Binary Space Partitioning Research Articles

A nonrevisiting genetic algorithm based on multi-region guided search strategy

Recently, nonrevisiting genetic algorithms have demonstrated superior capabilities compared with classic genetic algorithms and other single-objective evolutionary algorithms. However, the search efficiency of nonrevisiting genetic algorithms is currently low for some complex optimisation problems. This study proposes a nonrevisiting genetic algorithm with a multi-region guided search to improve the search efficiency. The search history is stored in a binary space partition (BSP) tree, where each searched solution is assigned to a leaf node and corresponds to a search region in the search space. To fully exploit the search history, several optimal solutions in the BSP tree are archived to represent the most potential search regions and estimate the fitness landscape in the search space. Except for the conventional genetic operations, the offspring can also be generated through multi-region guided search strategy, where the current solution is first navigated to one of the candidate search regions and is further updated towards the direction of the optimal solution in the search history to speedup convergence. Thus, multi-region guided search can reduce the possibility of getting trapped in local optima when solving problems with complex landscapes. The experimental results on different types of test suites reveal the competitiveness of the proposed algorithm in comparison with several state-of-the-art methods.

Trapezoidal neutrosophic teaching learning-based optimization in enhancing accuracy of diabetes prognosis

Diabetes is one of chronic diseases in which blood glucose (sugar) level soar up high where human body are incapable to absorb it properly. It is important to have an appropriate diagnosis for proper management and treatment. The aim of this manuscript is to provide a more accurate diabetes prediction model through the new adaptive Trapezoidal Neutrosophic Teaching Learning-Based Optimization (TLBO) method. In order to address the inherent uncertainties and imprecisions in medical data, the suggested model makes use of the resilience of Trapezoidal Neutrosophic sets. The Trapezoidal Neutrosophic set theory provides a suitable basis for developing rule/knowledge-based systems in the medical field. The present investigation makes use of the dataset acquired from the Pima Indians Diabetes Database (PIDD) website, which has an extensive global collection of diabetes datasets. The performance of our model is evaluated against several existing methodologies, including Intuitionistic Neuro-Fuzzy System (INFS) Structure, Fuzzy Logic based Diabetes Diagnosis System (FLDDS), Fuzzy Verdict Mechanism (FVM) for Diabetes Decision, (Fuzzy Expert System) FES, and Hierarchical Neuro-Fuzzy Binary space partitioning System (HNFB-1). Quantitative analysis validates that proposed methodology achieves an exceptional predictive accuracy of 99.89 %, which is substantially higher than the comparative methodologies, namely INFS Structure (88.76 %), FLDDS (87.2 %), FVM for Diabetes Decision (85.03 %), FES (81.7 %), and HNFB-1 (78.26 %). These enhancements demonstrate show how well the suggested model works to lower diagnostic errors and increase dependability.

Entropy‐driven Progressive Compression of 3D Point Clouds

Abstract3D point clouds stand as one of the prevalent representations for 3D data, offering the advantage of closely aligning with sensing technologies and providing an unbiased representation of a measured physical scene. Progressive compression is required for real‐world applications operating on networked infrastructures with restricted or variable bandwidth. We contribute a novel approach that leverages a recursive binary space partition, where the partitioning planes are not necessarily axis‐aligned and optimized via an entropy criterion. The planes are encoded via a novel adaptive quantization method combined with prediction. The input 3D point cloud is encoded as an interlaced stream of partitioning planes and number of points in the cells of the partition. Compared to previous work, the added value is an improved rate‐distortion performance, especially for very low bitrates. The latter are critical for interactive navigation of large 3D point clouds on heterogeneous networked infrastructures.

