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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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 ...
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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
24 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 ...
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What is tensor diffusion?

When I was studying "wickart diffusion", I came across the tensor diffusion of Fick's law. What is tensor diffusion?
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Tiny world image manipulation

I have a tiny planet image, and I need to turn it inside out. Inversion, I think. I'm trying to figure out an algorithm that can turn it inside out/slowly...I should be able to interpolate it on a ...
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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
9 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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22 views

Transformation matrix of 2D image

I have 2D image with 256x256 pixels, while top left point is [0,0]. My task is to create transformation matrix, which will mirror this image by 10th row and then rotate it clockwise by the [5,5] ...
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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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2answers
66 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
33 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 ...
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1answer
58 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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25 views

Edge detecting - how to detect the most accurate edges using the Canny and Sobel methods?

For some reason, I believe this question belongs here and not to the StackOverflow. Anyways, Here's an exercise I have to solve: Repeate Lab Exercise 2 but with the matlab eight.tif image. The ...
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16 views

How can I apply inverse Abel Transform to a Data?

I have a data with X values and corresponding Y values. When I plot intensity map (2D histogram) of the data, I get a good image. I want to apply inverse Abel Transform to this image. How can I do it? ...
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28 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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15 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 ...
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1answer
36 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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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
47 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 ...
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11 views

Introduce break after operation

I have made a function to select manually feature points in two images. However I can keep clicking endless because I don't have a limit for feature points. I now want to introduce a kind of button on ...
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1answer
60 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, ...
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reducing data that are very close to one another

so, I have this problem. I have to do image analysis to get the boundary of an image. I perform image analysis to get a boundary representation of the object. The problem is, there is an overlap of ...
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1answer
33 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 ...
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1answer
25 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 ...
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19 views

How to calculate discrete cosine transform for a matrix

I have a 8x8 matrix and I want to calculate its discrete cosine transform (DCT-II). I have this formula but I don't know to use it with a matrix. In the French Wikipedia they gave an example for ...
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2answers
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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
39 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 ...
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1answer
24 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 ...
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14 views

Optimize the distribution if it is left unsmoothed

I have a question about distribution. Let see my problem The paper said that the distributions p and q are left unsmoothed, so we can ignore Kernel density. But I don't understand what is left ...
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21 views

Papers related to Tomography and compressive sensing.

Recently I studied about Radon transformation and its applications. I got to know that they are lots of application in tomography and am very much interest after reading that. Now I wanted to read ...
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1answer
25 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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40 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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35 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 ...
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1answer
94 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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21 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 ...
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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 ...
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1answer
23 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
75 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 ...
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1answer
108 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: ...
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14 views

Histogram Separation Energy Equation

I am working in level set method, specially Lankton method paper. I try to implement Histogram Separation (HS) Energy problem (Part III.C). It based on Bhattacharyya to control the evolution of ...
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1answer
33 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 ...
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1answer
17 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 ...
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21 views

What is the equation for an anisotropic Hanning window (cosine wave) in two or three dimensions?

I do not exactly know how to ask this question, so I will explain myself thoroughly. I am really stuck on this one, and it is crucial for my research, so if anyone has any ideas on where I may find ...
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24 views

Low pass filter to maintain edge information

I am looking for a kernel as low pass filter that satisfy as:I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The gaussian ...
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2answers
56 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 ...
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1answer
64 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) ...
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70 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 ...
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1answer
40 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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38 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 ...
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Is there any common formula to estimate the salience of peaks of a histogram?

I need to use some quantitative measure to estimate the salience of peaks and the flatness of valleys of a histogram which represents the distribution of lightness of an image. For example, if an ...