Binary Space Partitioning Research Articles

Dynamic optimization facilitated by the memory tree

Memorizing the past information for later environments is an effective and widely employed approach to optimize dynamic problems. Although the existing explicit memories for dynamic optimization differ widely in the literature, all of them organize memory entries in a linear list. This naive structure leads to problems, such as heavy computational overhead and small memory capacity, and thus restricts the performance of the memories. In this paper, the binary space partition tree is adopted to organize the memory entries, and then a memory tree is constructed. The memory tree partitions the search space into regions. In order to make use of the memory tree, a neighbor shift strategy is proposed. When a new individual is generated in a region that has never been visited since the last change, the new individual is shifted to the neighboring memory individual of that region, if it is less fit than the memory individual. The proposed approach can be easily combined with many population-based algorithms for dynamic optimization in the real space. As examples, the proposed approach was combined with a basic particle swarm optimizer and two state-of-the-art dynamic optimizers. The experimental results showed that it significantly enhanced the performance of the three optimizers on various test problems. The proposed approach demonstrates the importance of memory structure in memory approaches.

Trinary-Projection Trees for Approximate Nearest Neighbor Search

We address the problem of approximate nearest neighbor (ANN) search for visual descriptor indexing. Most spatial partition trees, such as KD trees, VP trees, and so on, follow the hierarchical binary space partitioning framework. The key effort is to design different partition functions (hyperplane or hypersphere) to divide the points so that 1) the data points can be well grouped to support effective NN candidate location and 2) the partition functions can be quickly evaluated to support efficient NN candidate location. We design a trinary-projection direction-based partition function. The trinary-projection direction is defined as a combination of a few coordinate axes with the weights being 1 or -1. We pursue the projection direction using the widely adopted maximum variance criterion to guarantee good space partitioning and find fewer coordinate axes to guarantee efficient partition function evaluation. We present a coordinate-wise enumeration algorithm to find the principal trinary-projection direction. In addition, we provide an extension using multiple randomized trees for improved performance. We justify our approach on large-scale local patch indexing and similar image search.

An Attack-resistant Watermark Resynchronization Scheme using LDFT and BSP

Image watermarking is a method that embeds a watermark in the digital image by making small changes in the host data. In watermarking applications, the robustness of the watermark to the common signal processing and geometric desynchronization attacks(DAs) is essential to the system. Most image watermarking resynchronization schemes can survive global DAs (e.g., rotation, scaling, translation, and other affine transforms), but few are resilient to cropping and local DAs. In this paper, We present a watermarking resynchronization scheme against local transform attack. It uses a local invariant transform called Local Daisy Feature Transform(LDFT) and Binary Space Partitioning(BSP) Tree to partition the LDFT space. Watermark is embedded in the leaf nodes of the BSP tree. Here, attacks to the watermarked image can also be detected using

Flow cytometry bioinformatics.

Flow cytometry bioinformatics is the application of bioinformatics to flow cytometry data, which involves storing, retrieving, organizing, and analyzing flow cytometry data using extensive computational resources and tools. Flow cytometry bioinformatics requires extensive use of and contributes to the development of techniques from computational statistics and machine learning. Flow cytometry and related methods allow the quantification of multiple independent biomarkers on large numbers of single cells. The rapid growth in the multidimensionality and throughput of flow cytometry data, particularly in the 2000s, has led to the creation of a variety of computational analysis methods, data standards, and public databases for the sharing of results. Computational methods exist to assist in the preprocessing of flow cytometry data, identifying cell populations within it, matching those cell populations across samples, and performing diagnosis and discovery using the results of previous steps. For preprocessing, this includes compensating for spectral overlap, transforming data onto scales conducive to visualization and analysis, assessing data for quality, and normalizing data across samples and experiments. For population identification, tools are available to aid traditional manual identification of populations in two-dimensional scatter plots (gating), to use dimensionality reduction to aid gating, and to find populations automatically in higher dimensional space in a variety of ways. It is also possible to characterize data in more comprehensive ways, such as the density-guided binary space partitioning technique known as probability binning, or by combinatorial gating. Finally, diagnosis using flow cytometry data can be aided by supervised learning techniques, and discovery of new cell types of biological importance by high-throughput statistical methods, as part of pipelines incorporating all of the aforementioned methods. Open standards, data, and software are also key parts of flow cytometry bioinformatics. Data standards include the widely adopted Flow Cytometry Standard (FCS) defining how data from cytometers should be stored, but also several new standards under development by the International Society for Advancement of Cytometry (ISAC) to aid in storing more detailed information about experimental design and analytical steps. Open data is slowly growing with the opening of the CytoBank database in 2010 and FlowRepository in 2012, both of which allow users to freely distribute their data, and the latter of which has been recommended as the preferred repository for MIFlowCyt-compliant data by ISAC. Open software is most widely available in the form of a suite of Bioconductor packages, but is also available for web execution on the GenePattern platform.

