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.

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12 views

bwmorph(image, ‘skel’, inf) and edge(image, ‘log’, 0, 2) in matlab with same result in python

What are example of two functions in python with this result? bwmorph(image, ‘skel’, inf) and edge(image, ‘log’, 0, 2) in matlab with same result in python? My problem is that result in python not ...
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Optimal transport as a metric between two color images

I am trying to characterize a distance between two images in relation to the colors present in these images. Therefore I would like to solve Earth mover's distance/1-st Wasserstein distance with ...
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How to determine objects pixel size in an image given sensor/camera spec?

if the resolution is 1080x1920, FOV = .9, and the object is 3000 meters from the camera what is the pixel size of an object that is 3 meters diagonal? What's the general formula for solving problems ...
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Spectral norm of a difference matrix

Let $M,N\in\mathbb{N}\setminus\{1\}$ and suppose that $x\in\mathbb{R}^{M N}$. Denote $x$ by \begin{align} x = \begin{bmatrix} x_{1} \\ \vdots \\ x_{N} \\ \end{bmatrix} \end{align} where $x_{i}\in\...
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Difference in the interpretation of cross-correlation and convolution?

I'm confused on the interpretation between convolution and cross-correlation integral transforms. The convolution integral is defined as $f (t) \otimes g (t) = \int f(\tau) g(t-\tau) d\tau$ and the ...
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2D convolution of two circles

Imagine if two circles exist with definitions of $f_1(r) = circ(\frac{r}{R_1})$ and $f_2(r) = circ(\frac{r}{R_2})$ where circ is defined in a 2d dimension as: $ circ(\frac{r}{R}) = \begin{cases} 1, &...
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Remove outliers from a noisy curve

Allow me to present some images so that I may explain my problem. The images on the left contain a smooth curve surrounded by noise. Is there any approach that would help in eliminating the noise and ...
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Bspline interpolation vs Bspline transform

I saw in the internet mostly Bspline is talking about interpolation. We have some points and we can get a interpolated function from these points. But I am not sure how it works in transformation for ...
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Can a quadruple integral be simplified through 2D autocorrelation definition?

I am trying to calculate this integral $$P(l) = \int \int \int \int \langle\Psi^*(x',y',z)\Psi(x,y)\rangle \phi^*(x,y,z)\phi(x',y',z) dx' dy' dx dy, \qquad (1)$$ which corresponds to the detection ...
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How to find all points inside circle sector of 2 concentric circles in an optimized way

I have 2 concentric circles with known radiuses and sector start and end points of each circle($A, B, C, D$ and $O$ in figure is known) . I detected the circles from image. I have 2 points on the ...
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How many different hues, saturations and values are possible when converting RGB to HSV?

If we specify a colour in the RGB space, there are $2^{24}$ different colours, as R, G and B are 8 bit numbers. When a colour is converted to the HSV colour space (find the conversion formulas here ...
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How can I compute the gradient of a noiseless image?

I need to generate an image with 11x11 pixels having in the center of the image a square of 5x5 pixels, with the gray level of the background 0 and the gray level of the square is 50. I need to ...
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Comparing pixels for color difference - taking Alpha into account

Say I want to compare pixels to see how similar in color they are. This wikipedia article describes how: https://en.wikipedia.org/wiki/Color_difference it says: My question is, there not just a R,G,B ...
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How can I compute the gradient of the image function given by the compass operator?

I have an 11×11 image having in its center a 5×5 square, image it's noiseless and I don't know how to compute the gradient of the image function given by the compass operator for this image. If I ...
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CCM $3\times3$ into $4\times4$ (image processing)

Preface Color Correction Matrix (a.k.a. CCM or CMX) is applied to raw image data (before de-mosaicking, usually from a standard bayer $RGGB$ or $BGGR$ pattern) to correct for the physical ...
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How can I compute the gradient of image function of an noise-less image?

I have an $11\times11$ image having in its center a $5\times5$ square, image it's noiseless and I don't know how to compute the intensity of contour for this image. If I remember correctly, I should ...
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Harris corner detection vs. PCA

A lot of classes shows that Harris corner detector is actually PCA (example, page 5), but I'm having trouble with that since Harris doesn't have mean subtraction in the algorithm (not in the paper and ...
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Fourier Transform: Why use the Inversion of the Laplace Operator for Integration?

