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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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1answer
141 views

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 ...
3
votes
1answer
227 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 ...
2
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0answers
135 views

Lower bound for the sum of cosines between singular vectors of diagonally dominant matrices

Let $A \in \mathbb{R}^{n \times n}$ be a nonsymmetric diagonally dominant matrix with $a_{ij} < 0$ $\forall i \ne j$ and $a_{ii}>0$. Let the singular value decomposition of $A$ be $A=U \Sigma V^...
4
votes
2answers
170 views

Geometrical interpretation of pictures transforms and other “high dimensional everyday objects”

During the preparation of a general audience talk on why mathematicians use dimensions higher than three (or four) even for concrete applications, I came up with the following enjoyable observation : ...
5
votes
2answers
304 views

Mathematical physics applications in present-day image processing

During the past few years several important areas of image processing and image classification or generation became dominated by convolutional neural networks. I'm interested if there are any methods ...
11
votes
2answers
563 views

Why does this Moiré pattern look this way?

I was making some gifs of Mobius transformations in Matlab, and some strange patterns began to appear. I'm not sure if a deeper knowledge of the filetype/algorithm is needed to understand this ...
1
vote
0answers
53 views

The jump set of $SBV$ function for different value of parameter in image denoising problem

The classical Mumford-Shah image denoisng problem study the minimizer of the following functional, for each $\alpha>0$ where $\Omega\subset \mathbb R^2$ is open bounded with sommth boundary, $$ u_\...
7
votes
1answer
551 views

When is a mapping the proximity operator of some convex function?

Is there a characterization of mappings $p : \mathbb R^n \rightarrow \mathbb R^n$ which are proximity operators (in the sense of Moreau) of l.s.c (extended) real-valued functions ? That is, given $p : ...
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0answers
93 views

Can Mumford-Shah functional be adapted to lower $L^1$ space?

The well know Mumford-Shah functional functional $$ F(u)=\int_\Omega|\nabla u|^2+\mathcal H^{N-1}(S_u) \tag 1 $$ where $u\in SBV(\Omega)$ and $\nabla u$ is the absolutely continuous part of ...
3
votes
1answer
106 views

Why is it important to know if a frame is a Parseval frame?

I understand that a Parseval frame is one in which both upper and lower frame bounds equal 1. What's the main advantage to having this be the case? Or, more specifically, if I'm constructing a frame ...
3
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0answers
94 views

The best constant in Poincare-liked inequality in $BV$ and $BD$ space

This question has been posted on Math Stack exchange for a while and received no response. So I decide to move it here to get more attention. Let $\Omega\subset \mathbb R^N$ be open, bounded and with ...
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vote
1answer
95 views

question about $TGV^2$ space

Let us just stay in $\mathbb R^1$. The space $TGV^k$ is defined as the function $u\in L^1(I)$ and $$ TGV^k(u,I):=\sup\left\{\int_I u\,\phi^{(k)}\,d\mu, \,\phi\in C_c^\infty(I),\,\|\phi\|_{L^{\infty}(...
4
votes
3answers
1k views

Looking for techniques of How to measure the Similarity/Dissimilarity between two images?

I would like to compute the similarity/dissimilarity between two images L and R. I know one way which is : computing the histogram of blocks of each image, and then using Bhattacharyya measure I ...
2
votes
0answers
117 views

sets with positive reach with complementary set with positive reach

I am interested in bibliographical references about a special class of sets, those who have positive reach and which complementary has also positive reach. I recall that the reach $R\geq 0$ of a set ...
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0answers
129 views

Indecomposability of image transformations (pure algebra). Open questions

W-transformations -- definitions We will consider a class called finite window transformations $\ T:C^\mathbb Z\rightarrow C^\mathbb Z\ $ defined a paragraph below; $\ \mathbb Z\ $ is the ring of ...
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2answers
3k views

Switching from pure mathematics (e.g. geometry) to more applied areas (e.g imaging) after Ph.D., as postdoc and chance of getting such a postdoc?

Before I start my question, I should probably mention that this question might not be the right question to ask here, but I tried academiabeta, and stackoverflow, but without getting any to-the-point ...
2
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0answers
856 views

Optimal transport warping implementation in Matlab

I am implementing the paper "Optimal Mass Transport for Registration and Warping", my goal being to put it online as I just cannot find any eulerian mass transportation code online and this would be ...
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2answers
279 views

Smooth a matrix

I have a matrix in which each element contains the coordinates of a 3D surface. Sometimes, some points will be "out of line" meaning that they will not conform to the general shape. For example you ...
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votes
0answers
557 views

Decomposing max-convolution of sum of functions ?

Hello. $R, F_1, F_2, F_3$ are random (not-convex, not-concave) 2D matrices of size 100x100. $R$ is a linear combination of $F_1, F_2, F_3$. Explicitly, $R = w_1 F_1 + w_2 F_2 + w_3 F_3$ where $w_1,...
11
votes
1answer
4k views

How to un-pixelate pixelated regions in films?

Everybody knows the effect of pixelated objects (e.g. faces) on TV. Is there a way - and which mathematical method lies behind it - to un-pixelate the region? Beware: I am not talking about smoothing ...