Thanks!
I'm using the sprite system from the SDK but not its collision system. It seems to be nice and fast but it only checks for rectangles and I wanted to have slopes and loops. I also don't see how you can use it with tilemaps, so I wrote my own system instead.
For tilemaps, I am associating each tile with two mathematical functions. It makes the player movement smoother than checking collision with the image mask:
I then check the functions of the tile located under/over the player to know where he should land after a jump.
And between sprites I am using hitboxes, like the SDK:
