Vertex Distance Research Articles

Mixed reality infrastructure based on deep learning medical image segmentation and 3D visualization for bone tumors using DCU-Net.

Segmenting and reconstructing 3D models of bone tumors from 2D image data is of great significance for assisting disease diagnosis and treatment. However, due to the low distinguishability of tumors and surrounding tissues in images, existing methods lack accuracy and stability. This study proposes a U-Net model based on double dimensionality reduction and channel attention gating mechanism, namely the DCU-Net model for oncological image segmentation. After realizing automatic segmentation and 3D reconstruction of osteosarcoma by optimizing feature extraction and improving target space clustering capabilities, we built a mixed reality (MR) infrastructure and explored the application prospects of the infrastructure combining deep learning-based medical image segmentation and mixed reality in the diagnosis and treatment of bone tumors. We conducted experiments using a hospital dataset for bone tumor segmentation, used the optimized DCU-Net and 3D reconstruction technology to generate bone tumor models, and used set similarity (DSC), recall (R), precision (P), and 3D vertex distance error (VDE) to evaluate segmentation performance and 3D reconstruction effects. Then, two surgeons conducted clinical examination experiments on patients using two different methods, viewing 2D images and virtual reality infrastructure, and used the Likert scale (LS) to compare the effectiveness of surgical plans of the two methods. The DSC, R and P values of the model introduced in this paper all exceed 90%, which has significant advantages compared with methods such as U-Net and Attention-Uet. Furthermore, LS showed that clinicians in the DCU-Net-based MR group had better spatial awareness of tumor preoperative planning. The deep learning DCU-Net algorithm model can improve the performance of tumor CT image segmentation, and the reconstructed fine model can better reflect the actual situation of individual tumors; the MR system constructed based on this model enhances clinicians' understanding of tumor morphology and spatial relationships. The MR system based on deep learning and three-dimensional visualization technology has great potential in the diagnosis and treatment of bone tumors, and is expected to promote clinical practice and improve efficacy.

Mechatronic Device Used to Evaluate the Performance of a Compliant Mechanism and Image Processing System in Determining Optometric Parameters

The work presented in the paper describes a mechatronic test stand and technique employed to determine the accuracy of a system developed by the authors to assist optometrists in measuring parameters used in the customization of progressive lenses, as well as regular lenses. The system aims to offer information about interpupillary distance, pantoscopic angle, and vertex distance, as well as measurements useful in correctly mounting the lenses in the frames. This is conducted by attaching a marker support system to the user’s frame and determining the user’s dimensions by using image acquisition techniques performed via a custom application built for this purpose. In this paper, a test mannequin is used to determine the accuracy of the system, with measurements being compared to those obtained by using classic methods. This method is used to determine the accuracy of the measurements in a controlled environment. Following the good results obtained in this paper and pending some improvements to the application, clinical tests will be performed on a small scale in selected optometrist offices.

Enhanced Molecular Descriptors Using Degree-Distance Invariants And Their Efficacy In QSPR Quadratic Modelling Of Chemical Compounds

In this study, we introduce an enhanced version of topological descriptors based on degree-distance invariants of connected graphs designed to effectively capture the structural characteristics of graphs with convex cuts, utilizing both vertex degrees and distances. We use this concept to analyze the Schultz and Gutman indices from reverse and neighbourhood degree perspectives. Motivated by the necessity for more effective descriptors in graph theory, our approach involves the development of algebraic expressions facilitating efficient computation, illustrated in some generalized benzenoid hydrocarbons. Moreover, the efficacy of the newly derived descriptors is evaluated through Linear and Quadratic Quantitative Structure-Property Relationship (QSPR) modelling on a dataset of carboxylic acids, and a set of structural isomers of saturated hydrocarbons revealing their effectiveness compared to existing descriptors.

YOLOv8-MU: An Improved YOLOv8 Underwater Detector Based on a Large Kernel Block and a Multi-Branch Reparameterization Module.

