We present Octopus, a learning-based model to infer the personalized 3D shape of people from a few frames (1-8) of a monocular video in which the person is moving with a reconstruction accuracy of 4 to 5mm, while being orders of magnitude faster than previous methods. From semantic segmentation images, our Octopus model reconstructs a 3D shape, including the parameters of SMPL plus clothing and hair in 10 seconds or less. The model achieves fast and accurate predictions based on two key design choices. First, by predicting shape in a canonical T-pose space, the network learns to encode the images of the person into pose-invariant latent codes, where the information is fused. Second, based on the observation that feed-forward predictions are fast but do not always align with the input images, we predict using both, bottom-up and top-down streams (one per view) allowing information to flow in both directions. Learning relies only on synthetic 3D data. Once learned, Octopus can take a variable number of frames as input, and is able to reconstruct shapes even from a single image with an accuracy of 5mm. Results on 3 different datasets demonstrate the efficacy and accuracy of our approach.