Boundary Map Research Articles

Replica Rényi wormholes and generalised modular entropy in JT gravity

We consider the problem of computing semi-classical Rényi entropies of CFT on AdS2 backgrounds in JT gravity with nongravitating baths, for general replica number n. Away from the n → 1 limit, the backreaction of the CFT twist fields on the geometry is nontrivial. For one twist field insertion and general n, we show that the quantum extremal surface (QES) condition involves extremisation of the generalised modular entropy, consistent with Dong’s generalisation of the Ryu-Takayanagi formula for general n. For multiple QES we describe replica wormhole geometries using the theory of Fuchsian uniformisation, explicitly working out the analytically tractable case of the n = 2 double trumpet wormhole geometry. We determine the off-shell dependence of the gravitational action on the QES locations and boundary map. In a factorisation limit, corresponding to late times, we are able to relate this action functional to area terms given by the value of the JT dilaton at the (off-shell) QES locations, with computable corrections. Applied to the two-sided eternal black hole, we find the n-dependent Page times for Rényi enropies in the high temperature limit.

Determination of five-parameter grain boundary characteristics in nanocrystalline Ni-W by scanning precession electron diffraction tomography

Determining the full five-parameter grain boundary characteristics from experiments is essential for understanding grain boundaries impact on material properties, improving related models, and designing advanced alloys. However, achieving this is generally challenging, in particular at nanoscale, due to their 3D nature. In our study, we successfully determined the grain boundary characteristics of an annealed nickel-tungsten alloy (NiW) nanocrystalline needle-shaped specimen (tip) containing twins using Scanning Precession Electron Diffraction (SPED) Tomography. The presence of annealing twins in this face-centered cubic (fcc) material gives rise to common reflections in the SPED diffraction patterns, which challenges the reconstruction of orientation-specific virtual dark field (VDF) images required for tomographic reconstruction of the 3D grain shapes. To address this, an automated post-processing step identifies and deselects these shared reflections prior to the reconstruction of the VDF images. Combined with appropriate intensity normalization and projection alignment procedures, this approach enables high-fidelity 3D reconstruction of the individual grains contained in the needle-shaped sample volume. To probe the accuracy of the resulting boundary characteristics, the twin boundary surface normal directions were extracted from the 3D voxelated grain boundary map using a 3D Hough transform. For the sub-set of coherent Σ3 boundaries, the expected {111} grain boundary plane normals were obtained with an angular error of <3° for boundary sizes down to 400 nm². This work advances our ability to precisely characterize and understand the complex grain boundaries that govern material properties.

Combining statistical analyses and GIS-based approach for modeling the sanitary boundary of drinking water wells in Yaoundé, Cameroon

In slums and urban areas with unplanned housing such as in the city of Yaounde, Cameroon, poor water quality and inadequate sanitation pose significant health risks. The absence of locally-defined sanitary boundaries, tailored to hydrogeological conditions, hinders effective zoning and land use planning, exacerbating environmental degradation and health hazards. In this study, the sanitary boundary between drinking water wells and sources of pollution in the city of Yaoundé was defined using statistical analysis techniques and Geographic Information Systems (GIS). The Groundwater Quality Index (GWQI) and certain significant parameters affecting water quality notably the transmissivity of the aquifer and well depth were used to establish the sanitary boundary equation which was then interpolated in a GIS environment to obtain the sanitary boundary map of the study area. The linear equation deduced from the significant factors was defined to map the health boundaries between wells and pollution sources for a nominal value of the GWQI (GWQI = 25). Of the 112 wells analysed, 37 % had an excellent GWQI, 16 % were good while the remaining 47 % were poor. Statistical analysis showed a strong correlation between the GWQI and significant factors of groundwater pollution, such as the distance between well and pit latrines (r = −0.753), the aquifer transmissivity of the formation (r = 0.671) and the depth of the wells (r = - 0.855) but no correlation with elevation (r = 0.017) and well age (r = 0.090). Linear regression analysis confirmed the association of the GWQI with the main factors of pollution (p ≤ 0.05). A coefficient of determination of R2 = 0.85 was obtained when validating the linear regression plot based on independent data between measured and predicted GWQI. The sanitary boundary map shows that the wells in our study area should be located between 39 m and 370 m, with an average value of 215 m. New regulations on the distance between well and pit latrines are essential to prevent groundwater pollution.

