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One option is to use the PCL , as suggested by NEngelhard. There's a tutorial on how to compute an oriented bounding box here. This algorithm is based on PCA (Principal Component Analysis), which works well for most "longish" objects; for more compact objects (like cubes), the computed bounding box is not optimal.

Alternatively, you could use octomap to generate a voxel map from your point cloud. It will give you a better estimate of the object's volume, and a much better approximation of its shape.