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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4
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0answers
60 views

I am looking for a mathematical equation to warp an image [on hold]

Theoretically, I know that to warp an image, each pixel $(x,y)$ in the source image is transformed to $(x', y')$ using a function f (i.e. $x'=f(x,y)$ & $y'=f(x,y)$ ). But what mathematical ...
-6
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0answers
22 views

Image denoising code [on hold]

Could someone help me to find the code of the following paper : Image restoration combining a total variational filter and a fourth-order filter Fang Li, Chaomin Shen, Jingsong Fan, Chunli Shen
0
votes
0answers
12 views

gradient of total variation norm in total variation denoising

I am learning total variation denoising. The gradient of TV norm need calculated. From the link: http://www.numerical-tours.com/matlab/denoisingsimp_4_denoiseregul/ It says that the gradient is ...
0
votes
1answer
17 views

Is there any approach to computer vision that doesn't make use of geometry?

I've long been interested in applying my background in functional analysis (especially wavelets) and other related areas to actually create something with "real world" value (not that I don't enjoy ...
0
votes
0answers
10 views

What different between huffman and EBCOT?

I have a question about entropy coding and Image compression. Huffman coding and EBCOT coding are entropy coding. correct or not? I knew about huffman coding but I don't know EBCOT, How it working?...
0
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0answers
16 views

Fourier Transform Deformation [closed]

Let f(x,y) denote an original image containing an object. After deformation the image is expressed as f(a⋅x+b⋅y, c⋅x+d⋅y). Find the Fourier transform of f(a⋅x+b⋅y,c⋅x+d⋅y) in terms of F(w1,w2).
0
votes
1answer
411 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 ...
0
votes
1answer
514 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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0answers
38 views

Compute two 1D lookup tables for computing DCT of a 2D Laplacian

I am following a paper that I have to implement through coding and I am struggling understanding what it means exactly with the sentence "create two 1D lookup tables for computing the DCT of a 2D ...
0
votes
0answers
7 views

Morphological operations with even sized structuring elements

The well-known morphological operations, such as dilation/erosion, opening/closing, top-hat... , widespread in digital image processing, are defined by means of so-called structuring elements. For ...
0
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0answers
9 views

Phase correlation vs. normalized cross-correlation

In 2-dimensional discrete signal analysis (specifically image processing), a definition I found for the normalized cross-correlation between two images, both of size MxN $g_1(x, y)$ and $g_2(x, y)$ is:...
-1
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0answers
13 views

Best 3D reconstruction method.

I'm looking for a method to generate a 3D point cloud from one or more cameras (I know the position of each camera). I need the point cloud to be generated each frame (of video from the camera) and ...
2
votes
3answers
70 views

Maximum Eigenvalue of the Discrete Laplace Operator (Image Processing)

Given the derivative operator in image processing $$ A = \begin{bmatrix} 1 & -1 & 0 & 0 & \ldots & 0 & 0 & 0 \\ 0 & 1 & -1 & 0 & \ldots & 0 & 0 &...
1
vote
2answers
597 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 ...
0
votes
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 ...
0
votes
0answers
36 views

Alignment of one 3D Coordinate system to another 3D Coordinate system

I'm working on a project depicted by this picture(taken from internet) where there are different coordinate system involved which corresponds to camera coordinate system and local 3D coordinate system ...
1
vote
0answers
31 views

Estimate original matrix from matrix multiplication result

Let $A$ be $m \times n$ real matrix. Let $B$ be $n \times k$ real matrix. Let $C= A \times B$ ($m \times k$ matrix). Now, the question is: given $C$ and $A$, give an estimate for $B$. Possible ...
0
votes
0answers
29 views

recursive least squares for nearly singular matrices

I have an image reconstruction problem which I want to solve as a linear system $Ax=y$. A matrix is big, but for the beginning I can shrink the imaging region to $nPix$ = 2000 pixels. number of ...
0
votes
0answers
13 views

Thinning vs. medial axis transform

Both thinning and medial axis transform of a binary image produce a simplified version of the image, reducing the connected components to single-pixel wide subsets, also called skeletons. The one ...
0
votes
1answer
22 views

Minimizing $ E(q)=\lambda(q-p)^T(q-p)+q^TLq $

Let $ E(q)=\lambda(q-p)^T(q-p)+q^TLq $, where $\lambda$ is a scalar, q and p are n by 1 column vectors, L is an n by n positive definite matrix (Actually Laplacian matrix, in image processing field)....
5
votes
0answers
46 views

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 ...
0
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0answers
12 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 ...
1
vote
1answer
60 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, ...
0
votes
0answers
16 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
vote
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 ...
0
votes
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} \int_{\Omega_i}K_\sigma\big(...
1
vote
0answers
379 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
votes
0answers
32 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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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
votes
0answers
13 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
votes
2answers
56 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
votes
2answers
59 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 $P_1(...
2
votes
1answer
33 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 l^{'...
0
votes
0answers
24 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 ...
0
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0answers
36 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
33 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
votes
0answers
20 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' ...
0
votes
0answers
10 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 ...
0
votes
0answers
27 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
votes
0answers
16 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
vote
1answer
41 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 ...
0
votes
0answers
361 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
vote
1answer
64 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
50 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
15 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
votes
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 =[ 1/3&2/3&1&1&1&1&1&...
2
votes
1answer
71 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
votes
1answer
29 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 ...
0
votes
0answers
23 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 ...
1
vote
0answers
39 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 ...