2D CWT, is there frequency?

Hello, I have a question about 2D continuous wavelet transforms. Whist i have managed quite successfully to use the cwtft2 function to detect the location, scale and orientation of semi-periodic features in an image. It appears to me that there is no information about the period of these features (i.e. space (2D location), orientation AND a time (period, wavelength) discrimination). Is this correct or am I missing something here? Is there any 2D wavelet analysis that will measure the period of a feature in an image, as well as the location and the orientation?

Thank you for your time!

Answer 1

[David Ding]

Hi Chris,

For cwtft2, unfortunately the output does not directly provide the frequency information. However, there is a function called "scal2frq" (documentation attached as PDF) that would be able to convert scale information into frequency. The scale information is provided as part of the output for the cwtft2 function. I have brought to attention your use case, and in future releases of MATLAB, the development team will consider directly incorporating frequency data into "cwtft2" just as the 1-D cwt case currently.

Thanks,

David

[Chris Unsworth]

Many thanks David, this is a fantastic answer. If i understand this correctly, one can never know the frequency perfectly due to the Heisenberg uncertainty principle. You either get good approximations of scale or frequency - never both at the same time?

[David Ding]

Hi Chris,

Yes you are absolutely correct.

Thanks,

David