The construction of a three-dimensional object model from a set of images taken from different viewpoints is an important problem in computer vision. One of the simplest ways to do this is to use the silhouettes of the object (the binary classification of images into object and background) to construct a bounding volume for the object. To efficiently represent this volume, we use an octree, which represents the object as a tree of recursively subdivided cubes. We develop a new algorithm for computing the octree bounding volume from multiple silhouettes and apply it to an object rotating on a turntable in front of a stationary camera. The algorithm performs a limited amount of processing for each viewpoint and incrementally builds the volumetric model. The resulting algorithm requires less total computation than previous algorithms, runs in close to real-time, and builds a model whose resolution improves over time.