We propose a new method for free space detection and description for Advanced Driver Assistance Systems (ADAS) and autonomous vehicles. The detection is based on successive morphological image processing steps that are applied to an occupancy grid map-based environment representation acquired by an automotive radar sensor. The boundary of the found free space segment is traced and serves as a virtual measurement for a time-variant Kalman Filter in order to estimate and track the control points of a two-dimensional B-spline closed free space contour over time. In contrast to existing free space detection methods, the proposed solution incorporates knowledge about the vehicle’s dimensions and does not exclude free space that is not directly in the line of sight, but mapped beforehand, as well as free space behind obstacles. Furthermore, the algorithm shows advantages in terms of an intuitive control over spatial and temporal smoothness of the solution as well as an inherent robustness due to model-based filtering. Moreover, the control points of the B-spline curve are proposed as a new low-dimensional representation of drivable free space of arbitrary shape. The effectiveness of the algorithm is demonstrated in real traffic scenarios.