Kd-tree Method Research Articles

Solving Fokker–Planck equations using deep KD-tree with a small amount of data

The Fokker–Planck (FP) equation can deterministically describe the evolution of the probability density function, which plays an extremely significant role in the fields of stochastic dynamics. Unfortunately, the limited samples that arise from the consideration of engineering practice are inevitable, which restricts the solving of the FP equation. Accordingly, in the present study, a super-DL-FP framework is established to solve the steady-state FP equation with a small amount of data, through combining the deep KD-tree and the DL-FP approach proposed in [Chaos 30, 013133 (2020)]. It should be emphasized that the normalization condition is of great importance and has to be considered in solving the steady-state FP equation. An appropriate integral estimation for the normalization condition under non-uniform meshing can effectively improve the precision of the solution, but it is still a challenging problem, especially for the case of small data. Thus, the so-called deep KD-tree method is innovatively proposed to estimate the normalized integral with a small random dataset. The main target is to obtain the appropriate discrete integral points and corresponding integral volumes by executing multiple KD-tree segmentation based on random data on the integral region. Several numerical experiments and comparisons are implemented to illustrate the superior performance of the super-DL-FP method. The obtained results indicate that the proposed algorithm can accomplish higher accuracy in the sense of lower cost than the well-known algorithms like center difference scheme, Chebyshev spectrum algorithm, and normalized flow approach.

KD-Box: Line-segment-based KD-tree for Interactive Exploration of Large-scale Time-Series Data.

Time-series data-usually presented in the form of lines-plays an important role in many domains such as finance, meteorology, health, and urban informatics. Yet, little has been done to support interactive exploration of large-scale time-series data, which requires a clutter-free visual representation with low-latency interactions. In this paper, we contribute a novel line-segment-based KD-tree method to enable interactive analysis of many time series. Our method enables not only fast queries over time series in selected regions of interest but also a line splatting method for efficient computation of the density field and selection of representative lines. Further, we develop KD-Box, an interactive system that provides rich interactions, e.g., timebox, attribute filtering, and coordinated multiple views. We demonstrate the effectiveness of KD-Box in supporting efficient line query and density field computation through a quantitative comparison and show its usefulness for interactive visual analysis on several real-world datasets.

Deep learning network for point cloud classification based on k-dimensional tree neighbor query

PointNet++ is one of the effective deep learning methods to deal with the point cloud classification. However, there are some problems in this method including low precision, being time-consuming and sensitive to the noise of input points. In order to deal with these problems, we propose an efficient neighbor query method in which a k-dimensional tree (kd tree) structure is constructed to find the neighbor points within a specified radius around the query points, and the local features are extracted at the grouping layer of PointNet++. Aiming at the overfitting problem existing in the original network training process, we introduce the dropout regularization and thus reduce the training time of network convergence. The experiment environment is TensorFlow framework under Ubuntu14.04 system. The training and testing experiments are conducted based on ModelNet40 dataset. The classification accuracy of this method reaches 91.1%, 92.1% and 94.3% when the query radius is 0.1, 0.2 and 0.3, which is higher than PointNet++, and the kd tree method takes less time than the original method. At the same time, the improved structure has better semantic segmentation performance on the Stanford 3D semantic analysis dataset (mean intersection over union reaches 57.2%), which demonstrates the proposed method being more robust to occlusion objects.

Study on the Composite EM Scattering from Sea Surface with Ship Based on Kd-Tree Accelerated Hybrid Model

A hybrid model based on the geometrical optics and physical optics (GO-PO) method and facet-based asymptotical model (FBAM) for the composite EM scattering from sea surface with ship has been previously developed. But, the GO-PO method faces a difficult problem that the lower efficiency in testing the visibility of patches to the incident and reflected waves. Hence, to improve the computation efficiency of the GO-PO method, a kd-tree accelerated hybrid model is presented in this paper. The kd-tree method firstly carries out the intersection test between the ray and the bounding box where the patch is located before the operation between the ray and the patch. If the distance parameters of the bounding box do not meet the requirement, the ray is not necessary to enter the bounding box, which can reduce the needless intersection tests. Numerical results show that the proposed kd-tree accelerated hybrid model could improve the efficiency about three times and could be applied to the study of composite EM scattering characteristics of electrically large sea surface with a ship target.

Object tracking with an effective composite similarity

How to achieve a robust performance remains an intractable problem with the various object tracking algorithms, due to some unfavorable factors, e.g., occlusion, appearance change, etc. A robust object-tracking approach is proposed based on a composite similarity measure. Based on the first several frames in a video sequence, an initial dictionary is constructed by searching for the best candidates via the kd-tree method. For a target candidate, a likelihood value is computed by weighting the sparse representation coefficients of local patches obtained via the adaptive structural local sparse appearance (ASLSA) model. In order to alleviate the effect of occlusion, a smoothing operation is designed in computing the likelihood value. Meanwhile, after obtaining the codebook by applying the k-means clustering algorithm on the randomly sampled positive and negative templates, a confidence value is computed, via the sparse collaborative model (SCM), for each of the candidates. Furthermore, a composite similarity measure is devised, which combines the likelihood value and the confidence value for each candidate. Finally, the best candidate is searched for, according to the composite similarity measure. Due to the complementarity of SCM and ASLSA, the proposed algorithm is a more robust approach to object tracking. Experimental results on several challenging sequences demonstrate the effectiveness and feasibility of the proposed method.

