Grey Felt Hat

I think I may be a distant relative of the Grey Felt Hat in this painting. The Hat is resting on the head of the dude who painted this self portrait in 1887. It is in the Van Gogh Museum in Amsterdam. The dude painted another self portrait in the same year with a Straw Hat. I think these Hats could be cousins. Since I am also a straw hat, I wonder if the Straw Hat is my ancestor...