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Questions tagged [image-processing]

This tag is for the mathematics involved in the field of image processing. Many such questions are also appropriate for Signal Processing Stack Exchange.

5
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278 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 ...
4
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0answers
73 views

Shearlets - Understanding Anisotropic Features

For $\psi \in L^2(\mathbb R^2)$, the continuous shearlet system $SH(\psi)$ is defined by $SH(\psi) = \{\psi_{a,s,t} = T_t D_{A_a}D_{S_s}\psi:a>0,s\in \mathbb R, t \in \mathbb R^2$}, where $D_{A_a}...
4
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0answers
665 views

Reprojecting/converting an orthographic image/grid into a cartesian grid

I'm trying to dewarp a fisheye image into a simple rectilinear image of a subset of the fisheye. As part of this, I'm trying to map the azimuth/altitude values into a point on the image. The points ...
3
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0answers
267 views

Initial Contour in Level-Set-Method

I am learning Level-Set-Method for the image segmentation. I have a simple question, how people draw the initial contour in the given image, when people need to deform it? Is there a command in ...
3
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0answers
103 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')}{...
3
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0answers
241 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 k|}\...
3
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290 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 ...
3
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0answers
67 views

what is the significance of Eigen values of autocorrelation matrix?

I am trying to find auto correlation matrix of an image to get Harris corners.Paper I am referring suggest that if eigen values of auto correlation matrix are large the point will be corner point.so ...
3
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0answers
43 views

Detecting camera shake

I have a bunch of data captured from a worm tracker that consists of a B&W camera that stares down at a few dozen worms for an hour at a time. The tracker captures the outline of each worm ("blob"...
2
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0answers
19 views

Gradient of function with index operation

First of all, please let me know if anything is off with my notation. I am a computer scientist and as such I am not that strict about notation. In my problem I want to optimize an objective function ...
2
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0answers
38 views

Graph-cut and pairwise MRF

I try to use graph-cut method but I got some trouble with it. I want to segment an image into foreground and background. For each pixel $x$, I got the probability that it belongs to the background $p(...
2
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0answers
320 views

Compute real length from perspective

Given the two green lines and the real distance between them (blue lines), is it possible to calculate where in the picture would be placed a point 4.5m away from a certain initial point (red line)? ...
2
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0answers
15 views

Multiphase levelset Chan Vese algorithm

I am implementing the multiphase level Chan Vese algorithm. I am using IPOL document as reference (http://www.ipol.im/pub/art/2012/g-cv/article.pdf) Everything is clear for me, except the stopping ...
2
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0answers
48 views

Detect clusters in an RGB space

With OCR one of the first stages in a processing pipeline is to accurately identify what is print and what is paper, generally achieved by some form of binarization. In the good old days most scans ...
2
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0answers
26 views

How to deblur a image matrix blured by two circulant matrix?

We suppose an image matrix $X\in \mathbb{R}^{n_1\times n_2}$ is blurred by two circulant matrices $\Phi_1 \in \mathbb{R}^{n_1\times n_1},\Phi_2 \in \mathbb{R}^{n_2\times n_2}$. We can observe the ...
2
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0answers
36 views

Increasing the accuracy with techniques of interpolation

I am currently pursuing my Masters in electrical engineering and the class I am taking is Image Processing. Last night my professor introduced an interesting idea of ways of "guessing" the color of ...
2
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0answers
40 views

Aligning image contour to map coordinates - ways to solve?

Got an exotic problem I guess, but still. Let's say, I have an random image contour, created bu Laplace or Sobel algorithm. Also - I have a random set of coordinates (pretty dense one for example). ...
2
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0answers
62 views

How to arrange these detected points from one end points to other, edge to edge of an object?

Please suggest what topic to tag this question if I have tagged it in the wrong topic, after going through this. I have detected partial edge of an object like this after image processing. I have ...
2
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0answers
68 views

How to do 3D reconstruction using matched points (with stereo images)?

I have 2 images, called left and right images. I have some matched points $[c_l,r_l]$ and $[c_r,r_r]$ in both of them (these points are in pixel coordinates). For a 3D point in the real world, they ...
2
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0answers
43 views

calculating the effect of a point-spread function in the frequency domain

If my point spread function looks like: h(x) = 1, |x| <= W (where W is a positive integer) 0, |x| > W then i want to measure how it would effect the frequency content of some function f(x),...
2
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0answers
4k views

Calculate the height of a person on a picture

I am experimenting with an app to calculate the length of a person with the camera of my phone. I put my phone on the ground against the wall and make a picture. This situation is shown in the image ...
2
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0answers
184 views

What does the eigenvalue tell us?

Given an grayscale image and a position $(x,y)$ at which i've calculated the Hessian $H(x,y) = \left( \begin{matrix}I_{xx} & I_{xy} \\ I_{xy} & I_{yy} \end{matrix} \right)$, where the $I_{xx/...
2
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0answers
61 views

Reference request: Dictionary learning

I am interested in understanding more about sparsity coding and dictionary learning. I am aware of the paper that describes K-SVD. Can someone please suggest a good resource for understanding more ...
2
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0answers
61 views

SVD of Image: What do the two bases signify?

