Deformable segmentation via sparse representation and dictionary learning Shaoting Zhang a , Yiqiang Zhan b,⇑ , Dimitris N. Metaxas a a Department of Computer Science, Rutgers University, Piscataway, NJ, USA b Syngo R&D, Siemens Healthcare, Malvern, PA, USA article info Article history: Received 21 January 2012 Received in revised form 4 July 2012 Accepted 27 July 2012 Available online 23 August 2012 Keywords: Shape prior Segmentation Sparse representation Dictionary learning Mesh partitioning abstract ‘‘Shape’’ and ‘‘appearance’’, the two pillars of a deformable model, complement each other in object seg- mentation. In many medical imaging applications, while the low-level appearance information is weak or mis-leading, shape priors play a more important role to guide a correct segmentation, thanks to the strong shape characteristics of biological structures. Recently a novel shape prior modeling method has been proposed based on sparse learning theory. Instead of learning a generative shape model, shape priors are incorporated on-the-fly through the sparse shape composition (SSC). SSC is robust to non- Gaussian errors and still preserves individual shape characteristics even when such characteristics is not statistically significant. Although it seems straightforward to incorporate SSC into a deformable segmentation framework as shape priors, the large-scale sparse optimization of SSC has low runtime efficiency, which cannot satisfy clinical requirements. In this paper, we design two strategies to decrease the computational complexity of SSC, making a robust, accurate and efficient deformable segmentation system. (1) When the shape repository contains a large number of instances, which is often the case in 2D problems, K-SVD is used to learn a more compact but still informative shape dictionary. (2) If the derived shape instance has a large number of vertices, which often appears in 3D problems, an affinity propagation method is used to partition the surface into small sub-regions, on which the sparse shape composition is performed locally. Both strategies dramatically decrease the scale of the sparse optimization problem and hence speed up the algorithm. Our method is applied on a diverse set of biomedical image analysis problems. Compared to the original SSC, these two newly-proposed modules not only significant reduce the com- putational complexity, but also improve the overall accuracy. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction In various applications of medical image segmentation, deform- able models have achieved tremendous success, thanks to the com- bined use of shape and appearance characteristics. While appearance features provide low level clues of organ boundaries, shapes impose high level knowledge to infer and refine deformable models. However, in some medical image analysis problems, appearance cues are relatively weaker or even misleading. In those cases, the best ‘‘guess’’ of the organ boundaries can only come from shape priors, which should be effectively modeled from training shapes. Effective shape modeling faces the following challenges, (1) shape variations are complex and cannot always be modeled by a parametric probability distribution; (2) a shape instance de- rived from image appearance cues (input shape) may have gross errors; and (3) the local details of the input shape are difficult to preserve if they are not statistically significant in the training data. Traditional deformable model, e.g., Active Shape Model (Cootes et al., 1995), as well as its extensions (Heimann and Meinzer, 2009; Nahed et al., 2006), cannot tackle them in a uniform way. (More detailed reviews are presented in Section 2.1.) Recently, a new non-parametric method has been proposed to tackle these three challenges in a unified framework (Zhang et al., 2011a, 2012). Instead of using any parametric model of shape statistics, this method incorporates shape priors on-the-fly through sparse shape composition. More specifically, there are two general sparsity observations: (1) given a large shape repository of an or- gan, a shape instance of the same organ can be approximated by the composition of a sparse set of instances in the repository; and (2) gross errors from local appearance cues might exist but these errors are sparse in spatial space. This setting shows three major advantages: (1) General: There is no assumption of a para- metric distribution model (e.g., a unimodal distribution assump- tion in ASM), which facilitates the modeling of complex shape statistics. (2) Robust: Since it explicitly models gross errors, erro- neous information from appearance cues can be effectively de- tected and removed. (3) Comprehensive: It exploits information from all training shapes. Thus it is able to recover detail informa- tion even if the detail is not statistically significant in training data. 1361-8415/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.media.2012.07.007 ⇑ Corresponding author. Tel.: +1 610 574 1968. E-mail address: yiqiang@gmail.com (Y. Zhan). Medical Image Analysis 16 (2012) 1385–1396 Contents lists available at SciVerse ScienceDirect Medical Image Analysis journal homepage: www.elsevier.com/locate/media