Geodesic Kernel Research Articles

Enhancing estimation accuracy of nonstationary hydrogeological fields via geodesic kernel-based Gaussian process regression

In this study, the combined application of the geodesic kernel and Gaussian process regression was explored to estimate nonstationary hydraulic conductivity fields in two-dimensional hydrogeological systems. Specifically, a semianalytical form of the geodesic distance based on the intrinsic geometry of the manifold was derived and used to define positive definite geodesic covariance matrices that were used for the Gaussian process regression. Furthermore, the proposed approach was applied to a series of synthetic hydraulic conductivity estimation problems. The results show that the incorporation of secondary information, such as interpretations of geophysical explorations or geological surveys, can considerably improve the accuracy of the estimation, especially in nonstationary fields. In addition, groundwater flow and solute transport simulations based on estimated hydraulic conductivity fields reveal that the accuracy of the simulation is strongly affected by the inclusion of secondary information. These results suggest that incorporating secondary information into manifold geometry can remarkably improve the accuracy of the estimation and provide new insights into the underlying structure of geological data. This proposed approach has critical implications for hydrogeological applications, such as groundwater resource management, safety assessments, and risk management strategies related to groundwater contamination.

Geodesic Kernel embedding Distribution Alignment for domain adaptation

Domain adaptation is a method to classify the new domain accurately by using the marked image of the old domain. It shows a good but a challenging application prospect in computer vision. In this article, we propose a unified and optimized problem modeling method, which is called as Geodesic Kernel embedding Distribution Alignment (GKDA). Specifically, GKDA aims to reduce the domain differences. GKDA avoids degenerated feature transformation by using geodesic kernel mapping feature, and then adjusts the weight of cross-domain instances in the process of dimensionality reduction in principle, finally, constructs a new feature to represent the difference of distribution and unrelated instances. The experiment result shows that GKDA has obvious superiority in cross-domain image recognition.

Artifact Suppression with Geodesic Kernel Filter for Defocused Images Restored by Wiener Filtering

Abstract—The Wiener-filter restoration of images degraded by defocus blur usually causes specific low frequency artifacts. In this work, we propose to suppress such low frequency artifacts with a filter based on the geodesic distance affinity. A multispectral signal model is considered and the main idea of the proposed algorithm is based on assumption that low frequency outliers and additive noise in different image channels are uncorrelated. Thus, the affinity space formed by opposite channels can be used to efficiently suppress the Wiener filter restoration artifacts. The performance of the proposed filter is analyzed and compared in terms of the PSNR accuracy.

Development of cortical shape in the human brain from 6 to 24 months of age via a novel measure of shape complexity

The quantification of local surface morphology in the human cortex is important for examining population differences as well as developmental changes in neurodegenerative or neurodevelopmental disorders. We propose a novel cortical shape measure, referred to as the ‘shape complexity index’ (SCI), that represents localized shape complexity as the difference between the observed distributions of local surface topology, as quantified by the shape index (SI) measure, to its best fitting simple topological model within a given neighborhood. We apply a relatively small, adaptive geodesic kernel to calculate the SCI. Due to the small size of the kernel, the proposed SCI measure captures fine differences of cortical shape. With this novel cortical feature, we aim to capture comparatively small local surface changes that capture a) the widening versus deepening of sulcal and gyral regions, as well as b) the emergence and development of secondary and tertiary sulci. Current cortical shape measures, such as the gyrification index (GI) or intrinsic curvature measures, investigate the cortical surface at a different scale and are less well suited to capture these particular cortical surface changes. In our experiments, the proposed SCI demonstrates higher complexity in the gyral/sulcal wall regions, lower complexity in wider gyral ridges and lowest complexity in wider sulcal fundus regions. In early postnatal brain development, our experiments show that SCI reveals a pattern of increased cortical shape complexity with age, as well as sexual dimorphisms in the insula, middle cingulate, parieto-occipital sulcal and Broca's regions. Overall, sex differences were greatest at 6months of age and were reduced at 24months, with the difference pattern switching from higher complexity in males at 6months to higher complexity in females at 24months. This is the first study of longitudinal, cortical complexity maturation and sex differences, in the early postnatal period from 6 to 24months of age with fine scale, cortical shape measures. These results provide information that complement previous studies of gyrification index in early brain development.

Shape index distribution based local surface complexity applied to the human cortex.

The quantification of local surface complexity in the human cortex has shown to be of interest in investigating population differences as well as developmental changes in neurodegenerative or neurodevelopment diseases. We propose a novel assessment method that represents local complexity as the difference between the observed distributions of local surface topology to its best-fit basic topology model within a given local neighborhood. This distribution difference is estimated via Earth Move Distance (EMD) over the histogram within the local neighborhood of the surface topology quantified via the Shape Index (SI) measure. The EMD scores have a range from simple complexity (0.0), which indicates a consistent local surface topology, up to high complexity (1.0), which indicates a highly variable local surface topology. The basic topology models are categorized as 9 geometric situation modeling situations such as crowns, ridges and fundi of cortical gyro and sulci. We apply a geodesic kernel to calculate the local SI histrogram distribution within a given region. In our experiments, we obtained the results of local complexity that shows generally higher complexity in the gyral/sulcal wall regions and lower complexity in some gyral ridges and lowest complexity in sulcal fundus areas. In addition, we show expected, preliminary results of increased surface complexity across most of the cortical surface within the first years of postnatal life, hypothesized to be due to the changes such as development of sulcal pits.

Poster #261 A PROSPECTIVE STUDY OF FACTORS ASSOCIATED TO READMISSIONS IN ADULT SCHIZOPHRENIC PATIENTS DISCHARGED FROM A SHORT-SAY PSYCHIATRIC INPATIENT UNIT OF A UNIVERSITY GENERAL HOSPITAL

The quantification of local surface morphology in the human cortex is important for examining population differences as well as developmental changes in neurodegenerative or neurodevelopmental disorders. We propose a novel cortical shape measure, referred to as the ‘shape complexity index’ (SCI), that represents localized shape complexity as the difference between the observed distributions of local surface topology, as quantified by the shape index (SI) measure, to its best fitting simple topological model within a given neighborhood. We apply a relatively small, adaptive geodesic kernel to calculate the SCI. Due to the small size of the kernel, the proposed SCI measure captures fine differences of cortical shape. With this novel cortical feature, we aim to capture comparatively small local surface changes that capture a) the widening versus deepening of sulcal and gyral regions, as well as b) the emergence and development of secondary and tertiary sulci. Current cortical shape measures, such as the gyrification index (GI) or intrinsic curvature measures, investigate the cortical surface at a different scale and are less well suited to capture these particular cortical surface changes. In our experiments, the proposed SCI demonstrates higher complexity in the gyral/sulcal wall regions, lower complexity in wider gyral ridges and lowest complexity in wider sulcal fundus regions. In early postnatal brain development, our experiments show that SCI reveals a pattern of increased cortical shape complexity with age, as well as sexual dimorphisms in the insula, middle cingulate, parieto-occipital sulcal and Broca's regions. Overall, sex differences were greatest at 6 months of age and were reduced at 24 months, with the difference pattern switching from higher complexity in males at 6 months to higher complexity in females at 24 months. This is the first study of longitudinal, cortical complexity maturation and sex differences, in the early postnatal period from 6 to 24 months of age with fine scale, cortical shape measures. These results provide information that complement previous studies of gyrification index in early brain development.