Quad trees a data structure for retrieval on composite keys

Finkel, Raphael A.; Bentley, Jon Louis

doi:10.1007/bf00288933

Cited by 1,648 publications

(758 citation statements)

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“…Those are all based on a hierarchy of minimum bounding rectangles (MBRs). Quad trees [39] are an example of a space driven indexing technique. Quad trees, in the case of two-dimensional points, recursively partition the plane into four equal parts, until each part only contains one element.…”

Section: Indexing Feature Vectorsmentioning

confidence: 99%

Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval

Haesevoets¹,

Kuijpers

Révész

2017

IJGI

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Abstract:In the geometric data model for spatio-temporal data, introduced by Chomicki and Revesz , spatio-temporal data are modelled as a finite collection of triangles that are transformed by time-dependent affinities of the plane. To facilitate querying and animation of spatio-temporal data, we present a normal form for data in the geometric data model. We propose an algorithm for constructing this normal form via a spatio-temporal triangulation of geometric data objects. This triangulation algorithm generates new geometric data objects that partition the given objects both in space and in time. A particular property of the proposed partition is that it is invariant under time-dependent affine transformations, and hence independent of the particular choice of coordinate system used to describe the spatio-temporal data in. We can show that our algorithm works correctly and has a polynomial time complexity (of reasonably low degree in the number of input triangles and the maximal degree of the polynomial functions that describe the transformation functions). We also discuss several possible applications of this spatio-temporal triangulation. The application of our affine-invariant spatial triangulation method to image indexing and retrieval is discussed and an experimental evaluation is given in the context of bird images.

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Section: Indexing Feature Vectorsmentioning

confidence: 99%

Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval

Haesevoets¹,

Kuijpers

Révész

2017

IJGI

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“…The alternative to VR-tree is to index network Voronoi cells using Quad-tree [18,3], termed Voronoi Quad-tree (VQ-tree), that enables disjoint decomposition of the underlying space. The main observation behind VQtree is that each color coded area in Figure 4 is a spatially contiguous region in the network space.…”

Section: The Voronoi Quad-tree (Vq-tree)mentioning

confidence: 99%

Indexing Network Voronoi Diagrams

Demiryurek

Shahabi

2012

Database Systems for Advanced Applications

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Abstract. The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to efficiently evaluate various spatial proximity queries such as k nearest neighbor (kNN), reverse kNN, and closest pair. Although the existing approaches successfully utilize the network Voronoi diagram as a way to partition the space for their specific problems, there is little emphasis on how to efficiently find and access the network Voronoi cell containing a particular point or edge of the network. In this paper, we study the index structures on network Voronoi diagrams that enable exact and fast response to contain query in road networks. We show that existing index structures, treating a network Voronoi cell as a simple polygon, may yield inaccurate results due to the network topology, and fail to scale to large networks with numerous Voronoi generators. With our method, termed Voronoi-Quad-tree (or VQ-tree for short), we use Quad-tree to index network Voronoi diagrams to address both of these shortcomings. We demonstrate the efficiency of VQ-tree via experimental evaluations with real-world datasets consisting of a variety of large road networks with numerous data objects.

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“…However, this approach fails to take into account the fact that anatomical structures manifest in different scales. Consequently, we employ a quadtree-based strategy [10] to partition the slice into structurally adaptive patches. Since the intermediate slice is not available beforehand, we partition the slices immediately superior and inferior to the intermediate slice.…”

Section: Quadtree-based Patch Partitionmentioning

confidence: 99%

Non-local Means Resolution Enhancement of Lung 4D-CT Data

Zhang

Yap

et al. 2012

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2012

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Abstract. Image resolution in 4D-CT is a crucial bottleneck that needs to be overcome for improved dose planning in radiotherapy for lung cancer. In this paper, we propose a novel patch-based algorithm to enhance the image quality of 4D-CT data. Our premise is that anatomical information missing in one phase can be recovered from complementary information embedded in other phases. We employ a patch-based mechanism to propagate information across phases for reconstruction of intermediate slices in the axial direction, where resolution is normally the lowest. Specifically, structurally-matching and spatially-nearby patches are combined for reconstruction of each patch. For greater sensitivity to anatomical nuances, we further employ a quad-tree technique to adaptively partition each slice of the image in each phase for more fine-grained refinement. Our evaluation based on a public 4D-CT lung data indicates that our algorithm gives very promising results with significantly enhanced image structures. Introduction4D-CT is becoming increasingly popular in lung cancer treatment for providing respiratory-related information that is essential for guiding radiation therapy effectively. However, due to the risk of radiation [1], only a limited number of CT segments are usually acquired, which often results in very low resolution along the inferior-superior direction. This low-resolution (LR) data are usually plagued with visible imaging artifacts such as vessel discontinuity and partial volume effect. More importantly, insufficient resolution further distorts the shape of a tumor. This distortion might finally interfere with optimal dose planning. Super-resolution (SR) reconstruction is an effective approach for improving image resolution. Classical SR methods can be divided into two major categories: interpolation-based and model-based. The main advantage of interpolation-based methods is their simplicity. However, blurred edges and undesirable artifacts are inevitable. Currently, more attention has been directed to model-based SR approach. The general assumption of model-based SR approaches is that the LR image is a degraded version

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Quad trees a data structure for retrieval on composite keys

Cited by 1,648 publications

References 0 publications

Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval

Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval

Indexing Network Voronoi Diagrams

Non-local Means Resolution Enhancement of Lung 4D-CT Data

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