7 votes
Accepted

Metric Spaces: Why $L_\infty$ selects the maximum value

In the general case, let $x = (x_1,\dots,x_n)$ be a finite-length vector (in a finite dimensional space). The finite sequence of absolute values $|x_i|$ does attain its maximum (because the sequence ...
Laurent Duval's user avatar
5 votes
Accepted

Semantic Distance Measure Between Images

One of the most known image similarity metric is the SSIM. You can take a look to the next links: https://en.wikipedia.org/wiki/Structural_similarity https://www.imatest.com/docs/ssim/ https://www....
Arritmic's user avatar
  • 301
4 votes

Is maximizing hamming distance the same as minimizing correlation?

Two codewords $c_1$ and $c_2$ of length $n$, with elements in $\lbrace +1, -1 \rbrace$, and Hamming distance $d$, have a cross-correlation given by $$(n-d) -d = n-2d.$$ The reason is that there are $n-...
MBaz's user avatar
  • 15.3k
3 votes
Accepted

Is maximizing hamming distance the same as minimizing correlation?

Well, as you can easily verify, these two criteria aren't the same if you define "minimum correlation" to mean that the absolute value of the correlation coefficient is minimized (i.e. 0): In $\...
Marcus Müller's user avatar
2 votes
Accepted

Range Estimation Based on Distance Differences

Without loss of generality, let's define your anchor positions to be on the $x$ axis with $x_0=0$ and the gap between each position be $g$. Thus $$ x[n] = n \cdot g $$ Obviously, this can be ...
Cedron Dawg's user avatar
  • 7,560
2 votes
Accepted

Is SSIM a measure of mutual information?

...is the quality measure SSIM between two images (one base-line, one distorted) directly correlated to the mutual information between the two [?] The short answer to this is "yes" but it tells you ...
A_A's user avatar
  • 10.7k
2 votes
Accepted

What Distance Measure Is Proper for Image Patches?

Well, You're asking on one of the most researched topics. There is no single "Right" answer. Many models have been suggested and many of them works pretty well. In the Non Local Means they ...
Royi's user avatar
  • 19.6k
1 vote
Accepted

What is the condition under which the length of shortest 4-path equal to $D_4$ distance?

The $ D_4 $ distance in your definition is basically what's called the $ L_1 $ norm based distance or Manhattan Distance. It is also called Taxicab Distance or Taxicab Geometry. From its name you can ...
David's user avatar
  • 144
1 vote
Accepted

Is `xcov()` More Accurate Than `xcorr()` to Compute the Cross Correlation of Signals with Non Zero Mean Values?

When trying to measure similarity between signals we're basically building a metric. When doing so we need to ask what we want to be sensitive about. For instance, if you don't remove the DC Component ...
Royi's user avatar
  • 19.6k
1 vote

Can the colors of an image be interpreted as "virtual" Doppler effect?

Say the intensity signal at one of the color channels changes linearly from 1 to 0.5 relative to full scale when the wavelength changes by 5 nm near 580 nm, and you have a laser for illumination at ...
Olli Niemitalo's user avatar
1 vote

Can the colors of an image be interpreted as "virtual" Doppler effect?

Practically very difficult isn't it ? Speed of ordinary objects in an office environment will be so slow compared to light speed that the resulting shift in the color (wavelength) would be exremely ...
Fat32's user avatar
  • 28.2k
1 vote

Images similarity measure using Jeffrey’s Divergence (j Divergence)

According to the paper the definition is given by: All you need is to find a function which implements the Kullback Leibler Divergence and apply it twice (Will be inefficient). In MATLAB you may use <...
Royi's user avatar
  • 19.6k
1 vote

Measuring similarity between two very similar pictures

This measure really depends on how your images look like. A very basic thing would be the calculate the point-wise difference between both images and summing them up. The smaller this value is, the ...
Maximilian Matthé's user avatar
1 vote
Accepted

Gaussian weighted distance between pixel amplitudes: motivations and sources?

Maybe not an exact answer, but I'll to give a direction. What you are using is essentially an RBF-Kernel. First, it has a ready interpretation as a similarity measure (satisfies Mercer's conditions). ...
Tolga Birdal's user avatar
  • 5,465
1 vote

Metric Spaces: Why $L_\infty$ selects the maximum value

The $L_p$ norm is $$ d_p(\mathbf{x}, \mathbf{y}) \triangleq \left( \sum\limits_{i=1}^{n} |x_i - y_i|^p \right)^{\frac{1}{p}} $$ there exists a positive value that is the maximum value: $$ M \...
robert bristow-johnson's user avatar
1 vote
Accepted

Looking for pratical quantitative comparison metrics for scaled, delayed and warped Signals

I'm answering the question the way I understood it - How can one find a similarity measure which isn't sensitive to scaling and shifting. An approach could be borrowed from the Computer Vision world ...
Royi's user avatar
  • 19.6k
1 vote

What is a good distance measure for matching SIFT descriptors depending on the distribution of their noise?

For obtaining distributions or modes in your, a basic approach is to cluster the data. That will of course bias the distribution towards the metric, or in other words the distribution will be tied to ...
Tolga Birdal's user avatar
  • 5,465

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