Detecting the boundaries of objects is a key step in separating foreground objects from the background, which is useful for robotics and computer vision applications, such as object detection, recognition, and tracking. We propose a new method for detecting object boundaries using planar laser scanners (LIDARs) and, optionally, co-registered imagery. We formulate boundary detection as a classification problem, in which we estimate whether a boundary exists in the gap between two consecutive range measurements. Features derived from the LIDAR and imagery are used to train a support vector machine (SVM) classifier to label pairs of range measurements as boundary or non-boundary. We compare this approach to an existing boundary detection algorithm that uses dynamically adjusted thresholds. Experiments show that the new method performs better even when only LIDAR features are used, and additional improvement occurs when image-based features are included, too. The new algorithm performs better on difficult boundary cases, such as obliquely viewed objects.