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.
Karthik Srinivasan /
npub160…76fkd
2024-03-03 07:55:34
in reply to nevent1q…ulqm
Author Public Key
npub160cfnc8ucrqhs3n85wtnhvje5v6sms4jtj0jeg9ltqxgq3meuftq776fkdPublished at
2024-03-03 07:55:34Event JSON
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"content": "nostr:npub10l88929ze7h5h7g7pu7y0e0077c03zqtp9zk63zpx4gg7m2ypcnq8eath2 \n\nOnly partially so. No? \n\nI 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. \n\nIrrespective, I think it is an important inverse problem to be solved. \n\nI 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.",
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