Questions tagged [gaussian]

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12
votes
2answers
7k views

What is the relationship between the sigma in the Laplacian of Gaussian and the two sigmas in the Difference of Gaussians?

I understand that a Laplacian-of-Gaussian filter can be approximated by a Difference-of-Gaussians filter, and that the ratio of the two sigmas for the latter should be 1:1.6 for the best approximation....
1
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1answer
6k views

Question about Difference of Gaussian (DoG) algorithm

I am recently learning about Computer Vision and I am having a trouble understanding Difference of Gaussian (DoG) algorithm. I get how the algorithm works in high level idea, but I am trying to ...
10
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5answers
8k views

Low-pass filter parameters for image downsampling

I need to downscale an image in a factor of $s_x$ horizontally and $s_y$ vertically ($s_x$, $s_y$ < $1$). I want to use a finite $n\times m$ low-pass filter before downsampling. How should I ...
0
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1answer
591 views

FFT function of Gaussian pulse

I need gaussian pulse fft. I set the sigma of gaussian pulse 1e-10 and define the gaussian function in time and use the fft. as you know the amplitude of should be unit in frequency domain. but my ...
0
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1answer
1k views

Why/How a Gaussian Channel is both band-limited and Power limited?

All physical channels are band-limited, such that, X(f) = 0 for |f| > W A Gaussian Channel is limited in both power and bandwidth. For this reason we encounter phrases, such as, "A band-limited ...
0
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1answer
103 views

Can we decompose a correlated random variable into correlated plus uncorrelated?

Assume a random sequence $ Y_k = X_k \cdot H_k + W_k $ where $X_k$ is a deterministic quantity, $H_k$ is a correlated random sequence, $W_k$ is Additive White Gaussian random sequence. Can we ...
0
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1answer
423 views

Is there a closed form expression for noise other than white noise?

For white noise, where the PSD is constant, we can model that as a simple Gaussian. Is there any way to model the probability density function of other types of noise (pink noise, red noise, blue ...
0
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1answer
74 views

What type of sensors have complex Gaussian noise?

What type of sensors have complex Gaussian noise? Do strain gauges also exhibit such noise?
1
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0answers
133 views

Effect of Gaussian Smoothing to mean image intensity

I am implementing Perona-Malik Diffusion in using the formulas: Creating image at time k+1 using equation This is my implementation: ...
1
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1answer
47 views

How to determine stopband of discrete Gaussian, stdev sigma, support N

I would like to analyse a gaussian smoothing kernel with a set standard deviation and support (let's say, in MATLAB, fspecial('gaussian', [5 1], 1.3) so sigma is 1.3 and support is 5) in the DTFT ...
0
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0answers
56 views

Relation between Gaussian and Savitsky-Golay kernels

I would like to make a mathematical comparison between two methods in my field. One smooths with a Gaussian filter, and one smooths using a second-order Savitsky-Golay filter. Let's say the window ...
1
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2answers
288 views

imshow command for Gaussian function

I'm trying to plot 2D gaussian function using "imshow" in MATLAB. However I could not see any white points in image. I tried to change sampling values and limits of x and y values. In addition to this,...
2
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2answers
851 views

carrier frequency difference

Papers use wireless device-dependent radio-metrics as fingerprints. A radio-metric is a component of radio signal, amplitude, frequency and bandwidth. Each device creates a unique set of radio-metrics ...
3
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1answer
15k views

Fit data to Gaussian distribution

I want some data to fit the corresponding Gaussian distribution. The data is meant to be Gaussian already, but for some filtering reasons, they will not perfectly match the prescribed and expected ...
1
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1answer
301 views

Spacing between gaussian windows for STFT

I'm computing discrete short time Fourier transform. Data is split into overlapping chunks and gaussian window is used for each chunk. However, I'm not sure how much overlap there should be between ...
2
votes
2answers
4k views

Discrete approximation to Gaussian filter

One method of producing a discrete approximation kernel to a Gaussian filter of variance $\sigma^2$ is to assume a cutoff of $5\sigma$. This seems to suggest the following procedure: Create a uniform ...
0
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1answer
56 views

Different results for seperable filtering v/s direct filtering on 2-D image in MATLAB

I compared the difference between seperable and direct filtering for MATLAB's cameraman image. The difference is huge. I would like to understand the reason for this. Code below. ...
0
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5answers
23k views

noise of zero mean and variance?

