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 do I solve Euler Lagrange equation for image de-blurring?

This is one of the two Euler Lagrange equations for de-blurring which I need to solve: $$ u_r(-x,-y)\star\big(u_r(x,y)\star k-u_0\big) - \lambda_1\nabla \cdot \bigg(\frac{\nabla k}{|\nabla ...
0
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1answer
187 views

Given an intensity histogram,we apply an histogram equalization.Calculate the new intensity of the pixels in the original histogram had a150 intensity

It's a question from an exam that I can't understand its result. Given the following intensity histogram of an image: After an histogram equalization applied for this histogram, we've got the ...
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0answers
118 views

Using the Kuramoto-Sivashinsky operator applied on the Korteweg–de Vries Soliton as a filter for image processing

When the Kuramoto-Sivashinsky operator (Kuramoto-Si) is applied to the Korteweg–de Vries Soliton (Soliton) we obtain a very interesting filter which is able to process an image via convolution. An ...
2
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1answer
50 views

Finding the best fit of 3 categories ( restaurants/meal/person analogy problem )

I have this problem that sounds tedious and long and I'm not sure if there exist an intuitive way to solve it. The problem is related to image recognition but I will try to give an analogy to it You ...
3
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0answers
122 views

The mathematics of anaglyph images

Note: I'm not quite sure whether this question properly belongs to the Mathematica or to the mathematics Stack Exchange. But because my question mainly concerns general mathematical principles rather ...
0
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1answer
82 views

Which topics in maths should I know before I dive into programming for image processing?

I am a student who wants to start out with programming for Image processing but as I do not have a good mathematical background(I haven't studied A-level Maths) I would like to know what are the ...
2
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2answers
160 views

How can I convert camera motion into zoom?

I try to reconstruct a camera of a video sequence via match moving techniques. After the reconstruction process all seemed to work as expected, but then I've realized my camera is moving forward ...
3
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1answer
122 views

Geometric Transformations of Images

Related to image processing, I'm familiar with different types of geometric transformations. Translation, scaling, similarity, Affine, Perspectivity, and Projective Transformation. Is there a ...
2
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0answers
60 views

Homography matrix form for decomposition

I am trying to decompose a homography matrix. I read that there are a few methods to do that (e.g. Faugeras, Zhang). But I wasn't able to produce a useful output yet. I am not sure which form my ...
1
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1answer
50 views

Image analysis camera

A camera has the following data: CCD-chip Horizontal solution 5120 pixels Vertical solution 3840 pixels Pixels size $6.4 \mu$m $\cdot$ $6.4 \mu$m Pixels placement $6.4 \mu$m (center to center) ...
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1answer
106 views

Move coordinate system of a 3x3 homography matrix

I have a $3 \times 3$ homography matrix $H$. It was computed the way so that I can multiply a point of my image ($1000 \times 1000$px with coordinates $0/0$ to $1000/1000$) e.g. $1/1$ and get the new ...
2
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0answers
91 views

Understanding JPEG compression.

I have some problems in understanding a passage of the JPEG compression algorithm: Consider an $8\times8$ matrix $M$ that in our case is a "piece'' of a channel (for example the red channel $R$) of ...
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1answer
93 views

Get 1d kernel from 2d gaussian

I calculated the following gaussian 2d kernel: 0.011344 0.083820 0.011344 0.083820 0.619347 0.083820 0.011344 0.083820 0.011344 This kernel is the outer ...
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0answers
30 views

Why does one compute the power spectrum of an image from the Fourier transform of its autocorrelation and from the square of its spectrum?

image: f(x,y) fourier transform of f is F(u,v) my Goal is to compute its power spectrum. [denoted by P(u,v)] the first way to compute is by using the magnitude of fourier transform: ...
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3answers
775 views

Combining two convolution kernels

Is it possible to combine two convolution kernels (convolution in terms of image processing, so it's actually a correlation) into one, so that covnolving the image with the new kernel gives the same ...
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1answer
167 views

How correctly define the pixel intensity of an image?

