ABSTRACT
The above method is fast, but favors the horizontal and vertical directions; "if you want a subband that is oriented at 30 degrees (instead of 0 or 90) you are out of luck," says Ted Adelson of MIT. If the goal is analysis rather than image compression, than it's desirable to forego this computational simplicity and to use a transform in which wavelets can be oriented in any direction. This makes for a special kind of "mathematical microscope." As J. C. van den Berg writes in Wavelets in Physics, "a real-world microscope is not more sensitive in one direction than in another one.. . . But the mathematical microscope as embodied in twodimensional wavelets has an extra feature: these wavelets can be designed in such a way that they are directionally selective. Apart from dilation and translation, one can now also rotate the wavelet."
