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85
The quadtree and related hierarchical data structures
 ACM Computing Surveys
, 1984
"... A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics ..."
Abstract

Cited by 421 (11 self)
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A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics. There is a greater emphasis on region data (i.e., twodimensional shapes) and to a lesser extent on point, curvilinear, and threedimensional data. A number of operations in which such data structures find use are examined in greater detail.
Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
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Cited by 291 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
Hybrid Image Segmentation Using Watersheds and Fast Region Merging
 IEEE transactions on Image Processing
, 1998
"... Abstract—A hybrid multidimensional image segmentation algorithm is proposed, which combines edge and regionbased techniques through the morphological algorithm of watersheds. An edgepreserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate est ..."
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Cited by 90 (1 self)
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Abstract—A hybrid multidimensional image segmentation algorithm is proposed, which combines edge and regionbased techniques through the morphological algorithm of watersheds. An edgepreserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate estimate of the image gradient. Then, an initial partitioning of the image into primitive regions is produced by applying the watershed transform on the image gradient magnitude. This initial segmentation is the input to a computationally efficient hierarchical (bottomup) region merging process that produces the final segmentation. The latter process uses the region adjacency graph (RAG) representation of the image regions. At each step, the most similar pair of regions is determined (minimum cost RAG edge), the regions are merged and the RAG is updated. Traditionally, the above is implemented by storing all RAG edges in a priority queue. We propose a significantly faster algorithm, which additionally maintains the socalled nearest neighbor graph, due to which the priority queue size and processing time are drastically reduced. The final segmentation provides, due to the RAG, onepixel wide, closed, and accurately localized contours/surfaces. Experimental results obtained with twodimensional/threedimensional (2D/3D) magnetic resonance images are presented. Index Terms — Image segmentation, nearest neighbor region merging, noise reduction, watershed transform. I.
Image segmentation based on oscillatory correlation
 Neural Computation
, 1997
"... We study image segmentation on the basis of locally excitatory globally inhibitory oscillator networks (LEGION), whereby the phases of oscillators encode the binding of pixels. We introduce a potential for each oscillator so that only those oscillators with strong connections from their neighborhood ..."
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Cited by 78 (23 self)
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We study image segmentation on the basis of locally excitatory globally inhibitory oscillator networks (LEGION), whereby the phases of oscillators encode the binding of pixels. We introduce a potential for each oscillator so that only those oscillators with strong connections from their neighborhood can develop high potentials. Based on the concept of potential, a solution to remove noisy regions in an image is proposed for LEGION, so that it suppresses the oscillators corresponding to noisy regions, without affecting those corresponding to major regions. We show analytically that the resulting oscillator network separates an image into several major regions, plus a background consisting of all noisy regions, and illustrate network properties by computer simulation. The network exhibits a natural capacity in segmenting images. The oscillatory dynamics leads to a computer algorithm, which is applied successfully to segmenting real graylevel images. A number of issues regarding biological plausibility and perceptual organization are discussed. We argue that LEGION provides a novel and effective framework for image segmentation and figureground segregation. DeLiang Wang and David Terman Image Segmentation 1.
Segmentation and boundary detection using multiscale intensity measurements
 IN: CVPR. VOLUME I., HAWAII
, 2001
"... Image segmentation is difficult because objects may differ from their background by any of a variety of properties that can be observed in some, but often not all scales. A further complication is that coarse measurements, applied to the image for detecting these properties, often average over prope ..."
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Cited by 49 (6 self)
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Image segmentation is difficult because objects may differ from their background by any of a variety of properties that can be observed in some, but often not all scales. A further complication is that coarse measurements, applied to the image for detecting these properties, often average over properties of neighboring segments, making it difficult to separate the segments and to reliably detect their boundaries. Below we present a method for segmentation that generates and combines multiscale measurements of intensity contrast, texture differences, and boundary integrity. The method is based on our former algorithm SWA, which efficiently detects segments that optimize a normalizedcutlike measure by recursively coarsening a graph reflecting similarities between intensities of neighboring pixels. In this process aggregates of pixels of increasing size are gradually collected to form segments. We intervene in this process by computing properties of the aggregates and modifying the graph to reflect these coarse scale measurements. This allows us to detect regions that differ by fine as well as coarse properties, and to accurately locate their boundaries. Furthermore, by combining intensity differences with measures of boundary integrity across neighboring aggregates we can detect regions separated by weak, yet consistent edges.
