The linear algebra portion went by very quickly for someone who hasn't worked with them in several years. I guess this video is more tailored for current researchers?
Great vid! Quick question - it wasn't clear how many of these second-order matrices we're making. One for each patch, right? A single one for the whole image wouldn't provide us with local information. The explanation confused me a bit Also, if I understand correctly, the intuition is that the second-order matrix helps us compute the curvature of the edge in the patch. And checking the eigenvalues provides us with info on that curvature. Is my mind in the right place? 😅
Thanks! For every pixel location, we will form a second-order matrix. So yes, it's one for each patch. The eigenvalues of the second-order matrix tell us how fast the summed square error (between the reference patch and the translated patch) will go up. The eigenvectors tell us where we should move to get the fastest or the slowest error changes. So, to find a corner, we look for patches with a *large smallest eigenvalue*. This means that the error still goes up quickly, even in the direction with the slowest change. That's the criterion for good features to track.
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The linear algebra portion went by very quickly for someone who hasn't worked with them in several years. I guess this video is more tailored for current researchers?
Ah, sorry about that! I probably should slow down a bit on those math derivations. Will do so in future videos!
Great vid!
Quick question - it wasn't clear how many of these second-order matrices we're making. One for each patch, right? A single one for the whole image wouldn't provide us with local information. The explanation confused me a bit
Also, if I understand correctly, the intuition is that the second-order matrix helps us compute the curvature of the edge in the patch. And checking the eigenvalues provides us with info on that curvature. Is my mind in the right place? 😅
Thanks!
For every pixel location, we will form a second-order matrix. So yes, it's one for each patch.
The eigenvalues of the second-order matrix tell us how fast the summed square error (between the reference patch and the translated patch) will go up. The eigenvectors tell us where we should move to get the fastest or the slowest error changes. So, to find a corner, we look for patches with a *large smallest eigenvalue*. This means that the error still goes up quickly, even in the direction with the slowest change. That's the criterion for good features to track.
This looks like covariance matrix 🤔
Yes, second-moment matrix is a local covariance matrix of the gradient vector field. It captures the local image structure.