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We describe a computational architecture of a collision early-warning system for vehicles and other principals. Early-warnings allow drivers to make good judgments and to avoid emergency stopping or dangerous maneuvering. With many principals (vehicles, pedestrians, bicyclists, etc.) coexisting in a dense intersection, it is difficult to predict, even a few seconds in advance, since there are many possible scenarios. It is a major challenge to manage computational resources and human attention resources so that only the more plausible collisions are tracked, and of those, only the most critical collisions prompt warnings to drivers. In this paper, we propose a two-stage collision risk assessment process, including the following: 1) a preliminary assessment via simple efficient geometric computations, which thoroughly considers surrounding principals and identifies likely potential accidents, and 2) a specialized assessment that computes more accurate collision probabilities via sophisticated statistical inference. The whole process delivers an expected utility assessment to available user interfaces (UIs), allowing the UIs to make discriminating choices of when to warn drivers or other principals.