Man-made objects, such as chairs, often have very large shape variations, making it challenging to detect them. In this work we investigate the task of finding particular object shapes from a single depth image. We tackle this task by exploiting the inherently low dimensionality in the object shape variations, which we discover and encode as a compact shape space. Starting from any collection of 3D models, we first train a low dimensional Gaussian Process Latent Variable Shape Space. We then sample this space, effectively producing infinite amounts of shape variations, which are used for training. Additionally, to support fast and accurate inference, we improve the standard 3D object category proposal generation pipeline by applying a shallow convolutional neural network-based filtering stage. This combination leads to considerable improvements for proposal generation, in both speed and accuracy. We compare our full system to previous state-of-the-art approaches, on four different shape classes, and show a clear improvement.