Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [gradient]

46 questions
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How to Detect Gradients and Edges in Images?

I want to be able to find points in images that are the centre of a radial gradient like the one shown in the left picture below. Any ideas on how I could use a Hough transform or some other computer vision method? Thanks example search image:
waspinator
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How Does a Convolution Can Be Expressed as a Matrix Multiplication (Matrix Form)?

I know this question may not be very relevant to programming, but if I don't understand the theory behind image processing I'll never be able to implement something in practice. If I got it right Gaussian filters are convolved with an image for…
Matteo
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Shape of structuring elements for morphological gradients

I am looking to understand recommended shapes of structuring elements used in calculating morphological gradients. According to Pierre Soille: Morphological Image Analysis: Only symmetric structuring elements containing their origin are considered.…
penelope
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Gradient of Total Variation of Magnitude of Complex Function for Denoising

Say I have a complex function $f^*$ (e.g. a MRI image) that has a near piece-wise constant magnitude, but a non constant phase. If I have an optimization problem to find $f^*$ and set up an objective function with a total variation term (e.g. for…
Stiefel
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Regarding the choice of cost function in adaptive control - squared error vs absolute error

I did search the question database regarding this question, and although one or two questions came close, they didn't really address my specific question. In adaptive control based on minimizing tracking error (e.g. between plant and model), the…
docscience
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kernels to compute second order derivative of digital image

For an image $I$, its first order derivatives can be computed using several oprators, such as $$K_{sobel} = \left[ \begin{array}{ccc} -1 &0 &1 \\ -2 &0 &2 \\ -1 &0 &1 \end{array}\right]$$ $$I_{x} = I * K_{sobel},\ I_{y} = I * K_{sobel}.T$$. And to…
avocado
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Derivative of $l_1$ norm

I want to compute the following derivative with respect to $n\times1$ vector $\mathbf x$. $$g = \left\lVert \mathbf x - A \mathbf x \right\rVert_1 $$ My work: $$g = \left\lVert \mathbf x - A \mathbf x \right\rVert_1 = \sum_{i=1}^{n} \lvert x_i -…
user153245
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Banding in the derivative of a lock-in amplifier signal

I'm analysing several measurements taken with a SR830 lockin amplifier. These measurements look similar to this one. Since I'm interrested in the derivative of the signal I took the numerical difference. What I found was this. One can clearly see…
P3trus
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The Gradient / Derivative of Least Squares of 2D Image Convolution

Given the objective function: $$ \frac{1}{2} {\left\| h \ast x - y \right\|}_{2}^{2} $$ Where $ h $ is the 2D convolution kernel and $ x $ is the 2D convolution image and $ y $ is a given 2D image. What would be: $$ \frac{\mathrm{d} \frac{1}{2}…
Royi
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Derivative with respect to complex conjugate

I have a real function $C$ of a complex vector $x$. While taking the gradient of the function $C$ for minimising the same, why do we take the derivatives with respect to the complex conjugate of $x$, i.e. $\bar{x}$ and not the actual vector $x$? I…
Sal
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How Could One Accelerate the Convergence of the Least Mean Squares (LMS) Filter?

How can the convergence of an LMS filter be accelerated? Can we do better than the vanilla algorithm?
Thomas
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Compute the Second Order Derivative of Digital Image with Finite Differences

I was looking for how to compute second order derivative of an image and came across the question kernels to Compute Second Order Derivative of Digital Image. In the top voted answer, it gives an example to get $3\times 3$ kernel $I_{xx}$ and…
ciel
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What Is an Oriented Gaussian Second Derivative Filter

In the paper: Detecting and Localizing Edges Composed of Steps, Peaks and Roofs, the authors refer to an image filter as an oriented second-derivative Gaussian filter. I'm trying to figure out what this means. From my understanding a Gaussian filter…
IntegrateThis
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Use of the Sobel Filter for Image Gradient [MATLAB]

I am using the Sobel filter for an RGB image. I have found two different ways to do that and the results look a little different. What is the difference between these two methods? Method 1 sbl=fspecial('Sobel'); …
AL B
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The Mathematical Relationship Between Derivative and Convolution

What I'm looking for is the mathematical proof of why we can calculate derivatives as a simple convolution of a mask, and how do we get that mask? I know it has something to do with how the derivative is approximated Can anyone direct me to some…
Marin
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