Detecting primitives, like lines and planes, is a popular first step for the interpretation of range images. Real scenes are, however, often cluttered and range measurements are noisy, such that the detection of pure lines and planes is unreliable. In this paper, we propose a new primitive that combines properties of planes and lines: Linear Plane Borders (LPB). These are planar stripes of a certain width that are delineated at one side by a linear edge (i.e. depth discontinuity). The design of this primitive is motivated by the contours of many man-made objects. We extend the J-Linkage algorithm to robustly detect multiple LPBs in range images from noisy sensors. We validated our method using qualitative and quantitative experiments with real scenes.