Object parsing and segmentation from point clouds are challenging tasks because the relevant data is available only as thin structures along object boundaries or other features, and is corrupted by large amounts of noise. To handle this kind of data, flexible shape models are desired that can accurately follow the object boundaries. Popular models such as active shape and active appearance models (AAMs) lack the necessary flexibility for this task, while recent approaches such as the recursive compositional models make model simplifications to obtain computational guarantees. This paper investigates a hierarchical Bayesian model of shape and appearance in a generative setting. The input data is explained by an object parsing layer which is a deformation of a hidden principal component analysis (PCA) shape model with Gaussian prior. The paper also introduces a novel efficient inference algorithm that uses informed data-driven proposals to initialize local searches for the hidden variables. Applied to the problem of object parsing from structured point clouds such as edge detection images, the proposed approach obtains state-of-the-art parsing errors on two standard datasets without using any intensity information.