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Questions tagged [gradient]

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Expression related to Tellegen's theorem and signal flow graphs

I'm reading the paper "Signal Flow Graphs-Computer-Aided System Analysis and Sensitivity Calculations" by Arnold Y Lee and my question in about expression/equality (59) in the paper. The expression ...
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48 views

Is discrete cosine transform differentiable?

Is DCT differentiable? I.e. is d(DCT(x))/dx defined? I've seen a few implementations in automatic differentiation software packages, so I suppose the answer is positive, but I'm still missing a ...
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1answer
33 views

Computer Vision - Does implementation of Hough Transform for lines require a loop for angle parameter?

I am trying to understand how Hough Transform is implemented in real world applications. Consider a line with equation: $y = mx + b$ In parametric form, this line can be represented using (d, $\...
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3answers
282 views

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 $x$, ...
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1answer
663 views

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 ...
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1answer
99 views

Finding filaments in an image

I am at the moment working on images such as this one: What you see are filamentous structures / bundles. Other images coming from slightly different experiments could have more sparse / thick / ...
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1answer
286 views

how sobel edge detector as a first order derivative is turned to a 2 dim filter?

I want to know theorem behind sobel operator. basically a first order derivative is -1/2 0 1/2 . its a vector. the question is how this vector is turned to a matrix below and what was theory and ...
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1answer
250 views

Unable to understand the derivation of the update equation for LMS

I am trying to follow the derivation of the Least Mean Square https://en.wikipedia.org/wiki/Least_mean_squares_filter#Proof but I cannot get the update rule. I am stuck in the following steps and ...
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1answer
117 views

Two type of calculating R in steepest-descent modeling algorithm

I have wrote this algorithm for steepest descent: ...
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31 views

What are the methods of optimizing the well known Stochastic Gradient Tap Update Algorithm Performance?

As the Stochastic Gradient Algorithm tap update equation is: $$ w[n+1]=w[n]-\mu \bigtriangledown J(w) $$ $w$ are the filter tap weights So what are the methods for optimizing the performance of this ...
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1answer
398 views

Prewitt operator and central difference?

When taking the gradient of an image one can do $I * \begin{bmatrix}+1 \ 0 \ -1\end{bmatrix}$ (x direction). As I understand this is basically applying central differences in the x direction, $\...
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1answer
116 views

Contour sharpening: Optimal direction for derivation

Talking about sharpening a contour in an image. What's the optimal direction for derivation? What's the maximum value of derivative? I think that the optimal direction for derivation is the direction ...
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93 views

Gradient descent applying chain rule in state space setup

Trying to perform system identification in the following state-space model $$ \begin{bmatrix} x_{1}(n)\\ x_{2}(n) \\ x_{3}(n)\end{bmatrix}=\begin{bmatrix} a_{11} && a_{12} && a_{13} \\ ...
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1answer
198 views

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 ...
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484 views

Average gradient of pixels and sum of absolute diference

Studying the research paper Multidirectional Scratch Detection and Restoration in Digitized Old Images, E. Ardizzone et al., 2011: I have several questions regarding this section (5. Restoration), ...
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1answer
73 views

Is it appropriate to use Sobel operators to find the derivatives of an image?

Strictly speaking, the $x$ direction derivative should be the difference between the left and right pixel of each pixel. So, then I should be using a $1\times 3$ filter: \begin{bmatrix}-1&0&1\...
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2answers
982 views

Gradient of Total Variation (TV) Norm in Total Variation Denoising

In this link, it says that the gradient is as follow The Gradient of the TV norm is $$ \mathrm{Grad}J(f)=\mathrm{div}\left(\frac{\nabla f}{\lVert\nabla f\rVert}\right). $$ From this other link, ...
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1answer
457 views

Are the RLS filter and Kalman filter gradient methods?

I would like to extend my previous question What is difference between LMS and gradient-descent adaptation? with this other question. I found out, that RLS and Kalman filter learning seems to be ...
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113 views

Is it possible to rewrite gradient magnitude of Sobel in continuous formula?

Let $*$ denote a convolution operation, $G$ denote a kernel, and $I$ is a given image. The gradient of the image $I$ is equivalent: $\nabla (G*I) = (\nabla G) * I$ The Sobel filter approximtes two ...
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1answer
87 views

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 \...
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1answer
221 views

How to estimate filters using conjugate gradient?

An image $I$ is computed by performing convolution and summation: $$ \sum_{k=0}^{K-1} z_k * f_k = I $$ Given only the feature maps $z_k$ and the resulting image $I$, how do I compute the filters $...
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1answer
529 views

How do I compute the gradient vector of pixels in an image?

I'm trying to find the curvature of the features in an image and I was advised to calculate the gradient vector of pixels. So if the matrix below are the values from a grayscale image, how would I go ...
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1answer
104 views

Adaptive Filter Gradient Descent

The quadratic performance surface of an adaptive filter is a paraboloid. Its minimum can be found wherever the gradient is zero. However, since there are two types of paraboloids (elliptical and ...
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1answer
58 views
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1answer
143 views

Morphological gradient versus linear gradient

To obtain the gradient from an image, one can use a linear filter that for example is derrived from the derrivative of a gaussian. Then convolving the image with this linear filter gives you the ...
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84 views

How do i detect if an image has a gradient or not?

I have coloured images, some may be just clipart, some may be artwork, both could be with or without gradients. Before i run a colour counting algorithm on them, i want to detect if the image has ...
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1answer
127 views

Finding the gradient of a norm in a minimization problem

I have to find the gradient of the following term with respect to $X_{1}$: $\|\Phi\circ(X_{1}-X_{2})-u\|_F^2$ , where $u\in\mathbb{R}^{n}$; $X_{1}, X_{2}\in\mathbb{R}^{N\times J}$ and $\Phi\in\...
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742 views

Measuring spectral tilt

I have quite a few noisy signals and I want to calculate their spectral tilt over time, preferably using a method from literature. So far, I can only come up with the slope of the line between the F0 ...
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1answer
77 views

Iterative Blind Sinus Signal Suppression

There are two real signals in the form of $A_i sin(wt+p_i), i=1,2$. Suppose frequency $w$ of both the signals is the same and amplitude $A_i$ and phase $p_i$ are different. The first signal has ...
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138 views

Encoding the HOG features

I have got a video containing 200 frames and i am extracting low level features at pixel level. Then i am dividing the entire frame in to small spatial patches (say of size 7x7) and creating a feature ...
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1answer
367 views

MATLAB gradient derivative troubleshooting

I have an array $A$ having the next 145 values I would like to calculate the $\frac{dA}{dX}$, having a 1D grid, $x$: 1:286:41468 I use the function gradient: ...
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0answers
127 views

How to estimate gradient orientation?

I have a general task of discriminating images of shaded cylinders that significantly vary in 3d orientation, and almost insignificantly in size and shape. I have treated it as a regression problem ...
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2answers
8k views

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{...
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2answers
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How to compute Image Gradients?

How to compute Image gradients? In X Direction - Kernel : -1 0 1 In Y Direction - Kernel : -1 0 1 Let's assume my input image is: unsigned char* imgImage; ...
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1answer
242 views

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 ...
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3answers
14k views

How do convolutions become matrix multiplications?

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 ...
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1answer
401 views

Downsampling and Gradient filtering

Are the following sequence of operations the same - Down-sampling filtering followed by gradient filtering with kernel [-1 0 1] Gradient filtering with kernel [-1 0 1] followed by down-sampling ...
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1answer
829 views

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 ...
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3answers
1k views

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 ...
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3answers
7k views

How to detect gradients 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 ...