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Images and matrices are 2D data structures of numbers, but that is where the similarities end. An image is more like a vector, which matrices can be applied to.
by oivey 6y ago
Images and matrices are 2D data structures of numbers, but that is where the similarities end. An image is more like a vector, which matrices can be applied to. You would never matrix multiply an image onto another vector. Still, it isn’t uncommon to visualize matrices as images.
- sjg007 6y agoWell a matrix is a collection of vectors so... I guess I somewhat agree.. You can certainly apply projections to images, I mean this is what photoshop does.
- gspr 6y ago> Well a matrix is a collection of vectors so That's like saying "a matrix is a collection of real numbers, so anything you say about one applies to the other". > You can certainly apply projections to images, I mean this is what photoshop does. This doesn't seem to refer to anything in the comment you're replying to.
- sjg007 6y agoWould you please elaborate on your last point?
- gspr 6y agoIn reply to a comment that said nothing about projections, you wrote: > You can certainly apply projections to images, I mean this is what photoshop does. What's the relationship of this to anything in the comment you replied to?
- sjg007 6y ago"You would never matrix multiply an image onto another vector."
- gspr 6y ago> "You would never matrix multiply an image onto another vector." That wasn't me. But I can still elaborate: while you can certainly consider a non-color image as a matrix, the operation of multiplying this matrix with a vector is rather meaningless. While a lot of things can be made into or viewed as matrices, a matrix is typically only meaningful as a representation of a linear map.
- ladberg 6y agoEven if you never matrix multiply with an image, it's still useful to have it in matrix form for other things like PCA/SVD.
- newen 6y agoTypical use on PCA/SVD on image, what you do is treat each image as a vector, create a matrix out of a collection of images, and then do PCA/SVD on the matrix to analyze the distribution of the images, normalize, get the eigen-images (principal components), etc.
- ladberg 6y agoYeah, in retrospect that seems like the way to do it. The toy examples I learned from in college did it on a single image split up by row, but I can’t think of a great use case for that besides some naive compression.