A Non-local Measure for Mesh Saliency via Feature Space Reduction

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed.

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An Improved Deep Residual Network Prediction Model for the Early Diagnosis of Alzheimer’s Disease

Sensors ◽

10.3390/s21124182 ◽

2021 ◽

Vol 21 (12) ◽

pp. 4182

Author(s):

Haijing Sun ◽

Anna Wang ◽

Wenhui Wang ◽

Chen Liu

Keyword(s):

Alzheimer’S Disease ◽

Alzheimer's Disease ◽

Early Diagnosis ◽

Spatial Information ◽

Feature Space ◽

Attention Mechanism ◽

Residual Network ◽

Long Distance ◽

Distance Correlation ◽

Non Local

The early diagnosis of Alzheimer’s disease (AD) can allow patients to take preventive measures before irreversible brain damage occurs. It can be seen from cross-sectional imaging studies of AD that the features of the lesion areas in AD patients, as observed by magnetic resonance imaging (MRI), show significant variation, and these features are distributed throughout the image space. Since the convolutional layer of the general convolutional neural network (CNN) cannot satisfactorily extract long-distance correlation in the feature space, a deep residual network (ResNet) model, based on spatial transformer networks (STN) and the non-local attention mechanism, is proposed in this study for the early diagnosis of AD. In this ResNet model, a new Mish activation function is selected in the ResNet-50 backbone to replace the Relu function, STN is introduced between the input layer and the improved ResNet-50 backbone, and a non-local attention mechanism is introduced between the fourth and the fifth stages of the improved ResNet-50 backbone. This ResNet model can extract more information from the layers by deepening the network structure through deep ResNet. The introduced STN can transform the spatial information in MRI images of Alzheimer’s patients into another space and retain the key information. The introduced non-local attention mechanism can find the relationship between the lesion areas and normal areas in the feature space. This model can solve the problem of local information loss in traditional CNN and can extract the long-distance correlation in feature space. The proposed method was validated using the ADNI (Alzheimer’s disease neuroimaging initiative) experimental dataset, and compared with several models. The experimental results show that the classification accuracy of the algorithm proposed in this study can reach 97.1%, the macro precision can reach 95.5%, the macro recall can reach 95.3%, and the macro F1 value can reach 95.4%. The proposed model is more effective than other algorithms.

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Efficient Image Inpainting Using Dimensional Space Reduction via Adaptive Patch-based Concept and Rank Lowering Technique

International Journal of Artificial Intelligence Tools ◽

10.1142/s0218213021500147 ◽

2021 ◽

Vol 30 (03) ◽

pp. 2150014

Author(s):

Kimia Peyvandi ◽

Farzin Yaghmaee

Keyword(s):

Dimensional Space ◽

Image Inpainting ◽

Feature Space ◽

Low Rank ◽

Target Region ◽

Original Space ◽

Space Reduction ◽

Quad Tree ◽

New Space ◽

Low Dimensional

In this paper, we present a new algorithm for image inpainting using low dimensional feature space. In our method, projecting a low dimensional space from the original space is accomplished firstly using SVD, which is named low rank component, and then the missing pixels are filled in the new space. Finally, the original image is inpainted so that adaptive patch size is considered by quad-tree based on the previous step. In our algorithm, the missing pixels in the target region are estimated twice, one in low dimension feature space and another in the original space. It is noticeable that both processes estimate the unknown pixels using patch-based idea and rank lowering concept. Experimental results of this algorithm show better consistency in comparison with state-of-the-art methods.

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