geometric transformation
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Information ◽  
2022 ◽  
Vol 13 (1) ◽  
pp. 38
Author(s):  
Jijun Tong ◽  
Shuai Xu ◽  
Fangliang Wang ◽  
Pengjia Qi

This paper presents a novel method based on a curve descriptor and projection geometry constrained for vessel matching. First, an LM (Leveberg–Marquardt) algorithm is proposed to optimize the matrix of geometric transformation. Combining with parameter adjusting and the trust region method, the error between 3D reconstructed vessel projection and the actual vessel can be minimized. Then, CBOCD (curvature and brightness order curve descriptor) is proposed to indicate the degree of the self-occlusion of blood vessels during angiography. Next, the error matrix constructed from the error of epipolar matching is used in point pairs matching of the vascular through dynamic programming. Finally, the recorded radius of vessels helps to construct ellipse cross-sections and samples on it to get a point set around the centerline and the point set is converted to mesh for reconstructing the surface of vessels. The validity and applicability of the proposed methods have been verified through experiments that result in the significant improvement of 3D reconstruction accuracy in terms of average back-projection errors. Simultaneously, due to precise point-pair matching, the smoothness of the reconstructed 3D coronary artery is guaranteed.


2021 ◽  
Vol 5 (2) ◽  
pp. 135
Author(s):  
Nur Ainun Lubis ◽  
Dharma Kelana Putra ◽  
Amrul Badri ◽  
Wahyu Wiji Astuti

<p>This research explores the origins of the Ambe-ambeken Dance from Singkil Regency, the form of the Ambe-ambeken Dance, and analyzes the ethnomathematics. As a cultural entity, the Singkil people have a dance known as the Ambe-ambeken or Sakhindayong dance. This study uses a descriptive qualitative method to describe the Ambe-ambeken dance based on historical, anthropological and mathematical approaches. Although the variety of movements looks simple at first glance, this dance is a form of technology of enchantment that is full of wisdom and has an essential role in shaping the community's personality and the spread of Islam in Singkil through the poems that are sung during the dance. Then from a different perspective, it was found that there is a mathematical element that many people do not realize in a traditional dance, namely a geometric transformation. This fact leads to a new assumption that culture in the past was built on spirituality and aesthetic values and by applying mathematical principles in various aspects of life.</p><p align="left"> <em>Penelitian ini mengungkap asal-usul Tari Ambe-ambeken dari Kabupaten Singkil, bentuk Tari Ambe-ambeken serta menganalisis etnomatematika pada Tari Ambe-ambeken Sebagai sebuah entitas kultural, masyarakat Singkil memiliki sebuah tarian yang dikenal sebagai tari Ambe-ambeken atau Sakhindayong.. Penelitian ini menggunakan metode kualitatif deskriptif, yang bertujuan untuk mendeskripsikan tari ambe-ambeken berdasarkan pendekatan Sejarah, Antropologi dan Matematika. </em><em>Meskipun sepintas ragam geraknya terlihat sederhana, tetapi tarian ini merupakan bentuk technology of enchantment yang sarat akan kearifan dan memiliki peranan penting dalam pembentukan kepribadian masyarakat serta penyebaran agama Islam di Singkil melalui syair-syair yang dibawakan selama tarian berlangsung. Kemudian dari sisi yang berbeda, ditemukan bahwa ada unsur matematika yang tidak disadari oleh banyak orang dalam suatu tarian tradisional, yakni berupa transformasi geometri. Fakta ini mengarahkan pada asumsi baru bahwa kebudayaan di masa lalu tidak hanya dibangun atas dasar spiritualitas dan nilai estetika semata, tetapi juga dengan menerapkan</em> <em>prinsip matematika dalam berbagai aspek kehidupan.</em></p>


MaPan ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 233
Author(s):  
Suri Toding Lembang ◽  
Yusem Ba’ru

This research aims to examine the mathematical concepts in traditional Tongkonan houses' carving and provide information about the meaning of each carving in the Tongkonan house. The research method used is the qualitative research method. The results of the study are obtained by observation and interview. The results showed that it turns out, in some Toraja carvings, contain the concept of transformational geometry, namely reflection. The information also obtained that the carvings in the Tongkonan house are very loaded with meaning, especially about advice, prayer, or hope to all members of the Tongkonan.


