0$ I'm (and so is the author) interested in is given by an image and hence decomposes into ...
0xbadf00d's user avatar
  • 13.9k
0 votes
0 answers
29 views

Spatial discretization of the PDE $\partial_tu=\nabla\cdot\kappa(t,\nabla u)\nabla u$ for image processing

The question is basically in the title. I want to evolve an image $u_0$ (i.e. a $n_1\times n_2$ resolution set of discrete values in $[0,1)$, which is a discrete function on $\{0,\ldots,n_1-1\}\times\{...
0xbadf00d's user avatar
  • 13.9k
1 vote
1 answer
60 views

Numerical Method for (Total Variation) TV Norm Minimization of Linear Combination of Matrices

I have a matrix $\mathbf{A} \in \mathbb{R}^{2000 \times 2000}$ represented in memory by an array of $2000 \times 2000$ float32 elements and I also have $10$ arrays $...
VojtaK's user avatar
  • 368
1 vote
1 answer
44 views

Is there any method that can optimize the problem whose regularizer is kurtosis term?

I recently worked on an optimization problem, whose regularizer $g(x)$ is kurtosis. The overall optimization formula is as follows. $$\begin{align} \arg \min_x \frac12 \Vert Ax-b\Vert_2^2 + \lambda g(...
Leung Joe's user avatar
6 votes
0 answers
94 views

Similarity between the mathematics used in PDEs and in image processing

Sorry if this question is a bit vague I took a course on PDEs and learned or reviewed a lot of math revolving around Fourier transforms, convolutions, distributions, Gaussian functions, etc, all ...
summersfreezing's user avatar
0 votes
0 answers
39 views

Additive white Gaussian noise (AWGN)

In my research work regarding wireless communication, I came across many research papers wherein AWGN is assumed to be modelled as "complex Gaussian with zero mean and unit variance". I ...
Heretolearn's user avatar
1 vote
0 answers
87 views

Get 3d ray in world coordinates from a 2d pixel location

I am trying to project a 3d ray from a 2d image pixel location. I have the actual 3d coordinates of a pixel location and want the ray from the camera to intersect this point but currently, my line is ...
Mattcc18's user avatar
1 vote
0 answers
266 views

Discrete Fourier Transform of the Gaussian

I encountered the following question in a Digital Image Processing examination: Find the 2D DFT of $\frac{1}{2 \pi \sigma^2} e^{-\frac{(x - x_0)^2 + (y - y_0)^2}{2 \sigma^2}}$ where $x_0, y_0$ are ...
kaddy's user avatar
  • 93
1 vote
0 answers
19 views

$2$-dimensional Fourier transform of the same function after different sample resolution

I have a function $f :\mathbf{R}^2 \to \mathbf{R}$ under different discretizations, e.g., $64 \times 64$ and $32 \times 32$ (can be viewed as a $64 \times 64$ image downsampled to $32 \times 32$). Now,...
Jason Miller's user avatar
4 votes
0 answers
149 views

What are the family of geodesics/curves between point weights/balls on an elastic sheet?

ASSUMPTIONS: no deformation is separate, all deformations touch with at least another points deformation, i.e., no deformation is by itself. point force preferred, but small dense balls okay too. The ...
Teg Louis's user avatar
0 votes
0 answers
21 views

histogram equalization and CDF

Im having hard time understading one of the derivation steps in histogram equalization, Wikipedia (added picture). derivation In the last sentence it seems to me like they are suggesting that the CDF ...
Oy3's user avatar
  • 1
1 vote
0 answers
34 views

Efficient algorithms to detect connected components

I am reading the book "Computational Homology" by Tomasz Kaczynski, Konstantin Mischaikow and Marian Mrozek and in several places it says something to the effect of "of course, from the ...
12345's user avatar
  • 187
0 votes
0 answers
23 views

Mean Squared Error incompatible definitions

Let $x$ be a vectorial estimator, and we aim to estimate $y$. Then the mean squared error can be defined as $MSE(x) = \mathbb{E}[\|x-y\|^2]$. On the other hand, in image processing the mean squared ...
lightxbulb's user avatar
  • 2,109
1 vote
1 answer
41 views

