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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.

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Meaning of <a,b> symbol

I am reading some lecture notes about image science and active contours, and I come across the following: $J_1(c)=\int_a^b\left|\frac{\partial c}{\partial q}(t,q)\right|^2dq + \int_a^b g^2(|\nabla I(...
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Image Stitching using Homography Matrix

I'm currently working on an assignment where I have to take two images of the same object taken at different angles and stitch them to create a panorama - image mosaicing. I have already computed the ...
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How to Create a Homography Matrix in Matlab from n Pairs of Points?

I'm trying to create a homography matrix using the procedure shown below within Matlab: However, I'm having trouble actually coding it. I don't want to use SVD if possible and I'm not allowed to use ...
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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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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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Transform $\beta^* = \arg \min_\beta \|\beta \ \ln H -\ln J\|^2_2 +\lambda\|\nabla \beta\|^2_2$ to standard linear equation

I am struggling with transforming this eq. $$\beta^* = \arg \min_\beta \|\beta \ \ln H -\ln J\|^2_2 +\lambda\|\nabla \beta\|^2_2$$ to standard linear equation. I have looked into several papers that ...
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28 views

Need help understanding an equation: composition, addition and inverse

I have found an interesting paper on a digital image registration algorithm. There are many equations in the paper that I only understand partially, but there is a particular one I would like to ...
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12 views

Minimization in Chan-Vese convex relation model

I am working on an assignment with the Chan-Vese convex relaxation model for two-phase image segmentation, i.e., coming up with two regions — the object and the background. Specifically, I need to ...
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21 views

Cost function: minimizing algebraic error vs minimizing geometric/statiscal error (Simple Words)

Can anybody explain the differences between algebraic error and geometric error in image processing? I am trying to understand DLT (direct linear transform) algorithm to calculate homography that ...
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36 views

how to improve Normalized cross correlation

I used the Normal cross correlation (NCC) calculation to find an equation between two signals or images. now I'm trying to improve the calculations but have no idea. I just need a little improvement. ...
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18 views

How can I calculate the GPS coordinate of an object in an image using the distance, angle and GPS coordinate of the center of the image in python? Ask

I'm trying to find the GPS location of an object within an aerial image at an altitude of 10m. I already have the GPS coordinates of the image itself (center) and the distance between the center and ...
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0answers
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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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1answer
62 views

Numerical Implementation: Solution for the Euler Lagrange Equation Of the Rudin Osher Fatemi (ROF) Total Variation Denoising Model

I am watching some wonderful videos on Variational Methods in Image Processing, and the presenter talks about how variational methods are used to de-blur or denoise images, as well as other ...
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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 ...
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1answer
20 views

What is the resulting $\sigma$ after applying successive gaussian blur?

From Wikipedia Gaussian Blur it said that Applying multiple, successive Gaussian blurs to an image has the same effect as applying a single, larger Gaussian blur, whose radius is the square root of ...
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Permutative Constraint on Image Approximation

Motivation I am trying to explore the idea of constraining the approximation of an image represented by an $m$-by-$n$ matrix $A$ by the values on a linearly-spaced interval of $mn$ elements $L$ ...
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14 views

Insert new control points over an image

I'm trying to make an automatic non-rigid image registration using B-Splines as a deformation model, but I'm having some problems: Initially, I put a few control points (5x5), and after a long time, ...
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1answer
24 views

How to transform the given function to be defined in another range?

I have the following weighting function: $$ w(\rho) = k \cdot(\rho^\alpha)\cdot(1-\rho)^\beta,$$ where $\rho$ represents a pixel value expressed as a double, i.e., ...
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28 views

Iterative gaussian convolution and decimation when the decimation/convolution ratios are not divisible by two?

I have a bit of a mathematics problem. I have an image $I_1$ that I have previously blurred (from an image $I_0$) with a Gaussian of standard deviation $\sigma_1$. I would like to blur image $I_1$ ...
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1answer
26 views

Images Aspect Ratio

How to change the aspect ratio of an image while maintaining its area? I would like to know the math behind it because I can't make any sense of it. Example: image with $h = 128$, $w = 128$, area $= ...
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1answer
134 views

Recovering original image from its edges

Suppose we read an image $X$ with $1\times P$ dimensions (a single row and $P$ columns) and apply to it the simplest edge detector, that calculates the horizontal derivative say, $F = [1, 0, −1]$ to ...
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1answer
44 views

What does this equation imply?

I am reading a paper on seam carving to implement, and got stuck in understanding the convention used in the equation below. 1) I understand, $\{ ( x ( i ) , i ) \} _ { i = 1 } ^ { n } , \text { s.t....
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2answers
48 views

How to complete a noisy perspective rectangle?

