Automated Tumor Segmentation using Kernel Sparse Representations Jayaraman J. Thiagarajan, Deepta Rajan, Karthikeyan Natesan Ramamurthy, David Frakes and Andreas Spanias SenSIP Center and Industry Consortium, School of ECEE, Arizona State University, Tempe, AZ, USA 85287. Abstract— In this paper, we describe a pixel based approach for automated segmentation of tumor components from MR images. Sparse coding with data-adapted dictionaries has been successfully employed in several image recovery and vision problems. Since it is trivial to obtain sparse codes for pixel values, we propose to consider their non-linear similarities to perform kernel sparse coding in a high dimensional feature space. We develop the kernel K-lines clustering procedure for inferring kernel dictionaries and use the kernel sparse codes to determine if a pixel belongs to a tumorous region. By incorporating spatial locality information of the pixels, contiguous tumor regions can be efficiently identified. A low complexity segmentation approach, which allows the user to initialize the tumor region, is also presented. Results show that both of the proposed approaches lead to accurate tumor identification with a low false positive rate, when compared to manual segmentation by an expert. Index Terms—MRI, tumor segmentation, sparse representa- tions, kernel methods I. I NTRODUCTION A robust method to automatically segment a medical image into its constituent heterogeneous regions can be an extremely valuable tool for clinical diagnosis and disease modeling. Given a reasonably large data set, performing manual seg- mentation is not a practical approach. Brain tumor detection and segmentation have been of interest to researchers over the recent years and currently, there exists no comprehensive algorithm built and adopted in the clinical setting [1]. Although patient scans can be obtained using different imaging modali- ties, Magnetic Resonance Imaging (MRI) has been commonly adopted for brain imaging over other modalities because of its non-invasive and non-ionizing nature, and ability for direct multi-plane imaging. Tumors may be malignant or benign as determined by a biopsy, and are known to affect brain symmetry and cause damages to the surrounding brain tissues. Automated tumor segmentation approaches are often challenged by the vari- ability in size, shape and location of the tumor, the high degree of similarity in the pixel intensities between normal and abnormal brain tissue regions, and the intensity variations of identical tissues across volumes. As a result, unsupervised thresholding techniques have not been very successful in accurate tumor segmentation [2]. Furthermore, approaches that incorporate prior knowledge of the normal brain from atlases require accurate non-rigid registration [3], [4], and hence generating adequate segmentation results potentially calls for user-intervention and/or a patient specific training system. In addition, these methods require elaborate pre-processing and they tend to over-estimate the tumor volume. Approaches for tumor segmentation can be either region- based or pixel based. The active contours method [5] is a widely adopted region-based approach that is usually com- bined with a level-set evolution for convergence to a region of interest [6]. However, it is sensitive to the contour initial- ization, and has a high computational cost due to its iterative nature. Model-based approaches [7] employ geometric priors to extend the Expectation Maximization (EM) algorithm to augment statistical classification. In relatively homogeneous cases such as low grade gliomas, the outlier detection frame- work proposed by Prastawa et al. [2], [8] was shown to perform well. Pixel based approaches such as Fuzzy C-Means (FCM) using neighborhood labels [9], Conditional Random Fields [10], Bayesian model-aware affinities extending the SWA algorithm [1], and the more recent graph-based techniques combined with Cellular-Automata (CA) algorithm [11] have also achieved some success in tumor segmentation. However, processing issues with respect to contour initialization, noise reduction, intensity standardization, cluster selection, spatial registration, and the need for accurate manual seed-selection leaves substantial room for improvement. In addition, building a robust automated approach that does not require user in- tervention is very important, particularly for processing large datasets. In this paper, we propose a novel pixel based segmen- tation technique to automatically segment enhancing/active and necrotic tumor components from T1-weighted contrast- enhanced MR images. The success of sparse coding and dictio- nary learning in several image reconstruction applications has motivated us to apply them in the tumor segmentation problem. Sparse coding is typically performed on image patches or feature vectors, and it is trivial to obtain codes for pixel intensities, since they are one-dimensional. Hence we propose to perform kernel sparse coding, an approach where the codes for pixels are obtained using non-linear similarities measured between them in a high dimensional feature space. Further- more, we develop the kernel K-lines clustering algorithm to learn kernel dictionaries for coding the pixels. We also describe two different approaches for incorporating spatial locality information of the pixels to localize the active tumor regions. Finally, we present a semi-automated segmentation technique for improved computational efficiency, wherein the