It might be a very silly question, however I'm facing problem with it. Now, the Gaussian noise is a signal with zero mean and variance. I understand what the mean and the variance mean however, I'm ...
0
votes
1answer
965 views

Fixed SNR with unitary noise variance

I've just one question : How can I write a model like y = x + w,( with w a white gaussian noise) with a fixed SNR and a noise variance equal to 1. What coefficient may I have before x ? Thanks !
0
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0answers
151 views

What is purpose of correlation kernel? IIs it high pass filter or low pass filter?

I am research about correlation kernel and I have some questions that need your help. Let see the pp. 3302-3303 in the paper: Changyang Li, et al., Robust Model for Segmenting Images With/Without ...
2
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1answer
3k views

What is correlation kernel and compare with gaussian kernel

I read a paper that said about correlation kernel that defined: $$W(x-y)=(α/1+d(|y − x|))$$ where $α = (\int(1+d(y − x)dy)^{-1}$, $(d(|y − x|))$ is spatial Euclidean distance from the central pixel. ...
2
votes
1answer
415 views

Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary process in time (in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary ...
1
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1answer
703 views

Intuition behind the Gaussian Filter in Image Processing

I've been using a Gaussian Filter and know how to use it but I don't understand the physical significance behind using the filter. We use it but why? What is the significance? I'm just starting out in ...
1
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1answer
641 views

Expectation of product of Filtered White Gaussian Noise

Assume I have a random process $X(t)$ that is white gaussian noise with psd $S(f)$. Now, let's filter that noise through a LPF of bandwidth $B$. How would I evaluate the following expression: $$E[S(...
1
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2answers
1k views

Computer Vision - Gaussian Pyramid, Scale Space and Pattern Matching

I am planning to implement a pattern matching algorithm using something like correlation as a matching metric. I know that the template I am going to use will, if present, have different sizes in the ...
0
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0answers
52 views

Localization of a Gaussian

Studying for an exam I'll have I ran into a question about computing the localization of a Gaussian Filter in 1D, but sadly I have no idea of what such localization is. Can you give me a hint? ...
1
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1answer
245 views

Standard deviation of Gaussian corresponding to perfect low pass filter [1,1]

For a time discrete signal, the rect-filter (for 1D signal [1,1]) is a perfect low pass filter. I was wondering, what is the best gaussian approximation of this filter? For a current problem, I ...
0
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0answers
529 views

Constant amplitude, uniform phase - what's the distribution of the complex signal then?

The well-known relationships for zero-mean circularly-symmetric complex Gaussian $z = a + jb = |z| \exp(j\varphi)$ signals are the amplitudes $|z| = \sqrt{a^2 + b^2}$ are Rayleigh-distributed the ...
2
votes
3answers
4k views

Which sigma to use for edge detection

I know that in many edge detection algorithm the first step is choosing a scale to work on. We actually operate on the chosen scale by applying a gaussian blur on the original image. I wanted to ...
0
votes
1answer
134 views

frequency components of discrete Gaussian-windowed signal

When we are do a discrete Gabor transform on a 1D signal, we apply a Gaussian window on a segment of the signal. However, due to the tapering ends of the Gaussian window, the magnitude of the data ...
1
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0answers
57 views

Thresholding for Movement Classification

I have an application which creates a Gaussian model of the background based on consecutive frame difference and auto-generates a threshold for separating no-changes to movements. The application ...
1
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0answers
66 views

Is a Stationary VAR Process with Zero Mean Gaussian Innovations a Gaussian Stationary Process?