Dam Break Analysis of Batu Dam Using Hec-Ras

In Malaysia, dams are commonly built because they benefit the local community in several ways, especially through agricultural production and flood control. Nevertheless, an unexpected containment breach could result in the loss of life and property in a populated area downstream due to its huge potential energy reservoir. Dam break event simulations are essential for identifying and mitigating risks associated with possible dam breaches. Batu Dam has the highest percentage of the population at risk (PAR) and most likely exposed to the flood disaster due to dam break. From flood boundary maps, it was estimated that 78% of residential areas would be affected if a dam break disaster occurs. From the simulation, the maximum depth can reach up to 18 m with an estimated flow speed between 0.2 m/s – 3 m/s. At these depth and flow speed, people may lose strength and unable to control themselves in flood and would cause death and injury. Flood arrival time took 15 to 22 hours for flooding to arrive downstream with a maximum flood depth of 5.07 m at Persiaran Jasa Utama and the highest depth of 12.62 m at Kampung Baru Batu Caves with flood velocity between 1.60 m/s to 1.46m/s. Analysis and simulation of embankment dam breach events and the resulting floods are crucial for distinguishing and mitigating dangers from potential dam failures. Accurate forecast of inundation levels and the time of flood wave arrival at downstream key places is required for the development of effective emergency response plans.

Fortifying Patient Data Security in the Digital Era: A Two-Layer Approach with Data Hiding and Electrocardiogram

In an era dominated by digital technology, the imperative of securing patient data cannot be overstated. The deployment of advanced protective measures, including encryption, firewalls, and robust authentication protocols, is an absolute necessity when it comes to preserving the confidentiality and integrity of sensitive patient information. Furthermore, the establishment of stringent access controls serves as a fundamental safeguard, ensuring that only authorized personnel are granted access to this invaluable data. An innovative development in the realm of patient data protection is the utilization of ElectroCardioGram (ECG) as a unique identifier for individuals. In the context of this study, ECG data is ingeniously embedded within cover images using a technique known as Reversible Data Hiding (RDH). RDH offers a distinctive advantage by ensuring that the original image can be fully restored without loss of data after extraction. This achievement is made possible through the application of inventive pixel interpolation and histogram shifting algorithms. Crucially, the study's simulations, conducted across a diverse array of images, underscore the enhanced embedding capacity of the RDH technique while maintaining a commendable balance in terms of the Peak Signal to Noise Ratio (PSNR) and boundary map. This empirical evidence corroborates the efficacy of the approach and its potential to provide an advanced level of security for patient data in the digital landscape.

Spatial analysis of electrical distribution system in obio-akpor local government area, rivers state, Nigeria

The distributions of quality electrical energy to end users and, achieving a reasonable level of customer’s satisfaction from the electricity distribution companies servicing most area are faced with divers’ spatial problems particularly with the use of dilapidated infrastructures and poor services. This study used spatial techniques to analyze the spatial characteristics of the electrical distribution system in Obio-Akpor Local Government Area, Rivers State. It also examined the ward pattern of Port Harcourt Electricity Distribution (PHED) customer’s satisfaction and also predicted the ward level of customer’s satisfaction within the study area. Primary and secondary data were used for the study. The primary data on customer’s satisfaction of PHED services was obtained from questionnaire survey. Purposive sampling method was used for this study and the population for the study is the entire customers of PHED in the study area. The secondary data consist of ward boundary map of the study area, satellite image, PHED network spatial data and attribute data of all the 3200 (three thousand two hundred) transformers (11/0.415KVA and 33/0.415KVA) within the study area as at the time of this study. Geospatial analysis such as clip analysis, buffering were carried. The data attribute were analyzed using average nearest neighbor analysis, kernel density, zonal statistics, inverse distance weighting and geographical weighted regression to obtain the desired aim of the study. The result show that, the location pattern of PHED transformers are clustered. Result further reveal that the ward pattern of customer’s satisfaction are geography dependent with either positive, negative or mixed relationship.

