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Image appearance cues are often used to derive object shapes, which is usually one of the key steps of image understanding tasks. However, when image appearance cues are weak or misleading, shape priors become critical to infer and refine the shape derived by these appearance cues. Effective modeling of shape priors is challenging because: 1) shape variation is complex and cannot always be modeled by a parametric probability distribution; 2) a shape instance derived from image appearance cues (input shape) may have gross errors; and 3) local details of the input shape are difficult to preserve if they are not statistically significant in the training data. In this paper we propose a novel Sparse Shape Composition model (SSC) to deal with these three challenges in a unified framework. In our method, training shapes are adaptively composed to infer/refine an input shape. The a-priori information is thus implicitly incorporated on-the-fly. Our model leverages two sparsity observations of the input shape instance: 1) the input shape can be approximately represented by a sparse linear combination of training shapes; 2) parts of the input shape may contain gross errors but such errors are usually sparse. Using L1 norm relaxation, our model is formulated as a convex optimization problem, which is solved by an efficient alternating minimization framework. Our method is extensively validated on two real world medical applications, 2D lung localization in X-ray images and 3D liver segmentation in low-dose CT scans. Compared to state-of-the-art methods, our model exhibits better performance in both studies.