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.
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How can I write graham scan algorithm in C# without using pre-written library?
I am trying to write the Graham Scan algorithm but I do not understand how I can write it without using pre-written library. I am researching this for a long time but I really could not find any ...
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Integer algorithm to rotate a bitmap image(2d array) on small angle?
The task is - if you want to rotate a bitmap image on the small angle , so the most of the pixels will remain on its place or will be just shitted strict horizontally or vertically a little bit, is ...
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Hough voting or RANSAC voting, which strategy is better for pixel-wise object's center location estimation?
If we know all the pixels of the object in an image and draw a unit vector from all the known pixels of the object body towards the center direction of the object, and then apply some voting ...
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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,...
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How do I detect which of N objects appears in an image, and classify it's "state"? [closed]
Suppose I have a finite number of N objects O.
In every image I, strictly 1 of these objects exist.
And each object is in 1 of M states S. You can think of Q as a set R positions P, where each ...
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Combining two fundamental matrices
Let $\mathcal{F_{ab}}$ be the fundamental matrix obtained from images $A$ and $B$
$$ \mathcal{F_{ab}} = \begin{bmatrix}
ab_{11} & ab_{12} & ab_{13} \\
ab_{21} & ab_{22} & ab_{23} \\
...
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Frequency peak always appearing at half of Nyquist frequency in Fourier transform
When taking the FT of a signal I always get a sharp peak at exactly half the Nyquist frequency. My signal is shown here:
and its FT here:
The Nyquist frequency is 36.7 KHz. As can been seen in the ...
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notation for replacing values in one matrix with another with condition
I have two matrices of equal size. $'A'$ is a binary image, and '$B$' has values ranging between $0$ and $1$.
What's the correct notation which would demonstrate that foreground elements of A (equal ...
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Is there transfomation that transform the image to a space that I can use a small amount of function of fit it?
Now what I want to do is that I want to reprentation(just fitting) a image with neural network with as less error as possible,like paper NeRF(neural reprentation field) and FFN and Sire. The input is ...
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How to solve system of equations with complex exponentials (in medical imaging)
In the context of medical imaging, I need to solve the following equations for $\phi_1$ and $\phi_2$:
\begin{alignat}{2}
I_1(\boldsymbol{X}) &= \left\{A(\boldsymbol{X})+B(\boldsymbol{X})\cos(k_e ...
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How to get Information Entropy and Chi-Square Test value for an encrypted image
I was reading this paper. Under the section 4.3 and 4.5 they add The Chi-Square Test Analysis of Cipher Image and Information ...
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What is the Linear Shading Correction Algorithm accurately?
I want to right a code in C# without using pre-written libraries for removing shadows on the edges of the image and there is a algorithm for this(Linear Shading Algorithm) but I can not understand ...
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Image Deblurring Resources?
I have been researching about image deblurring methods and would like to know if anyone had some good entry points to this. I am looking for references about basic image deblurring, and mainly the ...
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How to calculate the properties of the resultant 2D Gaussian from the deconvolution of one anisotropic, 2D Gaussian with another?
Anisotropic, two-dimensional Gaussians, are described by the equation (from here):
$f(x,y)=A\exp \left( -(a(x-x_0)^2 + 2b(x-x_0)(y-y_0) + c(y-y_0)^2 )\right)$
where A is the amplitude of the peak, $...
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Calculate the distance of object from perspective drawing
Hello!
I would like to know if there is any way to calculate a distance based of this single point perspective drawing of a 17th century theatrical scenery :
We have this elements:
The real-life size ...
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Concatenate 2D-Discrete Wavelet Transform Horizontal,vertical and diagonal coefficients to generate new 2D image features [closed]
I am working on a classification task and I used 2D-DWT as a feature extractor. I want to ask about more details why I can concatenate 2D-DWT coefficients to generate image of features. I am thinking ...