LDFT-Based Watermarking Resilient to Local Desynchronization Attacks

Up to now, a watermarking scheme that is robust against desynchronization attacks (DAs) is still a grand challenge. Most image watermarking resynchronization schemes in literature can survive individual global DAs (e.g., rotation, scaling, translation, and other affine transforms), but few are resilient to challenging cropping and local DAs. The main reason is that robust features for watermark synchronization are only globally invariable rather than locally invariable. In this paper, we present a blind image watermarking resynchronization scheme against local transform attacks. First, we propose a new feature transform named local daisy feature transform (LDFT), which is not only globally but also locally invariable. Then, the binary space partitioning (BSP) tree is used to partition the geometrically invariant LDFT space. In the BSP tree, the location of each pixel is fixed under global transform, local transform, and cropping. Lastly, the watermarking sequence is embedded bit by bit into each leaf node of the BSP tree by using the logarithmic quantization index modulation watermarking embedding method. Simulation results show that the proposed watermarking scheme can survive numerous kinds of distortions, including common image-processing attacks, local and global DAs, and noninvertible cropping.

Determination of Power Distribution Network Configuration Using Non-Revisiting Genetic Algorithm

A non-revisiting genetic algorithm (NrGA) was used to determine distribution network configuration for loss reduction. By advocating binary space partitioning (BSP) to divide the search space and employing a novel BSP tree archive to store all the solutions that have been explored before, NrGA can quickly check for revisits by communicating with BSP tree archive when a new solution is generated by genetic algorithm (GA), and can mutate an alternative unvisited solution through a novel adaptive mutation mechanism that based on BSP tree while a revisit has occurred, which achieves no duplicates in the entire search. A method for getting independent loops of distribution network was realized using breadth-first search algorithm. Furthermore, the extended intermediate crossover mode, which requires no tuning parameter such as crossover rate and extends the crossover results, is employed for improving the performance of NrGA in solving distribution network configuration problem. The proposed approach has been successfully tested on three sample systems and three practical systems. Numerical studies have revealed its accuracy and efficient performance.

Open-source surface mesh-based ultrasound-guided spinal intervention simulator

Ultrasound is prevalent in image-guided therapy as a safe, inexpensive, and widely available imaging modality. However, extensive training in interpreting ultrasound images is essential for successful procedures. An open-source ultrasound image simulator was developed to facilitate the training of ultrasound-guided spinal intervention procedures, thereby eliminating the need for an ultrasound machine from the phantom-based training environment. Anatomical structures and surgical tools are converted to surface meshes for data compression. Anatomical data are converted from segmented volumetric images, while the geometry of surgical tools is available as a surface mesh. The pose of the objects are either constants or coming from a pose-tracking device. Intersection points between the surface models and the ultrasound scan lines are determined with a binary space partitioning tree. The scan lines are divided into segments and filled with gray values determined by an intensity calculation accounting for material properties, reflection, and attenuation parameters defined in a configuration file. The scan lines are finally converted to a regular brightness-mode ultrasound image. The simulator was tested in a tracked ultrasound imaging system, with a mock transducer tracked with an Ascension trakSTAR electromagnetic tracker, on a spine phantom. A mesh model of the spine was created from CT data. The simulated ultrasound images were generated at a speed of 50 frames per second, and a resolution of [Formula: see text] pixels, with 256 scan lines per frame, on a PC with a 3.4GHz processor. A human subject trial was conducted to compare the learning performance of novice trainees, with real and simulated ultrasound, in the localization of facet joints of a spine phantom. With 22 participants split into two equal groups, and each participant localizing 6 facet joints, there was no statistical difference in the performance of the two groups, indicating that simulated ultrasound could indeed replace the real ultrasound in phantom-based ultrasonography training for spinal interventions. The ultrasound simulator was implemented and integrated into the open-source Public Library for Ultrasound (PLUS) toolkit.

