# Tag Info

Accepted

### Why should an image be blurred using a Gaussian Kernel before downsampling?

An image "should not be blurred using a Gaussian Kernel" in general. This however can be a safe bet for a lot of basic image processing needs, and a smoothing is almost mandatory when you ...

### Why is Gaussian noise called so?

Noise is random, but like most random phenomena, it follows a certain pattern. Different patterns are given different names. Consider rolling a die. This is clearly random. Roll the die 1000 times, ...

### How to Calculate Gaussian Kernel for a Small Support Size?

Gaussian Kernel is made by using the Normal Distribution for weighing the surrounding pixel in the process of Convolution. Since we're dealing with discrete signals and we are limited to finite length ...
Accepted

### Gaussian Filter Close to Image Border

Pixels outside the image borders must be extrapolated. Now, you need to chose the model of your extrapolation. For instance, if you're working within the Discrete Fourier model a periodic ...
Accepted

### Correct way to add AWGN to a signal

Short answer 10*log(bw/fs) to take into account the oversampling operation because the awgn() function specifies the signal-to-...

### Why is random noise assumed to be normally distributed?

normal distribution (i like to call it "gaussian") remains normal after addition of normally distributed numbers. so if gaussian goes into an LTI filter, a gaussian distribution comes out. but because ...
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### How to approximate gaussian kernel for image blur

The continuous Gaussian, whatever its dimension (1D, 2D), is a very important function in signal and image processing. As most data is discrete, and filtering can be costly, it has been and still is, ...

### Gaussian Blur - Standard Deviation, Radius and Kernel Size

It turns out that the rows of Pascal's Triangle approximate a Gaussian quite nicely and have the practical advantage of having integer values whose sum is a power of 2 (we can store these values ...
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### Multi Scale Shape and Detail Enhancement from Multi Light Image Collections

What the authors meant is to create a matrix of Weights, ${U}^{\left( i, j \right)}$. It is a matrix of the size of the image. The given calculation is by the exponent of two terms (Each of them is ...

### Capacity of AWGN channel

The capacity formula $$C = 0.5 \log (1+\frac{S}{N}) \tag{1}$$ is for discrete time channel. Assuming you have a sequence of data $\left\lbrace a_n \right\rbrace$ to send out, you need an orthonormal ...

### Why is random noise assumed to be normally distributed?

I'll try to clear one possible source of confusion. If picking each sample value from a single distribution feels "not random enough", then let's try to make things "more random" by adding another ...
Accepted

### Simulating Range Bearing Sensor with MATLAB with Gaussian Noise (Generating Gaussian Colored Random Vector)

Few notes: First you should multiply the noise by the Standard Deviation (Root of the Variance for zero mean noise). You can do that by multiplying the Lower Cholesky Decomposition of matrix by a ...
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### Why Does the Odd Multiple of $\frac{\pi}{4}$ on Gaussian Cause Loss in Repeatability Under Image Rotations?

The answer boils down to 2 issues with the practical approximations of the Gaussian Kernel: Though the Gaussian Kernel is radially symmetric its discrete approximation has a rectangle support. ...
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### Decorrelating Stationary Colored Gaussian Noise -- Effect On The Desired Signal

Yes, the "Whitening" is basically filtering the signal using an LTI System. The Result would be the signal $\mathbf{s}$ filtered by the system which whitens the noise. In the framework of Matched ...

### Additive White Gaussian Noise (AWGN) and Undecimated DWT

One property of Orthogonal Transformations is that White Noise stays White (Uncorrelated) under Orthogonal Transformations (One could say it's a property of White Noise). Usually this property ...

### Parameters of Gaussian Kernel in the Context of Image Convolution

When dealing with Gaussian Blur in the Image Processing context the following holds: The Standard Deviation, $\sigma$, is sometimes called radius. I think this ...
Accepted

### How Is Laplacian of Gaussian (LoG) Implemented as Four 1D Convolutions?

I think Chris Luengo's answer is perfect. The trick is that you can calculate the 2nd derivative of the image (Using Finite Differences -> Convolution) and then blur it with Gaussian Filter. Since ...
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### The Effect of the Standard Deviation ($\sigma$) of a Gaussian Kernel when Smoothing a Gradients Image

Let's analyze it in 1D as the intuition is the same. First, let's have a look on a few different Gaussian Kernels: As expected, they are wider as the Standard Deviation (STD) increase. It means that ...