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Find DFT of $f(m,n)=0.5\cdot\left((-1)^{m+n}+1\right)$
I was trying to solve the following question:
Consider an image $8\times 8$ so:
$$
f(m,n)=0.5\cdot\left((-1)^{m+n}+1\right)
$$
Find the DFT of the image.
In the solution they did: (sorry in advanced ...
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What is the size of the convolution matrix?
In my Image Processing course, I had to operate a filter on image. Mathematically it's a convolution between the image $A$ (matrix $M\times N$) and a filer $F$ (matrix $m\times n$):
$$
A\star F
$$
The ...
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Pattern identification in real (conically deformed) images
I'm trying to solve the following problem:
I'm in an analysis process of some photographs (as taken by a camera, thus they are conically deformed).
I'm already able to automatically identify some ...
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Having difficulties to construct a B-spline tight frame
I am having difficulties constructing a B-spline tight frame. The method to construct such a wavelet multilevel decomposition is given as follows. However, I do not understand how the resultant matrix ...
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Getting width and height values that best fit a certain amount of pixels in an image
If I have n number of pixels, what's the best way to get the factor of n that most resembles a square shape when using it as a dimension of an image?
Using n == 512 as an example, its factors are:
<...
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What tools are used when images are displayed in a scatter plot?
I have seen a lot of scatter plots where the data inside the scatter plot has come from images.
But an image is like a matrix. It has a height and a width. And a scatter plot only write out the data ...
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How to check if a circle lies in a certain range
I've a problem where I need to calculate the score on this board. I was able to detect the ranges, and detect the bullets.
I would like to make a loop to check whether the bullet holes that are marked ...
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How to find ranges in a target score problem?
https://www.istockphoto.com/photo/hitting-the-target-a-paper-gun-target-with-a-very-high-score-gm928791034-254727306
image 2
image 3
So I do have similar images to the ones linked above, I already ...
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Given a point in an image find another point that is a certain distance away when projected to world coordinates
I have a point in image space p1 = (u1, v1) where u and v are the pixel coordinates. I project this point out in to 3D coordinates, using the projection matrix of the camera, to intersect with a plane ...
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How to calculate 3D depth reconstruction of an image using a set of 3 similar images?
I have tried asking this in computer science SE, but sadly get no answers. Since this is fundamentally mathematical, I hope someone could give pointers to an answer for this, please.
From a set of 2 ...
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How to construct a 2D Convolution matrix
I have a problem in understanding this explanation stated in an article, which is as below:
$error = a-Bf$
where, vector $error$ is in lexicographic ordering, vector $a$ is a lexicographic ordering of ...
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DFT of the discrete function $f(x,y)=1$
I want to solve the following question from the Digital Image Processing by Gonzalez and Woods book:
Show that the DFT of the discrete function $f(x,y)=1$ is:
$$
\Im\left\{ 1\right\} =\hat{h}(u,v)=\...
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Cover all 2D points given a 2D template with minimum distance between them
I am looking for an algorithm that gets a binary image similar to the below image
and given a circle(as a template) with radius R, returns the location of instances of this circle needed to cover all ...
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Why is the prewitt operator a 3x3 matrix instead of 1x3?
I was trying to understand how edge detection works in digital image processing works. Here is what I understand so far.
if we have a continuous intensity function of a row of an image, I(x), the ...
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Homography 3d matrix projection
enter image description here
(Sorry due to the reputation thing, I am not able to embed the image in my post)
Hi good day all,
I am currently doing the homography transformation using OpenCV and now ...
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mathematical operation in image scaling
I am trying to understand the resizing of an image, I understand that it is a matrix and the concept of where the values change when changing its size, but I don't know if this is some operation in ...
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Simplfy variance of an image
Today we learned variance of an image in my class. Its formula like below:
$\sigma^2 = \frac{1}{M \cdot N} \cdot \sum\limits_{x=0}^{M-1}\sum\limits_{y=0}^{N-1}(f(x,y)-m)^2$
$m = \frac{1}{M \cdot N} \...
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Some weird notations
I'm reading an article in imaging processing and i've been stuck in some notation details that i think that are not allowing me to procede my mathematical adventure...