I came across multiple papers (e.g. here and here) where an inversion of the 2D Laplace operator $\Delta = \partial_x^2+\partial_y^2$ was obtained via Fourier transform. This was applied to obtain ...
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How can I apply math on paper to compute the intensity of the contour for an image?

I need to build the matrix for an 11x11 image having In the center of it a square of 5x5 pixels. The gray level of the background is 0 and the gray level of the square is 50. How can I compute the ...
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How can I compute the result of the intensity of edges given by the compass operator of an image?

I have an image with 11x11 pixels and in the center of the image is a square of 5x5 pixels, with the gray level of the background 0 and the gray level of the square is 50. How can I compute the result ...
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calculate HD resolutions for an image

I have an image with height=75pixels and width=75pixels (75x75). I want to calculate what the resolution for this image would be in different resolutions [480p (640x480), 720p (1280x720), and 1080p (...
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What are “vectors on the unit-sphere”?

I currently read and try to understand this paper and stumbled upon the following sentence: Given a distribution of vectors $x$ on the $d$-dimensional unit sphere, we consider a set... and later: ...
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How to add Jaccard similarity coefficients?

I have a brain image and made a segmentation of two tumors with MATLAB. I want to compare my segmentations to the ground truth, which includes both tumors. Suppose an overlap coefficient $D$ is ...
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187 views

How can I compute closure/morphology and dilution for an image using math?

Suppose we have image A and the structuring element B from figure 2. How can I compute A dilated by B and A closed(or can be called morphology) by B? How can I apply math on paper for this?
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How to compare the angles of pixels of an image in different noises?

I am working on a project that needs the angles of pixels of images. I have found the way to do it in matlab for a clean image. Now, I need to add different amounts of additive white Gaussian noise to ...
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35 views

Structure Tensor definition, what is the point?

The structure tensor is defined like this where $(G^i_x, G^i_y)$ the i’th gradient in a square area around a point. I know that structure tensors are used in image analysis - here one could use the ...
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Compute Optical Flow-based features by deriving Optical Flow components

I'm trying to understand some optical flow-based features as a pre-processing step in order to reproduce some experiments of a paper public available at https://arxiv.org/pdf/1303.6021.pdf. Suppose ...
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How to perform 2d deconvolution for the Gaussian kernel and the gradient operator?

I have an images $u \in R^{M \times N}$, a Gaussian kernel $G$ and the gradient operator $\nabla u_{i,j}=[\nabla_{x} u_{i,j},\nabla_{y} u_{i,j}] \in (R^{2})^{M \times N}$ and I need to perform 2d ...
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What is the best iterative scheme to find the solution of a linear minimization problem in image processing?

I have a linear minimization problem as, $$ \inf_u E(u)=‎ \inf_u \frac{\mu}{2} \int_{\Omega}(u-f)^{2}d\Omega+\frac{c}{2}||u||^{2}-\langle u, g \rangle, $$ where $f$ and $g$ are fixed and c is a ...
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37 views

What is the correct notation for binary digital image and dice score?

I wanted to ensure the correctness of notation regarding some concepts of digital images. If I have a binary image $X$ of width $W$ and height $H$ is the correct notation for describing image $X$: $$X ...
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Given a signal I(m,n) = a + b*m + c*n and a non linear filter e.g. median filter, find the response.

I stumbled upon this question and I can't seem to solve it correctly "Given a signal $x(n,m) = a +b{\cdot}m + c{\cdot}n $ and a filter, find the processing system response defined in a finite ...
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1answer
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Morphological Closing. Formula understanding

I am trying to do use the morphological closing operation on a greyscaled image. As I found out closing is a combination of dilation and erosion. Now I am trying to understand the formulas of dilation ...
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1answer
54 views

$\lim _{z\rightarrow -i}\dfrac{1}{z-i}=\dfrac{i}{2}$ Why this answer?

