著作 |
名稱 | Some problems related to the sigma_k Yamabe problem |
年度 | 2011 |
類別 | 期刊論文 |
摘要 | In this thesis, we study the boundary-blow-up problem for the negative k-Ricci equations in bounded domains of R^n. By adopting the method of Loewner-Nirenberg for the scalar curvature, we generalize their results to the negative k-Ricci equations. When k 1; 2; and n, the necessary condition for the existence of the solutions satisfying the k-Ricci equations is that the codimension of the portion of boundary has to be bounded from above by some constants depending on n and k. For other cases, we believe that the similar argument can be developed. |
關鍵字 | Yamabe, conformal metric, |
名稱 | The Liouville Property forPseudoharmonic Maps with Finite Dirichlet Energy |
年度 | 2014 |
類別 | 期刊論文 |
摘要 | In this paper, we first derive the CR Bochner formula and the CR Katos inequality for pseudoharmonic maps. Secondly, by applying the CR Bochner formula and the CR Katos inequality we are able to prove the Liouville property for pseudoharmonic maps with finite Dirichlet energy in a complete (2n+1)-pseudohermitian manifold. This is served as CR analogue to the Liouville theorem for harmonic maps in Riemannian Geometry. |
關鍵字 | CR Bochner formula, CR Katos inequality, Dirichlet energy, Heisenberg group, Liouville property, pseudoharmonic map, pseudohermitian manifold, pseudohermitian Ricci tensor, pseudohermitian torsion, subhessian, sub-Laplacian |
名稱 | Applications of integral geometry to geometric properties of sets in the 3D-Heisenberg group |
年度 | 2016 |
類別 | 期刊論文 |
摘要 | By studying the group of rigid motions,PSH(1), in the 3D-Heisenberg group H1, we define density and a measure in the set of horizontal lines. We show that the volume of a convex domainD⊂H1is equal to the integral of the length of chords of all horizontal lines intersecting D. As in classical integral geometry, we also define the kinematic density for PSH(1)and show that the measure of all segments with length`intersecting a convex domainD⊂H1can be represented by the p-area of the boundary ∂D, the volume of D,and2`. Both results show the relationship between geometric probability and the natural geometric quantity in [10] derived by using variational methods. The probability that a line segment be contained in a convex domain is obtained as an application of our results. |
關鍵字 | Heisenberg Group; kinematic formula; Integral Geometry; CR-manifolds; method of moving frame |
名稱 | An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group |
年度 | 2017 |
類別 | 期刊論文 |
摘要 | We show the fundamental theorems of curves and surfaces in the 3-dimensional Heisenberg group and find a complete set of invariants for curves and surfaces respectively. The proofs are based on Cartans method of moving frames and Lie group theory. As an application of the main theorems, a Crofton-type formula is proved in terms of p-area which naturally arises from the variation of volume. The application makes a connection between CR geometry and integral geometry. |
關鍵字 | CR manifolds; Heisenberg groups; moving frames. |
名稱 | The differential geometry of curves in the Heisenberg groups |
年度 | 2018 |
類別 | 期刊論文 |
摘要 | We study the horizontally regular curves in the Heisenberg groups H_n. We prove a fundamental theorem for curves in H_n and define the order of horizontally regular curves. We also show that the curve γ is of order k if and only if, up to a Heisenberg rigid motion, γ lies in H_k but not in H_{k-1} ; moreover, two curves with the same order differ in a rigid motion if and only if they have the same invariants: p-curvatures and contact normality. Thus, combining these results with our previous work [3] we get a complete classification of horizontally regular curves in H_n for n>1. |
關鍵字 | |
名稱 | Automatic surface area and volume prediction on ellipsoidal ham using deep learning |
年度 | 2019 |
類別 | 期刊論文 |
摘要 | This article presents novel methods to predict the surface area and volume of ham through a camera. By doing so, conventional methods of obtaining volume through measuring weight can be neglected, as they are not very economically effective. Both the surface area and volume are obtained in the following two ways: manually and automatically. The former is assumed as the true or exact measurement and the latter is done through a computer vision technique together with some geometrical analysis that includes mathematically‐derived functions. For the automatic implementation, most of the existing approaches extract the features of the food material based on handcrafted features and to the best of our knowledge, this is the first attempt to estimate the surface area and volume of ham with deep learning features. We address the estimation task with a Mask Region‐based CNN (Mask R‐CNN) approach, which will perform the ham detection and semantic segmentation from a video. The experimental results demonstrate that the algorithm proposed is robust and promising as surface area and volume estimation are obtained from two angles of the ellipsoidal ham (i.e., horizontal and vertical positions). Specifically, when the ham is measured from a vertical angle, the overall accuracy achieved is up to 95% whereas from the horizontal angle, accuracy is around 80%. |
關鍵字 | |
名稱 | OFF-ApexNet on micro-expression recognition system |
年度 | 2019 |
類別 | 期刊論文 |