Developing a framework for heterotopias as discursive playgrounds: a comparative analysis of non-immersive and immersive technologies

The discursive space represents the reordering of knowledge gained through accumulation. In the digital age, multimedia has become the language of information, and the space for archival practices is provided by non-immersive technologies, resulting in the disappearance of several layers from discursive activities. Heterotopias are unique, multilayered epistemic contexts that connect other systems through the exchange of information. This paper describes a process to create a framework for Virtual Reality, Mixed Reality, and personal computer environments based on heterotopias to provide absent layers. This study provides virtual museum space as an informational terrain that contains a “world within worlds” and presents place production as a layer of heterotopia and the subject of discourse. Automation for the individual multimedia content is provided via various sorting and grouping algorithms, and procedural content generation algorithms such as Binary Space Partitioning, Cellular Automata, Growth Algorithm, and Procedural Room Generation. Versions of the framework were comparatively evaluated through a user study involving 30 participants, considering factors such as usability, technology acceptance, and presence. The results of the study show that the framework can serve diverse contexts to construct multilayered digital habitats and is flexible for integration into professional and daily life practices.

Rapid survey method for large-scale outdoor surveillance cameras using binary space partitioning

Video surveillance systems have been widely used in public security and urban management. Following the increasing demand for video surveillance in various countries worldwide, the number of outdoor surveillance cameras is rising. Their unified management and layout optimization have become a great challenge in the construction of video surveillance. Although there is a large number of outdoor surveillance cameras, there exists a lack of spatial location information, leading to difficulties regarding their quantification, space management, and construction status analysis. Hence, a method for estimating the location and orientation of outdoor surveillance cameras based on spatial segmentation and the use of a rapid survey device was proposed. Using the position information obtained from the movement of a designed marker and surveillance images simultaneously captured by each camera, we constructed an initial camera space and segmentation plane using binary space partitioning. By recursive segmentation, the real location of each camera is gradually approximated, and the azimuth angle of the camera orientation is calculated, achieving the rapid estimation of the spatial location and orientation of all surveillance cameras. A city area spanning 2.8 km2 was selected as an experimental area to verify the method proposed here, yielding an average error of 1.78 m between the estimated and actual locations of the cameras and a maximum error of 3.87 m. The average offset between the estimated and actual orientation was 3.13°, with a maximum offset of 6°. Thus, the target of the surveillance camera's estimated deviation is still in the visible range of the operator. The proposed method represents a new way for the rapid investigation of outdoor surveillance cameras and provides a basis for their unified management and layout optimization.

A Web3D Rendering Optimization Algorithm for Pipeline BIM Models

BIM (building information modeling) plays a pivotal role in the construction industry. BIM technology tailored for pipelines offers in-depth semantic information and spatial data, bolstering the utility and implementation of digital twin-associated technologies in both architecture and urban planning. This paper introduces a rendering optimization algorithm rooted in the BSP Tree (Binary Space Partitioning Tree). The algorithm is used to address the challenges of slow loading and poor rendering quality of pipeline BIM models when displayed on the web, which stem from large amounts of model data and complex geometric configurations. Initially, the algorithm delves into the geometric distribution traits of the pipeline BIM model from multiple perspectives, pinpointing the spatial division dimension. Subsequently, it employs an adaptive step size technique for spatial segmentation, harmonizing it with real-world application contexts. Concurrently, any superfluous data that emerge are refined to uphold the structural wholeness of the BIM model. This algorithm is adept at systematically arranging and overseeing the BIM model data. Trial outcomes reveal that the AKDT (Adaptive K-Dimensional Tree) algorithm significantly trims the browser’s initial rendering duration while maintaining the model’s accuracy and semantic uniformity. Moreover, it excels in areas such as rendering frame rate, user interaction responsiveness, and data transmission duration. In essence, the algorithm stands out for its efficiency and precision in rendering pipeline BIM models on web platforms, achieving the desired optimization results.

