How to get which part is on the direction of a ray on 2d image?

Hi,

I have several small parts in the binary image. Besides, I define a ray based on two points. I want to get which small parts being traversed by the ray. The input is the binary image and two points to define the ray. I make a sketch map below, the ray is in red. Obviously, the part in the green circle will be get. (The origin binary map is in the attachments.) Could someone give me some hints or method to realize this goal? Thank you very much.