Karthik Srinivasan on Nostr: npub10l889…eath2 Only partially so. No? I remember the Schwartz going through this ...
npub10l88929ze7h5h7g7pu7y0e0077c03zqtp9zk63zpx4gg7m2ypcnq8eath2 (npub10l8…ath2)
Only partially so. No?
I remember the Schwartz going through this problem in 780 with us. I can't find the reference in my emails, but I distinctly remember it as a paper from John Daugman... who showed with different low/bandpass filtered versions of the same image, you get these overlapping zero crossings (as the image representation), yet, you can't construct back which one is correct (when all are correct, I am using the word "correct" loosely). So, that Logan "unique" zeros condition might be an over restrictive one.
Irrespective, I think it is an important inverse problem to be solved.
I think we can reframe the Daugman critique of zero crossings in general as a primary motivation for the plemelj-schwartz-hay formulation: avoid the above issue either in the original image domain (or its equivalent hilbert transform domain), convert/extend the signal to analytical continuity, so the bands (of filters or filtered images) can be composed by simple linear superpositions of "paths" that are ultimately along a contour.
Only partially so. No?
I remember the Schwartz going through this problem in 780 with us. I can't find the reference in my emails, but I distinctly remember it as a paper from John Daugman... who showed with different low/bandpass filtered versions of the same image, you get these overlapping zero crossings (as the image representation), yet, you can't construct back which one is correct (when all are correct, I am using the word "correct" loosely). So, that Logan "unique" zeros condition might be an over restrictive one.
Irrespective, I think it is an important inverse problem to be solved.
I think we can reframe the Daugman critique of zero crossings in general as a primary motivation for the plemelj-schwartz-hay formulation: avoid the above issue either in the original image domain (or its equivalent hilbert transform domain), convert/extend the signal to analytical continuity, so the bands (of filters or filtered images) can be composed by simple linear superpositions of "paths" that are ultimately along a contour.