Most officers get less than six months of training.
In other countries (with much lower rates of officer involved homicides), officers receive years of training.
It is exactly perceived threat.
But they're so untrained that they perceive many things as threats that are not threats (a man with autism rocking back and forth on the ground while holding a toy firetruck, for example).
Surely, most average people's first instinct isn't approach any interaction with hand on weapons? I doubt that's due to lack of training. I think that's due to an entirely wrong sort of implicit and explicit training.
Walking around with a gun + license to kill + fostering sense of us vs them for years will probably teach you that escalation and confrontation is the way to get people to back down. So that's what you do.
By incentivizing them to take a second look at their assumptions, maybe we can make progress?
I'd say just the opposite. Normal people don't react to others this way. The violent hair trigger that cops are set on is a result of their training - they're taught to do this.
The solution is not to train them more. The solution is to change the relationship between police and the public, and train them to respect that.
Police are presently trained to shoot first, to pull out their guns first, and perhaps not formally trained for this but they're taught by at least their peers and mentors to be hostile and aggressive first.
Better training changes this. Better training fosters their membership and relationship with the community. Better training gets them to pull out their guns only when they intend to use them, not when they first pull someone over. Better training will get NYC cops to stop shooting passerbies while trying to kill suicidal people (http://www.nytimes.com/2013/12/05/nyregion/unarmed-man-is-ch...).
The present training is overly focused on violent intervention. And for the majority of police-civilian interaction no violence is intended by the civilians or needed by the police. But their mindset is entirely predicated on "be violent before they are".