摘要 | When a person attempts to conceal an emotion, the genuine emotion is manifest as a micro-expression. Exploration of automatic facial micro-expression recognition systems is relatively new in the computer vision domain. This is due to the difficulty in implementing optimal feature extraction methods to cope with the subtlety and brief motion characteristics of the expression. Most of the existing approaches extract the subtle facial movements based on hand-crafted features. In this paper, we address the micro-expression recognition task with a convolutional neural network (CNN) architecture, which well integrates the features extracted from each video. We introduce the Optical Flow Features from Apex frame Network (OFF-ApexNet). This is a new feature descriptor that combines the optical flow guided context with the CNN. Firstly, we obtain the location of the apex frame from each video sequence as it portrays the highest intensity of facial motion among all frames. Then, the optical flow information are attained from the apex frame and a reference frame (i.e., onset frame). Finally, the optical flow features are fed into a pre-designed CNN model for further feature enhancement as well as to carry out the expression classification. To evaluate the effectiveness of OFF-ApexNet method, comprehensive evaluations are conducted on three public spontaneous micro-expression datasets (i.e., SMIC, CASME II and SAMM). The promising recognition result suggests that the proposed method can optimally describe the significant micro-expression details. In particular, we report that, in a multi-database with leave-one-subject-out cross-validation (LOSOCV) experimental protocol, the recognition performance reaches 74.60% of recognition accuracy and F-measure of 71.04%. We also note that this is the first work that performs cross-dataset validation on three databases in this domain. |
關鍵字 | Apex CNN, Optical flow, Micro-expression, Recognition |
名稱 | A Statistical Approach in Enhancing the Volume Prediction of Ellipsoidal Ham |
年度 | 2020 |
類別 | 期刊論文 |
摘要 | In literature, there exist many attempts to determine the surface area and volume of an irregular object using automated image processing techniques. This paper expanded previous work on predicting the volume of ellipsoidal hams by using both image processing techniques and numerical methods. Novel algorithms were proposed to improve the prediction accuracy and robustness of the volume estimation mechanism. Particularly, the work focused on the ham’s position in the horizontal viewpoint. An industrial robotic arm was utilized to lift the ham object and rotate it at a fixed controlled speed to maximize data consistency. Then, a Mask Region-based convolutional neural network approach was used to extract the ham object’s features. Experiments were conducted on 16 newly collected ham datasets. In this paper, performance comparisons between this and the previous work were reported and detailed analyses presented. Particularly, three numerical algorithms (i.e., based on the minor axis, Y-direction, and k-nearest neighbor) were introduced to enhance volume prediction in the two databases. The new algorithm exhibited a 27% higher performance than that of the previous work’s algorithm. Related theoretical and conceptual frameworks were discussed to further provide evidence and insights on the proposed mechanism. |
關鍵字 | Mask R-CNN, Ham, Numerical algorithm, Volume |
名稱 | Leather defect classification and segmentation using deep learning architecture |
年度 | 2020 |
類別 | 期刊論文 |
摘要 | The defects on a leather surface may be caused by the poor material handling process during the production and manufacturing stages. It is essential to eliminate the natural variations and artificial injuries on the leather surfaces, in order to control the quality of the products and achieve customer satisfaction. To date, the visual inspection of the leather defects is performed manually by human operators. Thus, this paper aims to introduce an automatic defect detection technique by employing a deep learning method. Specifically, the proposed method consists of two stages: classification and instance segmentation. The former stage distinguishes whether the piece of the leather sample contains a defective part or not, whereas the latter is to localize the precise defective location. To accomplish the tasks, the dataset is first collected under a proper laboratory environment. Among 250 defective samples and 125 non-defective samples, the proposed method has been demonstrated its feature learning capability by producing promising performance when considering relatively fewer training samples. Particularly, the defect types focused in this study are the black lines and wrinkles. The best performance obtained is ∼95% for the classification task, whereas the segmentation task reaches an Intersection over Union rate of 99.84% |
關鍵字 | Leather, defect, classification, segmentation, U-Net |
名稱 | Automated leather defect inspection using statistical approach on image intensity |
年度 | 2020 |
類別 | 期刊論文 |
摘要 | Leather is a very important raw material in many manufacturing industries. For example to produce footwear, garments, bags and accessories. Prior to the mass production of certain product, a professional leather visual inspection process for defection spotting is essential as the quality control step. However, to date, there is a lack of fully-automated leather inspection systems in the industry, whereby most manufacturers rely on experienced and trained experts to mark out the defects in the leather. This kind of human assessment work is inefficient and inconsistent. Therefore, this paper proposes a method that based on image processing techniques, namely, gray level histogram analysis, to detect defects of the leather. Specifically, the histogram characteristics such as the mean and standard deviation are extracted and treated as the features. Then, the statistical Kolmogorov–Smirnov’s two-sample test is utilized to perform feature selection. Followed by a thresholding method to reduce the dimensionality of the features. Finally, the features are categorized by several well-known classifiers. The best classification accuracy obtained are 99.16% and 77.13% on two different datasets respectively. |
關鍵字 | Leather · Defect · Statistical · Classification · Feature selection |
名稱 | Who Is the Designer? ARC-100 Database and Benchmark on Architecture Classification |
年度 | 2020 |
類別 | 期刊論文 |