Underwater visual detection technology is crucial for marine exploration and monitoring. Given the growing demand for accurate underwater target recognition, this study introduces an innovative architecture, YOLOv8-MU, which significantly enhances the detection accuracy. This model incorporates the large kernel block (LarK block) from UniRepLKNet to optimize the backbone network, achieving a broader receptive field without increasing the model's depth. Additionally, the integration of C2fSTR, which combines the Swin transformer with the C2f module, and the SPPFCSPC_EMA module, which blends Cross-Stage Partial Fast Spatial Pyramid Pooling (SPPFCSPC) with attention mechanisms, notably improves the detection accuracy and robustness for various biological targets. A fusion block from DAMO-YOLO further enhances the multi-scale feature extraction capabilities in the model's neck. Moreover, the adoption of the MPDIoU loss function, designed around the vertex distance, effectively addresses the challenges of localization accuracy and boundary clarity in underwater organism detection. The experimental results on the URPC2019 dataset indicate that YOLOv8-MU achieves an mAP@0.5 of 78.4%, showing an improvement of 4.0% over the original YOLOv8 model. Additionally, on the URPC2020 dataset, it achieves 80.9%, and, on the Aquarium dataset, it reaches 75.5%, surpassing other models, including YOLOv5 and YOLOv8n, thus confirming the wide applicability and generalization capabilities of our proposed improved model architecture. Furthermore, an evaluation on the improved URPC2019 dataset demonstrates leading performance (SOTA), with an mAP@0.5 of 88.1%, further verifying its superiority on this dataset. These results highlight the model's broad applicability and generalization capabilities across various underwater datasets.

New Relations Between Zagreb Indices and Omega Invariant.

In this work, we studied the problem of determining the values of the Zagreb indices of all the realizations of a given degree sequence. We first obtained some new relations between the first and second Zagreb indices and the forgotten index sometimes called the third Zagreb index. These relations also include the triangular numbers, order, size, and the biggest vertex degree of a given graph. As the first Zagreb index and the forgotten index of all the realizations of a given degree sequence are fixed, we concentrated on the values of the second Zagreb index and studied several properties including the effect of vertex addition. In our calculations, we make use of a new graph invariant, called omega invariant, to reach numerical and topological values claimed in the theorems. This invariant is closely related to Euler characteristic and the cyclomatic number of graphs. Therefore this invariant is used in the calculation of some parameters of the molecular structure under review in terms of vertex degrees, eccentricity, and distance.

Soft Contact Lenses as a Good Option for Adolescent with Anisometropia

Introduction : Anisometropia is a condition of asymmetric refraction between the two eyes. Adequate anisometropia treatment, such as SCL (Soft Contact Lens) is required to provide binocular vision, patient comfort and also adolescent’s appearance.
 Case Illustration : A 16 years old woman came to the RS Khusus Mata Sumatera Selatan. She complained of blurred vision since 6 years ago, and not feeling comfortable using spectacle. The ophthalmologic examination revealed that uncorrected visual acuity was 2/60 ph 6/12 for right eye and on left eye is 6/30 ph 6/7.5. Best corrected visual acuity was 6/6 using S-7.00 on the right eye and left eye was 6/6 using correction S-3.00 but she was not comfortable. The base-curve measurement of the SCL was 8.60 mm for the both eyes and the diameter was 14.2 mm. After the contact lenses attached , obtained that S-7.00 D for the right eye and S-3.00 for the left eye could reach 6/6 in both eyes, she was more comfortable wearing SCL than spectacle.
 Discussion : Anisometropia can cause aniseikonia which is characterized by differences in the size of the image in the two eyes. One way to reduce aniseikonia by reducing the vertex distance, soft contact lenses canbe a choices to maintain binocular vision and minimalized the aniseikonia. Contact lenses significantly improved Adolescent’s appearance and activities, which lead to an overall improvementin satisfaction with vision correction, compared using spectacle.
 Conclusion : SCL is one of a good option for Adolescent with anisometropia that can provide good visual acuity, and also adolescent’s appearance.

Exploring reliable photogrammetry techniques for 3D modeling in anatomical research and education.

In anatomical research and education, three-dimensional visualization of anatomical structures is crucial for understanding spatial relationships in diagnostics, surgical planning, and teaching. While computed tomography (CT) and magnetic resonance imaging (MRI) offer valuable insights, they are often expensive and require specialized resources. This study explores photogrammetry as an affordable and accessible approach for 3D modeling in anatomical contexts. Two photogrammetry methods were compared: conventional open-source software (Colmap) and Apple's RealityKit Object Capture. Human C3 vertebrae were imaged with a 24 MP camera, with and without a cross-polarization filter. Reconstruction times, vertex distances, surface area, and volume measurements were compared to CT scans. Results revealed that the Object Capture method surpassed the conventional approach in reconstruction speed and user-friendliness. Both methods exhibited similar vertex distance from reference mesh and volume measurements, although the conventional approach produced larger surface areas compared to CT-based models. Cross-polarization filters eliminated the need for pre-processing and improved outcomes in challenging lighting conditions. This study demonstrates that photogrammetry, especially Object Capture, as a reliable and time-efficient tool for 3D modeling in anatomical research and education. It offers accessible alternatives to traditional techniques with advantages in texture mapping. While further validation of various anatomical structures is required, the accessibility and cost-effectiveness of photogrammetry make it a valuable asset for the field. In summary, photogrammetry would have the potential to revolutionize anatomical research and education by providing cost-effective, accessible, and accurate 3D modeling. The study underscores the promise of advancing anatomical research and education through the integration of photogrammetry with ongoing improvements in user-friendliness and accessibility.

