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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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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0answers
10 views

What are kernel space, functions and data?

I'm reading Kernelized Locality-Sensitive Hashing, which is obviously based on the concept of kernel applied to space, functions and data. It seems particular relevant in image processing domain, but ...
0
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1answer
504 views

Gaussian distribution and its parameters

I need to learn more about Gaussian distribution and given a set of data, plot a Gaussian distribution of it. Using the following code sample, could you please tell me how I can plot a Gaussian ...
0
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1answer
392 views

What is the matrix representation of Radon transform?

Just as the title, my question is what is the matrix representation of Radon transform (Radon projection matrix)? I want to have an exact matrix for the Radon transformation. (I want to implement ...
1
vote
2answers
492 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 ...
1
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1answer
58 views

Geometric explanation of a methodology in the article about Image Denoising

In article Ghimpeteanu G., et al. - A Decomposition Framework for Image Denoising Algorithms, I found as below: Let $\displaystyle I : \Omega \subset R^2\mapsto R$ be a gray-level image, and $(x, ...
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0answers
12 views

Learning point spread function image processing

Given a set of images, that are blurred by Gaussian point spread function, how can I learn the parameters of the PSF, i.e. standard deviation of the Gaussian kernel. One way that I can think of is to ...
1
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0answers
118 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 ...
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0answers
18 views

How to represent the function of variables?

I have a function as $$E=\int_\Omega -\log\big( p_i(x)\big) dx$$ where $p_i(x)$ is density distribution which estimated by Parzen window method. $p_i(x)=\frac{1}{\Omega_i} ...
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0answers
374 views

Produce a 4:2:2 sub sampled Y matrix, Cr matrix, Cb matrix for an image

I have write the matlab code below for to extract Y, Cb, Cr information from the picture: ...
0
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0answers
29 views

Determinant of Hessian approximation

I have a question regarding formula in SURF article by Bay et al. Theory Given a point $p=(x,y)$ in an image $I$, the Hessian matrix $\mathcal{H}$ in $x$ at scale $\sigma$ is defined as follows $$ ...
0
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2answers
2k views

Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
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0answers
26 views

Image processing, optimization via regularization - efficient strategy

i would like to solve the following system: $J(x) = |Ax-b|_2^2+\gamma|\nabla x|_2^2$ subject to: $x \geq 0, \sum_i x_i = 1$ The underlying problem is to derive the PSF from a sharp and blurry ...
0
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0answers
12 views

To get boundary of xy coordinates around object inside an image using active contour method

Trying to extract the XY coordinates around the boundary of an lesion object inside an image of plain background. I am using the active contour method as suggested to find x and y coordinates along ...
3
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2answers
54 views

Largest four line segments of polygon

I have some polygon (see darkblue contour): It consists of very small segments, pixel by pixel, so angles differ although they seem to be the same. Visually we see 4 large line segments. How can I ...
-1
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2answers
54 views

An algorithm for finding the intersection point between a center of vision and a surrounding rectangle

In plane $\mathbb{R}^2$, a rectangle $R$ with center $P_2(x_2,y_2)$ and vertices $(x_2 \pm w, y_2 \pm h)$ (sides parallel to axes) is given. We consider the transformation which, to a given point ...
2
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1answer
30 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 ...
0
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0answers
21 views

Contour and perimeter recognition in binary image

I need to detect contour (object) and find the perimeter of a detected object. For example, I have the following image: http://i.stack.imgur.com/40TTX.png All images are binary, so they consist of ...
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0answers
25 views

Relation between focus and camera intrinsic parameters

Does a focus tuning affect the camera intrinsic parameters? More precisely, if the focus of a camera is changed, does the camera intrinsic parameters matrix remain unchanged? Apparently, since this ...
0
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0answers
32 views

Does the ring in this Fast Fourier Transform image of a hexagonally close packed structure have significance?

I have a picture of a hexagonally close-packed lattice and I took the FFT of the image using ImageJ. Below are the results. I expected the FFT to also be a lattice with reciprocal lattice spacing, I ...
0
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0answers
19 views

I downloaded the SPARCO package (MATLAB)and when setting it up a problem has occured

I downloaded SPARCO1.2 (MATLAB) from http://www.cs.ubc.ca/labs/scl/sparco/ and when I use the command 'sparcoSetup' it says everything is successful. But then when I use the command 'checkProblems' ...
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0answers
9 views

Number of operations in convolution of an image with a sequence of kernel

In the vein as this question, I'm trying to see how many operations convolution takes (in the context of image processing), as illustrated by the following GIF: I'm interested in the naive ...
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0answers
23 views

Distance between a map and a point using bicubic interpolation

I have an image (i.e., a two dimensional regular grid) with pixel values that represent elevations. To interpolate points of the surface described by the grid, I use bicubic interpolation. The image, ...
0
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0answers
13 views

Transformation between camera velocity and projection of a tube's cut

I have a vision sensor / flying camera inside a circular tube as shown below: The camera is using the pinhole model and I am using edge detection to detect the "black" hole that is forming due to ...
1
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1answer
39 views

Calculate if image dimensions are too horizontal or vertical

I'm working on a PHP script that adds images to articles automatically. A common problem I've encountered is that the image dimensions can be too wide or too tall. In terms of aspect ratio of wide ...
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0answers
351 views

Maximum absolute deviation

Let $I$, $J$ be two gray scale images. How will I be able to interpret the maximum absolute deviation between the histograms of these images?
1
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1answer
54 views

Pyramidal Histogram Of Oriented Gradients - Trilinear interpolation

Hello im struggling with an implementation of this article: https://goo.gl/8mpIuq I performed bilinear interpolation over the histogram bins and the results are better with this interpolation, ...
0
votes
1answer
45 views

Method for finding basis of an image

I know the traditional method for finding an image of a matrix is finding the pivot columns of the rref of the matrix and then the corresponding columns are the basis of the image, but I'm wondering ...
0
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0answers
12 views

determine the absolute difference in bits between using an indexed colour

Given the following 4 x 4 image, determine the absolute difference in bits between using an indexed colour (where the index uses the lowest number of bits possible, but the colour is represented as ...
0
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0answers
18 views

finding image and kernel from convolution result

given a one dimension image/(signal) I and three kernels K,L,J. given the results of the convolution of I with each kernel, for example \begin{matrix}I*K =[ ...
2
votes
1answer
67 views

Fourier transform of a 2D image, and noise cancelation

I'm a statistics grad student, and I just started getting into Digital-Image-Processing (an analogy for processing super-large contingency tables). In the book "Digital Image Processing" by Gonzalez ...
0
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1answer
28 views

SVD for Seam Carving

Could SVD be used for Seam Carving ? I am making a small program for a uni course and I'm looking for different ways to calculate pixel energy; which made me come across SVD. Among others, I have ...
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0answers
22 views

Temerature and Strain images comparison & interpolation: finding offsets in X,Y coordinates systems.

I have two kind of 2D images from a Strain test, which show temperature and strain distributions in X and Y cordinate systems. One is thermal image, which gives temperature T values in a 200x300 ...
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0answers
37 views

Derivative of an Euclidean-Vector norm.

Consider: x a $N \times 1$ vector , with elements $x_i$ b a $N \times 1$ vector , with elements $b_i$ A a $M \times N$ matrix , with elements $a_{ij}$ ( Symmetric matrix - Block Circulant ) As we ...
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0answers
18 views

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 ...
0
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0answers
16 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? ...
0
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2answers
79 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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0answers
26 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
23 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
90 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 ...
0
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0answers
18 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
78 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 ...
2
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0answers
45 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
24 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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0answers
30 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
29 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
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 ...
0
votes
1answer
20 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
70 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
88 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 ...