Let's do easy: I have an image IM and p(i,j) is the discrete intensity value of a pixel in the image IM (not necessarily 2-dimensional)..... How can I mathematically correctly define this? Thank you ...
0
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1answer
392 views

What is the matrix representation of Radon transform?

Just as the title, my question is what is the matrix representation of Radon transform (Radon projection matrix)? I want to have an exact matrix for the Radon transformation. (I want to implement ...
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0answers
31 views

Averaging and approximation

I read a paper reference at http://arxiv.org/pdf/1101.1764.pdf that if we average a set $V=\{V(t_0,\nu_0), V({t_1,\nu_1),..., V(t_n,\nu_n)}\}$; with $V(t_i,\nu_i)=e^{i\sigma(t_i,\nu_i)}$ then we can ...
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0answers
19 views

Enlarge a 2d plot of f(x,y) while keeping the moiré patterns at the same size

I have some function $z=f(x,y)$ with $x,y,z$ real numbers. I wrote a script that generates a $600\times 600$ pixels plot of this function for, say, $0 < x < 1$ and $0 < y<1$, by mapping z ...
0
votes
1answer
185 views

sinc in 2d: how to interprete this in spatial domain?

The following two images are the ideal low pass filter in the frequency domain. As you can see, the origin (low frequency component), can pass through this filter while the high frequency are blocked. ...
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0answers
38 views

how does the following parameters affect the peak ( radius ,theta) of the its frequency spectrum?

The following is the similar magnified picture to the second image that it indicates the parameter i am going to talk about. Suppose i am going to fourier transform (DFT) of the following picture ...
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1answer
73 views

Minimizing image compression error (DCT)

I'm doing an assignement on image compression. I have to quantify the error given as $||A-\hat{A}||^2/||A||^2$, where $|\cdot|$ is the Eucledian norm. I really need help, so please just give some ...
2
votes
1answer
122 views

Generate evenly spaced points on 2D graph

I want to draw dots on an image that is W by W pixels. The image is stored as a 1-D array of pixels. The pixel (x,y) is at array index x + y * W. I am thinking that I can use a fixed step size, N, ...
0
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1answer
135 views

Convex Sets Pre-image

I am struggling with the following question: Let $a \in \mathbb{R}^n $ and $ b \in \mathbb{R}$ and define $ f: \mathbb{R}^n \rightarrow$ $\mathbb{R} $ by $f(x) = \langle x,a \rangle + b, x \in ...
0
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1answer
47 views

Multiply image kernels

If I have 3 image kernels (edge detection, sharpen, box blur) and want to perform each to an image in that order. Can I multiply the 3 together in some way and apply them to my image in one go? Here ...
2
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2answers
132 views

Integration of dirac function explanation

I have a problem that need your help. I have a gray image. We denotes $I(x)$ is gray level of a pixel in the image and $f(z)$ is a function of $z$(ie: histogram function...)-where $z$ is the set of ...
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2answers
50 views

Using difference of average for identifying features in an image

I'm working with this paper: Textural Features Corresponding to Visual Perception, by Tamura, Mori, and Yamawaki. There's a part where you have to calculate neighborhoods of one image (matrix of, for ...
2
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1answer
40 views

How to orthogonalize a set of 2x2 matrices?

I have set of 2D affine transformations of images and I need to modify the transformations such way that they become as close to rotations as possible to minimize distortions of images. Let the ...
0
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1answer
27 views

Check whether an image is proportional to a given one

I wonder how can I test whether the size of an image is proportional to $250\times 167$. For example, I have an image size of $1000\times 668$ and would like to see if it is proportional to ...
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0answers
42 views

Compressing an image by merging pixels [duplicate]

Let's say you have an image with dimensions (height, width) $h,w$ pixels. It is stored in a table $T[y][x]$ Unfortunately, the software you are using to generate this image can only use rectangles. ...
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1answer
70 views

About Radon Transform

Recently I got to Know that, Radon Transformation has huge contribution to Computer Tomography. So I would like to know about Radon transformation in Mathematical point of view. Can any one suggest ...
4
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1answer
276 views

How to mark rational points on a sphere

I found this picture on mathoverflow, which I find very intriguing and so I like to know how to draw such an image with a simple computer program. To calculate the rational point, I can draw a line ...
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0answers
46 views

Distributional Representation of Perimeter in Chan-Vese

While re-implementing the classic Chan-Vese Algorithm for image segmentation, I stumbled upon the following statement, which I have problems to understand: Let $H: \mathbb{R} \to \mathbb{R}$ be the ...
2
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1answer
238 views

Is 2D FFT separable?