Abjadia ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 144-159
Author(s):  
Devita Amalia ◽  
Dwi Noviani ◽  
M. Fadil Djamali ◽  
Imam Rofiki

Ethnomathematics are different ways of doing mathematics taking into account the academic mathematical knowledge developed by different sectors of society as well as taking into account the different modes in which different cultures negotiate their mathematical practices (ways of grouping, counting, measuring, designing tools, or playing). Based on this research, this study aims to describe the results of ethnomathematics exploration in Jember batik motifs. The method of analysis used in this research was a qualitative approac with an ethnographic design. Data collection techniques were observation, documentation, and interviews. This research was conducted at Rumah Batik Rolla Jember and Rezti'z Batik Tegalsari Ambulu Jember. The research was conducted for one week. The results of this study indicate that the ethnomathematics in the Jember batik motif has a philosophical value that describes the natural wealth of Jember Regency in each of its motifs, and there are mathematical concepts in the form of geometric transformation concepts (reflection, translation, rotation, and dilation) along with the concept of number patterns.


2021 ◽  
Author(s):  
Li Ding ◽  
Tony Kang ◽  
Ajay E. Kuriyan ◽  
Rajeev S. Ramchandran ◽  
Charles C. Wykoff ◽  
...  

<div>We propose a novel hybrid framework for registering retinal images in the presence of extreme geometric distortions that are commonly encountered in ultra-widefield (UWF) fluorescein angiography. Our approach consists of two stages: a feature-based global registration and a vessel-based local refinement. For the global registration, we introduce a modified RANSAC algorithm that jointly identifies robust matches between feature keypoints in reference and target images and estimates a polynomial geometric transformation consistent with the identified correspondences. Our RANSAC modification particularly improves feature point matching and the registration in peripheral regions that are most severely impacted by the geometric distortions. The second local refinement stage is formulated in our framework as a parametric chamfer alignment for vessel maps obtained using a deep neural network. Because the complete vessel maps contribute to the chamfer alignment, this approach not only improves registration accuracy but also aligns with clinical practice, where vessels are typically a key focus of examinations. We validate the effectiveness of the proposed framework on a new UWF fluorescein angiography (FA) dataset and on the existing narrow-field FIRE (fundus image registration) dataset and demonstrate that it significantly outperforms prior retinal image registration methods. The proposed approach enhances the utility of large sets of longitudinal UWF images by enabling: (a) automatic computation of vessel change metrics and (b) standardized and co-registered examination that can better highlight changes of clinical interest to physicians.</div>


2021 ◽  
Author(s):  
Li Ding ◽  
Tony Kang ◽  
Ajay E. Kuriyan ◽  
Rajeev S. Ramchandran ◽  
Charles C. Wykoff ◽  
...  

<div>We propose a novel hybrid framework for registering retinal images in the presence of extreme geometric distortions that are commonly encountered in ultra-widefield (UWF) fluorescein angiography. Our approach consists of two stages: a feature-based global registration and a vessel-based local refinement. For the global registration, we introduce a modified RANSAC algorithm that jointly identifies robust matches between feature keypoints in reference and target images and estimates a polynomial geometric transformation consistent with the identified correspondences. Our RANSAC modification particularly improves feature point matching and the registration in peripheral regions that are most severely impacted by the geometric distortions. The second local refinement stage is formulated in our framework as a parametric chamfer alignment for vessel maps obtained using a deep neural network. Because the complete vessel maps contribute to the chamfer alignment, this approach not only improves registration accuracy but also aligns with clinical practice, where vessels are typically a key focus of examinations. We validate the effectiveness of the proposed framework on a new UWF fluorescein angiography (FA) dataset and on the existing narrow-field FIRE (fundus image registration) dataset and demonstrate that it significantly outperforms prior retinal image registration methods. The proposed approach enhances the utility of large sets of longitudinal UWF images by enabling: (a) automatic computation of vessel change metrics and (b) standardized and co-registered examination that can better highlight changes of clinical interest to physicians.</div>


2021 ◽  
Vol 13 (24) ◽  
pp. 5152
Author(s):  
Kaiqiang Song ◽  
Fengzhi Cui ◽  
Jie Jiang

