Recent Patents on Engineering - Volume 16, Issue 5, 2022

Background: In recent geometric design, many effective toolkits for geometric modeling and optimization have been proposed and applied in practical cases, while effective and efficient designing of shapes that have desirable topological properties remains to be a challenge. The development of computational topology, especially persistent homology, permits convenient usage of topological invariants in shape analysis, geometric modeling, and shape optimization. Persistence diagram, the useful topological summary of persistent homology, provides a stable representation of multiscale homology invariants in the presence of noise in original data. Recent works show the wide use of persistent homology tools in geometric design. Objective: In this paper, we review the geometric design based on computational topological tools in three aspects: the extraction of topological features and representations, topology-aware shape modeling, and topology-based shape optimization. Methods: By tracking the development of each aspect and comparing the methods using classical topological invariants, motivations, and key approaches of important related works based on persistent homology are clarified. Results: We review geometric design through topological extraction, topological design, and shape optimization based on topology preservation. Related works show the successful applications of computational topology tools of geometric design. Conclusion: Solutions for the proposed core problems will affect the geometric design and its applications. In the future, the development of computational topology may boost computer-aided topological design.

Background: Shape segmentation is commonly required in many engineering fields to separate a 3D shape into pieces for some specific applications. Although there are different methods proposed to segment the 3D shape, there is a lack of analyses of their efficiency and accuracy. It is a challenge to select an effective method to meet a particular requirement of the shape segmentation. Objective: This paper reviews existing methods of the shape segmentation to summarize the methods and processes to identify their pros and cons. Methods: The process of the shape segmentation is summarized in two steps: feature extraction and model separation. Results: Shape features are identified from the available methods. Different methods of the shape segmentation are evaluated. The challenge and trend of the shape segmentation are discussed. Conclusion: Clustering is the most used method for shape segmentation. Machine learning methods are a trend of 3D shape segmentations for identification, analysis and reconstruction of large-scale models.

Background: 3D facial image data has become an important data source in many biometric computing applications due to the increasing availability of 3D surface image collection technologies. Objective: In this survey paper, we aim to review recent advances in 3D geometry-based techniques for facial image analysis and their roles in several critical applications. Methods: We first study the 3D facial landmark detection techniques which are often required for many facial data analysis applications. We then review the literature related to several critical 3D facial image based applications, including face recognition, medical diagnosis, and 3D face reconstruction. Conclusion: Our review shows that while 3D facial image data has been widely used as an important biometric data source, critical solutions still need to be developed in applications that require substantial understanding of the underlying anatomic and geometric structures of human faces.

Background: Implicit surface is a kind of surface modeling tool, which is widely used in point cloud reconstruction, deformation and fusion due to its advantages of good smoothness and Boolean operation. The most typical method is the surface reconstruction with Radial Basis Functions (RBF) under normal constraints. RBF has become one of the main methods of point cloud fitting because it has a strong mathematical foundation, an advantage of computation simplicity, and the ability of processing nonuniform points. Objective: Techniques and patents of implicit surface reconstruction interpolation with RBF are surveyed. Theory, algorithm, and application are discussed to provide a comprehensive summary for implicit surface reconstruction in RBF and Hermite Radial Basis Functions (HRBF) interpolation. Methods: RBF implicit surface reconstruction interpolation can be divided into RBF interpolation under the constraints of points and HRBF interpolation under the constraints of points and corresponding normals. Results: A total of 125 articles were reviewed, in which more than 30% were related to RBF in the last decade. The continuity properties and application fields of the popular global supported radial basis functions and compactly supported radial basis functions are analyzed. Different methods of RBF and HRBF implicit surface reconstruction are evaluated, and the challenges of these methods are discussed. Conclusion: In future work, implicit surface reconstruction via RBF and HRBF should be further studied in fitting accuracy, computation speed, and other fundamental problems. In addition, it is a more challenging but valuable research direction to construct a new RBF with both compact support and improved fitting accuracy.