摘要 | Architecture is about evolution, there exist many types of architectural styles that depend on the geography, traditions, and culture of the particular regions. An architectural designer may have a similar preference in creating the new architectural building, which can be easily recognized from the physical attributes and characteristics. This paper performs an architect classification based on the outward appearance of the building. An architecture database with 100 images (ARC-100) that have balanced class distribution is constructed. Among the architectural buildings, the best performance is 71% for 5-class classification. Convolutional neural networks (CNNs) have demonstrated breakthrough performance on various classification tasks in recent studies, and even outperform human experts in specific tasks. Thus, for the baseline evaluation, multiple pretrained CNN models are employed with slight modifications. Prior to the feature extraction and classification processes, the removal of background noise is performed using two approaches: manually and automatically. The former approach requires high human intervention, while the latter utilizes the cutting-edge object segmentation technology, namely mask regional convolutional neural network (R-CNN). The illustration of the experiment training progress and the confusion matrix are reported, to allow further interpretation and analysis for the model trained. Notably, this is the first work that performs automatic classification based on architectural styles. This framework can be used to improve the cultural understanding and practices in providing education for holistic development and enhance the learning experience and progressions from an aesthetic perspective. |
關鍵字 | Architecture, Building, Classification, Segmentation, CNN |
名稱 | A note on the existence of horizontal envelopes in the 3D-Heisenberg group |
年度 | 2020 |
類別 | 期刊論文 |
摘要 | By using the support functions on the xy-plane, we show the necessary and sufficient conditions for the existence of envelopes of horizontal lines in the 3D-Heisenberg group. A method to construct horizontal envelopes from the given ones is also derived, and we classify the solutions satisfying the construction. |
關鍵字 | Sub-Riemannian manifolds; pseudo-hermitian geometry; envelopes |
名稱 | Automatic traditional Chinese painting classification: A benchmarking analysis |
年度 | 2020 |
類別 | 期刊論文 |
摘要 | In the recent years, there is a growing trend toward digitization of cultural heritage for better accessibility and preservation. For instance, the development of image processing techniques in traditional Chinese painting (TCP) has begun to attract researchers attention in the computer vision field. TCP is one of the representative of Chinese traditional arts. Evidenced by the successes of development in image processing techniques in various applications, this article aim to apply the deep learning approach on TCP for several purposes, which include automatic establishment of unified image library, facilitating update‐to‐date data in the database, reduction of cost required for image classification and retrieval. First, a unified database is established, that consists of more than a thousand of images from six major TCP themes. Then, several deep learning algorithms that are based on mathematical models are applied to examine the classification performance. In addition, the salient regions that denote significant features are identified, by adopting the instance segmentation technique. As a result, the modified pretrained neural network is capable to achieve 99.66% recognition accuracy. Qualitative results are also presented to demonstrate the effectiveness of the proposed method. We also note that this is the first work that performs multiclass classification on six categories in this domain. Furthermore, a 10‐class classification result of 96% is obtained when performing on one of the painting types, namely, ghost‐and‐god. |
關鍵字 | classification, deep learning, instance segmentation, traditional Chinese painting |
名稱 | Generalizations of the Theorems of Pappus-Guldin in the Heisenberg groups |
年度 | 2021 |
類別 | 期刊論文 |
摘要 | In this paper, we study areas (called p-areas) and volumes for parametric surfaces in the 3D-Heisenberg group H1 , which is considered as a flat model of pseudo-hermitian manifolds. We derive the formulas of p-areas and volumes for parametric surfaces in H1 and show that the classical result of Pappus-Guldin theorems for surface areas and volumes hold if the surfaces satisfy some geometric properties. Some examples are also provided, including the surfaces with constant p-mean curvatures. |
關鍵字 | Pappus-Guldin Theorem · Sub-Riemannian manifolds · Pseudo-hermitian geometry |
名稱 | Shallow Triple Stream Three-dimensional CNN (STSTNet) for Micro-expression Recognition |
年度 | 2019 |
類別 | 會議論文 |
摘要 | In the recent year, state-of-the-art for facial micro-expression recognition have been significantly advanced by deep neural networks. The robustness of deep learning has yielded promising performance beyond that of traditional handcrafted approaches. Most works in literature emphasized on increasing the depth of networks and employing highly complex objective functions to learn more features. In this paper, we design a Shallow Triple Stream Three-dimensional CNN (STSTNet) that is computationally light whilst capable of extracting discriminative high level features and details of micro-expressions. The network learns from three optical flow features (i.e., optical strain, horizontal and vertical optical flow fields) computed based on the onset and apex frames of each video. Our experimental results demonstrate the effectiveness of the proposed STSTNet, which obtained an unweighted average recall rate of 0.7605 and unweighted F1-score of 0.7353 on the composite database consisting of 442 samples from the SMIC, CASME II and SAMM databases. |
關鍵字 | convolutional neural nets , emotion recognition , face recognition , feature extraction , image sequences , learning (artificial intelligence) |