K-Means Algorithm Performance Analysis With Determining The Value Of Starting Centroid With Random And KD-Tree Method

Clustering methods that have high accuracy and time efficiency are necessary for the filtering process. One method that has been known and applied in clustering is K-Means Clustering. In its application, the determination of the begining value of the cluster center greatly affects the results of the K-Means algorithm. This research discusses the results of K-Means Clustering with starting centroid determination with a random and KD-Tree method. The initial determination of random centroid on the data set of 1000 student academic data to classify the potentially dropout has a sse value of 952972 for the quality variable and 232.48 for the GPA, whereas the initial centroid determination by KD-Tree has a sse value of 504302 for the quality variable and 214,37 for the GPA variable. The smaller sse values indicate that the result of K-Means Clustering with initial KD-Tree centroid selection have better accuracy than K-Means Clustering method with random initial centorid selection.

A new spin image based registration algorithm of 3D surrounding model in low-dimensional feature space

Most recently, cooperation and coordination among different robots (CCDR), e.g., the air robot and the ground robot, has gradually been a new researching topic in the field of robotics. Among several challenging problems in CCDR, surrounding model registration is very important and difficult, because the models from different robots are usually of different scale and obtained from completely different viewpoints. Currently, very little algorithms have been reported to be feasible for this problem, wherein spin-image based scheme has achieved much attention. However, researches have showed that spin-image based methods present disadvantages in computational efficiency and robustness. Therefore, in this paper, a new spin image based 3D surrounding model registration algorithm is proposed. The new algorithm is on the basis of a three-dimensional feature space, which is composed by the curvature, the Tsallis entropy of spin image, and the reflection intensity of the laser sensor, and combined with the concept of KD-tree to firstly realize the primary key point matching, i.e., to find the corresponding point candidate set (CPCS). After that, spin-image based corresponding point searching is conducted with respect to each CPCS to obtain the accurate corresponding point relation. The most absorbing advantages of the proposed scheme are as the following two aspects: on one hand, due to the three extra features, the fault corresponding relation can be reduced effectively and thus the algorithm precision and robustness can be improved greatly; on the other hand, the CPCS obtained by using the KD-tree method in the constructed low-dimensional feature space contains much less points and thus the computational burden due to spin-image searching is reduced greatly. Finally, in order to verify the feasibility and validity of the proposed algorithm, experiments are conducted and the results are analyzed.

마커리스 트래킹을 위한 특징 서술자의 데이터베이스 생성 및 검색방법

본 논문에서는 증강 현실 환경에서 실시간 마커리스 트래킹을 수행하기 위한 특징 서술자 데이터베이스 생성 및 검색 방법을 제안한다. 먼저, 특징 서술자를 효율적으로 검색하기 위하여 특징 서술자의 형태를 기준으로 정수 부호화 하여 총 4 단계의 인덱스 데이터베이스를 구성한다. 특정 특징 서술자의 검색은 데이터베이스에서 각 단계별로 유사성 있는 후보 특징 서술자의 인덱스를 탐색하고 입력된 특징 서술자와 탐색된 모든 후보 특징 서술자들의 유클리드 거리 값 비교를 통해 이루어진다. 본 연구에서 제안한 검색방법은 형태를 기반으로 유사하지 않은 특징 서술자들을 검색 대상에서 제외하여 검색의 효율을 높였다. 제안된 방법은 기존 KD-Tree 방법에 비해서 특징 서술자당 약 16ms의 검색 속도 개선이 있었음을 확인할 수 있었다.

A Dense Point-to-Point Alignment Method for Realistic 3D Face Morphing and Animation

We present a new point matching method to overcome the dense point-to-point alignment of scanned 3D faces. Instead of using the rigid spatial transformation in the traditional iterative closest point (ICP) algorithm, we adopt the thin plate spline (TPS) transformation to model the deformation of different 3D faces. Because TPS is a non-rigid transformation with good smooth property, it is suitable for formulating the complex variety of human facial morphology. A closest point searching algorithm is proposed to keep one-to-one mapping, and to get good efficiency the point matching method is accelerated by a KD-tree method. Having constructed the dense point-to-point correspondence of 3D faces, we create 3D face morphing and animation by key-frames interpolation and obtain realistic results. Comparing with ICP algorithm and the optical flow method, the presented point matching method can achieve good matching accuracy and stability. The experiment results have shown that our method is efficient for dense point objects registration.

Fast implementations of nearest neighbor classifiers

Standard implementations of non-parametric classifiers have large computational requirements. Parzen classifiers use the distances of an unknown vector to all N prototype samples, and consequently exhibit O( N) behavior in both memory and time. We describe four techniques for expediting the nearest neighbor methods: replacing the linear search with a new kd tree method, exhibiting approximately O(N 1 2 ) behavior; employing an L ∞ instead of L 2 distance metric; using variance-ordered features; and rejecting prototypes by evaluating distances in low dimensionality subspaces. We demonstrate that variance-ordered features yield significant efficiency gains over the same features linearly transformed to have uniform variance. We give results for a large OCR problem, but note that the techniques expedite recognition for arbitrary applications. Three of four techniques preserve recognition accuracy.