# Questions tagged [gradient]

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### Measures of edge image continuity and connectivity

Suppose I have a scalar image $I:\mathbb{Z}_{1,m} \times \mathbb{Z}_{1,n}\rightarrow [0,1]\subset \mathbb{R}$, where $\mathbb{Z}_{1,m} = \{1,\ldots, m\}$. (For instance, computed as the (scaled) ...
3answers
65 views

### Calculating the numerical gradient of a volume in one direction at a time

I want to calculate the gradient of an image volume in one direction at a time. Using the built-in function of Matlab gradient() I can get the ...
1answer
120 views

### Optimal trade-off between oversampling and filter length

For some sampling-frequency-preserving operations on Nyquist–Shannon sampled signals, such as: a shift a.k.a. translation, and differentiation by applying a derivative filter a.k.a. gradient filter, ...
2answers
37 views

### The Gradient 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. ...
3answers
7k views

### 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 ...
1answer
177 views

### Morphological Gradient Versus Linear Gradient in Image Processing

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 ...
2answers
12k views

### 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; ...
1answer
126 views

### Is discrete cosine transform differentiable?

Is DCT differentiable? I.e. is $\frac{\mathrm{d}\mathrm{DCT}(x)}{\mathrm{d} x}$ defined? I've seen a few implementations in automatic differentiation software packages, so I suppose the answer is ...
1answer
127 views

### Two type of calculating R in steepest-descent modeling algorithm

I have wrote this algorithm for steepest descent: ...
0answers
19 views

### What is meant by peak value of gradient magnitude?

I am trying to write MATLAB code for the research paper entitled Echocardiography Image Enhancement Using Adaptive Fractional Order Derivatives. The two thresholds are given by a=(peak+min(Gmag))/2 ...
0answers
19 views

### 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 ...
1answer
208 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 ...
1answer
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1answer
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### 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 ...
1answer
110 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 ...
1answer
1k 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 ...
1answer
870 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 ...
2answers
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### 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, ...
1answer
135 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 / ...
1answer
619 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 ...
1answer
358 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 ...
1answer
554 views

2answers
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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{...
1answer
267 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 ...
0answers
98 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 ...
0answers
822 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 ...
0answers
148 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 ...
1answer
377 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: ...
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 ...
0answers
130 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 ...
1answer
439 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 ...