Remote sensing (RS) image change detection (CD) is a critical technique of detecting land surface changes in earth observation. Deep learning (DL)-based approaches have gained popularity and have made remarkable progress in change detection. The recent advances in DL-based methods mainly focus on enhancing the feature representation ability for performance improvement. However, deeper networks incorporated with attention-based or multiscale context-based modules involve a large number of network parameters and require more inference time. In this paper, we first proposed an effective network called 3M-CDNet that requires about 3.12 M parameters for accuracy improvement. Furthermore, a lightweight variant called 1M-CDNet, which only requires about 1.26 M parameters, was proposed for computation efficiency with the limitation of computing power. 3M-CDNet and 1M-CDNet have the same backbone network architecture but different classifiers. Specifically, the application of deformable convolutions (DConv) in the lightweight backbone made the model gain a good geometric transformation modeling capacity for change detection. The two-level feature fusion strategy was applied to improve the feature representation. In addition, the classifier that has a plain design to facilitate the inference speed applied dropout regularization to improve generalization ability. Online data augmentation (DA) was also applied to alleviate overfitting during model training. Extensive experiments have been conducted on several public datasets for performance evaluation. Ablation studies have proved the effectiveness of the core components. Experiment results demonstrate that the proposed networks achieved performance improvements compared with the state-of-the-art methods. Specifically, 3M-CDNet achieved the best F1-score on two datasets, i.e., LEVIR-CD (0.9161) and Season-Varying (0.9749). Compared with existing methods, 1M-CDNet achieved a higher F1-score, i.e., LEVIR-CD (0.9118) and Season-Varying (0.9680). In addition, the runtime of 1M-CDNet is superior to most, which exhibits a better trade-off between accuracy and efficiency.


2021 ◽  
Vol 11 (24) ◽  
pp. 11917
Author(s):  
Wei Liu ◽  
Yun Ma ◽  
Mingqiang Gao ◽  
Shuaidong Duan ◽  
Longsheng Wei

In a connected vehicle environment based on vehicle-to-vehicle (V2V) technology, images from front and ego vehicles are fused to augment a driver’s or autonomous system’s visual field, which is helpful in avoiding road accidents by eliminating the blind point (the objects occluded by vehicles), especially tailgating in urban areas. Realizing multi-view image fusion is a tough problem without knowing the relative location of two sensors and the fusing object is occluded in some views. Therefore, we propose an image geometric projection model and a new fusion method between neighbor vehicles in a cooperative way. Based on a 3D inter-vehicle projection model, selected feature matching points are adopted to estimate the geometric transformation parameters. By adding deep information, our method also designs a new deep-affine transformation to realize fusing of inter-vehicle images. Experimental results on KIITI (Karlsruhe Institute of Technology and Toyota Technological Institute) datasets are shown to validate our algorithm. Compared with previous work, our method improves the IoU index by 2~3 times. This algorithm can effectively enhance the visual perception ability of intelligent vehicles, and it will help to promote the further development and improvement of computer vision technology in the field of cooperative perception.


Author(s):  
George Spackman ◽  
Louise Brown ◽  
Thomas Turner

AbstractCurrently, generation of 3D woven T-joint models with complex weave geometries, using TexGen software, is a manual process. One of the main challenges to automatic generation of these textiles is the order in which the weft yarns interlace within the bifurcation region. This paper will demonstrate a method for predicting the order, based on the pattern draft and the information contained within it such as the direction of weft insertion and the beating action of the loom. The path of the entangling weft yarns and the yarn cross section orientation can then be modelled. Finally, a geometric transformation is applied to simulate the opening of the flanges so that the final model reflects the T-shaped profile.


Author(s):  
A. Herraiz ◽  
M. Gutierrez ◽  
M. Ortega-Mier

AbstractWe define a geometric transformation of Euclidean Travelling Salesman Problem (TSP) tours that leads to a new formulation of the TSP. For every Euclidean TSP n-city tour, it is possible to construct an inscribed n-polygon (Equivalent Cyclic Polygon, ECP) such that the lengths of the edges are equal to the corresponding TSP tour links and follow the same sequence order. The analysis of the ECP elicits the possibility of defining a new objective function in terms of angles instead of distances. This modification opens the way to identify characterizing geometric parameters of the TSP as well as to explore new heuristics based on the inclusion of additional constraints. The experimentation with a set of cases shows promising results compared to the traditional compact formulations. The behavior of the ECP-based TSP formulations is better when the nodes of the TSP are randomly or evenly distributed.


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