An O(N4) algorithm to construct all Voronoi diagrams for k nearest neighbor searching

Semantic segmentation of the sensed point cloud data plays a significant role in scene understanding and reconstruction, robot navigation, etc. This work presents a Graph Convolutional Network integrating K-Nearest Neighbor searching (KNN) and Vector of Locally Aggregated Descriptors (VLAD). KNN searching is utilized to construct the topological graph of each point and its neighbors. Then, we perform convolution on the edges of constructed graph to extract representative local features by multiple Multilayer Perceptions (MLPs). Afterwards, a trainable VLAD layer, NetVLAD, is embedded in the feature encoder to aggregate the local and global contextual features. The designed feature encoder is repeated for multiple times, and the extracted features are concatenated in a jump-connection style to strengthen the distinctiveness of features and thereby improve the segmentation. Experimental results on two datasets show that the proposed work settles the shortcoming of insufficient local feature extraction and promotes the accuracy (mIoU 60.9% and oAcc 87.4% for S3DIS) of semantic segmentation comparing to existing models.

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k — Nearest — Neighbor Voronoi diagrams for sets of convex polygons, line segments and points

Graph-Theoretic Concepts in Computer Science - Lecture Notes in Computer Science ◽

10.1007/3-540-52292-1_24 ◽

1990 ◽

pp. 330-340 ◽

Cited By ~ 2

Author(s):

Thomas Roos

Keyword(s):

Nearest Neighbor ◽

Voronoi Diagrams ◽

K Nearest Neighbor ◽

Convex Polygons ◽

Line Segments

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Aggregate-MAX Top-k Nearest Neighbor Searching in the L1 Plane

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195915500053 ◽

2015 ◽

Vol 25 (01) ◽

pp. 57-76 ◽

Cited By ~ 4

Author(s):

Haitao Wang

Keyword(s):

Data Structure ◽

Nearest Neighbor ◽

Maximum Distance ◽

K Nearest Neighbor ◽

Nearest Neighbor Searching

We study the aggregate/group top-k nearest neighbor searching for the Max operator in the plane, where the distances are measured by the L1 metric. Let P be a set of n points in the plane. Given a query set Q of m points, for each point p ∈ P, the aggregate-max distance from p to Q is defined to be the maximum distance from p to all points in Q. Given Q and an integer k with 1 ≤ k ≤ n, the query asks for the k points of P that have the smallest aggregate-max distances to Q. We build a data structure of O(n) size in O(n log n) time, such that each query can be answered in O(m+k log n) time and the k points are reported in sorted order by their aggregate-max distances to Q. Alternatively, we build a data structure of O(n log n) size in O(n log2 n) time that can answer each query in O(m + k + log3 n) time.

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A Bidirectional Searching Strategy to Improve Data Quality Based on K-Nearest Neighbor Approach

Symmetry ◽

10.3390/sym11060815 ◽

2019 ◽

Vol 11 (6) ◽

pp. 815 ◽

Cited By ~ 1

Author(s):

Minghui Ma ◽

Shidong Liang ◽

Yifei Qin

Keyword(s):

Data Quality ◽

Traffic Control ◽

Intelligent Transportation Systems ◽

Nearest Neighbor ◽

Transportation Systems ◽

Traffic Data ◽

K Nearest Neighbor ◽

Time Dimension ◽

Nearest Neighbor Searching ◽

Searching Strategy

Traffic data are the basis of traffic control, planning, management, and other implementations. Incomplete traffic data that are not conducive to all aspects of transport research and related activities can have adverse effects such as traffic status identification error and poor control performance. For intelligent transportation systems, the data recovery strategy has become increasingly important since the application of the traffic system relies on the traffic data quality. In this study, a bidirectional k-nearest neighbor searching strategy was constructed for effectively detecting and recovering abnormal data considering the symmetric time network and the correlation of the traffic data in time dimension. Moreover, the state vector of the proposed bidirectional searching strategy was designed based the bidirectional retrieval for enhancing the accuracy. In addition, the proposed bidirectional searching strategy shows significantly more accuracy compared to those of the previous methods.

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