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

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-3
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1answer
42 views

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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0answers
54 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
180 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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0answers
20 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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0answers
31 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 ...
1
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1answer
73 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, ...
2
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0answers
22 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 ...
0
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0answers
66 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 ...
0
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1answer
393 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. ...
0
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1answer
22 views

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 ...
0
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1answer
49 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 ...
0
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1answer
25 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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0answers
27 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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0answers
30 views

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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0answers
35 views

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 ...
0
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1answer
32 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, ...
0
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1answer
147 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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0answers
36 views

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 ...
2
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1answer
123 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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0answers
25 views

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 ...
1
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1answer
54 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 ...
2
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0answers
27 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 ...
2
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0answers
17 views

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 ...
0
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0answers
15 views

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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0answers
12 views

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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0answers
35 views

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: ...
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0answers
24 views

Derivative of the Total Variation of a digital image?

Thanks for your time reading my thread. I am trying to calculate the derivative of the Total Variation (TV) of a digital image with respect to its gray-scale intensity. Say, there is an image: ...
2
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2answers
66 views

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 ...
1
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1answer
107 views

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 ...
0
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1answer
31 views

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 ...
2
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1answer
303 views

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 ...
0
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0answers
27 views

Given a N*M matrix determine the number of pairs that exist in a GLCM

This is an interesting problem for which I can't find a direct solution. Given a n*m matrix (in this case 5*5): 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 There exist a certain number of ...
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0answers
62 views

Normalizing a co-occurrence matrix with an energy function to create a conditional random field or markov random field.

I currently have a set of factors produced for a co-occurrence matrix : link I want to be able to move towards developing a conditional random field for pixel labelling and multi-class segmentation. ...
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0answers
83 views

How can the formulas for Energy, Entropy, Max prob, Contrast, Correlation be expressed informally?

I'm currently working on a project in OpenCV that requires me to classify textures. I've constructed co-occurence matrices for four directions, and I now need to use the following co-occurence ...
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0answers
33 views

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 ...
0
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1answer
155 views

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 ...
0
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0answers
39 views

What does an image of Fourier Transformation of an image tell us?

First time studying image processing... I just don't understand what does fourier transformed image of an image describe? For example consider given following pictures, The first one is the image, and ...
2
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1answer
114 views

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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0answers
63 views

How to interpret autocorrelation of images?

Say we have a multiple grayscale images $I_i$ collected as a matrix $M = [I_1\ I_2\ I_3\ldots I_n]$ What exactly does its autocorrelation $R_{MM} = M M^T /{n}$ tell me? According to Wikipedia ...
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0answers
157 views

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 ...
2
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1answer
428 views

Mathematical Background for Computer Vision

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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0answers
19 views

Convolution of an image with a kernel that is a product of two functions

Suppose that $G(i,j)$ is a Gaussian decay function on the distance between points $i$ and $j$ of an image. In addition, $D(i,j)$ is the difference between the VALUES of the image at those points. ...
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3answers
248 views

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 ...
1
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1answer
77 views

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 ...
1
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1answer
104 views

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 ...
2
votes
1answer
61 views

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 ...
2
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4answers
854 views

PCA - Image compression

I have 2 questions related to principal component analysis: The first is, how do you prove that the principal components matrix forms a orthonormal basis? Are the eigenvalues always orthogonal? The ...
3
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3answers
142 views

How to calculate the size of any rectangle to fit into an ellipse?

It's been a long time I do not review my math knowledge, please help me out. I have an ellipse image with fix size, let's say it has the bounding rect with width=w1, height=h1, and I have any random ...
0
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3answers
53 views

Getting $x,y$ position on an image based on given value

This should be simple but my math skills are really bad ... I have an image of 36 images (6 by 6 matrix). These small images are 36 instances of a direction arrow (like from Google maps GPS), each ...
0
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1answer
54 views

Help with least squares in paper on hough transform

I'm trying to understand this paper. I'm having trouble with a least squares problem. In the paper, equation (4) is $ E^2 = \sum_{r\in R}{\sum_{c \in C}{[ \alpha r + \beta c + \gamma - I(r,c)]^2 ...