The usually mistaken notion is that confidence is the complete opposite of humility. But in reality, one can be both at the same time. Truth is you can't truly be humble without being confident. For it is by knowing yourself that you'll get to learn your skills and abilities. You'll know what you can do and what you can't. You will realize which things you are good at and which you are not. And thus you'll become confident of doing things you know you are capable of. And by being aware of your capability, you accept the possibility of others doing things better than you. That you can still fail on something which you are good at. Thus, you will be humbled by being aware of your own limitation. And such awareness of limitation is a part of being confident.
On the other hand, lack of self-esteem and arrogance are the two contrasting characteristics of being confident and humble respectively. Though I was able to identify the co-relation between humility and confidence, I'm not so sure how the lack of self-esteem and arrogance can be mixed up. Can you?