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

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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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C++ code to compute 3d convolution [on hold]

I'm looking for a C++ package to perform 3d convolution between a 3d volume (for example, of size 384x13x13) and a 3d filter (for example of size 384x3x3). I tried googling, but found nothing ...
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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
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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
26 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
46 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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7 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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Radon Transformation

well for quite some time 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 ...
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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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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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18 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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45 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
39 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
55 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
22 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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32 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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41 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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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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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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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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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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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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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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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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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
51 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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19 views

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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30 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 ...
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1answer
119 views

Calculating translation value and rotation angle of a rotated 2D image using MATLAB

I have two images which one of them is the Original image and the second one is Transformed image. I have to find out how many degrees Transformed image was rotated using 3x3 transformation matrix. ...
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Hysteresis Image Thresholding

In Image Processing, is it possible to automatically determine the upper and lower levels for a Hysteresis thresholding stage?. I have been looking for a while for a paper mentioning any technique for ...
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1answer
30 views

Conventional unit mesh

I'm trying to find and outline a non-primitive conventional unit mesh, I'm not sure how to go about it. I'd also like to find any mirrors of planes and rotional symmetry axes. Would this look ...
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1answer
20 views

Fourier transform in image processing

I want to know what a Fourier transform do to a image, does magnitude of this transform represent the energy of radiations captured by image, or is there any other way to find out the energy of ...
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23 views

Euler Lagrange equations

I need to minimise $$\int\limits_\Omega|\nabla H_\epsilon(\phi)|\,dx\,dy$$ with respect to $\phi$. Where $H_\epsilon$ is the regularised Heaviside function, so that it is differentiable. This can be ...
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Corrections and Normalization for Power Spectrum Calculation

So I'm hoping I can get some help. I have a 2d image and need to get the 1d power spectrum. I know the basic steps: take fft, take fft^2 to get power, then take average power in radial bins to get 1d ...
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Non-convexity of an energy functional

How would I go about showing that the following Mumford Shah functional is not convex? $$E_{MS}(u,C)= \int_{\Omega} |u_{0}(x,y) -u(x,y)|^{2}\ dx\ dy + \mu \int_{\Omega \backslash C}|\nabla ...
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1answer
26 views

Most computationally efficient way to find convolution of a matrix kernel with impulse response?

Let say if we wish to filter an input sequence x[n1, n2, n3] of NxNxN points using an Linear Shift Invariance system with impulse response h[n1, n2, n3], where the filter is a separable sequence, ...
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80 views

Looking for a formula to calculate DCT/FFT frequencies when cropping a matrix/image.

Given: A is a matrix of dimensions W1 x H1 . Cropping: Few rows and/or few columns were deleted from matrix A. We got matrix B of dimensions W2 x H2. Not more than 5% of matrix A rows/columns ...
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How to calculate the combined frequencies of a DCT matrix?

Given a 2D matrix of dimensions w1,h1. I preform a DCT 2D transform on the matrix (DCT = DCT type 2). I get a 2D result matrix. This matrix has two frequency axes - x,y (which are simply the ...
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1answer
80 views

How does a cropping of a 2D matrix/image affect its DCT transform?

I apologize in advance: since I am not a mathematician, maybe my question is not well defined, but I hope that some of you will still understand my meaning. Given a 2D matrix, or an image of ...
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Rigid Deformation

I'm trying to parse through this paper on using the method of moving least squares for rigid transformations - http://www.cs.rice.edu/~jwarren/research/mls.pdf Under section 2.3, the author mentions ...
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1answer
39 views

Why we take transpose of Vector (Displacement Vector)?

I'm trying to understand some equations that involves transpose of vectors (displacement vectors to be precise) Two set of vectors F and G (with i,j) that corresponds to X,Y value in plane and ...
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25 views

Regularized least squares

In Image Restoration, a true image f (in vector form)can be related to degraded data y through a linear model of the form $$y = Hf + n$$ where H is 2d blurring matrix and n denotes noise vector and ...
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Detecting camera shake

I have a bunch of data captured from a worm tracker that consists of a B&W camera that stares down at a few dozen worms for an hour at a time. The tracker captures the outline of each worm ...
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Is the autocorrelation of a function the same if one term is flipped on the y axis?

I have some questions about autocorrelation. They are very related, so I thought that one single post was appropriate for the topic. The first question is already illustrated in the subject: if I ...
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Would like in understanding a specific part of the Additive Operator Splitting scheme.

Can anybody help me to understand why the discretized version of this equation: $ \partial_tu = \partial_x \left( g(|\partial_x u_\sigma|^2) \partial_xu \right) $ (1) is the following: $ ...
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Image histogram equalization using variational calculus

In an image processing course at Coursera.org, on the section on PDE and calculus of variations, the professor gave the following as the functional to be optimized for image histogram modification: ...