The Vertex Distance on Cayley Digraphs of Rectangular Groups with respect to the Cartesian Product Connection Sets

A rectangular group S is a semigroup isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. The Cayley digraph Cay(S,A) of a finite rectangular group S with respect to a nonempty subset A of S is defined as a digraph with vertex set S and arc set consisting of ordered pairs (u,ua) in SxS for some a in A. The set A is called a connection set of Cay(S,A). Let u and v be in S. The distance from u to v in Cay(S,A), denoted by d(u,v), is the number of arcs in the shortest directed u-v path if one exists and is infinity otherwise. In this paper, we characterize the distances of any two vertices in Cayley digraphs of rectangular groups with respect to the Cartesian product connection sets

Vertex distance variability of the Vision-S™ 700 refractors in normal population

Vertex distance variability of the Vision-S™ 700 refractors in normal population

Dissimilarity-based hypothesis testing for community detection in heterogeneous networks

Identifying communities within networks is a crucial and challenging problem with practical implications across various scientific fields. Existing methods often overlook the heterogeneous distribution of nodal degrees or require prior knowledge of the number of communities. To overcome these limitations, we propose an efficient hypothesis test for community detection by quantifying dissimilarities between graphs. Our approach centers around examining the dissimilarity between a given random graph and a null hypothesis which assumes a degree-corrected Erdös–Rényi type. To compare the dissimilarity, we introduce a measure that takes into account the distributions of vertex distances, clustering coefficients, and alpha-centrality. This measure is then utilized in our hypothesis test. To simultaneously uncover the number of communities and their corresponding structures, we develop a two-stage bipartitioning algorithm. This algorithm integrates seamlessly with our hypothesis test and enables the exploration of community organization within the network. Through experiments conducted on both synthetic and real networks, we demonstrate that our method outperforms state-of-the-art approaches in community detection.

Some inequalities for two simplices in the Euclidean space En

Simplices are used as building blocks to construct an interesting class of topological spaces called simplicial complexes, which exhibit remarkable symmetric properties. In this paper, we study the problems of inequalities for two simplices in the Euclidean space En. We establish some new inequalities for the vertex distances of two simplices and obtain some generalizations of the classical Neuberg-Pedoe inequality.

Graph clustering with Boltzmann machines

Graph clustering is the process of labeling nodes so that nodes sharing common labels form densely connected subgraphs with sparser connections to the remaining vertices. Because of its difficult formulation, we translate the intra-cluster density maximization problem to a distance minimization problem. To achieve this reformulation, we use a novel vertex–vertex distance that accurately reflects density. Specifically, we extend the recent binary quadratic K-medoids formulation to graph clustering. We also generalize a quadratic formulation originally designed for partitioning complete graphs. Because binary quadratic optimization is an NP-hard problem, we obtain numerical solutions for these formulations through the use of two novel Boltzmann machine (meta-)heuristics. For benchmarking purposes, we compare solution quality and computational performances to those obtained using a commercial solver, Gurobi. We also compare clustering quality to the clusters obtained using the popular Louvain modularity maximization method. Our initial results clearly demonstrate the superiority of our problem formulations combined with our Boltzmann machines. In the case of smaller less complex graphs, our formulations solved using Boltzmann machines provide the same solutions as Gurobi, but with solution times that are orders of magnitude lower. In the case of larger and more complex graphs, Gurobi either fails to return meaningful results within a reasonable time frame or returns inferior results. Finally, we also note that both our clustering formulations, the distance minimization and K-medoids, when solved using our Boltzmann machines, yield clusters of superior quality to those obtained with the Louvain algorithm.

Retinal shadows produced by myopia control spectacles.

