This tag is for the mathematics involved in the field of image processing.

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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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20 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
36 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
46 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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22 views

Resize an image along rows only or columns only in matlab

I'm writing a function in matlab to zoom or shrink an image using bicubic interpolation. However, my function resizes an image along both rows and columns. What if I want to enlarge the image along ...
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13 views

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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22 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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22 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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13 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
50 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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38 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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22 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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20 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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29 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
67 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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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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38 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 ...
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1answer
21 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
36 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
64 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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11 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
27 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
15 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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18 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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21 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
51 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
45 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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1answer
63 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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34 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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36 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 ...
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2answers
45 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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91 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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46 views

How can we represent an image using basis images?

I have read that using Fourier transformation we can decompose any arbitrary image into orthogonal basis images and reconstruct it back. But i don't understand terms like "orthogonal " and "basis ...
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42 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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22 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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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: ...
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Potts model for image analysis

I'm trying to get a hold of the Potts model for image analysis, and this is what is posted on Wikipedia, http://en.wikipedia.org/wiki/Potts_model#The_Potts_model_in_signal_and_image_processing $$ ...
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Eigenvalues and Eigenvectors of a singular Covariance matrix

I am working on a research in which my data matrix $\bf X$ has dimension of $N\times P$ where $P>>>>N$.ie. its a small sample size problem. I need to compute the covariance of $\bf X$, ...
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51 views

Perspective projection alternate matrix (SOLVED)

A lot of perspective projection matrices I've seen look something like this: $$\left [\matrix {1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&z&0}\right]$$ where $z$ is ...
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2answers
152 views

how to calculate vehicle speed using mathematics and Image processing?

i am doing my project in image processing.using segmentation i have detected the moving part(i.e the car) in the video successfully. But now i want to calculate speed of vehicle. in the above ...
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19 views

Catastrophe theory: scale of a catastrophe for a 1D function

Studying arguments around scale space I came across the catastrophe theory. While I got what it suppose to describe (when a catastrophe e.g. annihilation happens on a continuous context), I'm not ...
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30 views

Is there a way to check if 2D level set function has changed from representing an object of genus 0 to genus 1?

This question has been moved from stack overflow to here. My goal is image segmentation but I think my question is a math one: In computer vision level sets are regularly used to represent moving ...
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1answer
66 views

Essential mathematics for Image Processing

What are the most essential mathematical concepts one has to be familiar with for succeeding in the field of Image/Signal Processing and Machine Learning. I am somewhat familiar with Tensors, ...
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What is the difference between Bilinear interpolation and Bilinear filtering

I'd like to know that different between bilinear interpolation vs blinear filtering in the manner of image processing warp operation. Are those two operations are identical ? I try to sample a ...
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53 views

Looking for a simple algorithm to scale/resize a matrix, or an image.

I am looking for a simple algorithm to scale a matrix of any size. Given matrix A of dimensions [w1,h1]. Given a scaling factor (or resizing factor) SF, which is a real number (not necessarily ...