Adaptive Discretization using Voronoi Trees for Continuous POMDPs

Solving continuous Partially Observable Markov Decision Processes (POMDPs) is challenging, particularly for high-dimensional continuous action spaces. To alleviate this difficulty, we propose a new sampling-based online POMDP solver, called A daptive D iscretization using V oronoi T rees (ADVT). It uses Monte Carlo Tree Search in combination with an adaptive discretization of the action space as well as optimistic optimization to efficiently sample high-dimensional continuous action spaces and compute the best action to perform. Specifically, we adaptively discretize the action space for each sampled belief using a hierarchical partition called Voronoi tree, which is a Binary Space Partitioning that implicitly maintains the partition of a cell as the Voronoi diagram of two points sampled from the cell. ADVT uses the estimated diameters of the cells to form an upper-confidence bound on the action value function within the cell, guiding the Monte Carlo Tree Search expansion and further discretization of the action space. This enables ADVT to better exploit local information with respect to the action value function, allowing faster identification of the most promising regions in the action space, compared to existing solvers. Voronoi trees keep the cost of partitioning and estimating the diameter of each cell low, even in high-dimensional spaces where many sampled points are required to cover the space well. ADVT additionally handles continuous observation spaces, by adopting an observation progressive widening strategy, along with a weighted particle representation of beliefs. Experimental results indicate that ADVT scales substantially better to high-dimensional continuous action spaces, compared to state-of-the-art methods.

Multiclass Sparse Centroids With Application to Fast Time Series Classification.

In this article, we propose an efficient multiclass classification scheme based on sparse centroids classifiers. The proposed strategy exhibits linear complexity with respect to both the number of classes and the cardinality of the feature space. The classifier we introduce is based on binary space partitioning, performed by a decision tree where the assignation law at each node is defined via a sparse centroid classifier. We apply the presented strategy to the time series classification problem, showing by experimental evidence that it achieves performance comparable to that of state-of-the-art methods, but with a significantly lower classification time. The proposed technique can be an effective option in resource-constrained environments where the classification time and the computational cost are critical or, in scenarios, where real-time classification is necessary.

Research on 3D Geographic Fence Algorithm Based on Linear Equation

Three-dimensional spatial geo-fencing is a new application based on location-based services (LBS, Location Based Services), which can provide real-time, three-dimensional location change-based related services to fence associates, and its core is to judge the location relationship between target points and fence area, which can be abstracted as point and space figure location relationship discrimination in geometry and mathematics, i.e., point inclusion problem. At present, the mainstream ray method has singularity problem in boundary judgment, and although many improved algorithms have been proposed, most of them are limited to two-dimensional form, which cannot meet the demand of high-precision position discrimination for complex spatial three-dimensional environment. Therefore, this paper starts from the idea of solving a system of linear equations, transforms the judgment of the position relationship between points and polyhedral fences into the judgment of the position relationship between points and planes, and proposes a new algorithm of 3D geo-fencing based on linear equations, which can quickly and accurately complete the judgment of the position relationship between target points and fences. Firstly, the complex polyhedral fence is pre-processed and formed into a binary tree by combining the idea of convex dissection and BSP tree technology; secondly, the target point is recursively queried to be located in the binary tree and the sub-convex polyhedral fence data is obtained; finally, the linear equation algorithm is used to judge the point inclusion between the target point and the sub-convex polyhedron. Experimental results show that the new linear equation algorithm is 40%-48.49% more efficient in convex polyhedral fence position discrimination and 12.5%-20% more efficient in simple nonconvex polyhedral fences compared with the improved ray method.

An evaluation of Kd-Trees vs Bounding Volume Hierarchy (BVH) acceleration structures in modern CPU architectures

Ray tracing is a rendering technique that is highly praised for its realism and image quality. Nonetheless, this is a computationally intensive task that is slow compared to other rendering techniques like rasterization. Bounding Volume Hierarchy (BVH) is a primitive subdivision acceleration mechanism that is the mainly used method for accelerating ray tracing in modern solutions. It is regarded as having better performance against other acceleration methods. Another well-known technique is Kd-Trees that uses binary space partitioning to adaptively subdivide space with planes. In this research, we made an up-to-date evaluation of both acceleration structures, using state-of-the-art BVH and Kd-Trees algorithms implemented in C, and found out that the Kd-Trees acceleration structure provided better performance in all defined scenarios on a modern x86 CPU architecture.

