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 do you take the discrete Fourier transform (DFT) of a parallelogram or a Bravais lattice in general?

I'm working on implementing a method that extracts the corresponding wallpaper group given a gray-scale image/pattern. But to do so, I need to take the DFT of a unit cell in the image which, in the ...
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0answers
8 views

Filtration on simplicial complex as a grayscale image

If we make a filtration on the complex built from vertices and edges and faces(2dimensions) of a grayscale image according to grayscale value. Does it considered as a filtration on simplicial complex? ...
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0answers
20 views

Homography with line correspondences

When calculating a homography with line instead of point correspondences, what is the derivation of the formula: $$ l_i = H^T\cdot l^{'}_i $$ I know that: $$ l^T\cdot x = 0 \quad\text{and}\quad ...
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0answers
20 views

Mathematical morphology problem for a dog contest organization [closed]

I'm a computer programmer responsible to develop a program for a dog contest organization that has to track the movement of dogs in a large warehouse. The system has to work with an 360ยบ IP camera ...
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2answers
72 views

How/why does matrix multiplication work to do a linear fit? [closed]

Some background: I have a B.S. in physics. I have taken linear algebra. I do work that involves doing image analysis in IDL. One thing I have to do a lot is fit a linear equation $(y=mx+b)$ to the ...
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16 views

Explanation of Template Matching formula

Can someone please explain the formula f.) on OpenCV template matching Formula: Suppose template image is 3x4 and source image is 15x20 how would the mathematical operations follow...
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0answers
17 views

analyze convolution in spatial domain against multiplication in frequency domain

Lets say I have a image of $NxN$ and a separable filter that I want to apply on it. there are 2 ways to do that: 1. By convolution in spatial domain. 2. By multiplication in frequency domain. I need ...
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0answers
15 views

Why is the square of an image not equvalent to taking the autoconvolution of an image in fourier space?

Al right I know that in order to multiply in the normal domain I have to take the convolution in Fourier domain but when I do so in matlab and invert the result then I come up with nothing but a lot ...
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0answers
80 views

Relationship b/w PDE periodic boundary values

Consider the following homogeneous boundary value problem for function/potential $u(x,y)$ on the infinite strip $[-\infty,\infty]\times[0,\pi/4]$ w/positive periodic coefficient/conductivity ...
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0answers
45 views

Trigonometry Calculate Distance and Angle of object in camera frame

I have an application where I am trying to build a handheld scanner that can draw a 2d profile of a 3d surface (using structured light scanning). The handheld device consists of a line laser and a ...
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0answers
34 views

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 ...
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0answers
23 views

what do the coefficients means in this matrix multiplication?

I found this article about creating anaglyphs through matrix multiplications, but I do not know what do the coefficents mean and do to the images? the 0,299,0,587 and the others can someone please ...
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28 views

summation of even and odd numbers

In my video processing algoritm, I do some processing even and odd frames seperately. F = E(x) + O(x) where F is the video, E and O contains its even and odd ...
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0answers
19 views

How to calculate derivative with respect to time for Optical Flow

Suppose we have 2 images in motion for detecting the object in movement according to Lucas and Kanade [u, v] = inv(H)*[dxdt, dydt] where H is the Hessian for partial derivatives for image x and y ...
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1answer
8 views

Why do we scale by $\frac{1}{N-1}$ while calculating the covariance matrix in PCA?

When we perform the Principal Components Analysis (PCA) on a set of N d-dimensional vectors, we scale by a factor of $\frac{1}{N-1}$. Here's what we do in PCA: We calculate the mean of all the ...
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1answer
18 views

Gradient transpose along $x$ or $y$ direction in images

Gradient in images $$ \nabla I=\nabla_x I+\nabla _y I$$ can be approximated to forward or backward difference ($[1 -1], [-1 1] $etc.) and also calculated from sobel or prewitt operators but I came ...
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1answer
48 views

Cauchy Schwarz inequality in Normalized Cross Correlation

I'm currently using a normalized cross correlation(NCC) for measure the degree of similarity between two image. Almost two week studying about how NCC is derived from Cauchy Schwarz inequality but ...
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0answers
8 views

Solution for multiple level set equation

Is an exact solution to the following minimization problem known? Find $f$ such that: $$\sum_{k=1}^m\int_{\mathbb{R}^2}(g_k(\mathbf{x})-H(f(\mathbf{x})))^2+\int_{\mathbb{R}^2}|\nabla ...
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0answers
38 views

How to represent a given equation more clear, professional and short form?

I have a given $A_{m \times n}$ matrix whose $i, j$th component is $a_{ij}$, let $$\mu = \max \{ a_{ij} : 1 \leq i \leq m, 1 \leq j \leq n\}$$ Let $J_{m \times n}$ be the $m \times n$ matrix whose ...
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0answers
73 views

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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1answer
17 views

Need help coming up with (or finding) an image metric for $N\times M$ image.

So say you have the set of all unsigned $8$ bit grayscale, $N\times M$ images. This means there are $256^{NM}$ images in this space. If these images were binary, you could represent them with an $NM$ ...
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0answers
15 views

Energy functions for CRF/MRF

I am currently working in image segmentation. I have read several papers and books where Markov or Conditional Random Fields are used in order to segment images. Most of them also mention an energy ...
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0answers
41 views

Matrix values increasing after SVD, singular value decomposition

I am trying to learn SVD for image processing... like compression. My approach: get image as BufferedImage using ImageIO... get RGB values and use them to get the equivalent grayscale value (which ...
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0answers
64 views

Finding Position of an Object in an Image Relative to a Camera

Hopefully I have this in the correct place, but apologies if not. What I'm trying to do is given I know the pixel that I am measuring to, how would I find the x, y and z co-ordinates of that pixel ...
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0answers
15 views

Maintaining crop dimensions for a resized image

I have an image with a base of 250 and a height of 250. I crop the image with four values: X1, Y1, X2, Y2. I resize the image so that it is 270 by 270 but I would like to keep the same proportions ...
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1answer
20 views

what is the different between Positive curvature and negative curvature?

Can somebody tell me, if i rotate the image,will the Positive and negative change?For example, shape just like "O" in the image coordinate system used in opencv, does the upper part and lower part ...
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0answers
15 views

How to find a maximally orthogonal set of images according to a basis set?

I apologize in advance if there is an obvious answer to this question, or if it has already been addressed; I have tried to find information on it, but haven't come up with much. I have a basis set ...
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1answer
43 views

Understand about maximum a posteriori probability (MAP) in classfication task

I have a 2D image defined on a region $\Omega$. Let $I: \Omega \to R$ be a gray image. Assume that the region can be separated into $N$ sub-regions $\Omega_i$ such that $$\forall i,j=1... N:\Omega_i ...
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0answers
34 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
47 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
28 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
88 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
182 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
39 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
35 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
43 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
40 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
29 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
169 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
41 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
26 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
29 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
35 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
169 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
60 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
54 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
51 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
32 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
52 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 ...