The technology relates to controlling a vehicle in an autonomous driving mode. For instance, sensor data identifying an object in an environment of the vehicle may be received. A grid including a plurality of cells may be projected around the object. For each given one of the plurality of cells, a likelihood that the object will enter the given one within a period of time into the future is predicted. A contour is generated based on the predicted likelihoods. The vehicle is then controlled in the autonomous driving mode in order to avoid an area within the contour.