For many applications in computer vision, it is important to recover range, 3-D motion, and/or scene geometry from a sequence of images. However, there are many robot behaviors which can be achieved by extracting relevant 2-D information from the imagery and using this information directly, without recovery of such information. In this paper, we focus on two behaviors, obstacle avoidance and terrain navigation. A novel method of these two behaviors has been developed without 3-D reconstruction. This approach is often called purposive active vision. A linear relationship, plotted as a line and called a reference flow line, has been found. The difference between a plotted line and the reference flow line can be used to detect discrete obstacles above or below the reference terrain. For terrain characterization, slopes of surface regions can be calculated directly from optical flow. Some error analysis is also done. The main features of this approach are that (1) discrete obstacles are detected directly from 2-D optical flow, no 3-D reconstruction is performed; (2) terrain slopes are also calculated from 2- D optical flow; (3) knowledge about the terrain model, camera-to-ground coordinate transformation, or vehicle (or camera) motion is not required; (4) the error sources involved are reduced to a minimum, since the only information required is a component of optical flow. An initial experiment using noisy synthetic data is also included to demonstrate the applicability and robustness of the method.