Convolving an image with mean filter infinite times

I was taught in my image processing class that when a mean filter is applied infinite times on a given image, the intensity of each pixel reaches the same value. I understood this that time entirely ...
gkgkgkkgkgkgk's user avatar
1 vote
0 answers
38 views

Extrapolating 2D image pixels using second order derivative

I intend to use image pixel data prediction to improve image compression. This means that I need predict image pixels based on previous rows and columns. I cannot use the next rows and columns for the ...
barej's user avatar
  • 176
2 votes
1 answer
39 views

Weighted sum of N images, which minimizes their TV norm

I have $K$ images $I_i, i\in{1 \ldots K}$ of the size $M \times N$. I wish to find weights $w_i$, s.t. $w_i \in [0,1]$ and $\sum_1^K w_i = 1$ so that $$|\sum_{i=1}^{K} w_i I_i|_{TV}$$ is minimal. I ...
VojtaK's user avatar
  • 368
1 vote
1 answer
102 views

What determines the coefficients of the laplacian filter?

I am building an approximately isotropic Laplace kernel based on the guidance in Optimally Isotropic Laplacian Operator. What I don't understand is the derivation process from (2) to (3). I don't know ...
Ili a's user avatar
  • 29
0 votes
0 answers
70 views

Convolution of a $2$-dimensional function with a $1$-dimensional function

Below is the schematic diagram from a very popular paper in this field of retinotopy. In the diagram above, $g$ is a bivariate Gaussian function of the form $$ g (x,y) = \exp \left( - \left( \frac{ (...
skm's user avatar
  • 113
6 votes
3 answers
278 views

What is the distribution of distances between two random points in RGB space?

Suppose we pick pairs of triples from $\{ 0, 1, 2, \dots, 255\}^3$ with a uniform distribution and would like to find a closed form for the distribution of the Euclidean distances $$ d((x_1, x_2, x_3),...
Teg Louis's user avatar
0 votes
0 answers
191 views

How to choose pixel value in case of nearest neighbor image down scaling

I am working on implementing a fast algorithm for image resizing (more generally 2D array of numbers resizing). It is supposed to be fast, and should not add new values (meaning the result 2D array ...
Pierre Baret's user avatar
1 vote
1 answer
493 views

Pinhole camera projection of 3D multivariate Gaussian

Consider a 3D Gaussian with $3\times 1$ mean $\boldsymbol \mu$ and $3\times 3$ covariance $\boldsymbol \Sigma$ (which is symmetric positive semidefinite): $$ p(\mathbf x) = \frac{1}{\sqrt{\...
Daniel's user avatar
  • 282
0 votes
1 answer
60 views

Finding the dimensions of a box (cuboid) given a hexagon filled in to look like the box

Suppose I have hexagons that like the ones below but I know the area and the points of each hexagon that represent a cuboid of dimensions g,h,d. How can I find the values for g, h, and d? Any pointers ...
Teg Louis's user avatar
0 votes
1 answer
51 views

How is the convolution of images properly defined?

In the Wikipedia article, the convolution is defined as $$(g*f)(x,y):=\sum_{dx=-a}^a\sum_{dy=-b}^b\omega(dx,dy)f(x-dx,y-dy).\tag1$$ The image $f$ is obviously understood as a function on $[-a,a]\times[...
0xbadf00d's user avatar
  • 13.9k
-1 votes
1 answer
70 views

Why do these patterns appear in custom fractals? [closed]

Last year I programmed a fractal renderer and played around a lot with fractals such as the Julia set and Mandelbrot set. Eventually I got curious and inputted my own algorithms for the fractal, and ...
Caedmon's user avatar
  • 570
0 votes
0 answers
24 views

Trying to understand an application of expectation-Maximization algorithm

In the paper Johannes Kopf, Ariel Shamir, Pieter Peers - Content Adaptive Image Downscaling, the authors apply the Expectation-Maximization algorithm to solve an image downscaling problem. I've never ...
Babis's user avatar
  • 517
0 votes
1 answer
298 views

