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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1answer
19 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,$\sigma_1^2 + \sigma_2^2$) = ...
0
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0answers
18 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 ...
0
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0answers
101 views
+50

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} \\ ...
0
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3answers
22 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 ...
0
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0answers
20 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 ...
1
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0answers
21 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 ...
0
votes
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
-1
votes
1answer
39 views

Image restoration in matlab via PDE toolbox

I want to remove a noise for an image using matlab, when the observed image is $$f=u+v$$ where $u$ is the restored image (is the image i want recovered) and $v$ is the gaussian noise. To restore $u$, ...
2
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0answers
33 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 ...
1
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0answers
26 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, ...
1
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0answers
45 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 ...
0
votes
1answer
18 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 ...
1
vote
1answer
21 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 ...
0
votes
1answer
23 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 ...
0
votes
1answer
23 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?
0
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0answers
31 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 ...
0
votes
1answer
25 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: $m_{pq}=\underset{x,y}{\Sigma}x^py^qI(x,y)$ ...
2
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0answers
42 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 ...
1
vote
0answers
16 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 ...
0
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0answers
11 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
votes
1answer
79 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 ...
1
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0answers
22 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 ...
1
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1answer
38 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 ...
1
vote
1answer
48 views

Minimum matching convolution

Let $\text{SPD}^n$ and $\text{PD}^n$ be the 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 $||X||$ ...
0
votes
0answers
15 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
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0answers
46 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
votes
2answers
114 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 ...
7
votes
2answers
648 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 ...
3
votes
0answers
68 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: ...
5
votes
1answer
75 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 ...
0
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0answers
130 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: ...
1
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1answer
52 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 ...
2
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0answers
39 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
votes
1answer
76 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 !!!
0
votes
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 ...
3
votes
1answer
84 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} ...
-1
votes
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 ...
0
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0answers
106 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. ...
4
votes
1answer
33 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 ...
0
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0answers
16 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 ...
1
vote
1answer
17 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 ...
0
votes
1answer
72 views

Improvement over gamma correction for brightening images?

I'd like to brighten one of my own images for printing purposes, using a program I made. When I use the formula: pixelBrightness^0.6 to brighten an image (0.6 being an example, and where ...
0
votes
1answer
32 views

Is A+D-C-B really the correct formula to get sum over rectangle in summed area table?

Recently, I was taught about the summed area table (integral image) concept. This table represents a matrix, usually an image, so that every ${SAT}_{ij}$ (I used SAT as summed area table) equals to ...
3
votes
0answers
62 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 ...
0
votes
0answers
41 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
votes
1answer
78 views

Given an intensity histogram,we apply an histogram equalization.Calculate the new intensity of the pixels in the original histogram had a150 intensity

It's a question from an exam that I can't understand its result. Given the following intensity histogram of an image: After an histogram equalization applied for this histogram, we've got the ...
1
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0answers
108 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 ...
2
votes
1answer
40 views

Finding the best fit of 3 categories ( restaurants/meal/person analogy problem )

I have this problem that sounds tedious and long and I'm not sure if there exist an intuitive way to solve it. The problem is related to image recognition but I will try to give an analogy to it You ...
3
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0answers
69 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 ...
0
votes
1answer
69 views

Which topics in maths should I know before I dive into programming for image processing?

I am a student who wants to start out with programming for Image processing but as I do not have a good mathematical background(I haven't studied A-level Maths) I would like to know what are the ...