I think that wavelets were hyped in the 90s. Although the rationale behind and continous behaviour of wavelets may excite physicists and mathematicians, I think that the practical possibilities have (up until now) been quite similar to e.g. the time/frequency analysis filterbanks that have been used in e.g. electronic engineering for half a century or more.
-h
I don't know. I would agree there has been a lot of wavelet hype. However, when we image a subject, in first analysis we image 3D texture interacting with lighting: Moss, brick, clouds, water, snow, skin are not shaded solids.
Texture is not something well described by conventional geometry. An analysis of texture implies the understanding of the object under various transforms of which scale transforms seem to be part, and whether one likes it or not this is not something which Fourier does naturally. I mean, one can do it with Fourier constructions, but Fourier does not -to me at least- seem to be something that generates or analyses textures naturally. Speaking as a layman of course. I don't know whether wavelets really do it or have to be coerced - fractal methods seem to go some way there naturally, a lot of the CGI techniques are fractal-based- so it's interesting to look, to see what might be "catching the eye" when we perceive texture, and what the maths could be, and what one can then set as criteria for good texture reproduction.
One phenomenon I've noticed is that we seem to like images where the reproduction noise merges in some way with the imaged texture. This is the sort of thing which is an interaction of perception, capture technology and object geometry, and is an application that cannot be invented or predicted by mathematical theory alone.
Look, I'm not claiming I understand any of this stuff, I'm just saying that it needs to be looked at, and the methods we have been using were probably not the right ones, which is why people have been pretending that any object in a scene is an assemblage of smoothly shaded solids, and as a result many cameras yield images of people and landscapes that look as if they were ... dead assemblages of smoothly shaded solids.
I think it's time I went back and read some more of those references
Pseudo-scientific discussions are the written equivalent, I guess, of cat photographs.
Edmund