“…Figure 2 shows the translation of the normal vector n of point p , from the original surface to the unit sphere, where its origin coexists with the origin of the coordinate. Gaussian mapping is the name of the process, and the sphere is known as the Gaussian sphere 27 , 28 . Figure 2 Gauss map definition .…”
Alzheimer’s disease (AD) is considered one of the most spouting elderly diseases. In 2015, AD is reported the US’s sixth cause of death. Substantially, non-invasive imaging is widely employed to provide biomarkers supporting AD screening, diagnosis, and progression. In this study, Gaussian descriptors-based features are proposed to be efficient new biomarkers using Magnetic Resonance Imaging (MRI) T1-weighted images to differentiate between Alzheimer’s disease (AD), Mild Cognitive Impairment (MCI), and Normal controls (NC). Several Gaussian map-based features are extracted such as Gaussian shape operator, Gaussian curvature, and mean curvature. The aforementioned features are then introduced to the Support Vector Machine (SVM). They were, first, calculated separately for the Hippocampus and Amygdala. Followed by the fusion of the features. Moreover, Fusion of the regions before feature extraction was also employed. Alzheimer's disease Neuroimaging Initiative (ADNI) dataset, formed of 45, 55, and 65 cases for AD, MCI, and NC respectively, is appointed in this study. The shape operator feature outperformed the other features, with 74.6%, and 98.9% accuracy in the case of normal vs. abnormal, and AD vs. MCI classification respectively.
“…Figure 2 shows the translation of the normal vector n of point p , from the original surface to the unit sphere, where its origin coexists with the origin of the coordinate. Gaussian mapping is the name of the process, and the sphere is known as the Gaussian sphere 27 , 28 . Figure 2 Gauss map definition .…”
Alzheimer’s disease (AD) is considered one of the most spouting elderly diseases. In 2015, AD is reported the US’s sixth cause of death. Substantially, non-invasive imaging is widely employed to provide biomarkers supporting AD screening, diagnosis, and progression. In this study, Gaussian descriptors-based features are proposed to be efficient new biomarkers using Magnetic Resonance Imaging (MRI) T1-weighted images to differentiate between Alzheimer’s disease (AD), Mild Cognitive Impairment (MCI), and Normal controls (NC). Several Gaussian map-based features are extracted such as Gaussian shape operator, Gaussian curvature, and mean curvature. The aforementioned features are then introduced to the Support Vector Machine (SVM). They were, first, calculated separately for the Hippocampus and Amygdala. Followed by the fusion of the features. Moreover, Fusion of the regions before feature extraction was also employed. Alzheimer's disease Neuroimaging Initiative (ADNI) dataset, formed of 45, 55, and 65 cases for AD, MCI, and NC respectively, is appointed in this study. The shape operator feature outperformed the other features, with 74.6%, and 98.9% accuracy in the case of normal vs. abnormal, and AD vs. MCI classification respectively.
“…To quantitatively measure the shape similarity (or difference) between different types of the underlying lattice cells, a robust rotation based 3D shape descriptor (Pan et al, 2006) is used to computationally represent each unit cell in the form of a probability distribution curve. Minkowski L 2 norm of the distribution curves corresponding to the shape of different unit cells is computed to measure the geometric similarity between different unit cells [Figure 3(b)].…”
Section: Framework Overviewmentioning
confidence: 99%
“…In the present work, a rotation based 3D shape descriptor (Pan et al, 2006) is used to quantify shape similarity (or shape difference) of different Fourier series based defined unit cells.…”
Section: Shape Similaritymentioning
confidence: 99%
“…The periodic geometries are determined and mathematically computed by the sum of the selected sets of Fourier terms [Figure3(a)]. The mathematical modeling approach allows for simplicity in geometry alteration and automated generation of various periodic structures using only a small set of Fourier terms.To quantitatively measure the shape similarity (or difference) between different types of the underlying lattice cells, a robust rotation based 3D shape descriptor(Pan et al, 2006) is used to computationally represent each unit cell in the form of a probability distribution curve. Minkowski L 2 norm of the distribution curves corresponding to the shape of different unit cells is computed to measure the geometric similarity between different unit cells [Figure3(b)].…”
Purpose
This paper aims to clarify the relationship between mechanical behaviors and the underlying geometry of periodic cellular structures. Particularly, the answer to the following research question is investigated: Can seemingly different geometries of the repeating unit cells of periodic cellular structure result in similar functional behaviors? The study aims to cluster the geometry-functional behavior relationship into different categories.
Design/methodology/approach
Specifically, the effects of the geometry on the compressive deformation (mechanical behavior) responses of multiple standardized cubic periodic cellular structures (CPCS) at macro scales are investigated through both physical tests and finite element simulations of three-dimensional (3D) printed samples. Additionally, these multiple CPCS can be further nested into the shell of 3D models of various mechanical domain parts to demonstrate the influence of their geometries in practical applications.
Findings
The paper provides insights into how different CPCS (geometrically different unit cells) influence their compressive deformation behaviors. It suggests a standardized strategy for comparing mechanical behaviors of different CPCS.
Originality/value
This paper is the first work in the research domain to investigate if seemingly different geometries of the underlying unit cell can result in similar mechanical behaviors. It also fulfills the need to infill and lattify real functional parts with geometrically complex unit cells. Existing work mainly focused on simple shapes such as basic trusses or cubes with spherical holes.
“…The importance of a comparison of the shape of 3D objects' shape is increasing in the areas of computer vision, robotics, molecular biology, and others. The shape is usually expressed by a descriptor, which is a feature vector capturing some essence of a given shape [ 20 - 22 ]. A shape descriptor generally carries a number of desirable properties: transformation invariant, succinctness for representation, low computation expense, expressiveness of shape, etc.…”
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