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

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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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1answer
20 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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12 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 ...
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19 views

Find linear line of data following gaussian distribution

I have a data that following gaussian distribution $x=\{x_1,x_2...x_n\}, p(x) ~is ~N(\mu,\sigma)$ Now, I want to find a linear line fitting all the data such as $y=ax+b$ The line subject to ...
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13 views

Literature on 3 dimensional image segmentation

Currently I am working on a paper on 3d image segmentation and finding my way into the topic. However I can not find good mathematical literature on the topic. I am looking for a books or scripts that ...
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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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11 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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10 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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2answers
511 views

Scale Space - Scales and Octaves

So I'm desperately trying to understand scale space for signals, specifically for 2D images... I'm having trouble with algorithms that discuss creating a pyramid. Specifically, I don't understand how ...
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1answer
22 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 ...
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2answers
42 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 ...
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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: ...
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1k views

Explanation of this image warping (bulge filter) algorithm

I've been researching image warping algorithms lately and haven't found many comprehensive references. That said, there are of course code snippets from GIMP, jhlabs.com, and imagemagick.org but none ...
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12 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: ...
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374 views

Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
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23 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 ...
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32 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 ...
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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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28 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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25 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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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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1answer
48 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 ...
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25 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 ...
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159 views

To what extent can Gielis' so-called “Superformula” be used to improve the efficiency of WIFI antennas ? [closed]

In 2003, the Belgian plant biotechnologist Johan Gielis proposed a formula that allows for the description of a wide variety of shapes in 2$d$, 3$d$ and higher dimensions. This is the formula $$r( ...
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1answer
40 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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1answer
63 views

A function for forming a closing curve on all points on a 2D image

First of all, this is for image processing. The small circles above is on an image and are my list of points. The points are always in order from p1, p2, p3 to pn. And I am to create a curve that ...
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30 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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3answers
1k views

find the rotation of one image with respect to other in MATLAB

I have two images. One is the reference image and the other is the rotated version of the reference image. I would like to find what is the angle by which the second image is rotated with respect to ...
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1answer
51 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 ...
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3answers
234 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 ...
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80 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 ...
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1answer
130 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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17 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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4answers
181 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 ...
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1answer
53 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 ...
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1answer
48 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 ...
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3answers
245 views

Principal Component Analysis in Face Recognition - number of Eigenvalues?

I'm at the beginning of learning about the PCA as it is applied in the field of face recognition (Eigenface algorithm) and I came about the following question: "You're using a training set of 80 ...
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3answers
103 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 ...
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1answer
50 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 ...
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3answers
46 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 ...
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About Sum of Squared differences

I found a paragraph in the book about $SSD$, can't get one thing: Most commonly, the distance measure is the sum of squared differences. For two images $f(x, y)$ and $g (x, y)$ it is defined as ...
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31 views

For a given image $\mathbf X$, the equivalence class for pixels $p$ with labels $l$.

$\left[l\right]=\left\{p \in\mathbf X|\,p\sim l\right\}$. This is taken from this paper on image segmentation, page $2$. I don't know how to interpret this, do they mean "all the pixels on image ...
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1answer
104 views

Gradient of a norm with a linear operator

In mathematical image processing many algorithms are stated as an optimization problem, where we have an observation $f$ and want recover an image $u$ that minimizes a objective function. Further, to ...
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What are interesting ways to tile a square image? Or a transformation that make an image tilling-able?

I want a method to tile arbitrary square image. For most cases the boundaries do not agree. So I are looking for a transformation from a square image to a square image whose boundaries agrees. One ...
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32 views

Proportional Image Resizing

This is quite a simple one I guess (but my mind is dead currently and is getting cluttered by other numbers). I have an square image that is currently 256 width x 256 height. I am variably resizing ...
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77 views

Huffman Coding Integer Identifier Table

this might be trivial but I have a brainfog here! I am working through a JPEG compression problem using Huffman codes. According to our book, the process for coding a quantized matrix for a jpeg has ...
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May I know how to solve this Huffman coding-related question?

Question 1: An image is coded with 3 bits per pixel and the probabilities associated with each of the grey levels are P = [0.2 0.15 0.13 0.13 0.12 0.10 0.09 0.08]. (i) Using ...
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5answers
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How do I find/predict the center of a circle while only seeing the outer edge?

Question What formula would allow me to predict the center of this circle? In addition, what attributes of this image must be detected in order to predict the center? I figured understanding the ...
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Data preprocessing

How would you preprocess 2 dimensional data to have 0 mean? Say you have a matrix $M $ that is $p \times q $. Would you calculate the mean of each row, get a vector of length $q $ and subtract each ...