Background: Curved modeling technology originated from the geometric lofting and design of aircrafts, automobiles and ships. The control points of the traditional B-spline mesh should be placed regularly in whole rows and columns. A T-spline surface is a B-spline surface that allows T-junctions. It can overcome the limitations of traditional B-mesh topology and has its own advantages in surface splicing, surface fining, surface simplification, etc. T-spline has wide application prospects in product modeling, art design, animation production, numerical control machining, volume data expression, and other aspects. Objective: The objective of this paper is to summarize the properties, algorithms, and applications of T-splines. It helps scholars in determining the research status of T-splines and in further exploring the theories related to the applications of T-splines. Methods: This paper reviews the theories on T-splines and their applications from four aspects. First, we discuss the development of the concept, properties, and algorithms of T-splines and the Tspline reconstruction. Then, we conducted an isogeometric analysis using T-splines. Next, we demonstrate the applications of T-splines in actual scenarios. Finally, we present a brief summary of the paper and expectations for the future. Results: The paper provides a brief introduction to the relevant papers on T-splines. The research on T-spline technology is currently active, and there are many studies on T-spline theories and applications. Among these, the spline theory on T-mesh has aroused widespread interest in engineering, especially in Computer-Aided Geometric Design (CAGD) and computer graphics. Conclusion: The T-spline surface is the most important new spline surface in the CADG field since the creation of the B-spline surface and non-uniform rational B-spline surface. Although the surface modeling technology based on the T-spline surface is developing rapidly, there are still some problems that need to be further studied.

Background: Selective laser melting is a best-established additive manufacturing technology for high-quality metal part manufacturing. However, the technology is yet to be accepted widely, especially in critical applications, due to the absence of a thorough understanding of the technology although several benchmark test artifacts have been developed to characterize the performance of selective laser melting machines. Objective: The objective of this paper is to inspire new designs of benchmark test artifacts to better understand the selective laser melting process, and to promote the acceptance of the selective laser melting technology. Methods: The existing benchmark test artifacts for selective laser melting are analyzed comparatively, and the design guidelines are discussed. Results: The modular approach should still be adopted in designing new benchmark test artifacts in the future, and task-specific test artifacts may also need to be considered furtherly to validate machine performance for critical applications. The inclusion of the design model in the manufactured artifact, instead of the conformance to the design specifications, should be evaluated after the artifact is measured for the applications requiring high-dimensional accuracy and high surface quality. Conclusion: The benchmark test artifact for selective laser melting is still under development, and a breakthrough of the measuring technology for internal and/or inaccessible features will be beneficial for understanding the technology.

Background: A developable surface is a special ruled surface with vanishing Gaussian curvature. The study of developable surfaces is of interest in both academia and industry. The application of developable surfaces ranges from ship hulls, architecture to origami, clothes, etc., as they are suitable for the modeling of surfaces with materials that are not amenable to stretch like leather, paper, fiber, and sheet metal. Objective: We survey techniques and patents of developable surfaces in the field of geometric modeling. The theory, algorithms, and applications are discussed to provide a comprehensive summary for modeling developable surfaces. Methods: Prior methods that model smooth and discrete developable surfaces in diverse disciplines are collected and reviewed. In particular, our review focuses on C², C¹ and C⁰ developable surfaces, which are driven by the problems and challenges in the industry. Results: Many papers and patents of developable surface modeling are classified in this review paper. It is found that remarkable developments and improvements have been achieved in both analytical computations and practical applications. Conclusion: Global piecewise-developable surfaces, exploration of shape space of developable surfaces, joint optimization of geometry and physics, and other fundamental problems should be further studied.

Background: Learning discriminative representation from large-scale data sets has made a breakthrough in decades. However, it is still a thorny problem to generate representative embedding from limited examples, for example, a class containing only one image. Recently, deep learning- based Few-Shot Learning (FSL) has been proposed. It tackles this problem by leveraging prior knowledge in various ways. Objective: In this work, we review recent advances of FSL in a perspective of high-dimensional representation learning. The results of the analysis can provide insights and directions for future work. Methods: We first present the definition of general FSL. Then, we propose a general framework for the FSL problem and give the taxonomy under the framework. We survey two FSL directions: learning policy and meta-learning. Results: We review the advanced applications of FSL, including image classification, object detection, image segmentation and other tasks etc., as well as the corresponding benchmarks to provide an overview of recent progress. Conclusion: In future work, FSL needs to be further studied in medical images, language models and reinforcement learning. In addition, cross-domain FSL, successive FSL and associated FSL are more challenging and valuable research directions.