RAMI ZEWAIL AND AHMED HAG-ELSAFI: MULTISCALE SPARSE APPEARANCE MODELING AND SIMULATION OF PATHOLOGICAL DEFORMATIONS DOI: 10.21917/ijivp.2017.0225 1596 MULTISCALE SPARSE APPEARANCE MODELING AND SIMULATION OF PATHOLOGICAL DEFORMATIONS Rami Zewail and Ahmed Hag-ElSafi Smart Empower Innovation Labs Inc., Canada Abstract Machine learning and statistical modeling techniques has drawn much interest within the medical imaging research community. However, clinically-relevant modeling of anatomical structures continues to be a challenging task. This paper presents a novel method for multiscale sparse appearance modeling in medical images with application to simulation of pathological deformations in X-ray images of human spine. The proposed appearance model benefits from the non-linear approximation power of Contourlets and its ability to capture higher order singularities to achieve a sparse representation while preserving the accuracy of the statistical model. Independent Component Analysis is used to extract statistical independent modes of variations from the sparse Contourlet-based domain. The new model is then used to simulate clinically-relevant pathological deformations in radiographic images. Keywords: Appearance Model, Contourlet, Sparsity, Independent Component Analysis, Pathology Deformations 1. INTRODUCTION Within the field of medical imaging, machine learning and statistical modeling have drawn much attention in a wide range of applications. Examples include: computer-aided diagnosis, segmentation, registration, and surgical planning. However, specificity and generalizability continues to be two major challenges in statistical modeling and learning approaches in medical imaging. This is partly due to noise in the images, complexity of the anatomical structures of interest, and higher resolution of medical images. Lately, in the era of Big Data, this challenge has even escalated where there is an increasing demand for efficient modeling and analyzing of high resolution medical images and large scale of biomedical data in general. As a response to these renewed challenges, concepts of sparse representation and sparse learning have been drawing much attention lately within the medical imaging research community. In the machine learning paradigm, statistical appearance models fall under the category of Generative models. Generative models are often used in medical imaging to provide constrained solutions for various complex ill-posed problems. Over the last decade, the concept of sparsity of representation and its applications in computer vision has been gaining an increased interest from the research community. In the medical imaging paradigm, sparsity techniques have been used in applications such as image enhancement, segmentation, quantification of diseases. Despite being a promising approach, this continues to be a challenging task due to the complexity of anatomical structures, and scarcity of training sets with ground truth data. In this paper, we first present a novel method for localized sparse modeling of texture variability in medical images with application to simulation of pathological deformations in medical x-ray images of human spine. The proposed appearance model is based upon Contourlet transform and Independent Component Analysis (CTICA-AM). Contourlet transform is inherently suited for representation of higher order singularities in medical images. This is due to the multi-scale, directionality and anisotropy of Contourlet basis functions. Localized texture modes of variation are then captured using ICA modeling in the compressed Contourlet domain. The proposed appearance model benefits from the non-linear approximation power of Contourlets to achieve high data reduction rates while preserving the accuracy of the statistical model. This is particularly important in modeling high resolution images. Next, we present a general framework for simulation of various pathological deformations in x-ray images of human spine. Within the medical imaging community, this is particularly important due to the sacristy of ground truth data. Ground truth data is needed for a number of tasks such as: validation of segmentation and registration algorithms, and improving the training phase in statistical models. The proposed appearance simulation framework makes use of the new proposed sparse appearance model, along with the multi-scale shape model presented in [24]. The rest of the paper is organized as follows: Section 2 covers some of the related work in literature. Section 3.1 presents the details of the proposed Multiscale Sparse Appearance Model. Section 3.2 describes a general image framework for generation of spine x-ray images with simulated pathological deformations. Experiments and results are presented in section 4. Finally, conclusions are drawn in section 5. 2. RELATED WORK Since the introduction of Active Appearance Models, in [1], modeling of texture appearance in medical images has been predominantly performed using Principle Component Analysis (PCA) basis functions. In order to overcome limitations of Active Appearance Models, a number of researchers suggested different methods to impose locality in appearance modeling. Roberts and Cootes, [2], proposed a method to capture localized texture variations using linked active appearance models. Delac et al. [3], proposed a statistical appearance model using Independent Component Analysis (ICA). The model is used for face recognition. In [4], Zhang et al. presented a method for modeling human faces with parameterized local shape morphing. In [5], Mikkel Stegmann et al. presented a method for sparse modeling of landmark and texture variability using the Orthomax criteria. The model generates localized shape and texture variations. In [6], Wolstenholme and Taylor proposed using Haar-based wavelet compression in Active Appearance Models. A compression ratio of 20:1 was accomplished while maintaining acceptable accuracy of the model. In [7], Stegman and Cootes extended the work in