# 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### $2$-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,...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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,...