1. A method for monitoring a surrounding region of a vehicle, the method comprising: reading in a distance image with the aid of a sensor for stereo image recording and pertaining to the surrounding region of the vehicle sensed by the sensor, the distance image being a disparity map; assigning a distance value to each pixel of the distance image based on a brightness of the corresponding pixel; selecting a cut-away portion from the distance image, the cut-away portion being selected based on a correspondence of the cut-away portion to an area of the surrounding region situated at a predefined height above a ground surface; detecting an obstacle located in the surrounding region using the distance values assigned to the pixels in the cut-away portion; ascertaining (i) a count of relevant distance values representing the distance values that are assigned to the pixels included in the cut-away portion and are allocate-able to the obstacle, and (ii) a quality of the relevant distance values that are assigned to the pixels included in the cut-away portion and are allocate-able to the object, wherein the distance values are relevant if the distance values lie within a predefined collision-relevant distance, and wherein the quality of the relevant distance values is a measure of a probability that the distance values lie within the predefined collision-relevant distance; ascertaining a value of an existence measure for an existence of the obstacle within the cut-away portion, based on the count of the relevant distance values and the quality of the relevant distance values; and implementing an emergency braking operation as a function of the value of the existence measure.