Enhancing Geographic Information System Skills through Boundary Mapping Training at Pesantren Rahmatullah, Lempake, Samarinda

This program designed to enhance the skills and knowledge of students and teaching staff at Pesantren Rahmatullah (Islamic boarding school) regarding the use of Geographic Information System (GIS) technology in boundary mapping. The initiative was launched recognizing the importance of understanding territorial boundaries in the context of natural resource management, development planning, and disaster mitigation in the surrounding areas. The training includes a series of theoretical sessions and field practices. The first stage involves learning how to gather coordinate points in the field using the Garmin 60 CSX GPS device. The second stage focuses on field data processing and coordinate data correction, covering basic GIS knowledge, introduction to GIS software, and usage of Autodesk Map software and Arc GIS 10.8. The third stage is the scaled printing of processed field data. The duration of the training is one semester, following the curriculum set by the Rahmatullah Islamic boarding school. This training aims to equip participants with the necessary skills to produce accurate and informative boundary maps, which will later serve as tools for decision-making and strategic planning at Rahmatullah Lempake Islamic boarding school in Samarinda. Additionally, this activity also aims to enhance the boarding school’s awareness and capacity in utilizing geographic information technology for educational and environmental management purposes.

Exploring Classifiers with Differentiable Decision Boundary Maps

AbstractExplaining Machine Learning (ML) — and especially Deep Learning (DL) — classifiers' decisions is a subject of interest across fields due to the increasing ubiquity of such models in computing systems. As models get increasingly complex, relying on sophisticated machinery to recognize data patterns, explaining their behavior becomes more difficult. Directly visualizing classifier behavior is in general infeasible, as they create partitions of the data space, which is typically high dimensional. In recent years, Decision Boundary Maps (DBMs) have been developed, taking advantage of projection and inverse projection techniques. By being able to map 2D points back to the data space and subsequently run a classifier, DBMs represent a slice of classifier outputs. However, we recognize that DBMs without additional explanatory views are limited in their applicability. In this work, we propose augmenting the naive DBM generating process with views that provide more in‐depth information about classifier behavior, such as whether the training procedure is locally stable. We describe our proposed views — which we term Differentiable Decision Boundary Maps — over a running example, explaining how our work enables drawing new and useful conclusions from these dense maps. We further demonstrate the value of these conclusions by showing how useful they would be in carrying out or preventing a dataset poisoning attack. We thus provide evidence of the ability of our proposed views to make DBMs significantly more trustworthy and interpretable, increasing their utility as a model understanding tool.

Maritime Boundary Delimitation using Different Methods of GIS - A Case Study of the France-United Kingdom (Jersey Island) Boundaries

Abstract Maritime and territorial zone disputes have created tensions and conflicts between countries with contiguous or adjacent maritime zones. France escalated its fishing rights dispute with the UK by announcing that it had seized an unlicensed British vessel operating in French waters. This paper examines the incident by reviewing the geographical condition and creating a maritime boundary map between the France-United Kingdom (Jersey) that complies with the UNCLOS 1982 convention. This research uses GIS software and bathymetry data to create maritime boundaries according to the UNCLOS 1982 convention. GIS methods used include Buffer, Thiessen Polygon and Geocap Maritime Delimitation toolbox. According to the “geocap maritime delimitation” toolbox, the total water area measures 509 square miles, with an even division between the two areas. However, when utilizing the buffer and Thiessen polygon methods, there is a notable variation of 56 square miles between the water areas of Jersey and France. The delimitation method from the Geocap Maritime Delimitation toolbox was chosen as the best method because this tool can generate critical points and baselines from the closest point between two baselines that follow UNCLOS convention and produce a solution with the equidistance division between the two countries.