Persistent Predecessor Search and Orthogonal Point Location on the Word RAM

We answer a basic data structuring question (e.g., raised by Dietz and Raman [1991]): Can van Emde Boas trees be made persistent, without changing their asymptotic query/update time? We present a (partially) persistent data structure that supports predecessor search in a set of integers in {1, ..., U } under an arbitrary sequence of n insertions and deletions, with O (log log U ) expected query time and expected amortized update time, and O ( n ) space. The query bound is optimal in U for linear-space structures and improves previous near- O ((log log U ) 2 ) methods. The same method solves a fundamental problem from computational geometry: point location in orthogonal planar subdivisions (where edges are vertical or horizontal). We obtain the first static data structure achieving O (log log U ) worst-case query time and linear space. This result is again optimal in U for linear-space structures and improves the previous O ((log log U ) 2 ) method by de Berg et al. [1995]. The same result also holds for higher-dimensional subdivisions that are orthogonal binary space partitions, and for certain nonorthogonal planar subdivisions such as triangulations without small angles. Many geometric applications follow, including improved query times for orthogonal range reporting for dimensions ≥ 3 on the RAM. Our key technique is an interesting new van-Emde-Boas--style recursion that alternates between two strategies, both quite simple.

Steganography: Securing Message in wireless network

Steganography is the process of hiding a secret message with in a cover medium. However eavesdropper may guess the embedding algorithm like least significant bit (LSB) replacement of Chan et al, 2004; Wang et al, 2001; Wu et al, 2005, LSB matching of Mielikainen, 2006, addition and/or subtraction of Andead wastfield, 2001; F. Huang et al in 2011, Exploiting Modification Direction by Zhang and Wang, 2006, Binary Space Partition by Tsai and Wang, 2007, modulus function of Chin et al, 2011 and thus can apply the respective extraction method to detect the secret message. So challenges lies in the methodologies of embedding message. Capacity, security and robustness are the services to be demanded by users. Again the true-positive rate of secret message detection by eavesdropper should be lessened by applying firm technique. Thirdly operating domain should be less sensitive to the noise, margin level of losses or alteration of data while communicating through unguided medium like wireless network, sensor network and cellular network. This paper will briefly discuss the steganographic methods and their experimental results explained in the survey paper of Niels Provos and Peter Honeyman to hide and seek message. Finally the proposed results and the directions for future works are addressed.

The 2013 Virtual Reality Career Award

The 2013 virtual reality career award goes to Henry Fuchs, The University of North Carolina at Chapel Hill, for his lifetime contributions to research and practice in virtual environments, telepresence, and medical applications. Since the 1970s, Henry Fuchs has made pioneer contributions to many of the technologies needed to enable virtual and augmented reality: automatic construction of 3D models and scenes, fast rendering algorithms (BSP Trees), graphics hardware (Pixel-Planes), large-area tracking systems (HiBall), optical and video see-through head-mounted displays. Many of these advances were inspired by demanding applications such as augmenting visualization for surgical assistance (by merging real and virtual objects) and teleimmersion for remote medical consultation. He continues to innovate within a multi-national telepresence research center with sites at ETH Zurich, NTU Singapore, and UNC Chapel Hill. The IEEE VGTC is pleased to award Henry Fuchs the 2013 Virtual Reality Career Award.

An Enhanced Binary Space Partitioning Algorithm for Indoor Radio Propagation

An Enhanced Binary Space Partitioning Algorithm for Indoor Radio Propagation

Crdbrd: Shape Fabrication by Sliding Planar Slices

AbstractWe introduce an algorithm and representation for fabricating 3D shape abstractions using mutually intersecting planar cut‐outs. The planes have prefabricated slits at their intersections and are assembled by sliding them together. Often such abstractions are used as a sculptural art form or in architecture and are colloquially called ‘cardboard sculptures’. Based on an analysis of construction rules, we propose an extended binary space partitioning tree as an efficient representation of such cardboard models which allows us to quickly evaluate the feasibility of newly added planar elements. The complexity of insertion order quickly increases with the number of planar elements and manual analysis becomes intractable. We provide tools for generating cardboard sculptures with guaranteed constructibility. In combination with a simple optimization and sampling strategy for new elements, planar shape abstraction models can be designed by iteratively adding elements. As an output, we obtain a fabrication plan that can be printed or sent to a laser cutter. We demonstrate the complete process by designing and fabricating cardboard models of various well‐known 3D shapes.

