# Questions tagged [image-processing]

Mathematics of image processing, variational methods (i.e. methods from calculus of variations), questions about denoising, deblurring, segmentation, image registration, imaging modalities (e.g. computed tomography, ultrasound, magnetic resonance tomography)

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### 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 $\partial \Omega$, $f: \Omega \rightarrow \mathbb{R}$ ...
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1 vote
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### Reconstructing an object from its shadow

I'm looking into the section "Reconstructing an object from its shadow" in the book Introduction to the Mathematics of Medical Imaging by Charles L. Epstein. I have two questions The ...
129 views

### Graph Laplacians, Riemannian manifolds, and object collisions

To preface this question, I am a part-time game developer and full-time optimization fiend. I am working on object collisions at the moment and many resources I have found online are more-or-less just ...
106 views

### Is this formula for 2D Fourier integral of diffraction kernel correct?

Well I have a function parametrized by $z$ $$g_z(x,y) = \frac{z}{i \lambda r^2} e^{i k r}, \quad r = \sqrt{x^2+y^2+z^2},$$ where $\lambda > 0$ is real constant and $k = \frac{2\pi}{\lambda}$. This ...
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### 1D representation of 2D discrete Fourier transformation [closed]

I'm not too familiar with image processing, so I need a little help: In general, if we transform a discrete function $f$ with $n$-variables from the "spatial domain" using the Fourier ...
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### elaboration on the equation of directional derivative that lead to steepest gradient descent [closed]

I am reading the book Ian Goodfellow and Yoshua Bengio and Aaron Courville, Deep Learning, MIT Press, 2016. I am reaching to the point about directional derivative. Given the $u$ as the unit vector ...
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### Apply gaussian blur to get original image [closed]

Suppose I have an image A. Is it possible to construct an image A' from A so I can get the ...
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71 views

### Mandelbrot's lacunarity realized by fractal or stochastic field?

It is my understanding that Mandelbrot came up with the notion of lacunarity to classify the homogeneity of 2D functions that only take two distinct values see here. I wonder, does there exist a ...
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1 vote
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### Analytically compare two 3D heatmaps of the brain

I have two heatmaps of a 3D model of the brain, with the color of each pixel being an intensity of the response to a stimulus, and I want to get a metric of how "alike" those two heatmaps ...
220 views

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### Advantage of fractional Fourier transform over multiscale wavelet

What is the best argument of fractional Fourier transform over multiscale wavelet in data analysis purpose. Optimization of the good time-frequency domain parameter ? "Good" will be, find the %time-%...
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### Suggestions for Math Equation OCR tool with API [closed]

I am looking forward to converting equation images to tex/mathml. All the equations are computer printed. So, not so worried about the clarity. We have around 100K images and hence looking for some ...
62 views

### Calculating Average Ratios Of Human Faces From Images Of Differing Lengths To The Camera [closed]

For a project I'm creating a program that must analyse a database of images to define average ratios for certain parts of the face (i.e. distance between eyes, distance from nose to chin etc.). I've ...
5k views

### Mathematics of imaging the black hole

The first ever black hole was "pictured" recently, per an announcement made on 10th April, 2019. See for example: https://www.bbc.com/news/science-environment-47873592 . It has been claimed that ...
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### Why do we consider some weakening frames like K-frames, frame sequences, and upper semi-frames?

I have found some applications of the Frame Theory in engineering sciences like signal processing, image processing, data compression, sampling theory, optics, filter-banks, signal detection. As we ...
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418 views

### Updating Geman and Geman (1984) on image restoration

I am reading the seminal paper Stuart Geman and Donald Geman, Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine ...
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### Given a function $f(t): \mathbb{R}\to\mathbb{R}^n$, can 2D, or $n$D discrete Fourier transforms be used on $f(t)$ to perform frequency analysis?
$\DeclareMathOperator{\R}{\mathbb{R}}$Frequency analysis is often performed on wave forms (1D DFT = discrete Fourier transform), and images (2D DFT), where the function in question often takes the ...