The spatiotemporal epidemiological study on human brucellosis in shenyang, China from 2013 to 2022

BackgroundEpidemiological characteristics of human brucellosis (HB) have changed over the last decade. In this study, we depicted the spatiotemporal features of HB in Shenyang, China, from 2013 to 2022 and the objective was to visualise spatiotemporal patterns and identify high-risk regions with the purpose to provide evidence for HB prevention and control. MethodsWe performed an observational epidemiological study using HB data obtained from the National Notifiable Disease Reporting System (NNDRS). Joinpoint regression analysis was employed to determine the changing trends in the annual incidence. A vector boundary map of Shenyang was used to visualise spatial distribution. Spatial autocorrelation was identified using both global and local Moran's autocorrelation coefficients, while hotspot areas were determined using the Getis-Ord statistic. ResultsA combined sum of 4103 HB cases were analysed, and the average level of annual incidence of HB was 5.52 per 100,000. The incidence of HB showed obvious seasonality, with a notable peak observed from April to July (summer peak). The annual incidence in Shenyang has been on the rise since 2013, with an annual percentage change (APC) of 6.39% (95%CI 1.29%, 12.39%). Xinmin County exhibited the most elevated average annual incidence rate, with Faku County ranking second. The average annual incidence in rural areas exhibited a significantly greater disparity compared to suburban areas (P < 0.001), whereas the incidence rate in suburban areas demonstrated a significantly higher contrast when compared to urban areas (P < 0.001). A clustered distribution of the annual incidence of HB was observed for all years from 2013 to 2022. Abnormally high values were found in suburban areas, and no abnormally high values were found after 2017. The low-low clustering areas were found in urban as well as suburban areas from 2013 to 2022. Hotspots (P < 0.05) were located in rural areas, while cold spots (P < 0.05) were found in both urban and suburban areas. Since 2020, there have been no hotspots in Shenyang. ConclusionsRural areas are high-risk areas for HB and may be key to controlling HB epidemics. Although the annual incidence of HB in rural areas has increased, owing to the stability of spatial relationships and the disappearance of hotspots, there is little possibility of outbreaks; however, stricter monitoring should be applied in rural areas to prevent the emergence of new transmission routes.

Focus Group Discussion Pembuatan Peta Batas Wilayah Padukuhan di Kalurahan Kebonharjo, Kapanewon Samigaluh, Kabupaten Kulon Progo

Geospatial information has expanded widely, including development and regional aspects. Kebonharjo sub-district, which is in the Kapanewon Girimulyo administrative area, Kulon Progo Regency, is committed to participating in regional development by trying to optimize its various potentials. However, the database and profile of potentials (and problems) are still limited, need better documented, and are still limited to tabular data. The database and profile will have added value if presented with a spatial approach like a map. Community service programs were carried out to make a map as a basis for developing spatial data and profiles. In the preparation step, the agendas include discussion with the village official to scope the activities and products, downloading satellite image data as a basis for mapping, and collecting maps for initial reference for area boundaries. Next, the technical activities for making the map were started by carrying out the Focus Group Discussion with village officials and community representatives from all of the hamlets to obtain agreement on the boundaries of the hamlet and Rukun Tetangga (RT) areas. The results of the Focus Group Discussion were digitized and processed in the laboratory to obtain map products and an overview of public understanding regarding mapping. The output achieved from the community service was the Padukuhan and Rukun Tetangga Area Boundary Map products, both in printed and soft file versions.

Determining climate classifications and producing climate border maps with GIS of Safranbolu district, Karabük, Türkiye.