I have an image of a rectangle that is noisy (perspective image). I know the value of $x$, $y$, and angle $3$. Angles "$2$" and "$4$" are not accurate. Also, I know the real rectangle size. The angle ...
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9 views

Delta function representation for kernel decompositioning

Can anyone explain to me what is meant by Delta function representation for kernel (for instance a PSF) decompositioning and how you do this kind of decompositioning?
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1answer
27 views

Intuition or interpretation of the first term of the Mumford Shah functional in image processing

I was hoping someone could explain the intuition behind the first term of the Mumford-Shah functional, used in image segmentation problems. I have been watching an interesting video series on ...
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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 ...
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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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Comparing lacunarity vs. normalized lacunarity

Background: I'm computing lacunarity plots of binary images for a project. The lacunarity plot is basically the plot of lacunarity on the y axis with box sizes on the x axis. For reference. Lacunarity ...
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1answer
38 views

What does it mean to multiply two sine waves together

Suppose I have a wave pool with two sources, A and B. The two sources both produce sine waves of the same frequency, and the sources are separated by a distance of the period of the wave. So they ...
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1answer
26 views

Why averaging filter work?

To smooth an image we use often use a 3 by 3 matrix of ones divided by the average or mean filter Intuitively I understand that we take the average gray levels value so there will be no "high" or "low"...
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3answers
44 views

Fast Fourier Transform algoritm - simple explanation(step by step)

I can't find step by step explanation of the FFT algorithm. Why it is faster than common DFT? As I understand, we calculate DFT for $X$, and for $Y$, then merge them and got the final DFT.
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12 views

Using SVD to generate a transformation for calibration

Given the problem of trying to find a transformation matrix from one camera to another on a vehicle in a calibration room with the usual checkerboard floor and walls, we can capture images from both ...
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3answers
37 views

Resizing and scaling image

I'm trying to resize image bitmap in software development, in that my requirement is as following, Get the original height of image Get the original width of image Set a max threshold, output height ...
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2answers
23 views

Is histogram “function” linear?

I was ask to prove/disprove if for two given images $f_1(x,y)$ and $f_2(x,y)$ the histogram of $f_1(x,y)-f_2(x,y)$ and $h_1-h_2$ are equal, where $h_i$ is the histogram of image i. Intuitively it ...
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1answer
26 views

How do we find first order estimate of the given entropy of the following image

What is the solution for this answer? Should we use log base 2 in the formula?
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1answer
53 views

Application of topology in image processing

I've been reading through "topological vector spaces" lately. I've realized some of the notation usually used resemble the definition of some morphological operators usually defined in image analysis. ...
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0answers
24 views

Perspective Mappings Between Quadrilaterals

Given a quadrilateral represented by $(X_n, Y_n)\;$ I would like to obtain a specific point $\;(A, B)\;$ in the same quadrilateral when it changes perspective knowing only the vertex $\;(X'_j, Y'_j)\;$...
2
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1answer
65 views

Why is the Mean Square Error (MSE) used in the Peak Signal-to-Noise Ratio (PSNR) calculation rather than the Root Mean Square Error (RMSE)?

Peak signal-to-noise ratio (PSNR) is calculated with $$\text{PSNR} = 10 \log \frac{\;\text{MAX}^2}{\text{MSE}}\;,$$ with MSE the mean square error and MAX the maximum signal value. Why is the MSE ...
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2answers
59 views

Curve between 0 and 1 for contrast filtering

I was editing an image by increasing the contrast. For this I used the formula $(\tanh(\mathtt{CONTRAST\_FACTOR}*(x-0.5))+1)/2$ This formula has limits at 0 and 1, with y=0.5 at x=0.5. The problem ...
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1answer
57 views

Finding arrays of pixels perpendicular to a derivative

I have a question that I originally posted to Stackoverflow, but got no answers, and was encouraged to re-post here. I am developing a method for “straightening” binary-masks of pictures of carrot ...
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2answers
33 views

Filter that gives the max change in matrix value

I have a 3x3 matrix, I want to find the maximum change in value that any one element in the vector has with the centre element (given that this element has the opposite sign to the centre element). ...
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(...
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2answers
52 views

Is there a way to write the convolution form of a derivative?

In image filtering and computer simulations, derivatives can be applied to a image by performing a convolution of the image/data with an appropriate kernel matrix. For example, in 1D this could be $ ...
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1answer
49 views

Histogram equalization - Contrast (gray value) distribution using transforming function

I am looking for some guidance and explanation to be able to solve this exercise. I understand that I have to come up with a function T(x) such that h(x) becomes H(x) and then with a U(x) which ...
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0answers
12 views

Calculation of a point coordination from a camera

May you please help me how can I calculate the point A's coordination if the camera is placed in B side (ideal and with a focus distance of 2CM) Please see this image I've tried using the matrix ...
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0answers
67 views

How can I solve Image matrix homography?

I have a problem. I couldn't understand this question. I know homography formula. I implemented this formula for zero level of first image pyramid but I couldn't get second image pyramid points at ...
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0answers
12 views

log-likelihood applied to classification of image histograms

I have a reference histogram of an 8-bit image, and histograms of multiple test cases for which i'm trying to determine if they belong to the same reference class. If I understand the procedure, for ...
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0answers
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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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1answer
33 views

What is the definition in contrast-invariant?

I came across this "texture analysis" technique in a paper called "Identifying structural complexity in aeromagnetic data: An image analysis approach to greenfields gold exploration" by E. Holden et ...
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1answer
152 views

Minimizing Dirichlet energy defined on a open curve

As extension of this question, I was wondering what would be the Euler-Lagrange equations associated with the functional $$ E(u) = \frac{1}{2}\int_{\gamma} \lVert \nabla u \rVert^2 ds $$ The ...