Efficient Boundary Extraction of BSP Solids Based on Clipping Operations

We present an efficient algorithm to extract the manifold surface that approximates the boundary of a solid represented by a Binary Space Partition (BSP) tree. Our polygonization algorithm repeatedly performs clipping operations on volumetric cells that correspond to a spatial convex partition and computes the boundary by traversing the connected cells. We use point-based representations along with finite-precision arithmetic to improve the efficiency and generate the B-rep approximation of a BSP solid. The core of our polygonization method is a novel clipping algorithm that uses a set of logical operations to make it resistant to degeneracies resulting from limited precision of floating-point arithmetic. The overall BSP to B-rep conversion algorithm can accurately generate boundaries with sharp and small features, and is faster than prior methods. At the end of this paper, we use this algorithm for a few geometric processing applications including Boolean operations, model repair, and mesh reconstruction.

A Multiobjective Evolutionary Algorithm That Diversifies Population by Its Density

Most existing multiobjective evolutionary algorithms (MOEAs) assume the existence of Pareto-optimal solutions/Pareto-optimal objective vectors in a neighborhood of an obtained Pareto-optimal set (PS)/Pareto-optimal front (PF). Obviously, this assumption does not work well on the multiobjective problem (MOP) whose true PF and true PS are in the form of multiple segments-truly disconnected MOP (TYD-MOP). Moreover, these MOEAs commonly involve more than three control parameters; and some of them even involve nine control parameters. The stabilities of their performance against parameter settings are generally unknown. In this paper, we propose a MOEA, namely multiobjective density driven evolutionary algorithm (MODdEA), which can handle TYD-MOP. MODdEA stores all evaluated solutions by a binary space partitioning (BSP) tree. Benefiting from the BSP scheme, a fast solution density estimation by the archive is naturally obtained. MODdEA uses this estimated density together with the nondominated rank to probabilistically select mating individuals, which relaxes the neighborhood assumption on PF in a parameter-less manner. Moreover, two genetic operators, extended arithmetic crossover and diversified mutation, are proposed to enhance the explorative search ability of the algorithm. MODdEA is examined on two test problem sets. The first test set consists of six TYD-MOPs; the second test set consists of 17 benchmark MOPs which are commonly examined by the existing MOEAs. Comparing to 14 test MOEAs, MODdEA has superior performance on TYD-MOP and is competitive on MOP whose true PF and PS are one single connected segment.

SEPARABILITY OF POINT SETS BY k-LEVEL LINEAR CLASSIFICATION TREES

Let R and B be sets of red and blue points in the plane in general position. We study the problem of computing a k-level binary space partition (BSP) tree to classify/separate R and B, such that the tree defines a linear decision at each internal node and each leaf of the tree corresponds to a (convex) cell of the partition that contains only red or only blue points. Specifically, we show that a 2-level tree can be computed, if one exists, in time O(n2). We show that a minimum-level (3 ≤ k ≤ log n) tree can be computed in time nO( log n). In the special case of axis-parallel partitions, we show that 2-level and 3-level trees can be computed in time O(n), while a minimum-level tree can be computed in time O(n5).

Time-Varying Data Visualization Using Functional Representations

In many scientific simulations, the temporal variation and analysis of features are important. Visualization and visual analysis of time series data is still a significant challenge because of the large volume of data. Irregular and scattered time series data sets are even more problematic to visualize interactively. Previous work proposed functional representation using basis functions as one solution for interactively visualizing scattered data by harnessing the power of modern PC graphics boards. In this paper, we use the functional representation approach for time-varying data sets and develop an efficient encoding technique utilizing temporal similarity between time steps. Our system utilizes a graduated approach of three methods with increasing time complexity based on the lack of similarity of the evolving data sets. Using this system, we are able to enhance the encoding performance for the time-varying data sets, reduce the data storage by saving only changed or additional basis functions over time, and interactively visualize the time-varying encoding results. Moreover, we present efficient rendering of the functional representations using binary space partitioning tree textures to increase the rendering performance.

