I have a liquid bow wave that is recorded by a high-speed camera. This gives me a lot of images that I want to analyze automatically. I want to determine the outer contour of the liquid and preferably extract the coordinates of the individual pixels.

When using edge detection like canny, I run into the problem that there is an edge at the top that is caused by the drop in brightness of the lighting. Furthermore, I don't know how to delete the small edges and keep only the "main edge" for further evaluation.

To get rid of the small edges you can try to Erode an Dilate. By doing this the small gaps on the left will be filled and no edges may be found there anymore. Also you could search for the longest found edge. By combining these two approaches you should be able to resolve this problem. For more information:
https://docs.opencv.org/3.4/db/df6/tutorial_erosion_dilatation.html
For the top edge problem i have a few ideas you could try: