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
11 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 d-...
0
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1answer
21 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 ...
1
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1answer
74 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
10 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 H(f(\mathbf{x}))|...
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0answers
50 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 $i,...
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0answers
93 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 ...
0
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1answer
22 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
27 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
50 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 ...
1
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0answers
107 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
17 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 ...
0
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1answer
22 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
23 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 (...
1
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1answer
44 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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2answers
49 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 i,j=1....
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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
95 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) $$ \...
1
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2answers
577 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
45 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 {(I(x)-\mu_i)^2}{2\sigma_i^...
0
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1answer
37 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
48 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 ...
1
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1answer
44 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,$\sigma_1^2 + \sigma_2^2$) = g1D(...
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0answers
30 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} \\ a_{...
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3answers
54 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
27 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
32 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
37 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
327 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
80 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
55 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
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1answer
62 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
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1answer
35 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
78 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
28 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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0answers
42 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
107 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
44 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
48 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 ...
3
votes
1answer
93 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
vote
0answers
131 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 http://docs.opencv.org/doc/tutorials/features2d/trackingmotion/...
1
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1answer
51 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 $f(x,...
2
votes
1answer
107 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 $||...
0
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2answers
187 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
4k 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
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0answers
83 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: $$\dfrac{ddx(h')}{...
5
votes
1answer
106 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 ...
1
vote
1answer
138 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
105 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 ...