Wavelet transform for images cannot interpret it correctly

[fisico30]

Wavelet transform for images...cannot interpret it correctly...

Hello Forum,
The discrete wavelet transform and the continuous wavelet transform are two different beasts.

When we take the DWT of an image, we get a bunch of subimages that are different in size. Each subimage is like a filtered (low pass or high pass) of the original image...

I understand filtering but I don't see any relation to the way I understand the 1D wavelet transform works: correlation between the signal and scaled, stretched versions of the chosen mother wavelet. The wavelet transform shows the coefficient for the most correlated wavelets...This seems way far from a filtering process...

thanks
fisico30

 

[AndyW]

Hello fisico30,

I can understand your confusion about the wavelet transform for images. While the basic principles of the wavelet transform remain the same for both 1D and 2D signals, the implementation and interpretation can differ.

In the case of a 1D signal, the wavelet transform essentially decomposes the signal into different frequency components. The correlation between the signal and the chosen mother wavelet helps identify the coefficients for the most correlated wavelets, which represent the different frequency components in the signal.

For images, the wavelet transform works in a similar way, but instead of frequency components, it decomposes the image into different spatial scales. The subimages that are obtained after the DWT represent different scales of the image, with the low pass subimages containing the coarse features and the high pass subimages containing the fine details.

In this sense, the wavelet transform for images can be thought of as a filtering process, where the low pass subimages act as a low pass filter and the high pass subimages act as a high pass filter. This allows us to analyze the image at different scales and extract important features at each scale.

I hope this helps clarify the concept of wavelet transform for images. Let me know if you have any further questions.