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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12 views

Micro structure image to geometry [on hold]

How to create microstructure (2D voronoi diagram) from a microscopic image (tif) in MATLAB.
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18 views

Which correct sentence to explain the function $g(\nabla I)=\frac{1}{1+\beta |\nabla(G_{\sigma}*I)|^2}$

I have a edge indicator function that has formula as $$g(\nabla I)=\frac{1}{1+\beta |\nabla(G_{\sigma}*I)|^2}$$ where $\nabla$ is gradient operator, $*$ is convolution operator, $G_{\sigma}$ is a ...
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2answers
40 views

Expressing Math Equations

I'm confused how to express the following expressions in math equations for publication: $x =$ integer part of $y$ $x =$ fraction part of $y$ image $x =$ shifted version of image $y$ left with $z$ ...
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0answers
23 views

How to prove $\int_{\Omega} \sum_{i=1}^{N} f_i(x)dx$ is equivilant with $\sum_{i=1}^{N} \int_{\Omega} f_i(x)u_i(x)dx$

I have a 2D image in $\Omega$ space. Assume that the space can be separated into $N$ sub-regions $\Omega_i$ such that $\Omega_i \cap\Omega_j=\emptyset$; $\Omega_i \cup \Omega_j=\Omega, \forall ...
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0answers
36 views

How comes plotting affine curve as shadows of gray modulo integer resembles its real locus?

Let $f(x,y)$ be polynomial with integer coefficients. Pick integer $n>2$. Let $M$ be $n \times n$ matrix. Set $M_{i,j}=f(i,j) \mod n$. Plot $M$ as bitmap in shadows of gray where larger value is ...
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4answers
73 views

Integrating unit impulse function

Given that, $$ \delta(t) = \begin{cases} \infty & \text{if } t = 0 \\ 0 & \text{if } t \ne 0\\ \end{cases}$$ How is it that, (A) $$ \int_{-\infty}^\infty \delta(t) dt = 1 $$ (B) $$ ...
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2answers
35 views

How do I compute the gradient vector of pixels in an image?

I'm trying to find the curvature of the features in an image and I was advised to calculate the gradient vector of pixels. So if the matrix below are the values from a grayscale image, how would I go ...
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2answers
26 views

Does logarithm of Gaussian image still gaussian distribution?

I have an image 2D that pixel intensity follows multi Gaussian distribution such as $$p \left( I(x) \in \Omega_i \mid (I(x)\right)=\frac{1}{2\pi \sigma_i}\exp\left(-\frac ...
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1answer
31 views

Minimum matching convolution (part II)

We assume we are working in $\mathcal{H}(\mathbb{R}^n)$, the space of real symmetric matrices. We define the partial order $\ge$ defined as $\Sigma_1\ge \Sigma_2$ iff $\Sigma_1-\Sigma_2$ is in ...
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0answers
38 views

Curvature of a level set

I am using the level set method for image segmentation. In particular, the segmentation boundary $C(x, y)$ is represented as the zero level set of a level set function $\phi(x, y)$. As working on ...
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1answer
35 views

From 1D gaussian to 2D gaussian

I read this: The Gaussian kernel for dimensions higher than one, say N, can be described as a regular product of N one-dimensional kernels. Example: g2D(x,y,$\sigma_1^2 + \sigma_2^2$) = ...
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0answers
23 views

Sobel method on data points

From what I've seen of the Sobel method, one takes an source image $A$, and applies the matrices $G_x = \begin{pmatrix} -1 && -2 && -1 \\ 0 && 0 && 0 \\ 1 && 2 ...
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0answers
161 views

Solving a BTTB system by BCCB extension that is highly structured and fewer degree of freedom

Consider a BTTB system generated by a simple $3\times 3$ matrix, $$ Col_1 = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ ...
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3answers
30 views

How can mathematical models be applied to image analysis

I'm quite interested in how mathematical models can be used in analysing images. For example, I'm aware that mixed effect models can be using in image analysis but I was just wondering if there are ...
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0answers
24 views

Why input for 2D signal processing is always some kind of image?

I am dealing with 2D signals that are random. To be more specific my input is a matrix of 1's and 0's. Moreover, at any position (n1,n2) the probability of having a 1 or a 0 is same. One example is ...
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0answers
23 views

Haar wavelet transformation of a binary vector data over $GF(2)$

I am trying to perform Haar wavelet transformation on the following vector which is defined over $GF(2)$. $[1, 0, 1, 0, 1, 0, 1, 0]$ I am doing it as follows. $[1, 0, 1, 0, 1, 0, 1, 0]$ $\implies ...
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0answers
29 views

deconvolution of exp($x^2$)

I would like to know whether we can get the function of type exp($x^2$) by convoluting any functions. That is which function convolution gives exp($x^2$). Thanks in advance
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0answers
44 views

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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0answers
29 views

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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0answers
50 views

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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1answer
24 views

1D FFT on rotated image column by column

I am facing a problem: performing 1D FFT on a rotated column by column on a rotated image, described as following: Original Image: Rotated Image: What I have: original image convolution ...
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1answer
23 views

Singular Value Decomposition for an image understanding

I'm trying to get an intuitive understanding of what an SVD decomposition does to an image. From my understanding, for an image $A \in \Bbb R^{m \times n}$, the singular values are the roots of the ...
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1answer
30 views

Convert a pixel displacement to angular rotation?