So we know that $$u(t)=-\frac{d}{...
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Formula for grass green and greener
Within the science project we are watering grass with water using different level and technique of treatment and cleaning. We measure traces of biological and chemical materials within the soil as ...
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What is the gradient operator in this context?
I've been trying to learn math recently by implementing papers that I find related to projects I'm working on. Usually when I encounter a problem, I just google it, find the answer and continue on but ...
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Is double integral over general region a spatially invariant system?
Given a system H which gets as an input the image f(x,y) and outputs the image:
$$ g(x,y) = H\{f(x,y)\}=\int_{x}^{x+2}\int_{y-4}^{y} f(\alpha, \beta)d\alpha d\beta $$
Define if this system is ...
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The translation property of a 2-d discrete Fourier transform proof
Background
In a recent lecture about the (2-d discrete) Fourier transform, we were told there's a "translation property", which says that if you shift your function $f$ then the amplitude ...
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Design a LoG (Laplacian of gaussian) $1 \times5$ filter with sigma $=2$
Design a LoG (Laplacian of gaussian) $1 \times5$ filter with sigma $=2$.
Formula to calculate LoG:
$$\text{LoG}(x,y) \;=\; - \frac1{\pi\sigma^4}\left[1-\frac{x^2+y^2}{2\sigma^2}\right]e^{-\frac{x^2+y^...
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Matching nodes by comparing overlapping subsets of a graph
For an image stitching algorithm, I am trying to match keypoints of a moving object in multiple images.
I thought one way to do it is to create a graph of the keypoints in the image and compare the ...
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Confusion in Discrete Fourier transform derivation - DIP book 4th edition
In the Digital Image Processing Book by Rafael C. Gonzalez and Richard E. Woods, section 4.4 "The Discrete Fourier Transform of one variable". We get
$$
\tilde{F}(\mu)=\int_{-\infty}^{\infty}...
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2D Fourier Transform and Inverse Fourier Transform Bounds
My professor for a computer vision class introduced the 2-D Fourier Transform and Inverse Fourier Transform (in the context of images) as the following:
$$X(\omega_1, \omega_2)=\sum_{n_1}\sum_{n_2}x(...
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Finding object position using calibrated camera and object size
I have a calibrated camera. In other words, I calculated the extrinsic and intrinsic parameters as below using opencv (more info)...
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Least square fit of ellipse worsens with increasing border thickness
I use the least square method to fit ellipses to data points that originate from a binary image. The least square fit minimizes the sum of squared algebraic distances between data points and the ...
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2d convolution in analytic form
I have an image of a 2D-sinusoidal pattern $f(x, y)$ with wavelength $\lambda$ which I would like to convolve with a 2D circular pill-box function $h(x,y)$ of radius $r$.
The image is given by
$$
f(x,...
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A proper definition for homogeneous coordinates in geometric image formation
In my computer vision course, we apply homogenous coordinates to represent points in 2D or 3D space. However, in my course it lacks a proper definition of what homogeneous coordinates are.
I have ...
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Conflict for solving denoising problem as optimization problem by gradient descent method
I am new to image processing and optimization.
Let y be a noisy image described by the relationship y = x+n, where u is a noise-free image and n is the noise. The goal is to recover x from n.
min || y-...
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How can I calculate all possible combinations between a specific ratio range?
Not sure this is the right wording for this sort of problem, but let me explain by context.
Instagram displays specific image ratios when posted to a feed. These ratios are:
1:1 (square)
1.91:1 (...
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Jacobian Calculation with Homographic Coordinates
I'm trying to work my way through an image processing paper (Creating Full View Panoramic Image Mosaics and Environment Maps) and am stuck on how the Jacobian is calculated, especially terms ($J_{17}, ...
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Segment region into horizontal and vertical parts
My task is to draw rectangles around a given error shape to make it visible for the user.
Most of the time the smallest rectangle around the shape is good enough, but there are shapes where this is ...
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