Dynamic Boundary Optimization of Free Route Airspace Sectors

Free Route Airspace (FRA) permits users to freely plan routes between defined entry and exit waypoints with the possibility of routing via intermediate waypoints, which is beneficial to improve flight efficiency. Dynamic management of sectors is essential for the future promotion of full-time FRA applications. In this paper, considering the demand uncertainty at the pre-tactical level, we construct an FRA complexity indicator system and use the XGBoost algorithm to predict the ATC workload. A two-stage sector boundary optimization method is proposed, using Binary Space Partition (BSP) to generate sector boundaries and an A*-based heuristic algorithm to automatically tune them to conform to the operational structure and “direct to” characteristics of FRA. Finally, this paper verifies the effectiveness of the proposed method for balancing ATC workload in a pre-designed Lanzhou FRA in China.

Hedera Nepalensis Cutting Propagation Based on Fractal Theory for Promoting Green Environment

The green environment is the need of the hour. There are many techniques opted by the agriculture experts for Hedera nepalensis cutting propagation. In order to simulate the propagation pattern of Hedera nepalensis cuttings more vividly, the simulation method of Hedera nepalensis cuttings propagation based on fractal theory has been studied in this paper for promoting green environment. The rule of L-system to generate to Hedera nepalensis graphics is elaborated in detail. The composition of generators is represented by strings, and Hedera epalensis fractal images are generated repeatedly by recursive algorithm. Combining BSP technology (Binary Space Partitioning Tree) with L-system, the simulation model of Hedera nepalensis cutting propagation is designed. The mechanism and morphological difference of real Hedera nepalensis cutting propagation are investigated in detail. The different Hedera nepalensis organs are distinguished by static simulation and the mathematical model is established. With the help of GDI+, random functions are flexibly used in programming control to simulate the process of Hedera nepalensis cutting propagation. By determining the growth proportion coefficient of each organ and the growth coefficient of control parameters, the image of Hedera nepalensis cutting reproduction is generated continuously from the dynamic control parameters and the dynamic process of Hedera nepalensis cutting reproduction is simulated. The simulation results show that the simulation error of this method is less than 0.8%. The simulation process is simple and efficient, and the simulation results are vivid and viable to suggest newer solution for Hedera nepalensis cutting propagation to protect the environment.

Methodology for image retrieval based on binary spacepartitioning and perceptual image hashing

The paperfocuses on the content-based image retrieval systems building. The main challengesin the construction of such sys-tems are considered, the components of such systems are reviewed, and a brief overview of the main methods and techniques that have been used in this area to implement the main components of image search systems is given.As one of the options for solving such a problem, an image retrievemethodology based on the binary space partitioning method and the perceptual hashing method is proposed. Space binary partition trees are a data structuresobtained as follows: the space is partitioned by a hyperplane into two half-spaces, and theneach half-space is recursively partitioned until each node contains only a trivial part of the input features. Perceptual hashing algorithms make it possible to represent an image as a 64-bit hash value, with similar images represented by similar hash values. As a metric for determining the distance between hash values, the Hamming distance is used, this counts the number of dis-tinct bits.To organize the base of hash values, a vp-tree is used, which is an implementation of the binary space partitioning struc-ture.For the experimental study of the methodology, the Caltech-256 data set was used, which contains 30607 images divided into 256 categories, the Difference Hash, P-Hash and Wavelet Hash algorithms were used as perceptual hashing algorithms, the study was carried out in the Google Colab environment.As part of an experimental study, the robustnessof hashing algorithms to modification, compression, blurring, noise, and image rotation was examined. In addition, a study was made of the process of building a vp-tree and the process of searching for images in the tree. As a result of experiments, it was found that each of the hashing algorithms has its own advantages and disadvantages. So, the hashing algorithm based on the difference inadjacentpixel values in the image turned out to be the fastest, but it turned out to be not very robustto modification and image rotation. The P-Hash algorithm, based on the use of the discrete cosine transform, showed better resistance to image blurring, but turned out to be sensitive to image compression. The W-Hash algorithm based on the Haar wavelet transform made it possible to construct the most efficient tree structure and provedto be resistant to image modification and compression.The proposed technique is not recommended for use in general-purpose image retrieval systems; however, it can be useful in searching for images in specialized databases. As ways to improve the methodology, one can note the improvement of the vp-tree structure, as well as the search for a more efficient method of image representation, in addition to perceptual hashing.