I have camera at which i know the distance to it, its HFOV, and each frame has resolution axb. How would one convert a pixel displacement between the center of frame and the object into a propper ...
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1answer
24 views

The most efficient way to find a minimal value in a 2 dimensional matrix.

Suppose we have a matrix A with value of elements ranging from 0 to 255 ( a greyscale image). What is the most efficient algorithm that will return a minimal value found in this matrix?
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32 views

Perspective view and calculating based on it

I've got a project in which i'm asked to use an image captured in perspective view of a lane road (Assume the distance of the camera and the angle relative to the road are known). What I need to do ...
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1answer
36 views

Calculating an Intensity Centroid

I am trying to understand the theory behind calculating an Intensity Centroid (image processing), in particular defining moments. As defined by Rosin 1: $m_{pq}=\underset{x,y}{\Sigma}x^py^qI(x,y)$ ...
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0answers
43 views

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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0answers
19 views

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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0answers
15 views

CT helical scan artifacts

I did helical CT reconstruction but ended up with artifacts like following: This is water phantom using cone beam helical. The cone angle is small enough not to cause severe problems. So the ...
3
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1answer
85 views

New Horizons at Pluto

I recently posted this question on the signal processing site http://dsp.stackexchange.com/questions/23768/new-horizons-at-pluto The only answer was less detailed than I hoped for, so I'm trying here ...
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0answers
39 views

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 ...
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1answer
39 views

Why is my phase correlation not equal to the real correlation?

If I understand the correlation theorem correctly, it states: $ f(x,y) \unicode{x2606} \bar g(x,y) = \mathfrak{F}^{-1} \left\{ F^*(u,v) G(u,v) \right\}, $ also called a phase correlation. Above ...
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1answer
88 views

Minimum matching convolution

Let $\text{SPD}^n$ and $\text{PD}^n$ be the symmetric semi-positive and positive definite matrices in $\mathbb{R}^{n\times n}$, respectively. I want to find an $X\in \textrm{SPD}^n$ that minimizes ...
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0answers
19 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 ...
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0answers
64 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)= ...
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2answers
123 views

Features of phase and magnitude spectrum?

I have read in many books that whether the signal is 1D or multidimensional , The magnitude spectrum tells you how strong are the harmonics in the signal and The phase spectrum tells where this ...
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2answers
920 views

What are the limitations /shortcomings of Fourier Transform and Fourier Series?

I am fond of Fourier series & Fourier transform. But every approach has some outcomes and some shortcomings. It's limitations lead to innovation of new approach. So, can anybody explain about ...
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0answers
71 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: ...
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1answer
78 views

Compute the image intensity on a spherical surface under orthographic projection

I got stuck on the folllowing exercise: Consider a spherical surface of radius $r$ centered at the origin with equation:$$z = d - \sqrt{r^2 - x^2 - y^2}, \quad x^2 + y^2 \leq r$$. The surface is ...
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0answers
147 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: ...
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1answer
70 views

Displaying images on Matlab.

I'm working on image denoising problem and I have develop an optimization algorithm in Matlab for this prupose. The images are in a 256 grey level scale so mathematically what I have is a map from ...
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0answers
50 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 ...
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1answer
90 views

Can someone explain Wishart distribution?

I have to use Wishart distribution to model noise in images. Can someone explain or give intuition behind wishart distribution. Thank you !!!
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1answer
27 views

Why are there these patterns in these pathtraced images?

I've written a path tracing renderer for a technology class, and, while examining the histograms of the resulting images, I found a weird wavy pattern. The resultant image is the average of many ...
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1answer
89 views

Discrete Fourier Transform question

Let $R_{M\times N}$ be a space of size $M\times N$. Define the 2D Discrete Fourier Transform of $f\in R_{M\times N}$ to be \begin{equation} ...
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1answer
33 views

Help with Homework Problem for Img Processing class

I have this homework about Image Processing: Give the general equation of a complex or real-valued digital image that produces a delta function in the frequency domain. Demonstrate this function for ...
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0answers
130 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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1answer
34 views

What is the simplest way to extract a rough orientation statistics from images

Which is the fastest method to extract a rough orientation statistics from images. I think the most precise way is the scanning with local Gabor filters, but its very time consuming. Is it possible to ...
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0answers
20 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 ...
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1answer
21 views

discretization of $div(\psi(x, y)\nabla(u(x, y)))$ for image processing

I am trying to derive numerical scheme for optical flow In Euler-Lagrange equations i obtain following term $div(\psi(x, y)\nabla(u(x, y)))$ where $\psi, u : R^2 \rightarrow R$, $div(u)$ denotes ...