Suppose I have a 2D matrix (or image). Can I loop on the columns - compute the FFT of each column and then loop on the rows (of the result matrix) and compute the FFT of that? Would that be equivalent ...
0
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1answer
63 views

Energy functional in Geodesic Active Contours

I have read some papers about Geometric active contours of the author C.Gout and Le Guyader [1] Segmentation under geometrical conditions using geodesic active contours and interpolation using level ...
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1answer
3k views

Algorithms to increase or decrease the contrast of an image

While tinkering with image editing, I thought I might implement a contrast algorithm; something that would take a range of values and, based on the value that the user provides (from 0 to 255; the ...
1
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1answer
461 views

Minimize Energy in Image processing - Geodesic active contours

I've read some papers in Geodesic active contours (Image processing), which use the minimization of an Energy, consist of Internal Energy and External energy, for example, in the paper of Kass (Snake: ...
2
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1answer
80 views

Radon Transformation

I have been tinkering over the line segmentation of images. I found that it is very well implemented in matlab with the Hough algorithm. Now the Hough-transformation is just a special form of the ...
0
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1answer
42 views

Feature selection of Gabor filter

I am working with Gabor filter with level set method here. As you known, gabor filter gave many filter output. Some of them is not necessary. Could you suggest to me some method that can choose best ...
0
votes
2answers
98 views

Which is kernel similar gaussian kernel?

I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The purpose of that kernel is that it will take a weight for each points ...
2
votes
1answer
266 views

Horn–Schunck method. Explanation of iterative solution

I am reading this paper (explanation of Horn-Shunck method for finding optical flow) and trying to understand it. My stumbling block is obtainig solution of system of linear equations I(x, y, t) ...
0
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1answer
134 views

What is purpose of correlation kernel? IIs it high pass filter or low pass filter?

I am research about correlation kernel and I have some questions that need your help. Let see the pp. 3302-3303 in the http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6517250&tag=1 The special ...
0
votes
1answer
69 views

Top and bottom power spectral density of a height profile

Imagine I have a simple 1D height profile which is NOT symmetric. Now, what is truly important for me is to know what are the frequency content of the top profile (i.e. a cut profile above the ...
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0answers
59 views

Reversible smoothing of a two dimensional function (or an image)

Smoothing of an image, or a two dimensional function is quite easy, there are many methods to achieve it, using average of near elements. But how to make it reversible? Maybe DCT (discrete cosine ...
3
votes
2answers
65 views

Heat Equation derivative in terms of Laplace

If the heat equation is $ \frac{\partial u}{\partial t} - \alpha \nabla^2 u=0$ Is the second derivative of u w.r.t t is the laplacian of the lapacian?
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2answers
716 views

Image Reconstruction:Phase vs. Magnitude

Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels. $$ ...
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1answer
105 views

What are Basis images?

I have read that using Fourier transformation we can decompose any arbitrary image into orthogonal basis images and reconstruct it back. But what are basis images actually?
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0answers
214 views

what does autocorrelation matrix signifies in image processing?

I am trying to find out corners using auto correlation matrix in an image,what does it signifies?
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0answers
50 views

what is the significance of Eigen values of autocorrelation matrix?

I am trying to find auto correlation matrix of an image to get Harris corners.Paper I am referring suggest that if eigen values of auto correlation matrix are large the point will be corner point.so ...
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0answers
39 views

Batch Linear Unmixing

Linear unmixing means to solve a set of linear equations to get the proportions of basic elements in the final composit. It is a linear mixture. If we have $f$ features and $m$ basic elements: ...