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.
670 questions
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How to Correctly Apply an Affine Transform to a Grid of Overlapping Images?
I’m working with a grid where each cell contains an image with a bounding box, and adjacent images overlap. Users can click points on the grid to define source–destination point pairs, and I compute a ...
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How to turn an affine reconstruction to a metric reconstruction knowing angles?
I have an affine reconstruction of a 3d scene obtained by using the factorization algorithm (as described on chapter 18.2 of Multiple View Geometry in Computer Vision) on 3 views from affine cameras.
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Rectifying radial lens distortion
I have an image with lens distortion determined with 7 radial distortion terms $k_1$ thru $k_7$ calculated using the collinearity equation given by
where the lens distortion is given by
Since ...
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The rank of the matrix of Fourier coefficients
If I have a rank r matrix $A\in \mathbb{R}^{n\times n}$, $r<n$.
If we do a discrete fourier transform on $A$, we get $\hat{A}$.
my question is that the rank of $\hat{A}$ is still r or not.
I did ...
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Are There Segmentation Algorithms Based on Mathematical Morphology Other Than the Watershed Algorithm?
I’m a mathematics student currently working on my thesis, which focuses on implementing computational algorithms for image segmentation based on the theory of mathematical morphology. At this stage, I’...
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Transformation for Ellipse with Moving Focus Point
I am hoping that there exists a transformation as performed in this image that changes the eccentricity of an ellipse, but preserves the major axis length.
I have been spending today looking into ...
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Can matrix multiplication define rough "zero borders" in another matrix?
Imagine a grayscale image, $M$.
We know that somewhere within $M$ is a dark spot $S$ with brightness values of $0$.
Can we find the borders of $S$ using block matrix multiplication, such that the ...
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Why dominant singular values represent main character of an image?
Do Singular Value Decomposition (SVD) to an image (for simplicity we use gray-levels images, the matrix is made with gray values of pixels) and delete some smaller singular values to get a new signal ...
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Euclidean distance for RGB signal
Source: https://patentimages.storage.googleapis.com/0d/44/0f/acee7e8b5d6913/US8599269.pdf
How signal can be measure by using Euclidean distance? Given by the formula like this ones:
$\text{signal}(m, ...
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Taylor expansion of composite mapping
I'm trying to understand the derivation of equation 7 in this paper.
$\Phi_\theta^{AB}(x)$ and $\Phi_\theta^{BA}(x): \mathbb{R}^3 \to \mathbb{R}^3 $ are maps from the coordinate space of Image A to ...
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Trying to understand an algorithm for corner detection
There's a paper called "Corner detection based on tangent-to-point distance accumulation technique" that I'm trying to implement.
The basic premise of the paper is that you have a shape that ...
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Hough transformation: get line function from Hough parameters (rho, theta)
I have two an input image (256px x 256px) with a line and Hough space image (256px x 256px) with a mark where the corresponding ...
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Compressed image using SVD draws a clear line between part that's blank and part with a drawing. Why? [closed]
I'm trying to compress grayscale images using SVD. This is the original image:
Yes, there's a lot of blank space.
I then choose the x% largest singular values, perform the transformed matrices ...
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Solution of $V'(t)=AV(t)+V(t)A^T+\sigma^2I_m$, where $A$ is the discretized Neumann-Laplacian
I'm considering a PDE involving the Laplacian on $[0,1)^2$. I'm discretizing the problem using the finite difference approach. The resolution discretized Laplcian opertor $A$ with Neumann boundary ...
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Is it possible to extract the translation of an affine transformation matrix independent of rotation center and angle?
I have $2$ images rotated by $60^\circ$ to each other with different center of rotation. The here presented matrices are affine transformation matrices derived from OpenCV: https://docs.opencv.org/4.x/...
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Book Recommendation on Edge or Boundary Detection
I have recently being interested in the estimation of discontinuities or jumps from noisy signals or densities and spend some time reading "Image Processing and Jump Regression Analysis" by ...
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Numerical solution of Perona-Malik equation: How to handle the boundary properly?
In the paper Perona-Malik equation and its numerical properties, the following PDE is considered:
The $u_0$ I'm (and so is the author) interested in is given by an image and hence decomposes into ...
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Numerical Method for (Total Variation) TV Norm Minimization of Linear Combination of Matrices
I have a matrix $\mathbf{A} \in \mathbb{R}^{2000 \times 2000}$ represented in memory by an array of $2000 \times 2000$ float32 elements and I also have $10$ arrays $...
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Similarity between the mathematics used in PDEs and in image processing
Sorry if this question is a bit vague
I took a course on PDEs and learned or reviewed a lot of math revolving around Fourier transforms, convolutions, distributions, Gaussian functions, etc, all ...
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381
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Discrete Fourier Transform of the Gaussian
I encountered the following question in a Digital Image Processing examination:
Find the 2D DFT of $\frac{1}{2 \pi \sigma^2} e^{-\frac{(x - x_0)^2 + (y - y_0)^2}{2 \sigma^2}}$ where $x_0, y_0$ are ...
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What are the family of geodesics/curves between point weights/balls on an elastic sheet?
ASSUMPTIONS:
no deformation is separate, all deformations touch with at least another points deformation, i.e., no deformation is by itself.
point force preferred, but small dense balls okay too.
The ...
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Convolving an image with mean filter infinite times
I was taught in my image processing class that when a mean filter is applied infinite times on a given image, the intensity of each pixel reaches the same value. I understood this that time entirely ...
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Weighted sum of N images, which minimizes their TV norm
I have $K$ images $I_i, i\in{1 \ldots K}$ of the size $M \times N$. I wish to find weights $w_i$, s.t. $w_i \in [0,1]$ and $\sum_1^K
w_i = 1$ so that
$$|\sum_{i=1}^{K} w_i I_i|_{TV}$$
is minimal. I ...
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What is the distribution of distances between two random points in RGB space?
Suppose we pick pairs of triples from $\{ 0, 1, 2, \dots, 255\}^3$ with a uniform distribution and would like to find a closed form for the distribution of the Euclidean distances
$$ d((x_1, x_2, x_3),...
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Pinhole camera projection of 3D multivariate Gaussian
Consider a 3D Gaussian with $3\times 1$ mean $\boldsymbol \mu$ and $3\times 3$ covariance $\boldsymbol \Sigma$ (which is symmetric positive semidefinite):
$$
p(\mathbf x) = \frac{1}{\sqrt{\...
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