To analyse ocular coherence tomography (OCT) images of the retinal shadows caused by defocus and diffusion optics spectacles. One eye was fitted successively with the Hoya Defocus Incorporated Multiple Segments (DIMS) spectacle lens, two variations of the +3.50 D peripheral add spectacle (DEFOCUS) and the low-contrast dot lens (Diffusion Optics Multiple Segments, DOMS); each at a vertex distance of 12 mm. Simultaneously, a retinal image of the macular region with central fixation was obtained using infrared OCT. The corneal power and intraocular distances were determined using an optical biometer. The retinal images for the DIMS and DOMS lenses showed patterns of obvious retinal shadows in the periphery, while the central 10-11° remained clear. The DEFOCUS lens produced a darkened peripheral area. Dividing the size of the retinal pattern, measured with the calliper of the OCT software, by the actual size on the spectacle lens gave a magnification of -0.57 times. This is consistent with the incoming OCT beam being imaged to a position approximately 31 mm beyond the front of the eye. [Correction added on 26 October 2023 after first online publication: The preceding paragraph was corrected.] CONCLUSION: With device-specific correction, retinal OCT images can help visualise the regions affected by the defocus or lowered contrast induced by myopia control spectacles. This is of potential value for improving myopia therapies.

Die Anwendung des telezentrischen Strahlenganges in der Augenoptik zur Bestimmung des Hornhautscheitelabstandes

Purpose. Nowadays, a video centering system is often used to determine centering data. Nevertheless, these are often additionally checked manually afterwards. An important pa- rameter is the vertex distance (VD). This is often determined using a measuring ruler with a millimeter scale. Also during refraction a classical millimeter scale on the trial frame is used to determine the VD. Due to the difference between the location of the measuring scale used and the location of the real VD, there is a systematic measurement error. Material and Methods. At the Berlin University of Applied Sciences (BHT), a measurement tool was developed on the basis of an object-side telecentric beam path, which enables the determination of the real VD independent of distance. The validation of this measurement tool was performed in two different series of measurement. In the first series of tests, the measurements were performed on test subjects using a measuring tool, a video centering system (“visuReal” from Hoya) and a measuring ruler, and the results were compared. In the second series, VD measurements were taken using the measuring tool and millimeter scale on defined test sections for objectification purposes. Results. In the first series of measurements, the VD values obtained using the millimeter scale were lower than those de- termined with the other instruments (statistically significant at the 5% level with Friedman test). The difference between the VD values of the measuring tool and the video centering system, on the other hand, was small on average and not statistically significant. In the series of measurements on de- fined test sections, the measuring tool showed a significantly better approximation to the actual length of the defined test distance than the measuring ruler. Conclusion. The series of measurements show that the de- termination of the VD by the measuring tool and the video centering system are very similar on average and that the measured values of the measuring tool are closer to the orig- inal value than the measured values of the measuring ruler. Thus, the determination of the VD by means of a simple scale should be dispensed with in the future. Keywords telecentric beam path, vertex distance, vertex distance meas- urement, trial frame, refraction

Structural analysis of customized 3D printed plate for pelvic bone by comparison with conventional plate based on bending process

Pelvic bone fracture is highly complex, and its anatomical reduction is difficult. Therefore, patient-specific customized plates have been developed using three-dimensional (3D) printing technology and are being increasingly used. In this study, the reduction status in five representative pelvic fracture models was compared between two groups: the 3D printing plate (3DP) group using a patient-specific 3D printed plate after virtual reduction and the conventional plate (CP) group using a conventional plate by manual bending. The 3DP and CP groups included 10 and 5 cases, respectively. The fractured models were reduced virtually and their non-locking metal plates were customized using 3D printing. The process of contouring the conventional plates to fit the contact surface of the bone with the bending tool was conducted by an experienced pelvic bone trauma surgeon. The reduction and fixation achieved using the two different plate groups was compared, and the significance of differences in the results was analyzed using paired t-tests, after verifying the normality of data distribution. The vertex distances between the surface of the bone and the contact surface of the plate were significantly lower in the 3DP group than in the CP group (0.407 ± 0.342 and 2.195 ± 1.643, respectively, P = 0.008). Length and angular variations, which are measurements of the reduction state, were also lower in the 3DP group than in the CP group (length variation: 3.211 ± 2.497 and 5.493 ± 3.609, respectively, P = 0.051; angular variation: 2.958 ± 1.977 and 4.352 ± 1.947, respectively, P = 0.037). The customized 3D printed plate in the virtual reduction model provided a highly accurate reduction of pelvic bone fractures, suggesting that the customized 3D printed plate may help ensure easy and accurate reduction.

Vertex transitivity and distance metric of the quad-cube

The quad-cube is a special case of the metacube that itself is derivable from the hypercube. It is amenable to an application as a network topology, especially when the node size exceeds several million. This paper presents the following welcome properties of the graph, relating to its structure: (1) vertex transitivity that facilitates the working of an algorithm meant for a “local” context in the global context as well, and (2) an exact formula for the distance metric, which leads to a precise result on the distance-wise vertex distribution of the graph and an exact formula for the average vertex distance. Remarkably, the vertex distribution of the quad-cube resembles, to a large extent, the vertex distribution of the twin copies of a hypercube. In a parallel study, the author recently reported similar results with respect to the dual-cube (Jha in J Supercomput 78:17758–17775, 2022)

PAC-Net: Multi-pathway FPN with position attention guided connections and vertex distance IoU for 3D medical image detection.