$i$ is imaginary number. I think this quiestion. $$\lim _{z\rightarrow -i}\dfrac{1}{z-i}=\dfrac{i}{2}$$ I think this answer is $-\dfrac{1}{2i}$. I don't know why this answer is $\dfrac{i}{2}$. please ...
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Derivative of Energy function for image processing - Diffusion regularisation

I'm working through a topic concerning diffusion regularisation. The following energy function is given. $$ E(\mathbf u) = (u - f)^2 + \lambda \mathbf{ |\nabla u |}^2 $$ I understand that $(u-f)^2$ is ...
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In how many components/regions does this curve divide the complex plane and how can I color them (with an algorithm)?

I am reading a book (Creating symmetry, by Frank A. Farris) on how to construct "symmetric images" or wallpaper and came across the following curve: $$\gamma(t) = \exp(it)+\frac{1}{2}\exp(...
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Interpreting mathematical notation of the perspective transform according to openCV?

Below is two notations of the camera perspective transform acording to openCV: Link:http://opencv.jp/opencv-2.1_org/py/camera_calibration_and_3d_reconstruction.html What i literally don't understand ...
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66 views

How many points needed to compute the Homography?

I'm working on a project where i'm using planar homography. As seen in the above image, every point gives two equations and since the homography matrix has 8 degree of freedom, 4 points are enough to ...
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How can I numerically solve a least square problem with L2 penalty

I want to solve a least square problem that: \begin{equation*} \text{minimize } \frac{1}{2}\|Ax-b\|_2^2 + \frac{1}{2}\lambda\|x\|_2^2 \end{equation*} From the normal equation, I have to solve the ...
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How to generate lookup table from expression

There is a Research paper on image encryption based on finite algebraic structures. They gave following method to generate lookup table ( also known as S-box). S-box which is used in the proposed ...
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Mesh / Grid undistortion

I have a image which has pincushion distortion. I know nothing about the camera parameters, e.g. focal length, etc. Distorted Image I can, using SVD (singular value decomposition), successfully ...
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Reordering multi-channel image to minimise total variation of each channel.

I have a problem related to image processing, explained below. I'm not sure if the notation is completely correct, so please edit if necessary. The problem comes from an image with multiple patterns ...
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General method for finding the basis of the image of a linear transformation

Let $f: V \rightarrow W$ be a linear transformation, and let $\mathfrak{B}_V=\{b_i\}$ be a basis of $V$. If the images of the elements of the basis $\mathfrak{B}_V=\{b_i\}$ are $\{f(b_i)\}$, then how ...
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Image and kernel of quatient map $q: V \to V / U$, $q(x)=[x]$

Find image and kernel of the quotient map $q: V \to V / U$, $q(x)=[x]$ $U$ is a subspace of a linear vector space $V$. The definition of a quotient function is below: Let $U$ be a subspace of a ...
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Correlation via FFT for different image sizes

Right now I am trying to match a small template image to a bigger one to see where the correlation is the highest. I know that I can compute this by filtering the big image with a filter comprised by ...
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How to initialize the end size of image after affine transformation

How to initialize the end size of image after affine transformation. How can i calculate them? ...
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Metrics to order patches of images (arrays of pixels) to find best fit for a canvas

I have some 100000 patches of images as three dimensional arrays 24 (height) x 24 (width) x 3 (rgb channels). I have an image acting as a canvas to which I want to insert the best matching patches. ...
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Object detection uncertainty due to camera limitations

I have a 2-D image of an object, and am using this to detect an object and estimate the object's position relative to the camera's pose (say, as a vector between the origin of the camera's coordinate ...
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24 views

How this author calculates this discrete gradient?

In this paper on page 3 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.900.2273&rep=rep1&type=pdf author gives formula for finite difference of first order The discrete gradient ...
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Perform $2D$ convolution on a $2D$ unit step function

I am stuck with the following $2D$ convolution: Consider the sequence $f$ defined by the following: $f[m,n] = \begin{cases} 1 & \text{0 ≤ m ≤ n} \\\ 0 & \text{otherwise}\\ \...
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Reducing geodesic distance

I read in a paper (on image processing) about a dealing with a graph for some processing tasks. I found something surprising in the text and could not find out that completely. The authors stated that ...

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