# Tagged Questions

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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### 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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### 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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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 figure ...
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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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### 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, Scale-...
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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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### 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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### 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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### 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 correc ...
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### 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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### 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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### 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 ("blob"...
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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: U(...
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### Is it possible to formalize areas such as image processing and computer vision?

Is it possible to formalize areas such as image processing? By formalize I mean setup axioms, then derive theorems, and reason about image processing concepts and methods formally. I would say now ...
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### texture mapping from a camera image to a 3D surface acquired by a kinect

I have the following problem: A kinect camera capture a 3D surface and save it as a .obj files containing all the positions of the vertices (in the kinect coordinate system). If I take a picture ...
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### how to introduce time into calculus of variations for image processing?

I'm studying some topics about calculus of variation applied to image processing. I'd like to understand how to introduce time parameter to evolve an image in an iterative way. For example, let's ...
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### How can I combine affine transformations into one matrix?

So from what I understand from this picture, the box is stretched to twice its width. And it is then flipped from the x-axis. And then it is rotated 30 degrees anticlockwise. So these three ...
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### Which figure provides the greatest change in angle per change in distance? (trigonometry)

I have been having a lively discussion with others about the following: We (myself and others) are using triangulation to measure distance to an object with a linear image sensor (CCD) and a ...
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### Gaussian distribution and its parameters

I need to learn more about Gaussian distribution and given a set of data, plot a Gaussian distribution of it. Using the following code sample, could you please tell me how I can plot a Gaussian ...
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### Texture mapping from a camera image (knowing the camera pose)

I'm not sure if I should ask this question here or on stackoverflow, so forgive me if I'm wrong. I want to apply a texture (taken from a camera) on a 3D surface, let me explain my problem: I have ...
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### Area optimization: Packing rectangles inside rectangle

Background: I am scrambling to figure out the optimization algorithm to build sprite image, which is essentially a big container rectangular image, with multiple rectangular images. I have found an ...
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### Mathematical Background for Computer Vision [closed]

I am a PhD student and would like to do deep research in the area of computer vision and pattern recognition. I know to be successful I need strong mathematical background. Could you please introduce ...
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### Calculating the next value of sin(x) from previous sin.

(Please bare with me as I try to explain my problem to the best of my abilities) I have a computer program that draws a sine. Each y value of the sine is stored against the x value in an array like ...
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### fitting the content of an elliptical region in an image into the equivalent stretched circle

Assuming that I know the ellipse parameters (the major/minor axis, theta and the centre), and I could get the equivalent circle of this ellipse (I mean the equivalent x and y positions of the pixels ...
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### circle affine transformation

I am trying to convert a region of pixels surrounded by an ellipse into an equivalent stretched circle.This basically means affine transformation. Assume I want to extract the region in light blue ...
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### Poisson equation with dirichlet condition

I'm not sure whether this is a mathematics or stack overflow question, but I'll try here as my doubt are because of my lack of maths knowledge. I'm trying to implement an image editing paper that ...