Automatic medical image detection aims to utilize artificial intelligence techniques to detect lesions in medical images accurately and efficiently, which is one of the most important tasks in computer-aided diagnosis (CAD) systems, and can be embedded into portable imaging devices for intelligent Point of Care (PoC) Diagnostics. The Feature Pyramid Networks (FPN) based models are widely used deep-learning-based solutions for automatic medical image detection. However, FPN-based medical lesion detection models have two shortcomings: the object position offset problem and the degradation problem of IoU-based loss. Therefore, in this work, we propose a novel FPN-based backbone model, i.e., Multi-Pathway Feature Pyramid Networks with Position Attention Guided Connections and Vertex Distance IoU (abbreviated as PAC-Net), to replace vanilla FPN for more accurate lesion detection, where two innovative improvements, a position attention guided connection (PAC) module and Vertex Distance IoU Vertex Distance Intersection over Union loss, are proposed to address the above-mentioned shortcomings of vanilla FPN, respectively. Extensive experiments are conducted on a public medical image detection dataset, i.e., Deeplesion, and the results showed that i) PAC-Net outperforms all state-of-the-art FPN-based depth models in both evaluation metrics of lesion detection on the DeepLesion dataset, ii) the proposed PAC module and VDIoU loss are both effective and important for PAC-Net to achieve a superior performance in automatic medical image detection tasks, and iii) the proposed VDIoU loss converges more quickly than the existing IoU-based losses, making PAC-Net an accurate and also highly efficient 3D medical image detection model.

Theoretical performance of progressive addition lenses with poorly measured individual parameters.

The aim of this paper was to present a theoretical study of how poorly measured individual parameters affect the optical performance of progressive addition lenses (PALs). Modern progressive lenses can be prescribed based on parameters such as vertex distance, pantoscopic and wrap angles. These parameters can be measured from the lens wearer using specific devices; however, not all of them can be measured with the same precision, and the impact of measurement errors on the lens performance is still unknown. Data from 1900 patients were used to simulate the performance of four PAL designs with different degrees of complexity: perfect individual design, individual design with induced errors in the individual parameters, optimised design and conventional/basic design. For each patient and design, a quality metric was calculated to describe the optical performance of the lens. The design having the best performance was the perfect individual design, followed by the individual design with induced errors, the optimised design and finally the conventional/basic design. Individual designs with measurement errors have better optical performance than lenses with less complexity, such as the optimised or conventional designs. This knowledge is useful for the eye care professional to make informed choices when dispensing these lenses.

On spectral radius and Nordhaus-Gaddum type inequalities of the generalized distance matrix of graphs

If $Tr(G)$ and $D(G)$ are respectively the diagonal matrix of vertex transmission degrees and distance matrix of a connected graph $G$, the generalized distance matrix $D_{\alpha}(G)$ is defined as $D_{\alpha}(G)=\alpha ~Tr(G)+(1-\alpha)~D(G)$, where $0\leq \alpha \leq 1$. If $\rho_1 \geq \rho_2 \geq \dots \geq \rho_n$ are the eigenvalues of $D_{\alpha}(G)$, the largest eigenvalue $\rho_1$ (or $\rho_{\alpha}(G)$) is called the spectral radius of the generalized distance matrix $D_{\alpha}(G)$. The generalized distance energy is defined as $E^{D_{\alpha}}(G)=\sum_{i=1}^{n}\left|\rho_i -\frac{2\alpha W(G)}{n}\right|$, where $W(G)$ is the Wiener index of $G$. In this paper, we obtain the bounds for the spectral radius $\rho_{\alpha}(G)$ and the generalized distance energy of $G$ involving Wiener index. We derive the Nordhaus-Gaddum type inequalities for the spectral radius and the generalized distance energy of $G$.

Vertex transitivity, distance metric, and hierarchical structure of the dual-cube

The dual-cube, derivable from the hypercube, admits a number of good properties that render it as a good network topology, especially when the node size exceeds several million. This paper presents several other welcome characteristics of the graph. Prominent among them are: (1) vertex transitivity that facilitates the working of an algorithm meant for a “local” context in the global context as well, (2) an exact formula for the distance between two nodes, which leads to a precise result on the distance-wise node distribution of the graph and an exact formula for the average node distance, and (3) a hypercube-like hierarchical structure of the graph that is amenable to an inductive treatment.