Spectral and Shape Analysis in Medical Imaging

The human brain may be considered as a genus-0 shape, topologically equivalent to a sphere. Various methods have been used in the past to transform the brain surface to that of a sphere using harmonic energy minimization methods used for cortical surface matching. However, very few methods have studied volumetric parameterization of the brain using a spherical embedding. Volumetric parameterization is typically used for complicated geometric problems like shape matching, morphing and isogeometric analysis. Using conformal mapping techniques, we can establish a bijective mapping between the brain and the topologically equivalent sphere. Our hypothesis is that shape analysis problems are simplified when the shape is defined in an intrinsic coordinate system. Our goal is to establish such a coordinate system for the brain. The efficacy of the method is demonstrated with a white matter clustering problem. Initial results show promise for future investigation in these parameterization technique and its application to other problems related to computational anatomy like registration and segmentation.

Alzheimer’s disease (AD) and mild cognitive impairment (MCI) are the most prevalent neurodegenerative brain diseases in elderly population. Recent studies on medical imaging and biological data have shown morphological alterations of subcortical structures in patients with these pathologies. In this work, we take advantage of these structural deformations for classification purposes. First, triangulated surface meshes are extracted from segmented hippocampus structures in MRI and point-to-point correspondences are established among population of surfaces using a spectral matching method. Then, a deep learning variational auto-encoder is applied on the vertex coordinates of the mesh models to learn the low dimensional feature representation. A multi-layer perceptrons using softmax activation is trained simultaneously to classify Alzheimer’s patients from normal subjects. Experiments on ADNI dataset demonstrate the potential of the proposed method in classification of normal individuals from early MCI (EMCI), late MCI (LMCI), and AD subjects with classification rates outperforming standard SVM based approach.

In this paper we exploit the Functional maps approach for brain classification. The functional representation of brain shapes, or their subparts, enables us to improve the detection of morphological abnormalities associated with the analyzed disease. The proposed method is based on the spectral shape paradigm that is largely used for generic geometric processing but still few exploited in the medical context. The key aspect of the Functional maps framework is that it moves the estimation of correspondences from the shape space to the functional space enhancing the potential of spectral analysis. Moreover, we propose a new kernel, called the Functional maps kernel (FM-kernel) for the Support Vector Machine (SVM) classification that is specifically designed to work on the functional space. The obtained results for bipolar disorder detection on the putamen regions are promising in comparison with other spectral-based approaches.

This paper proposes a new method for describing parenchymatous organs by the set of volumetric primitives with simple shapes. The proposed method is based on our modified Self-organizing Deformable Model (mSDM) which maps an object surface model onto a target surface with no foldovers. By extending mSDM to apply to organ volume models, the proposed method, volumetric SDM (vSDM), finds the one-to-one correspondence between the volume model and its target volume. During the mapping, vSDM preserves geometrical properties of the original model while mapping internal structures of the model onto their corresponding primitives inside of the target volume. Owing to these characteristics, vSDM enables to obtain a new volume representation of organ volume models which simultaneously (1) represents by simple primitives the shapes of the whole organ and its internal structures and (2) describes the relationship among the external surface and internal structures of the organ.

We address the challenge of variability in the definition of anatomical structures over time in a single subject, using a template-based diffeomorphic mapping algorithm to filter out inconsistencies. Shape changes are parametrized through 2D surfaces, while data attachment is specified through dense 3D images. The mapping uses two geodesic trajectories through diffeomorphism space: template to baseline, and baseline through the timeseries. We apply this algorithm to a study of atrophy in the entorhinal and surrounding cortex in patients with mild cognitive impairment, characterized by rate of change of log-volume. We compare the uncertainty in atrophy rate measured from manual segmentations, to that computed with segmentations filtered using our longitudinal method, and to that computed from FreeSurfer. Our method correlates well with manual (correlation coefficient 0.9881, and results in significantly less variability than manual (p 8.86e-05) and FreeSurfer (p 1.03e-04).

The detection of pathological changes in neurodegenerative diseases that occur before clinical onset would be of great value for identifying suitable subjects and assessing drug efficacy in trials aimed at preventing or slowing onset. Using MRI derived volumetric information, researchers have been able to detect significant differences between patients in the presymptomatic phase of neurodegenerative diseases and healthy controls. However, volumetric studies provide only a summary representation of complex morphological changes. Shape analysis has already been successfully applied to model pathological features in neurodegeneration and represents a valuable instrument to model presymptomatic anatomical changes occurring in specific brain regions.In this study we propose a computational framework to model group-wise spatio-temporal shape differences, and to statistically evaluate the effects of time and pathological components on the modeled variability. The proposed approach leverages the geodesic regression framework based on varifolds, and models the spatio-temporal shape variability via dimensionality reduction of the subject-specific “residual” transformations normalised in a common reference frame through parallel transport. The proposed approach is applied to patients with genetic variants of fronto-temporal dementia, and shows that shape differences in the posterior part of the thalamus can be observed several years before the appearance of clinical symptoms.

Scoliosis is a complex 3D deformation of the spine leading to asymmetry of the external shape of the human trunk. A clinical follow-up of this deformation is decisive for its treatment, which depends on the spinal curvature but also on the deformity’s progression over time. This paper presents a new method for longitudinal analysis of scoliotic trunks based on spectral representation of shapes combined with statistical analysis. The spectrum of the surface model is used to compute the correspondence between deformable scoliotic trunks. Spectral correspondence is combined with Canonical Correlation Analysis to do point-wise feature comparison between models. This novel combination allows us to efficiently capture within-subject shape changes to assess scoliosis progression (SP). We tested our method on 23 scoliotic patients with right thoracic curvature. Quantitative comparison with spinal measurements confirms that our method is able to identify significant changes associated with SP.

Cochlear implants can restore hearing to completely or partially deaf patients. The intervention planning can be aided by providing a patient-specific model of the inner ear. Such a model has to be built from high resolution images with accurate segmentations. Thus, a precise segmentation is required. We propose a new framework for segmentation of micro-CT cochlear images using random walks combined with a statistical shape model (SSM). The SSM allows us to constrain the less contrasted areas and ensures valid inner ear shape outputs. Additionally, a topology preservation method is proposed to avoid the leakage in the regions with no contrast.

The aim of the paper is to develop a relaxed closed form for tensor principal component analysis (PCA) for the recognition, classification, compression and retrieval of volumetric data. The tensor PCA derives the tensor Karhunen-Loève transform which compresses volumetric data, such as organs, cells in organs and microstructures in cells, preserving both the geometric and statistical properties of objects and spatial textures in the space. Furthermore, we numerically clarify that low-pass filtering after applying the multi-dimensional discrete cosine transform (DCT) efficiently approximates the data compression procedure based on tensor PCA. These orthogonal-projection-based data compression methods for three-way data is extracts outline shapes of biomedical objects such as organs and compressed expressions for the interior structures of cells.

The Corpus Callosum (CC) has been a structure of much interest in neuroimaging studies of normal brain development, schizophrenia, autism, bipolar and unipolar disorder. In this paper, we present a technique which allows us to develop a shape preservation methodology in the deformation of CC for further global and regional shape analyzes between two sample corpora callosa. Source and target CC are superpositioned individually from eleven anchor points. Source CC is deformed in order to get superpositioned onto the target CC from these anchor points and superposition operation leads other anatomical landmarks to get placed automatically in all of the regions of source CC for further deformation analysis. Region construction via quadratic Bézier curves, deformation by using Gaussian RBF and quantifying the amount of deformation via generalized Procrustes analysis are used to infer the proper parameters used in minimum deformation. Amount of deformation can be analyzed both regionally and globally.