Shooting Permanent Rays among Disjoint Polygons in the Plane

We present a data structure for ray shooting and insertion in the free space between disjoint polygonal obstacles with a total of $n$ vertices in the plane, where each ray starts at the boundary of some obstacle. The portion of each query ray between the starting point and the first obstacle hit is inserted permanently as a new obstacle. Our data structure uses $O(n\log n)$ space and preprocessing time, and it supports $m$ successive ray shooting and insertion queries in $O((n+m)\log^2 n + m\log m)$ total time in the real RAM model of computation. We present two applications: (1) Our data structure supports efficient implementation of auto-partitions in the plane, that is, binary space partitions where each partition is done along the supporting line of an input segment. If $n$ input line segments are fragmented into $m$ pieces by an auto-partition, then it can now be implemented in $O(n\log^2n+m\log m)$ time. This improves the expected runtime of Patersen and Yao's classical randomized auto-partition algorithm for $n$ disjoint line segments in the plane to $O(n\log^2 n)$. (2) If we are given disjoint polygonal obstacles with a total of $n$ vertices in the plane, a permutation of the reflex vertices, and a half-line at each reflex vertex that partitions the reflex angle into two convex angles, then the convex partitioning algorithm draws a ray emanating from each reflex vertex in the prescribed order in the given direction until it hits another obstacle, a previous ray, or infinity. The previously best implementation (with a semidynamic ray shooting data structure) requires $O(n^{3/2-\varepsilon/2})$ time using $O(n^{1+\varepsilon})$ space for any $\varepsilon>0$. Our data structure improves the runtime to $O(n\log^2 n)$.

An Evolutionary Algorithm That Makes Decision Based on the Entire Previous Search History

In this paper, we report a novel evolutionary algorithm that enhances its performance by utilizing the entire previous search history. The proposed algorithm, namely history driven evolutionary algorithm (HdEA), employs a binary space partitioning tree structure to memorize the positions and the fitness values of the evaluated solutions. Benefiting from the space partitioning scheme, a fast fitness function approximation using the archive is obtained. The approximation is used to improve the mutation strategy in HdEA. The resultant mutation operator is parameter-less, anisotropic, and adaptive. Moreover, the mutation operator naturally avoids the generation of out-of-bound solutions. The performance of HdEA is tested on 34 benchmark functions with dimensions ranging from 2 to 40. We also provide a performance comparison of HdEA with eight benchmark evolutionary algorithms, including a real coded genetic algorithm, differential evolution, two improved differential evolution, covariance matrix adaptation evolution strategy, two improved particle swarm optimization, and an estimation of distribution algorithm. Seen from the experimental results, HdEA outperforms the other algorithms for multimodal function optimization.

Stochastic global optimization for robust point set registration

In this paper, we propose a new algorithm for pairwise rigid point set registration with unknown point correspondences. The main properties of our method are noise robustness, outlier resistance and global optimal alignment. The problem of registering two point clouds is converted to a minimization of a nonlinear cost function. We propose a new cost function based on an inverse distance kernel that significantly reduces the impact of noise and outliers. In order to achieve a global optimal registration without the need of any initial alignment, we develop a new stochastic approach for global minimization. It is an adaptive sampling method which uses a generalized BSP tree and allows for minimizing nonlinear scalar fields over complex shaped search spaces like, e.g., the space of rotations. We introduce a new technique for a hierarchical decomposition of the rotation space in disjoint equally sized parts called spherical boxes. Furthermore, a procedure for uniform point sampling from spherical boxes is presented. Tests on a variety of point sets show that the proposed registration method performs very well on noisy, outlier corrupted and incomplete data. For comparison, we report how two state-of-the-art registration algorithms perform on the same data sets.

Smart Nearest Neighbors

This document presents an implementation of two algorithms, Voronoi Neighbors and Binary Space Partition (BSP) Neighbors. These algorithms find neighbors of a point in a point set that are somehow better'' than aK nearest neighbors’’ or a ``all neighbors within a radius’’ query. This type of nearest neighbor query is more computationally expensive, but results in set of neighbors with more desirable properties. The BSP Neighbors search ensures that there is less local duplication, while the Voronoi Neighbors search ensures that the spatial arrangement of the neighbors is as uniform as possible.These algorithms are explained in ``Point Primitives for Interactive Modeling and Processing of 3D Geometry’’.The code is available here: https://github.com/daviddoria/SmartNearestNeighbors