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

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4
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1answer
87 views

How to solve cross-products including matrices?

I'm a programmer and I'm doing a whitebalance-transformation in RGB colorspace. This should work with this transformation matrix that I've found in literature: $$ \begin{pmatrix} R \\ G \\ B ...
2
votes
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 ...
1
vote
1answer
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 ...
4
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0answers
224 views

Reprojecting/converting an orthographic image/grid into a cartesian grid

I'm trying to dewarp a fisheye image into a simple rectilinear image of a subset of the fisheye. As part of this, I'm trying to map the azimuth/altitude values into a point on the image. The points ...
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0answers
15 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 ...
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0answers
94 views

2-D DFT of a matrix PxP and 1-D DFT of a vector of size P^2?

What is the difference between the following two things: make a 2-D Discrete Fourier Transform of a certain matrix A[p,p], first reshape this matrix into a 1-D vector a[p^2,1], and compute the 1-D ...
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0answers
196 views

Lloyd-Max Quantizer Problem

Consider the function $z = x^2 + y^2$ , for $0 \leq x \leq 10$ and $0 \leq y \leq 10$. Take a regular discretization with steps $\Delta x = \Delta y = 0.1$ and its histogram as the probability ...
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62 views

Principal Component Analysis software

I'm looking for a (non-MATLAB) software that can process a image using the PCA algorithm and output it like this: Regards.
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0answers
2k views

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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0answers
146 views

Singular Value Decomposition

I want to decompose an image $A$ using the Discrete Wavelet Transform and then find the singular values, $S$, such that $A=USV$. I will then do the same to another image such that $B=USV$. I will ...
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0answers
66 views

Intuition about moment function derivation [OR] derivatives involving a time varying integration domain

$$ m_{{pq}}(t)=\iint\limits_{R(t)}h(x,y) dx dy $$ where $ R(t)$ the domain of integration is time varying (In fact it is the only one which is time varying). And $$ h(x,y) = x^p y^q f(x,y) dx dy ...
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17 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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23 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
25 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 ...
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0answers
82 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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0answers
23 views

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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0answers
75 views

Whitening matrix for Fast ICA

I have a matrix $X $ with dimension say $ m \times n $ with $ m> n $. I am trying to whiten this matrix in matlab by first taking the $C= \operatorname{covariance}(X)$ followed by eigenvalue ...
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0answers
55 views

Anamorphotic Projections onto Awkward Solid Surfaces

I have been experimenting with some 19th century picture development techniques that involve photochemical image projection: For flat pictures you first mix equal parts of chemicals like ferric ...
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0answers
73 views

How to show that the Harris corner detector is rotation invariant

I understand what it means for the Harris corner detector to be rotation invariant. But what steps do you need to take to show that it is rotation invariant?
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0answers
65 views

Keeping a constant resolution scale of an image

Intro I'm writing a program that zooms in and out on an image and the only way to do it with the data I have is to change the limits of my graph. The aspect ratio (scale of x to y) always remains 1:1 ...
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0answers
79 views

viewing ray geometry - with multiple aerial photographs

I am working with multiple aerial images. My idea is to model 3d objects (only upper parts). I am having known orientation parameters. As I am new to this field so that, I want to clarify few general ...
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0answers
79 views

Produce a 4:2:2 sub sampled Y matrix, Cr matrix, Cb matrix for an image

I have write the matlab code below for to extract Y, Cb, Cr information from the picture: ...
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0answers
157 views

Calculating the aspect ratio of the rotated rectangle on the image

I need to determine the aspect ratio of the rectangular object (such as mobile phone or credit card) on the image. The problem is that the object might be photographed from an angle or perspective. So ...
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0answers
270 views

image classification problem using Matlab?

I have an image classification problem. I have an image which spesify classes' labels using "imread" funtion of Matlab $(A=imread('r.bmp'))$ the output for example for 3 classes is as $$A= ...
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178 views

Projection Slice theorem getting rid of artifacts?

I have employed the fourier(projection) slice theorem in matlab. I have a 3D image, P(x,y,z) defines their pixel intensities at a given location int he image volume, it is discrete and uniform. I ...
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4 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 ...
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13 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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14 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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0answers
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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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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0answers
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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0answers
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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23 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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29 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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27 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
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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31 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
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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26 views

Rearranging convolution equation: seismic image processing

I am looking at the theory of surface related multiple elimination and I have got to a point where it says: If we define an operator $a(t)$ as follows $$a(t) \ast s(t) = - \delta (t),$$ ...
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63 views

Moving from 1D to 2D space

In 1D space I can create a Gabor function $h(x)$ as the product of a sinusoid and a Gaussian envelope $ f(x) = sin(2\pi x)\\ g(x) = e^{-\frac{(x-x_0)^2}{2\sigma^2_x}}\\ h(x) = f(x)g(x) $ What I ...
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0answers
13 views

what exactly does scale mean in scale-space theory?

In image processing, scale-space is a technique to represent an image at different scales. But this really confuses me, since I always think that the word scale just means the size of an object, so ...
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0answers
97 views

AC component of Hadamard coefficients.

I want to generate the watermark strength map of two images. My book says that the watermark strength factor is calculated by: $a=b*mask1(j,k)*mask2(j,k)$ where a:watermark factor b=scaling factor ...
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31 views

Best transform for detecting frequencies of sinusoidal signals.

Between Discrete Fourier Transform (DFT) and Discrete Cosine Tranform (DCT) could we say that one of them is better than the other in detecting frequencies of sinusoidal signals?
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42 views

Mymultiple image geometry

I have to work with multiple aerial images. the objective is to reconstruct 3d features. For a particular object, i want to find the images which are giving good viewing geometry than others. so ...
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0answers
60 views

Limiting search space around line segment via rectangular buffer

I have 2D line segments extracted from an image. So i know end point coordinates of them. also, i have some reference 2d line segments. Both line segments are now in vector form. comparing to ...
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0answers
88 views

Can a matrix based “secret sharing scheme” be applied to image based secret sharing?

I was reading this and was wondering if it can be used to do secret sharing with images. I dont know a lot about image processing, but if the authors have given a scheme for matrices, how can be ...
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173 views

Maximum absolute deviation

Let be I , J a two gray scale image How I will be able to interpret the Maximum absolute deviation between the histograms of these images?
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258 views

Distance between two objects in a picture

lets say I have a photo that has a picture on a wall and a book upright on the desk. now i know the size of both of these objects. I want to find the distance between two of them on the photo, I was ...
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0answers
322 views

Circular to linear convolution with matrices

I know how to perform a circular convolution with vectors (http://engineering-matlab.blogspot.it/2010/12/matlab-program-for-implementing_5864.html) and I know that circular convolution can be obtained ...
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63 views

How can I convert lines intersecting a plane into a focused image?

I am writing a particle transport code. I would like to be able to obtain an image of my geometry when transporting photons given the following information: The photons are incident on a plane. For ...