It depends on the jurisdiction. When you show up to court you typically enter your plea with the court clerk. You can plead guilty with explanation (at least in MD and Portland you can) which gives you the opportunity to plead your case to the judge. Here in Portland, the clerk looks up your record and will offer you a reduced fine if you plea guilty & it's your first offense. If you plead innocent and the cop is there then you will absolutely lose unless you've got evidence to the contrary (traffic cam picture, etc.).