Segmentation of endocardium in ultrasound images based on sparse representation over learned redundant dictionaries Roberto Rosas-Romero a,n , Hemant D. Tagare b a Universidad de las Américas-Puebla, Puebla 72810, Mexico b Yale University, New Haven, CT, USA article info Article history: Received 28 May 2013 Received in revised form 2 August 2013 Accepted 2 September 2013 Available online 18 October 2013 Keywords: Echocardiographic image segmentation Sparse representation Dictionary learning abstract This paper considers the problem of segmenting the endocardium in 2-D short-axis echocardiographic images from rats by using the sparse representation of feature vectors over learned dictionaries during classification. We highlight important aspects of the application of the theory of sparse representation and dictionary learning to the problem of ultrasound image segmentation. Experiments were conducted following two directions for the generation of dictionaries for myocardium and blood pool regions; by manual extraction of image patches to build untrained dictionaries and by patch extraction followed by training of dictionaries. The results obtained from different learned dictionaries are compared. During classification of an image patch, instead of using features of the patch alone, features of neighboring patches are combined. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Advancements in ultrasound transducer design, improvements in image resolution, noninvasive nature, usefulness for medical diagnosis, portability as well as economy make segmentation of ultrasound images a motivating challenge; however, ultrasound data presents characteristics (such as speckle, non-homogeneities, shadowing, low contrast, and signal dropout) that make its seg- mentation a difficult task. Noble and Boukerroui (2006) provide an extensive review of different ultrasound segmentation methods. We consider the problem of segmenting the endocardium on short-axis echocardiographic images by dividing an image in patches (Kumar and Hebert, 2006), and classifying an image patch as belong- ing to one of two classes or regions, myocardium tissue or blood pool. This problem is approached using the promising research field of dictionary learning, early addressed by Olshausen and Field (1997), with the motivation that there are no reports of echocardiographic image segmentation using the framework of dictionary learning. This research field focuses on the development of algorithms to learn dictionaries with elements, called atoms, so that a signal of interest can be decomposed as a linear combination of a few atoms. The sparse representation of a signal possesses an implicit discriminative nature by choosing the subset of atoms that give the best compact recon- struction of the signal, and discarding other representations. Modeling of signals by means of their sparse representation is a natural and fundamental concept so that it becomes a very useful tool for different applications. The solution to the problem of dictionary learning for sparse representation of images has proven to be successful in many other applications such as image denoising (Aharon et al., 2006; Elad and Aharon, 2006), compression (Marcellin et al., 2000), super-resolution (Yang et al., 2010), hand- written digit classification (Mairal et al., 2008c, 2012), face recogni- tion (Wright et al., 2009), texture segmentation and classification (Mairal et al., 2008a; Wright et al., 2010), object detection (Agarwal and Roth, 2002), color restoration (Mairal et al., 2008b). There are different research directions that could be taken to push the frontiers of knowledge in this research field (Elad, 2012). An opposite alternative to the previously mentioned synthesis- based sparse representation model for signals is the analysis- based model where an analysis dictionary is learned so that this dictionary multiplies a signal to provide the corresponding sparse code (Rubinstein and Faktor Elad, 2012). Scale-Up of an image from a down-scaled noisy version with preservation of edges and small details has been accomplished by using sparse representa- tion models and regularization (Zeyde et al., 2012). It has been shown that dictionary learning outperforms off-the-shelf fixed dictionaries for the case of denoising of astronomical images (Beckouche et al., 2013). An image has been separated into its texture and piecewise smooth components by modeling these components as sparse combination of atoms from dictionaries (Starck et al., 2005). Algorithms for multi-scale dictionary learning combine characteristics from multi-scale representation models (wavelets) and single-scale dictionaries to sparsely represent Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/engappai Engineering Applications of Artificial Intelligence 0952-1976/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engappai.2013.09.008 n Corresponding author. Tel.: þ52 222 229 26 77. E-mail addresses: Roberto.rosas@udlap.mx (R. Rosas-Romero), hemant.tagare@yale.edu (H.D. Tagare). Engineering Applications of Artificial Intelligence 29 (2014) 201–210