Consider the stationary VAR process $${\bf X}_t = \sum_{\tau = 1}^{L} A_\tau {\bf X}_{t-\tau} +{\bf \epsilon}_t$$ If the innovations $\epsilon_t \sim MVN({\bf 0},\Sigma)$ then is ${\bf X}_t$ a ...
1
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0answers
62 views

Fitting VAR Process with Generalised Gaussian Noise

Consider the $m$-dimensional VAR process $${\bf x}_t = \sum_{l=1}^{P} A_l{\bf x}_{t-l} + {\bf e}_t$$ where the componenets of ${\bf e}_t$ are spatially and temporally independent and follow a ...
0
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2answers
265 views

Calculating information loss in a signal after smoothing?

I have a signal. I applied Gaussian smoothing to it and then for baseline reduction I appied Tophat filter to the smoothed version. This is the original signal: This is the final signal: I read ...
1
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1answer
205 views

Highpass filter applied to noise

Suppose the input signal is represented as $$y=x+w$$ where $x$ is the signal to be estimated and $w$ is AWGN. I design a high pass filter $H$. What does $$H^{T}Hw$$ represent? Will it be just AWGN but ...
2
votes
2answers
270 views

Situations where complexity is too big to exceed linearity and gaussianity

I'm studing about Kalman Filter and Particle Filter in multiple target tracking in computer vision (tracking pedestrians). Reading sientific papers I'm colliding with a lot of sentences like: The ...
3
votes
1answer
7k views

What is use of a gaussian filter over histogram?

I am working in the field of digital image processing and currently i am reading this paper and I have two questions about it.... After applying a gaussian filter to a histogram, will the pixel ...
0
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1answer
1k views

gaussian kernel and bionomial coefficients

The following image is from robert collins' ppt from http://www.cse.psu.edu/~rcollins/CSE486/ How to calculate sigma ? It shows [1 4 6 4 1] is corresponding to sigma=1. I learned that usually 3*...
16
votes
3answers
6k views

How do I add AWGN to an I and Q representation of a signal?

I have a wireless communication system that I am simulating in Matlab. I am performing some watermarking through slightly adjusting the phase of the transmitted signal. My simulation takes the ...
3
votes
1answer
820 views

Determine Parameters of gaussian distribution to fit a certain Image-Filter

I'd like to know what the parameters for the two-dimensional gaussian distributions are, which create this (I think) quite common image-processing filter: $$ h_\sigma(x,y)= \left[ \matrix { 1&2&...
1
vote
1answer
85 views

Is there a need of Point interpolation before proceeding for gaussian smoothing of an incomplete distribution?

Suppose there is a distribution that has values sampled on the interval 1-25 with corresponding sample values that have to be smoothed. For example: ...
7
votes
2answers
257 views

What is the difference between a simple gaussian filter and gaussian filter multiplied by its sum of it elements?

1 2 1 1 2 1 2 4 2 (A) (1/16) * 2 4 2 (B) 1 2 1 1 2 1 Both matrices are the same ...
3
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0answers
137 views

Compensate for standard deviation loss

I am not sure if this question will be a little off-topic on this forum, that I will give it a try anyway, since it implies signal process arguments. By using ...
7
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1answer
2k views

Choice of Gaussian kernel parameters when lowpass filtering before image resampling?

I need to decimate a signal by a factor of q. More specifically my signal is a 3D "image": $\ I(x_i,y_j,z_k)$, which I need to downsample by a factor of two in the z direction. I want to do lowpass ...
5
votes
1answer
110 views

Is there a transformation filter to decode light signal through Glass Bricks?

A friend is doing renovations and getting his entire ground-floor street-side wall replaced with glass bricks. I told him that with all those bricks giving similar distorted views of the same room, ...
5
votes
2answers
4k views

Standard Deviation in Gaussian Blur

I have a function that performs gaussian blur on image for some specific $\sigma$ (the standard deviation). It first computes kernel of size $\lceil 3\sigma \rceil$ and then performs convolution with ...