Unimodal thresholding
 Pattern Recognition
, 2001
"... Most thresholding algorithms have difficulties processing images with unimodal distributions. In this paper an algorithm, based on finding a corner in the histogram plot, is proposed that is capable of performing bilevel thresholding of such images. Its effectiveness is demonstrated on synthetic dat ..."
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Cited by 35 (3 self)
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Most thresholding algorithms have difficulties processing images with unimodal distributions. In this paper an algorithm, based on finding a corner in the histogram plot, is proposed that is capable of performing bilevel thresholding of such images. Its effectiveness is demonstrated on synthetic data as well as a variety of real data, showing its application to edges, difference images, optic flow, texture difference images, polygonal approximation of curves, and image segmentation. 1
Stochastic Relaxation on Partitions with Connected Components and Its Application to Image Segmentation
, 1998
"... We present a new method of segmentation in which images are segmented by partitions with connected components. For this, first we define two different types of neighborhoods on the space of partitions with connected components of a general graph; neighborhoods of the first type are simple but sma ..."
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Cited by 30 (0 self)
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We present a new method of segmentation in which images are segmented by partitions with connected components. For this, first we define two different types of neighborhoods on the space of partitions with connected components of a general graph; neighborhoods of the first type are simple but small, while those of the second type are large but complex; second, we give algorithms which are not computationally costly, for probability simulation and simulated annealing on such spaces using the neighborhoods. In particular Hastings algorithms and generalized Metropolis algorithms are defined to avoid heavy computations in the case of the second type of neighborhoods. To realize segmentation, we propose a hierarchical approach which at each step minimizes a cost function on the space of partitions with connected components of a graph.
A probabilistic approach to the semantic interpretation of building facades
 In Int. Workshop on Vision Techniques Applied
, 2004
"... Semanticallyenhanced 3D model reconstruction in urban environments is useful in a variety of applications, such as extracting metric and semantic information about buildings, visualizing the data in a way that outlines important aspects, or urban planning. We present a probabilistic imagebased app ..."
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Cited by 28 (0 self)
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Semanticallyenhanced 3D model reconstruction in urban environments is useful in a variety of applications, such as extracting metric and semantic information about buildings, visualizing the data in a way that outlines important aspects, or urban planning. We present a probabilistic imagebased approach to the semantic interpretation of building facades. We are motivated by the 4D Atlanta project at Georgia Tech, which aims to create a system that takes a collection of historical imagery of a city and infers a 3D model parameterized by time. Here it is necessary to recover, from historical imagery, metric and semantic information about buildings that might no longer exist or have undergone extensive change. Current approaches to automated 3D model reconstruction typically recover only geometry, and a systematic approach that allows hierarchical classification of structural elements is still largely missing. We extract metric and semantic information from images of facades, allowing us to decode the structural elements in them and their interrelationships, thus providing access to highly structured descriptions of buildings. Our method is based on constructing a Bayesian generative model from stochastic contextfree grammars that encode knowledge about facades. This model combines lowlevel segmentation and highlevel hierarchical labelling so that the levels reinforce each other and produce a detailed hierarchical partition of the depicted facade into structural blocks. Markov chain Monte Carlo sampling is used to approximate the posterior over partitions given an image. We show results on a variety of real images of building facades. While we have currently tested only limited models of facades, we believe that our framework can be applied to much more general models, and are currently working towards that goal. 1
Image Segmentation with Topological Maps and Interpixel Representation
, 1998
"... In this paper we present a data structure improving region segmentation of 2D images. This data structure provides an efficient access to the set of pixel of one region. It also provides topological informations like the frontier of a region, the neighbours of a region or the set of regions included ..."
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Cited by 25 (7 self)
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In this paper we present a data structure improving region segmentation of 2D images. This data structure provides an efficient access to the set of pixel of one region. It also provides topological informations like the frontier of a region, the neighbours of a region or the set of regions included in one region. Thanks to this data structure different segmentation algorithms can be combined to perform the segmentation of an image. Interactive refinement or merge of regions can also be performed efficiently. Keywords Segmentation, interpixel boundary, topological map. I. introduction The problem of extracting objects from a complex image has been widely studied for the last fifty years. It quickly appeared that this problem cannot be solved without an priori knowledge of the objects to be recognized. Segmentation algorithms can thus be categorized in two classes: domaindependent algorithms which attempt to recognize specific objects in a scene  for instance tumors in chest radi...