Does my xray show any signs of peri-implantitist or dental failure? (Photo)

My implant crown fell off (about 1 1/2yr old crown). I went to my dentist worried that my implant was also failing because the gum around the implant looks red, gum receded, and foil breath, but my dentist says that the implant looks fine and there is no sign of dental implant failure. Based on the xray shown below, does it look like there is any sign of infection or peri implantitis? should I have my dentist just recement the crown back?