MULTI VARIATE NEURO-STATISTICAL SPARSE TRANSFORM FOR GRAY SCALE IMAGES

Abstract-- The main objective of this paper is to examine the performance of Neuro- Statistical sparse transformation function for implementation in a still image vector coding based compression system. This paper discusses the important features of low bit-rate image coding which is based on recent developments in the theory of multivariate nonlinear piecewise polynomial approximation in still images. It combines Binary Space Partition (BSP) scheme with Geometric Wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The quality of the reconstructed image is measured objectively using Peak Signal to Noise Ratio. Experimental results show that the proposed image compression system yields higher compression with minimal loss.

Testing Performance (Time Analysis) of Nearest Neighbour (NN) Search Algorithms on K-d Trees

K-d tree (k-dimensional tree) is a space partitioning data structure for organizing points in a k-dimensional space. K-d tree, or Multidimensional Binary Search Tree is a useful data structure for several applications such as searches involving a multidimensional search key (e.g., Range Search and Nearest Neighbour Search). K-d trees are a special case of binary space partitioning trees.KNN Search is a searching algorithm with complexity O(N log N) {N= no. of data points}. This search algorithm is relatively better than brute force search {Complexity= O(n*k); where k=No. of neighbours searched, N=No. of Data Points in Kd tree} for dimensions N>>2D {N=No. of Points, D=Dimensionality of Tree}.Furthermore, Parallel KNN Search is much more efficient and performs better than KNN Search, as it harnesses parallel processing capabilities of computers and thus, results in better search time.This paper tests the time performance of KNN Search and Parallel KNN Search and compares them by plotting it on a 3D graph. A more comprehensive comparison is done by use of 2D graphs for each dimension(from 2 to 20).

Evaluation of Hidden Surface Removal Methods Using Open GL

The research aims to address one of the complex problems that may be encountered when generating computer images for three-dimensional (3D) objects, which is the hidden surface detection and elimination. Several methods have been devised, through the last three decades, to solve this problem. However, the most popular methods used widely nowadays are depth or Z-Buffer (ZB) and Binary Space Partition Tree (BSPT). The first method (ZB) is very simple and more general but requires additional memory to store depth values in addition to intensity. On the other hand, (BSPT) method is more complex to implement but requires memory for pixel intensity only. Modelling graphical database in a binary tree make the dealing with parts of the database feasible. This is so important for clipping a part or more of the database when outside the viewing zone. The focus of this paper is to study these two methods, design an algorithm to implement each of them. After that a reasonable procedure is to found and applied for testing the performance of each of the two methods using exactly the same graphic load. A step by step increase of this load should be possible so that the behavior of the execution time at different complexity level and on average bases can be reported. The outcome results of the two methods should be compared and a recommendation to use which one of them is to be concluded [1]. Since one of the most popular graphics library which is being used during the last ten years and nowadays is the Open Graphic Library( OpenGL) from(Silicon Graphic Incorporation (SGI)[2], the algorithms of this work are implemented and the related software is carried out using this library with visual C platform.

