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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 ...
15k 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 ...
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 ...
865 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 ...
207 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 ...
95 views

633 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 $x$, ...
1k 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, ...
110 views

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 ...
114 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 ...
376 views

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: ...
170 views

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 ...
92 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\...
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; ...
344 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 ...
544 views

122 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 ...
223 views

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 ...
437 views

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 ...
18 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 ...
132 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 / ...
127 views

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

I have wrote this algorithm for steepest descent: ...
100 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} \\ ...
557 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), ...
134 views

### Writing the 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 ...
96 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 ...
810 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 ...