Calculate point coordinates after image rotation

So I have two rectangle pictures with known Resolution On the first image we have a point on $(900, 300)$ $x,y$ pixel coordinate (guessed number, not exactly). The second picture is rotated by $15^\...
automatikz's user avatar
0 votes
2 answers
417 views

Linear algebra: is there a matrix representation of cropping an image? [closed]

Can I write a matrix description of cropping an image to a given size? It doesn't even need to be an image, simply some rectangle $\square ABCD$, and a crop boundary $\square EFGH$. Is there a ...
Saul Aryeh Kohn's user avatar
1 vote
0 answers
37 views

How can one construct polynomial bases for positional estimation?

In the field of signal processing a popular problem is to try and estimate how something has moved as compared to a previous point in time. In attacking this problem a long standing popular approach ...
mathreadler's user avatar
  • 26.1k
0 votes
2 answers
117 views

Solving a ratio of Lambert W branches: $y=\frac{W_{-1}(x)}{W_0(x)},$ where y is positive and real.

How might I go about solving a ratio of Lambert W branches? Namely, $y=\frac{W_{-1}(x)}{W_0(x)},$ where y is positive and real. Motivation: I want to define a Cauchy filter for edge detection given ...
Davey's user avatar
  • 113
2 votes
1 answer
58 views

Connection between image space and Hough space? [closed]

The other day I got very interested in learning about Hough Transform that is used to detect edges in images. After going through OpenCV documentation, I still couldn't piece together an understanding ...
kiyanuDevs's user avatar
1 vote
0 answers
55 views

Prerequisits on eulerian video magnification

From this article http://people.csail.mit.edu/mrub/papers/vidmag.pdf I became extremely interested in the subject, but I couldn't find too much content that starts from the "basics". This ...
underfilho's user avatar
1 vote
1 answer
40 views

How to normalize signal from 3 images

My question is mathematical related but it concerns a bit biology since they are images of cells. Image we have 3 images of negative control. Since I have to only use 1 I need to normalize these 3 ...
Alex's user avatar
  • 21
2 votes
0 answers
18 views

Name / type of image filter

Occasionally I stumble across a very pretty image filter and I always wonder what the underlying algorithm is. The term wavelet-transformation pops up in my head but my searches let to nothing. It ...
Suuuehgi's user avatar
  • 229
1 vote
0 answers
40 views

Unit and step of coordinates of spatial frequency Discret Fourier Transform

I'm trying to understand spacial frequency Fourier Transform. If I perform the 2D Fourier Transform of an image of $n_x*n_y$ pixels and I know that the measurement step is $\Delta L$ (in $\mu m$) in ...
kipgon's user avatar
  • 131
1 vote
0 answers
58 views

Viterbi algorithm for object-tracking

I have a sequence of images, and I need to find and track the creation of the objects, then their movement and then their disappearance. There can be up to $3$ objects overall, and sometimes there are ...
josh92's user avatar
  • 11
3 votes
1 answer
106 views

Summing the discretized values of the density function of $\mathcal{N}(0, \sigma)$ with a step of $1$ is equal to $1$?

Given the density function of the Gaussian distribution $\mathcal{N}(0, \sigma)$: $$ \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-0.5\,\frac{x^2}{\sigma^2}\right)$$ I have noted that emprically, summing ...
abc's user avatar
  • 121
2 votes
1 answer
89 views

Trying to implement a loss function read from a journal-article in python

Computer science undergrad here. I am trying to understand Eqn 12 from this paper so that I can implement it in python code. In this paper, the NN model takes a blurred image as input and outputs a ...
abu obaida's user avatar
0 votes
1 answer
160 views

Can we use mathematics and logic to estimate probability of extremely absurd events?

I'd like to detail my question over the example below. Let's say I have a random pixel generator which has $1024 \times 768$ screen resolution. It also has $24$ bit color which means $2^{24}= 16,777,...
Jaap's user avatar
  • 1

1
2 3 4 5
14