Extract a periodic pattern from an image in Matlab

I have a sinuous signal in my image that you watch in below image. (in other words more than one signal with it's shadow)

I want to extract this sinuous signal (such a 1d signal) and find it's duty cycle, frequency and etc. As you can see there is a lot of noisy pattern also in my image and finding threshold or finding edges did not help me to solve the problem.

Also, I want to have a automatic algorithm that have generalize for my other images such this. Therefore,I think the finding of ROI couldn't be done, because in general sinuous signal begin from different row.

What you said, is quite a project, not a question. I'd rather to study more about the similar projects and ask about some details in here. Although I could give you some hints:

1-Do a suitable thresholding on your image, like Otsu method (with a little change in the threshold value if it's needed).

2-On the binary image do an erode and a dilate successively to get rid of the small objects.

3-Do a horizontal dilation to get all parts of a curve stuck together. This gives you two firm curves.

4-Find connected components of each curve and with their prositions, find the lowest pixels (local minimum of signals)

5-Horizontal position of these local minimums, gives you the frequency.