Knowing climate characteristics enables the detection of particular climate characteristics and their boundaries. This situation is essential in terms of providing sustainable use of areal resources and directing land use plans. For this reason, in this study, climate boundary maps of the Safranbolu district were created based on the need to form a basis for planning. For this purpose, measurement data of all meteorological stations in the district for the last 30 years were obtained; data were associated with the location, and the water balance of each station was calculated using the Thornthwaite climate classification method. In addition, the climate type was determined using different climate classification methods, and the results were compared. All applied methods have shown that Safranbolu has a humid climate; however, the humidity value in the north of Safranbolu is slightly higher than that in the central and southern parts. In addition, water shortage in the north of Safranbolu is observed in July-August, while water shortage in the central and southern parts is observed in July-August-September. Considering the long-term precipitation average of the Safranbolu district, the highest annual precipitation is observed in March and the lowest in August. Etp and Etr throughout the district are highest in July and lowest in January. Surplus water and surface flow occur in the months between December and May, with the highest amount of surface flow occurring in March. There is no month without rain in Safranbolu. Safranbolu, which is on the UNESCO World Heritage List, is a visiting area for local and foreign tourists because of its cultural, architectural, and historical features and geotourism potential. In addition to its current agricultural activities, the cultivation of the "Saffron" plant, which gives its name to the district, and its forest assets cause an increase in both the tourism capacity and population of the district. Considering all of these, studies on climate change risk management and water resources management in Safranbolu have been conducted.

Planar matrices and arrays of Feynman diagrams: poles for higher k

Planar arrays of tree diagrams were introduced as a generalization of Feynman diagrams that enable the computation of biadjoint amplitudes mn(k) for k > 2. In this follow-up work, we investigate the poles of mn(k) from the perspective of such arrays. For general k, we characterize the underlying polytope as a Flag Complex and propose a computation of the amplitude-based solely on the knowledge of the poles, whose number is drastically less than the number of the full arrays. As an example, we first provide all the poles for the cases (k, n) = (3, 7), (3, 8), (3, 9), (3, 10), (4, 8) and (4, 9) in terms of their planar arrays of degenerate Feynman diagrams. We then implement simple compatibility criteria together with an addition operation between arrays and recover the full collections/arrays for such cases. Along the way, we implement hard and soft kinematical limits, which provide a map between the poles in kinematic space and their combinatoric arrays. We use the operation to give a proof of a previously conjectured combinatorial duality for arrays in (k, n) and (n − k, n). We also outline the relation to boundary maps of the hypersimplex Δ k,n and rays in the tropical Grassmannian Tr(k,n) .

How to characterise the anisotropy of laser powder bed fusion-processed parts? Towards a surrogate, non-destructive indentation-based approach

This work proposes a non-destructive indentation (NDI)-based surrogate mechanical testing framework for anisotropy and mechanical property evaluation of LPBF processed Inconel 718 superalloy. A Knoop-hardness tester was employed to develop the surrogate framework. Further post-heat treatments (PHTs) were performed at various cooling rates. The as-printed and PHT (SA, SB, SC, and SD) samples were characterized using X-ray diffraction (XRD) optical microscopy (OM), scanning electron microscopy (SEM), and electron back-scattered diffraction (EBSD) techniques. The yield locus plots show strong anisotropy for the as-printed sample. The IPF maps and pole figures for the as-printed samples showed elongated columnar grains with strong fiber texture along the (001) plane parallel to the build direction. They corroborated sufficiently with XRD, grain boundary map (GBM), and Kernel average misorientation (KAM) analysis. The yield locus shape of samples subjected to homogenization treatment becomes a nearly uniform ellipse with a reduction in the difference between σx and σy values, which can be attributed to the recrystallization of grains as observed by the transition from low-angle grain boundaries (LAGBs) to high angle grain boundaries (HAGBs). The PHT samples show a further increase in yield loci size due to the precipitation of γ’ and γ” strengthening phases due to aging treatment and corroborated with higher Taylor factor and dislocation density than the as-printed samples. The yield loci were sensitive to the PHT's cooling rates. Notably, among PHT ones, ‘SA’ samples exhibited a strong correlation (R2 ≈ 97.5 %) between the Taylor factor and yield locus. It was attributed to slower cooling rates (furnace cooled) with noticeably enhanced precipitation of strengthening phases, an increase in the volume fraction of recrystallized grains (from grain orientation spread (GOS) map), corroborating with higher dislocation density due to local strain as inferred from EBSD analysis. The proposed NDI surrogate approach was initially validated on an as-printed Inconel 718 stator blade. The yield locus showed a strong correlation between the stator blade and the as-printed sample, indicating the effectiveness of the proposed methodology.