Suppose we have an image and we store its pixel array as a matrix. Then, we compute the SVD of the matrix. What do $U$ and $V$ the two bases qualitatively signify? Please let me know if I am being ...
2
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0answers
374 views

About the Mumford Shah model in image-processing

The Mumford Shah method is to find the minimal function of the following functional $$F(u,K)=\int_{\Omega\setminus K}(u-u_0)^2+\alpha\int_{\Omega\setminus K}|\nabla u|^2+\beta Length(K),$$ where $\...
2
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0answers
55 views

Change of basis from RGB to different set of colors

Color images are defined by red, green, blue (RGB) values at each pixel. What if instead I wanted to define pixel colors by orange, black, and yellow? Is there a way to change the basis of colors from ...
2
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0answers
294 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 ...
2
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0answers
291 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 ...
2
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0answers
197 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 gradients?...
2
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0answers
1k 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 ...
2
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0answers
47 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 ...
2
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0answers
314 views

Homography matrix form for decomposition

I am trying to decompose a homography matrix. I read that there are a few methods to do that (e.g. Faugeras, Zhang). But I wasn't able to produce a useful output yet. I am not sure which form my ...
2
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0answers
220 views

Understanding JPEG compression.

I have some problems in understanding a passage of the JPEG compression algorithm: Consider an $8\times8$ matrix $M$ that in our case is a "piece'' of a channel (for example the red channel $R$) of ...
2
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0answers
70 views

Distributional Representation of Perimeter in Chan-Vese

While re-implementing the classic Chan-Vese Algorithm for image segmentation, I stumbled upon the following statement, which I have problems to understand: Let $H: \mathbb{R} \to \mathbb{R}$ be the ...
2
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0answers
149 views

What is the difference between Bilinear interpolation and Bilinear filtering

I'd like to know that different between bilinear interpolation vs blinear filtering in the manner of image processing warp operation. Are those two operations are identical ? I try to sample a ...
2
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0answers
116 views

Euler Lagrange equations

I need to minimise $$\int\limits_\Omega|\nabla H_\epsilon(\phi)|\,dx\,dy$$ with respect to $\phi$. Where $H_\epsilon$ is the regularised Heaviside function, so that it is differentiable. This can be ...
2
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0answers
962 views

Area optimization: Packing rectangles inside rectangle

Background: I am scrambling to figure out the optimization algorithm to build sprite image, which is essentially a big container rectangular image, with multiple rectangular images. I have found an ...
2
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0answers
194 views

2-D DFT of a matrix PxP and 1-D DFT of a vector of size P^2?

What is the difference between the following two things: make a 2-D Discrete Fourier Transform of a certain matrix A[p,p], first reshape this matrix into a 1-D vector a[p^2,1], and compute the 1-D ...
2
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0answers
495 views

Calculating the aspect ratio of the rotated rectangle on the image

I need to determine the aspect ratio of the rectangular object (such as mobile phone or credit card) on the image. The problem is that the object might be photographed from an angle or perspective. So ...
2
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0answers
562 views

Projection Slice theorem getting rid of artifacts?

I have employed the fourier(projection) slice theorem in matlab. I have a 3D image, P(x,y,z) defines their pixel intensities at a given location int he image volume, it is discrete and uniform. I ...
2
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0answers
206 views

Singular Value Decomposition

I want to decompose an image $A$ using the Discrete Wavelet Transform and then find the singular values, $S$, such that $A=USV$. I will then do the same to another image such that $B=USV$. I will ...
2
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0answers
105 views

Intuition about moment function derivation [OR] derivatives involving a time varying integration domain

$$ m_{{pq}}(t)=\iint\limits_{R(t)}h(x,y) dx dy $$ where $ R(t)$ the domain of integration is time varying (In fact it is the only one which is time varying). And $$ h(x,y) = x^p y^q f(x,y) dx dy $...
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0answers
18 views

Haar Normalization

In the pseudo code of haar transfom provided by Wavelets for Computer Graphics. Before implementing the decomposition step, we need to divide the coefficients C by $\sqrt{h}$ for normalization. Can ...
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0answers
17 views

Pure pursuit algorithm - Transform Global to vehicle coordinates?

project: autonomous driving car I have a small RC car, a Raspberry Pi and a camera which are fixed on the car. Now I want to let the car drive autonomous with image processing. So far I can detect ...
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0answers
20 views

Matching shapes between two images

I am working on a computer vision application for Arduino using a very low resolution camera (80x80 pixels). I want to detect moving shapes. The segmentation part works fine as i managed to detect ...
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0answers
29 views

Normalizing the x,y coordinates for images of different sizes and distances

A two part question: The output from a biomechanics program provides you with the $x$-$y$ coordinates for any joint within each image of a video. However this is relative to the image size and also ...
1
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0answers
23 views

Correlation between 2 signals of uneven dimensions

As a part of my work, I am trying to correlate the audio signal in a video with the pixels of each frame. The steps I follow are: 1] Audio sampling rate and frame rate of the video are known. So, ...
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0answers
13 views

How to obtain this equation of hyperspectral image restoration using total variation in the following equation?

While reading the paper "Total-Variation-Regularized Low-Rank Matrix Factorization for Hyperspectral Image Restoration" I came through the following equation. Can someone help me how the last equation ...
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0answers
26 views

Projection of portion of equirectangular image

I am working on a project and a doubt arises when thinking on image projections. I have and equirectangular image created using a cubemap like the following: Equirectangular projection If I draw a ...
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0answers
39 views

Studying behaviour of the following differential equation

I derived the following differential equation from a problem in signal analysis. $$ 0 = f - u - \frac{1}{2\lambda}\nabla^T\cdot\left(e^{-\lVert \nabla u \rVert/\lambda} \frac{\nabla u}{\lVert \nabla ...