1. A method comprising: identifying, using one or more computing devices, an object along a road, wherein the object is represented by a bounding box; projecting, using the one or more computing devices, a set of obstacle points within the bounding box corresponding to the identified object; identifying, using the one or more computing devices, a two-dimensional plane oriented perpendicular to a direction of movement of the vehicle; determining, using the one or more computing devices, which areas of the two-dimensional plane are occupied based on the set of obstacle points to generate a contour of the identified object; determining, using the one or more computing devices, a height profile of the identified object using the contour of the identified object; identifying, using the one or more computing devices, a height profile of the vehicle including a set of lateral distances from a center of the vehicle to a side of the vehicle at a plurality of different height measurements; and determining, using the one or more computing devices, a minimum clearance based on the height profile of the identified object and the height profile of the vehicle.