A characterization of crossed self-similarity on crossed modules in L-algebras

Abstract We introduce crossed modules in cycloids, as a generalization of cycloids, which are algebraic logical structures arising in the context of the quantum Yang–Baxter equation. As a spacial case, we in particular focus on the crossed modules of $L-$algebras. These types of crossed modules are exceptional, since the category of $L-$algebras is not protomodular, nor Barr-exact, but it nevertheless has natural semidirect products that have not been described in category theoretic terms. We identify crossed ideals of crossed module in $L-$algebras, and obtain some characteristics of these objects that are normally not encountered on crossed modules of groups or algebras. As a consequence, we characterize crossed self-similarity completely in terms of properties of $L-$algebras and the boundary map forming the crossed module.

A novel machine learning method to exploit EBSD and nanoindentation for TRIP steels microstructures analysis

The recognition of phases and microstructures in TRIP-assisted bainitic-ferritic steels is challenging and requires sophisticated techniques to gain insights and reveal mechanical features with nanoscale precision. EBSD and nanoindentation have been employed to assess the surface composition and their properties within a reporting depth of 30 nm. Correlative mechanical microscopy and data science were used to overcome the shortcomings associated with the lack of an inclusive solution that combines the metadata from both techniques. A modular methodology is presented, which involves routines for exploiting structural and mechanical data via reproducible Machine Learning models (code and data are shared). The approach is structured to facilitate reuse by research community for correlating characterization mapping data, not limited to nanoindentation and EBSD. Gaussian mixture models are adopted to extract mechanical phases utilizing the nanomechanical properties. The K-means++ method is used for the first time to mine information from Inverse Polar Figure (IPF) mapping about anisotropy and to extract the knowledge from images for each grain, including grain coordinates and size. Moreover, k-nearest-neighbours regression was used to perform data imputation to fill in the values of descriptors related to missing coordinates relative to those of nanoindentation, grain boundary, EBSD phase, and EBSD anisotropy maps.

Insights into thermomechanical fatigue behavior of nitrogen alloyed 316LN stainless steel under various temperature cycling ranges

Thermomechanical fatigue (TMF) failure has become one of the most important life-limiting factors of components exposure to the high temperature in the fourth-generation sodium-cooled fast reactor (SFR) nuclear power plant. Therefore, TMF tests at different temperature cycling ranges are performed to study the cyclic deformation behavior and damage mechanism of a nitrogen alloyed 316LN stainless steel. Moreover, the isothermal fatigue (IF) tests at the maximum temperature of TMF cycling are conducted for comparison. The cyclic hardening and softening response are analyzed, taking into account the phenomenon of dynamic strain aging which occurs at the temperature range of 350 °C–650 °C. Furthermore, the critical strain corresponding to the occurrence of serrated stress flow in engineering stress-strain curves keeps decreasing from 28.94% at 350 °C to 0.09% at 650 °C. The distribution of plastic deformation and the degree of strain localization are evaluated by the characterization results of kernel average misorientation map, high/low angle grain boundary map and dislocation configuration. The dominant damage mechanism and its corresponding cracking behavior in both IF and TMF tests are analyzed based on the observation of fracture surface morphology. In addition, the sequence order of fatigue life is determined as IF < IP-TMF < OP-TMF. Moreover, the maximum difference of fatigue life between IF test and TMF test occurs at the temperature range of 400 °C–600 °C, in which the IP and OP life is about 2.91 and 3.65 times larger than the IF life. The results in this work provide reliable data support and theoretical guidance for the fatigue design of high-temperature components in SFR.

