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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4
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283 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 ...
3
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0answers
63 views

How do I apply this PDE as an image filter?

I'm trying to preprocess a height map image with a helmholtz-type equation as described in this paper. The equation is: $$ddx(h') + ddy(h') + y(h'-h) = 0$$ I solved for h and got: ...
3
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0answers
56 views

How do I solve Euler Lagrange equation for image de-blurring?

This is one of the two Euler Lagrange equations for de-blurring which I need to solve: $$ u_r(-x,-y)\star\big(u_r(x,y)\star k-u_0\big) - \lambda_1\nabla \cdot \bigg(\frac{\nabla k}{|\nabla ...
3
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0answers
54 views

The mathematics of anaglyph images

Note: I'm not quite sure whether this question properly belongs to the Mathematica or to the mathematics Stack Exchange. But because my question mainly concerns general mathematical principles rather ...
3
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0answers
37 views

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 ...
3
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0answers
22 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 ...
3
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0answers
3k 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 ...
2
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0answers
30 views

Scale invariant Image Moments - not scale variant?

I came across a problem working with image moments [1]. It is stated that $\eta_{ij} = \frac{\mu_{ji}}{\mu_{00}^{k}}$ where $k = 1 + \frac{i+j}{2}$ is scale invariant. However, if I try to ...
2
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0answers
29 views

Homography matrix form for decomposition

I am trying to decompose a homography matrix. I read that there are a few methods to do that (e.g. Faugeras, Zhang). But I wasn't able to produce a useful output yet. I am not sure which form my ...
2
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0answers
40 views

Understanding JPEG compression.

I have some problems in understanding a passage of the JPEG compression algorithm: Consider an $8\times8$ matrix $M$ that in our case is a "piece'' of a channel (for example the red channel $R$) of ...
2
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0answers
29 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 ...
2
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0answers
43 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 a 2D blurring matrix and $n$ is a noise ...
2
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0answers
119 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 ...
2
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0answers
285 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 ...
2
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0answers
73 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.
2
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164 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 ...
2
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0answers
76 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 ...
1
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0answers
104 views

Using the Kuramoto-Sivashinsky operator applied on the Korteweg–de Vries Soliton as a filter for image processing

When the Kuramoto-Sivashinsky operator (Kuramoto-Si) is applied to the Korteweg–de Vries Soliton (Soliton) we obtain a very interesting filter which is able to process an image via convolution. An ...
1
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0answers
30 views

Averaging and approximation

I read a paper reference at http://arxiv.org/pdf/1101.1764.pdf that if we average a set $V=\{V(t_0,\nu_0), V({t_1,\nu_1),..., V(t_n,\nu_n)}\}$; with $V(t_i,\nu_i)=e^{i\sigma(t_i,\nu_i)}$ then we can ...
1
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0answers
26 views

how does the following parameters affect the peak ( radius ,theta) of the its frequency spectrum?

The following is the similar magnified picture to the second image that it indicates the parameter i am going to talk about. Suppose i am going to fourier transform (DFT) of the following picture ...
1
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0answers
35 views

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 ...
1
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0answers
64 views

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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0answers
115 views

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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0answers
20 views

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: ...
1
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0answers
21 views

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 $$ ...
1
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0answers
70 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 ...
1
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0answers
38 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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0answers
39 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
36 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 ...
1
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0answers
31 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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0answers
51 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
39 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 ...
1
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0answers
224 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
40 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 ...
1
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0answers
160 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 ...
1
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0answers
62 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 ...
1
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0answers
129 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?
1
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0answers
92 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
89 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 ...
1
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0answers
240 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: ...
1
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0answers
258 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 ...
1
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0answers
361 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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0answers
248 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 ...
0
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0answers
14 views

Derivative of convoluted 2D image w.r.t. to its coefficients

I am creating an image with the following variables with the following dimensions: $A: (1,i)\\ X_a: (i,x,y)\\ B: (1,j)\\ X_b: (j,x,y)\\ Image=A\cdot X_a\odot B\cdot X_b $ Where $\odot$ stands for ...
0
votes
0answers
29 views

Convert a nonconvex function to convex function

I have a image $I: \Omega \to \Bbb R$. It is separated into 2 non-overlapping region: $D$ and $\Omega \setminus D$ Each point $x$ in the image $I$, the $\phi$ function is defined as: $$\phi(x)= ...
0
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0answers
69 views

Converting Zhang's Whiteboard Rectification to Python problem.

I've posted this to stackoverflow, but it may be more appropriate here since requires converting a formula to a program. Here is the paper: ...
0
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0answers
80 views

Solve a equation involved differential operator in Matlab

I want to solve $F$ in the following equation in Matlab: $$ F + \partial_x F = Y, $$ where $F$ is a matrix (image), $\partial_x$ is the differential operator of $x$ axis, and $Y$ is a known matrix. ...
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0answers
15 views

Understanding second order derivatives in non max suppression

I am working on converting some old code that uses non max suppression on edge maps produced by an internal process. This process returns a maximum response at edge location but needs to be non ...
0
votes
0answers
34 views

Calculate change in distance to camera from scale

I have 2 pictues of an object. In one picture the object is close and in the other one it is far away. I have these values: $z$ = distance of object to camera in first picture $f$ = focal length ...
0
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0answers
20 views

What is tensor diffusion?

When I was studying "wickart diffusion", I came across the tensor diffusion of Fick's law. What is tensor diffusion?