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Mathematics
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Advances in Applied Mathematics in Computer Vision
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Advances in Applied Mathematics in Computer Vision

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 31 August 2024 | Viewed by 4025

Special Issue Editor

Prof. Dr. Shuai Liu

E-Mail Website
Guest Editor
School of Educational Science, Hunan Normal University, Changsha 410081, China
Interests: computer vision; artificial intelligence; intelligent system; complexity; nonlinear dynamics; fractals
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Computer vision is one of the most attractive domains in the field of artificial intelligence, and it includes tracking, understanding and recognition, etc., in both image and video. Due to the variety of its applications, many learning models for computer vision have become popular research topics in today’s world. Though many studies have been conducted in this field, many issues in the mathematical base are still left unsolved, including graphical computing, suitable loss function helping learning, sample selection, mathematical features for images or targets, etc. Therefore, the applications of sophisticated and robust applied mathematics are important, for example, in clustering, geometric analysis, statistical analysis, dynamics computing, and so forth.

This Special Issue aims to provide an opportunity for researchers to publish their theoretical and technological studies involving applied mathematics in computer vision, as well as novel engineering applications.

Dr. Shuai Liu
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • clustering
  • deep learning
  • GNN
  • complexity
  • computer vision
  • machine learning

Published Papers (3 papers)

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Research

13 pages, 1475 KiB  
Article
A Contrastive Model with Local Factor Clustering for Semi-Supervised Few-Shot Learning
by Hexiu Lin, Yukun Liu, Daming Shi and Xiaochun Cheng
Mathematics 2023, 11(15), 3394; https://doi.org/10.3390/math11153394 - 03 Aug 2023
Viewed by 758
Abstract
Learning novel classes with a few samples per class is a very challenging task in deep learning. To mitigate this issue, previous studies have utilized an additional dataset with extensively labeled samples to realize transfer learning. Alternatively, many studies have used unlabeled samples [...] Read more.
Learning novel classes with a few samples per class is a very challenging task in deep learning. To mitigate this issue, previous studies have utilized an additional dataset with extensively labeled samples to realize transfer learning. Alternatively, many studies have used unlabeled samples that originated from the novel dataset to achieve few-shot learning, i.e., semi-supervised few-shot learning. In this paper, an easy but efficient semi-supervised few-shot learning model is proposed to address the embeddings mismatch problem that results from inconsistent data distributions between the novel and base datasets, where samples with the same label approach each other while samples with different labels separate from each other in the feature space. This model emphasizes pseudo-labeling guided contrastive learning. We also develop a novel local factor clustering module to improve the ability to obtain pseudo-labels from unlabeled samples, and this module fuses the local feature information of labeled and unlabeled samples. We report our experimental results on the mini-ImageNet and tiered-ImageNet datasets for both five-way one-shot and five-way five-shot settings and achieve better performance than previous models. In particular, the classification accuracy of our model is improved by approximately 11.53% and 14.87% compared to the most advanced semi-supervised few-shot learning model we know in the five-way one-shot scenario. Moreover, ablation experiments in this paper show that our proposed clustering strategy demonstrates accuracy improvements of about 4.00% in the five-way one-shot and five-way five-shot scenarios compared to two popular clustering methods. Full article
(This article belongs to the Special Issue Advances in Applied Mathematics in Computer Vision)
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18 pages, 13753 KiB  
Article
A Multi-Scale Hybrid Attention Network for Sentence Segmentation Line Detection in Dongba Scripture
by Junyao Xing, Xiaojun Bi and Yu Weng
Mathematics 2023, 11(15), 3392; https://doi.org/10.3390/math11153392 - 03 Aug 2023
Viewed by 715
Abstract
Dongba scripture sentence segmentation is an important and basic work in the digitization and machine translation of Dongba scripture. Dongba scripture sentence segmentation line detection (DS-SSLD) as a core technology of Dongba scripture sentence segmentation is a challenging task due to its own [...] Read more.
Dongba scripture sentence segmentation is an important and basic work in the digitization and machine translation of Dongba scripture. Dongba scripture sentence segmentation line detection (DS-SSLD) as a core technology of Dongba scripture sentence segmentation is a challenging task due to its own distinctiveness, such as high inherent noise interference and nonstandard sentence segmentation lines. Recently, projection-based methods have been adopted. However, these methods are difficult when dealing with the following two problems. The first is the noisy problem, where a large number of noise in the Dongba scripture image interference detection results. The second is the Dongba scripture inherent characteristics, where many vertical lines in Dongba hieroglyphs are easily confused with the vertical sentence segmentation lines. Therefore, this paper aims to propose a module based on the convolutional neural network (CNN) to improve the accuracy of DS-SSLD. To achieve this, we first construct a tagged dataset for training and testing DS-SSLD, including 2504 real images collected from Dongba scripture books and sentence segmentation targets. Then, we propose a multi-scale hybrid attention network (Multi-HAN) based on YOLOv5s, where a multiple hybrid attention unit (MHAU) is used to enhance the distinction between important features and redundant features, and the multi-scale cross-stage partial unit (Multi-CSPU) is used to realize multi-scale and richer feature representation. The experiment is carried out on the Dongba scripture sentence segmentation dataset we built. The experimental results show that the proposed method exhibits excellent detection performance and outperforms several state-of-the-art methods. Full article
(This article belongs to the Special Issue Advances in Applied Mathematics in Computer Vision)
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20 pages, 2846 KiB  
Article
Simple and Robust Boolean Operations for Triangulated Surfaces
by Meijun Zhou, Jiayu Qin, Gang Mei and John C. Tipper
Mathematics 2023, 11(12), 2713; https://doi.org/10.3390/math11122713 - 15 Jun 2023
Viewed by 1963
Abstract
Boolean operations on geometric models are important in numerical simulation and serve as essential tools in the fields of computer-aided design and computer graphics. The accuracy of these operations is heavily influenced by finite precision arithmetic, a commonly employed technique in geometric calculations, [...] Read more.
Boolean operations on geometric models are important in numerical simulation and serve as essential tools in the fields of computer-aided design and computer graphics. The accuracy of these operations is heavily influenced by finite precision arithmetic, a commonly employed technique in geometric calculations, which introduces numerical approximations. To ensure robustness in Boolean operations, numerical methods relying on rational numbers or geometric predicates have been developed. These methods circumvent the accumulation of rounding errors during computation, thus preserving accuracy. Nonetheless, it is worth noting that these approaches often entail more intricate operation rules and data structures, consequently leading to longer computation times. In this paper, we present a straightforward and robust method for performing Boolean operations on both closed and open triangulated surfaces. Our approach aims to eliminate errors caused by floating-point operations by relying solely on entity indexing operations, without the need for coordinate computation. By doing so, we ensure the robustness required for Boolean operations. Our method consists of two main stages: (1) Firstly, candidate triangle intersection pairs are identified using an octree data structure, and then parallel algorithms are employed to compute the intersection lines for all pairs of triangles. (2) Secondly, closed or open intersection rings, sub-surfaces, and sub-blocks are formed, which is achieved entirely by cleaning and updating the mesh topology without geometric solid coordinate computation. Furthermore, we propose a novel method based on entity indexing to differentiate between the union, subtraction, and intersection of Boolean operation results, rather than relying on inner and outer classification. We validate the effectiveness of our method through various types of Boolean operations on triangulated surfaces. Full article
(This article belongs to the Special Issue Advances in Applied Mathematics in Computer Vision)
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