Overcoming the Challenge of Accurate Segmentation of Lung Nodules: A Multi-crop CNN Approach.

Lung nodules are generated based on the growth of small and round- or oval-shaped cells in the lung, which are either cancerous or non-cancerous. Accurate segmentation of these nodules is crucial for early detection and diagnosis of lung cancer. However, lung nodules can have various shapes, sizes, and densities, making their accurate segmentation a difficult task. Moreover, they can be easily confused with other structures in the lung, including blood vessels and airways, further complicating the segmentation process. To address this challenge, this paper proposes a novel multi-crop convolutional neural network (multi-crop CNN) model that utilizes different sized cropped regions of CT scan images for accurate segmentation of lung nodules. The model consists of three modules, namely the feature representation module, boundary refinement module, and segmentation module. The feature representation module captures features from the lung CT scan image using cropped regions of different sizes, while the boundary refinement module combines the boundary maps and feature maps to generate a final feature map for the segmentation process. The segmentation module produces a high-resolution segmentation map that shows improved accuracy in segmenting cancerous lung nodules. The proposed multi-crop CNN model is evaluated on two segmentation datasets namely LUNA 16 and LIDC-IDRI with an accuracy of 98.3% and 98.5%, respectively. The performances are measured in terms of accuracy, recall, precision, dice coefficient, specificity, AUC/ROC, Hausdorff distance, Jaccard index, and average Hausdorff. Overall, the proposed multi-crop CNN model demonstrates the potential to enhance the lung nodule segmentation accuracy, which could lead to earlier detection and diagnosis of lung cancer and ultimately reduce mortality rates associated with the disease.

Weighted product of point clouds and simplicial complexes

AbstractThis paper extends the concept of weighted point clouds and weighted simplicial complexes by introducing product point clouds and product simplicial complexes within a commutative ring with unity. Within an integral domain, the introduction of a weighted product chain group, along with the induced product weighted homomorphism and weighted product boundary maps, leads to significant outcomes and findings. To explore the algebraic characteristics of a weighted product structure, we introduce the concept of weighted product homology. This homology considers the relationship of weights assigned to elements within the structure and their impact on the structure’s underlying algebraic properties.

Occlusion Boundary Prediction and Transformer Based Depth-Map Refinement From Single Image

Due to the numerous applications of boundary maps and occlusion orientation maps (ORI-maps) in high-level vision problems, accurate estimation of these maps is a crucial task. The existing deep networks employ a single-stream network to estimate the relation between boundary map and ORI-map estimation. However, these networks fail to explore significant individual information separately. To resolve this problem, in this paper, we propose a novel two-stream generative adversarial network (GAN) for boundary map and ORI-map estimation, named OBP-GAN. The proposed OBP-GAN consists of two streams known as BP-GAN and OR-GAN. The BP-GAN estimates the boundary map, and the OR-GAN predicts the ORI-map. The boundary and ORI-map can also be useful cues for the task of depth-map refinement from single images. Therefore, in this work, we propose a transformer-based depth-map refinement network (TRANSDMR-GAN) for refining the depth estimated from monocular images using boundary and ORI-map. We conducted extensive analyses on indoor and outdoor datasets to validate our proposed OBP-GAN and TRANSDMR-GAN. The extensive experimental analysis and ablation study demonstrate the ability of the proposed OBP-GAN to generate state-of-the-art occlusion boundary maps. Furthermore, we show that the proposed network, TRANSDMR-GAN, can generate an edge-enhanced depth map without degrading the accuracy of the initial depth map.