# 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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### How to measure the irregularity of a hexagon?

I need to evaluate the quality of a list of machine parts, which roughly has one center point surrounded by 6 exterior points. If the quality is good, then the 6 exterior points will form a regular ...
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### When is a mapping the proximity operator of some convex function?

Sorry for cross-posting from MO. It's been a few days and the question hasn't received any attention there. So, is there a characterization of mappings $p : \mathbb R^n \rightarrow \mathbb R^n$ which ...
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### 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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### 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 ...
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### 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 ...
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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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### 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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### Math behind Photoshop's gradient tool

I want to implement something like Photoshop's gradient tool and I need to understand the math behind it. Can anyone explain the differences between linear, radial, angle, reflected, diamond gradients?...
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### 2D Discrete Fourier Transform on an Image - Example with numbers (rgb)

I am trying to write my own function that takes an image, an pixel by pixel it calculates that pixel value that will produce a 2D Fourier Transform image. I have no idea about signal processing, my ...
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### Eigenvalue and informations?

I have been wondering about this these last couple of days and cannot seem to understand how come this is the case.. I know about the eigevalues and the eigenvector, and that it can be found on for ...
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### 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 ...
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### 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 ...
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### 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 ...
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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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### 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 ...
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### 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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### 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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### 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.
191 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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### Algorithm for high contrast

Using this algorithm I can increase contrast but applications like Paint.Net can increase contrast significantly. For example it can convert to (by setting contrast to 100 and brightness to 100, ...
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### Given x,y,w,h can you generate a rainbow box/cuboid with rounded edges?

Given $x$, $y$, $w$, $h$ where $0 \leq x < w$ and $0 \leq y < h$ and $(x, y)=(0, 0)$ is bottom-left and $(x, y)=(w-1, h-1)$ is top-right and they're all integers, can you make a formula that ...
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### Interpolation of jacobians for point wise defined transformation

Here is my question: let's say that I have a transformation function T from the image A to the image B which is pointwise defined. That is, T(x) = J, where J is the jacobian representing the ...
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### Eigenvalues and Harris Matrix

In image processing is possible to detect a corner by looking at the eigenvalues of the Harris matrix. Harris matrix can be here http://docs.opencv.org/doc/tutorials/features2d/trackingmotion/...
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### Using the Kuramoto-Sivashinsky operator applied on the Kortewegâ€“de Vries Soliton as a filter for image processing

When the Kuramoto-Sivashinsky operator (Kuramoto-Si) is applied to the Kortewegâ€“de Vries Soliton (Soliton) we obtain a very interesting filter which is able to process an image via convolution. An ...
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### 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 ...
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### 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 (...
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### 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 ...
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### 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?
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: \begin{...