We develop an approach for the detection of ruins of livestock enclosures (LEs) in alpine areas captured by high-resolution remotely sensed images. These structures are usually of approximately rectangular shape and appear in images as faint fragmented contours in complex background. We address this problem by introducing a rectangularity feature that quantifies the degree of alignment of an optimal subset of extracted linear segments with a contour of rectangular shape. The rectangularity feature has high values not only for perfectly regular enclosures but also for ruined ones with distorted angles, fragmented walls, or even a completely missing wall. Furthermore, it has a zero value for spurious structures with less than three sides of a perceivable rectangle. We show how the detection performance can be improved by learning a linear combination of the rectangularity and size features from just a few available representative examples and a large number of negatives. Our approach allowed detection of enclosures in the Silvretta Alps that were previously unknown. A comparative performance analysis is provided. Among other features, our comparison includes the state-of-the-art features that were generated by pretrained deep convolutional neural networks (CNNs). The deep CNN features, although learned from a very different type of images, provided the basic ability to capture the visual concept of the LEs. However, our handcrafted rectangularity-size features showed considerably higher performance.