Binary space partitioning visibility tree for polygonal and environment light rendering

Binary space partitioning visibility tree for polygonal and environment light rendering

A new small area estimation algorithm to balance between statistical precision and scale

Combining national forest inventory (NFI) data with auxiliary information allows downscaling and improving the precision of NFI estimates for small domains, where normally too few field plots are available to produce reliable estimates. In most situations, small domains represent administrative units that could greatly vary in size and forested area. In small and poorly sampled domains, the precision of estimates often drop below expected standards.To tackle this issue, we introduce a downscaling algorithm generating the smallest possible groups of domains satisfying prescribed sampling density and estimation error. The binary space partitioning algorithm recursively divides the population of domains in two groups while the prescribed precision conditions are fulfilled.The algorithm was tested on two major forest attributes (i.e. growing stock and basal area) in an area of 7,500 km2 dominated by hardwood forests in the centre of France. The estimation domains consisted in 157 municipalities. The field data included 819 NFI plots surveyed during a 5 years period. The auxiliary data consisted in 48 metrics derived from a forest map, photogrammetric models and Landsat images. A model-assisted framework was used for estimation. For each forest attribute, the best model was selected using a best-subset approach using a Bayesian Information Criteria. The retained models explained 58% and 41% of the observed variance for the growing stocks and basal areas respectively. The performance of the algorithm was evaluated using a minimum of 3 NFI points per domain and estimation errors varying from 10 to 50%.For a target estimation error set to 10%, the algorithm led to a limited number of estimation domains (<23 for both attributes) of large size (~15,000 ha) having an average estimation error lower than 7.7% for both attributes. Relaxing the targeted error threshold to 50% led to a larger amount of smaller domains (80 domains of 4,176 ha in average) for both attributes, and maximum estimation errors reaching 42.8%. Among those domains 65% consisted in single municipalities. For the sake of comparison, the estimation was also conducted at the scale of municipalities. Out of the 157 municipalities studied, only 93 were sampled with at least 3 NFI points and therefore estimated. Missing values were generated for the remaining 64 municipalities. Average errors of 15.9% and 15.6% were obtained for growing stock and basal area respectively, but estimation errors greater than 50% were obtained for some municipalities.The algorithm provides a flexible estimation framework for small area estimation. The key advantages of the approach are relying on its capacity to produce estimations based on a preselected precision threshold and to produce results over the whole area of interest, avoiding areas without any estimates. The algorithm could also be used on any kind of polygon layers (not only administrative ones), provided that the field sampling design enable estimation. This makes the proposed algorithm a convenient tool notably for decision makers and forest managers.

Learning Mesh Representations via Binary Space Partitioning Tree Networks.

Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives.We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders.

Non-revisiting stochastic search revisited: Results, perspectives, and future directions

The non-revisiting genetic algorithm (NrGA) uses the entire search history with parameter-less adaptive mutation to significantly enhance search performance. In the past decade, a family of non-revisiting stochastic search (NrSS) methods has been developed. Using the entire (or partial) search history to assist evolutionary computation can achieve not only the goal of duplicated solution prevention, but also other utilizations such as adaptive parameter-less local search and fitness landscape estimation. In this survey, the focus is on the memory-assisted stochastic search techniques that store the search history in a binary space partitioning (BSP) tree. First, the basic NrGA is reviewed. Then, the development of the family of NrSS is reviewed from three aspects: 1) the basic NrSS algorithms, 2) conceptual extension of non-revisit and usage of the search history as novel operators and estimators, and 3) application of NrSS to different problem types, such as multi-objective problems, dynamic problems, and multi-modal problems. A comprehensive classification of search history-assisted algorithms suggests that the cumulative historical search information can be developed in a more functional manner; for example, a BSP tree can be simultaneously used for revisit prevention, fitness landscape estimation, and adaptive operation. Both the application on real-world problems and the theoretical analysis of NrSS are reviewed. Possible future work suggestions include a deeper understanding of the non-revisiting scheme in theory, a more comprehensive functional usage of search history, and a closer cooperation with data-driven techniques.