Surface shape analysis with an application to brain surface asymmetry in schizophrenia

Hyperbolic Wasserstein Distance for Shape Indexing

Shape space is an active research topic in computer vision and medical imaging fields. The distance defined in a shape space may provide a simple and refined index to represent a unique shape. This work studies the Wasserstein space and proposes a novel framework to compute the Wasserstein distance between general topological surfaces by integrating hyperbolic Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram algorithms. The resulting hyperbolic Wasserstein distance can intrinsically measure the similarity between general topological surfaces. Our proposed algorithms are theoretically rigorous and practically efficient. It has the potential to be a powerful tool for 3D shape indexing research. We tested our algorithm with human face classification and Alzheimer's disease (AD) progression tracking studies. Experimental results demonstrated that our work may provide a succinct and effective shape index.

Discrimination surfaces with application to region-specific brain asymmetry analysis

Discrimination surfaces are here introduced as a diagnostic tool for localizing brain regions where discrimination between diseased and nondiseased participants is higher. To estimate discrimination surfaces, we introduce a Mann-Whitney type of statistic for random fields and present large-sample results characterizing its asymptotic behavior. Simulation results demonstrate that our estimator accurately recovers the true surface and corresponding interval of maximal discrimination. The empirical analysis suggests that in the anterior region of the brain, schizophrenic patients tend to present lower local asymmetry scores in comparison with participants in the control group.

Putative structural neuroimaging endophenotypes in schizophrenia: a comprehensive review of the current evidence

The genetic contribution to schizophrenia etiopathogenesis is underscored by the fact that the best predictor of developing schizophrenia is having an affected first-degree relative, which increases lifetime risk by tenfold, as well as the observation that when both parents are affected, the risk of schizophrenia increases to approximately 50%, compared with 1% in the general population. The search to elucidate the complex genetic architecture of schizophrenia has employed various approaches, including twin and family studies to examine co-aggregation of brain abnormalities, studies on genetic linkage and studies using genome-wide association to identify genetic variations associated with schizophrenia. ‘Endophenotypes’, or ‘intermediate phenotypes’, are potentially narrower constructs of genetic risk. Hypothetically, they are intermediate in the pathway between genetic variation and clinical phenotypes and can supposedly be implemented to assist in the identification of genetic diathesis for schizophrenia and, possibly, in redefining clinical phenomenology.

Neurological imaging: statistics behind the pictures

Neurological imaging represents a powerful paradigm for investigation of brain structure, physiology and function across different scales. The diverse phenotypes and significant normal and pathological brain variability demand reliable and efficient statistical methodologies to model, analyze and interpret raw neurological images and derived geometric information from these images. The validity, reproducibility and power of any statistical brain map require appropriate inference on large cohorts, significant community validation, and multidisciplinary collaborations between physicians, engineers and statisticians.