Example of wavelet analysis of a surface

General Usage
1

Dear all,

I would like to analysis images of surface with variable roughness in space. In practice, I would like to quantify the roughness of signals and report it on 2D maps (in the original spatial coordinates). It seems that a discrete wavelet analysis could be the ideal tool for this. If I understand well, I could report the spatial distribution of energy for different frequencies… (I am a newbie on that topic)

Does anyone know an example that does such type of analysis using Julia-based tools?
It looks like it could be done with Wavelets.jl but I failed at finding a detailed example/tutorial.

Here’s an example of a synthetic signal that may be relevant. I would expect that a wavelet analysis will be able to detect energy in high frequency range in the upper right region. And energy at low frequency in the lower-left region.

Is Wavelets.jl the appropriate tool to carry out such analysis? Is there a tutorial that I could use to get started with this?
(If not I’d be happy to progress on this example and then contribute to the docs)

    # Synthetic signal
    nx, ny = 128, 150  
    x = LinRange(0, 1.0, nx)
    y = LinRange(0, 1.0, ny)

    # Create a low frequency part in the the upper-right region
    k         = (5., 10)     # Wavenumbers
    shift     = (0.75, 0.75) # Shift
    gauss     = @. exp(-((x .- shift[1]).^2 + (y' .- shift[2]).^2) / 0.1)  # Gaussian function for varying energy
    signal_HR = @. gauss * (sin(2π * k[1] * x) + cos(2π * k[2] * y'))

    # Create a low frequency part in the the lower-left region
    k         = (2., 2)      # Wavenumbers
    shift     = (0.25, 0.25) # Shift
    gauss     = @. exp(-((x .- shift[1]).^2 + (y' .- shift[2]).^2) / 0.1)  # Gaussian function for varying energy
    signal_LR = @. gauss * (sin(2π * k[1] * x) + cos(2π * k[2] * y'))

    # Total signal
    signal = signal_LR .+ signal_HR

edit: added the image corresponding to the test signal below

image
image600×400 62.4 KB

3

This quick guide to surface roughness measurements is quite clear and defines roughness profiles using wavenumber cutoffs. Is it applicable?

4

Thanks, it’s indeed a useful resource, I didn’t know the distinction between roughness and waviness.
I would still like to analyse the data maps using 2D wavelet analysis. I have tried GPT and Claude but none of them seem to know how to operate Wavelets.jl :smiley:

5

Another common method to analyse roughness is variogram analysis. You could compute the DirectionalVariogram along directions (1, 0) and (0, 1) and then derive properties from the resulting curves.

I explain the concept in this video:

The “behavior near the origin” is what you are after.

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