Landmark-based spherical quasi-conformal mapping for hippocampal surface registration.

Background: The cognitive decline induced by Alzheimer's disease (AD) is closely related to changes in hippocampal structure captured by magnetic resonance imaging (MRI). To accurately analyze the morphological changes of the hippocampus induced by AD, it is necessary to establish a one-to-one surface correspondence to compare the morphological measurements across different hippocampal surfaces. However, most existing landmark-based registration methods cannot satisfy both landmark matching and diffeomorphism under large deformations. To address these challenges, we propose a landmark-based spherical registration method via quasi-conformal mapping to establish a one-to-one correspondence between different hippocampal surfaces. Methods: In our approach, we use the eigen-graph of the hippocampal surface to extract the intrinsic and unified landmarks of all the hippocampal surfaces and then realize the parameterization process from the hippocampal surface to a unit sphere according to the barycentric coordinate theory and the triangular mesh optimization algorithm. Finally, through the local stereographic projection, the alignment of the landmarks is achieved based on the quasi-conformal mapping on a two-dimensional (2D) plane under the constraints of Beltrami coefficients which can effectively control the topology distortion. Results: We verified the proposed registration method on real hippocampus data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database and created AD and normal control (NC) groups. Our registration algorithm achieved an area distortion index (ADI) of 0.4362e-4±0.7800e-5 in the AD group and 0.5671e-4±0.602e-5 in the NC group, and it achieved an angle distortion index (Eangle) of 0.6407±0.0258 in the AD group and 0.6271±0.0194 in the NC group. The accuracy of support vector machine (SVM) classification for the AD vs. NC groups based on the morphological features extracted from the registered hippocampal surfaces reached 94.2%. Conclusions: This landmark-based spherical quasi-conformal mapping for hippocampal surface registration algorithm can maintain precise alignment of the landmarks and bijectivity in the presence of large deformation.

Developing univariate neurodegeneration biomarkers with low-rank and sparse subspace decomposition.

Cognitive decline due to Alzheimer's disease (AD) is closely associated with brain structure alterations captured by structural magnetic resonance imaging (sMRI). It supports the validity to develop sMRI-based univariate neurodegeneration biomarkers (UNB). However, existing UNB work either fails to model large group variances or does not capture AD dementia (ADD) induced changes. We propose a novel low-rank and sparse subspace decomposition method capable of stably quantifying the morphological changes induced by ADD. Specifically, we propose a numerically efficient rank minimization mechanism to extract group common structure and impose regularization constraints to encode the original 3D morphometry connectivity. Further, we generate regions-of-interest (ROI) with group difference study between common subspaces of Aß+AD and Aß-cognitively unimpaired (CU) groups. A univariate morphometry index (UMI) is constructed from these ROIs by summarizing individual morphological characteristics weighted by normalized difference between Aß+AD and Aß-CU groups. We use hippocampal surface radial distance feature to compute the UMIs and validate our work in the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort. With hippocampal UMIs, the estimated minimum sample sizes needed to detect a 25% reduction in the mean annual change with 80% power and two-tailed P=0.05are 116, 279 and 387 for the longitudinal Aß+AD, Aß+mild cognitive impairment (MCI) and Aß+CU groups, respectively. Additionally, for MCI patients, UMIs well correlate with hazard ratio of conversion to AD (4.3, 95% CI = 2.3-8.2) within 18 months. Our experimental results outperform traditional hippocampal volume measures and suggest the application of UMI as a potential UNB.

Cortical thickness computation by solving tetrahedron-based harmonic field.

Cortical thickness computation in magnetic resonance imaging (MRI) is an important method to study the brain morphological changes induced by neurodegenerative diseases. This paper presents an algorithm of thickness measurement based on a volumetric Laplacian operator (VLO), which is able to capture accurately the geometric information of brain images. The proposed algorithm is a novel three-step method: 1) The rule of parity and the shrinkage strategy are combined to detect and fix the intersection error regions between the cortical surface meshes separated by FreeSurfer software and the tetrahedral mesh is constructed which reflects the original morphological features of the cerebral cortex, 2) VLO and finite element method are combined to compute the temperature distribution in the cerebral cortex under the Dirichlet boundary conditions, and 3) the thermal gradient line is determined based on the constructed local isothermal surfaces and linear geometric interpolation results. Combined with half-face data storage structure, the cortical thickness can be computed accurately and effectively from the length of each gradient line. With the obtained thickness, we set experiments to study the group differences among groups of Alzheimer's disease (AD, N = 110), mild cognitive impairment (MCI, N = 101) and healthy control people (CTL, N = 128) by statistical analysis. The results show that the q-value associated with the group differences is 0.0458 between AD and CTL, 0.0371 between MCI and CTL, and 0.0044 between AD and MCI. Practical tests demonstrate that the algorithm of thickness measurement has high efficiency and is generic to be applied to various biological structures that have internal and external surfaces.

Fast discrete cross-modal hashing with semantic consistency.

Supervised cross-modal hashing has attracted widespread concentrations for large-scale retrieval task due to its promising retrieval performance. However, most existing works suffer from some of following issues. Firstly, most of them only leverage the pair-wise similarity matrix to learn hash codes, which may result in class information loss. Secondly, the pair-wise similarity matrix generally lead to high computing complexity and memory cost. Thirdly, most of them relax the discrete constraints during optimization, which generally results in large cumulative quantization error and consequent inferior hash codes. To address above problems, we present a Fast Discrete Cross-modal Hashing method in this paper, FDCH for short. Specifically, it firstly leverages both class labels and the pair-wise similarity matrix to learn a sharing Hamming space where the semantic consistency can be better preserved. Then we propose an asymmetric hash codes learning model to avoid the challenging issue of symmetric matrix factorization. Finally, an effective and efficient discrete optimal scheme is designed to generate discrete hash codes directly, and the computing complexity and memory cost caused by the pair-wise similarity matrix are reduced from O(n2) to O(n), where n denotes the size of training set. Extensive experiments conducted on three real world datasets highlight the superiority of FDCH compared with several cross-modal hashing methods and demonstrate its effectiveness and efficiency.

A novel cortical thickness estimation method based on volumetric Laplace-Beltrami operator and heat kernel.

Cortical thickness estimation in magnetic resonance imaging (MRI) is an important technique for research on brain development and neurodegenerative diseases. This paper presents a heat kernel based cortical thickness estimation algorithm, which is driven by the graph spectrum and the heat kernel theory, to capture the gray matter geometry information from the in vivo brain magnetic resonance (MR) images. First, we construct a tetrahedral mesh that matches the MR images and reflects the inherent geometric characteristics. Second, the harmonic field is computed by the volumetric Laplace-Beltrami operator and the direction of the steamline is obtained by tracing the maximum heat transfer probability based on the heat kernel diffusion. Thereby we can calculate the cortical thickness information between the point on the pial and white matter surfaces. The new method relies on intrinsic brain geometry structure and the computation is robust and accurate. To validate our algorithm, we apply it to study the thickness differences associated with Alzheimer's disease (AD) and mild cognitive impairment (MCI) on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. Our preliminary experimental results on 151 subjects (51 AD, 45 MCI, 55 controls) show that the new algorithm may successfully detect statistically significant difference among patients of AD, MCI and healthy control subjects. Our computational framework is efficient and very general. It has the potential to be used for thickness estimation on any biological structures with clearly defined inner and outer surfaces.