Quadtree

Dans cet article, nous avons étudié la segmentation des images médicales à laquelle nous avons appliqué les algorithmes génétiques. Nous allons réunir les deux modes pour pallier à ce problème. Dans un premier temps, nous avons utilisé l'algorithme de quadtree qui permet de découper l'image en quatre régions selon l'étendue, le gradient et la variance de chacune des régions. Nous réitérons ce découpage sur chaque rectangle obtenu. Le processus s'arrête lorsque les régions sont homogènes. Dans un deuxième temps, nous utilisons les algorithmes génétiques pour pouvoir fusionner les régions voisines qui se ressemblent. Ce processus est réitéré jusqu'a ce qu'il soit impossible de trouver deux régions voisines suffisamment semblables.

Three dimensional graphical user interfaces is a subject long studied, but due to its technical dependency on large amounts of processing power, it has not been possible to implement until recently. This is due to the recent advances of a computing technology that centers around special processors, created specifically for processing vertices and triangles, named graphical processing units or GPU's. By grouping small or large amounts of GPU's together, real time rendering with interactivity is now possible. Due to these recent advances in computing technology there has been a recent research interest in the HCI realm focused on spatial interactive devices and complementary technologies. Our own research focuses on creating and evaluating a 3D user interface system based on the fundamental principles that have made 2D user interface systems enhance user productivity and become widely adopted. 3D dimensional interfaces are now becoming important because of the recent advances and changes in input devices made commercially available to the public and industry. With the increase in networking technology and the advent of low-power inexpensive integrated circuits(IC's), new types of input devices are possible that capture input in 3D space and output recorded data formatted using 3D spatial coordinates.

Image segmentation is the process of subdividing a digital image into its systematized regions or objects which is useful in image analysis. In this review paper, we carried out an organized survey of many image segmentation techniques which are flexible, cost effective and computationally more efficient. We classify these segmentation methods into three categories: the traditional methods, graph theoretical methods and combination of both traditional and graph theoretical methods. In the second and third category of image segmentation approaches, the image is modeled as a weighted and undirected graph. Normally a pixel or a group of pixels are connected with nodes. The edge weights represent the dissimilarity between the neighborhood pixels. The graph or the image is then divided according to a benchmark designed to model good clusters. Every partition of the nodes or the pixels as output from these algorithms is measured as an object segment in an image representing a graph. Some of the popular algorithms are thresholding, normalized cuts, iterated graph cut, clustering method, watershed transformation, minimum cut, grey graph cut, and minimum spanning treebased segmentation.

This paper presents a new hybrid scheme for image data compression using quadtree decomposition and parametric line fitting. In the first phase of encoding, the input image is partitioned into quadrants using quadtree decomposition. To prevent from very small quadrants, a constraint of minimal block size is imposed during quadtree decomposition. Homogeneous quadrants are separated from non-homogeneous quadrants. In the second phase of encoding, the non-homogeneous quadrants are scanned row-wise. Luminance variation of each scanned row is fitted using parametric line at specified level of tolerance. The output data is entropy coded. Experimental results show that the proposed scheme performs better than well-known lossless image compression techniques for several types of synthetic images, e.

We present several algorithms and improvements for the PH-Tree [14], a general purpose multi-dimensional index. The algorithms include a skyline query, nearest neighbour queries (kNN queries), range queries and a special update() operator for moving data. The improvements include a solution for the problem of large nodes, resulting in much better scalability with high dimensionality k when updating the tree. Another improvement uses generic data preprocessing to avoid problems with special cases of clustered datasets such as the CLUSTER 0.5 dataset in [14]. Finally, we discuss how the PH-Tree can be used to store hyper-rectangles instead of points and how to perform efficient queries on stored hyper-rectangles.

Spatial sampling schemes are mainly developed to determine sampling locations that can cover the variation of environmental properties in the area of interest. Here we proposed the variance quadtree algorithm for sampling in an area with prior information represented as ancillary or secondary environmental data, and the covariance structure of the ancillary variable is non-stationary. The algorithm is based on the idea of a quadtree decomposition, where an area is successively divided into strata so each stratum has more-or-less equal variation. An observation point is then placed inside each stratum. This scheme samples sparsely in relatively uniform areas and more intensively where variation is large. It samples in the feature space and also takes into consideration the spread in the geographic space. We describe the algorithm, its software implementation, and present some examples of applications. r

The existing techniques of reversible data hiding in encrypted JPEG images vacates space for data hiding after encrypting the image. As the entropy of encrypted images is higher, there is a chance for information loss as well as the computational complexity of image reconstruction will be higher. The proposed method therefore finds space for data hiding before encrypting the image using the method of quadtree compression. The simplicity of quadtree data structure reduces computational complexity. The image is encrypted using RC4 encryption algorithm. The vacant spaces obtained after quadtree compression is used for data hiding with the help of a data hiding key. At the receiver side, data extraction and image recovery are made separable such that the data can be extracted without knowing the image contents. The original pixel restoration is done using prediction error method. The experimental results demonstrate that the proposed method is able to achieve better data hiding capacity and recovered image quality within an acceptable computational complexity range.

Fungsi pembangkit mesh adaptif, meshqt2d, telah berhasil dikembangkan dengan menggunakan bahasa pemrograman matematik MATLAB®. Keluaran program pembangkit mesh ini secara umum adalah file yang berisi data distribusi nodal dan data konektifitas elemen mesh hasil diskritisasi dari suatu domain geometri dua dimensi.

This paper presents a polygon soup representation for multiview data. Starting from a sequence of multi-view video plus depth (MVD) data, the proposed quad-based representation takes into account, in a unified manner, different issues such as compactness, compression, and intermediate view synthesis. The representation is extracted from MVD data in two steps. First, a set of 3D quads is extracted thanks to quadtree decomposition performed on depth maps. Second, a selective elimination of the quads is performed in order to reduce interview redundancies and thus provide a compact representation. Moreover, the proposed methodology for extracting the representation allows to reduce ghosting artifacts. Finally, an adapted compression technique is proposed that limits coding artifacts. The results presented on two real sequences show that the proposed representation provides a good trade-off between rendering quality and data compactness.

A method that combines region growing and edge detection for image segmentation is presented. The authors start with a split-and merge algorithm wherein the parameters have been set up so that an over-segmented image results. Region boundaries are then eliminated or modified on the basis of criteria that integrate contrast with boundary smoothness, variation of the image gradient along the boundary, and a criterion that penalizes for the presence of artifacts reflecting the data structure used during segmentation (quadtree in this case). The algorithms were implemented in the C language on a Sun 3/160 workstation running under the Unix operating system. Simple tool images and aerial photographs were used to test the algorithms. The impression of human observers is that the method is very successful on the tool images and less so on the aerial photograph images. It is thought that the success in the tool images is because the objects shown occupy areas of many pixels, making it is easy to select parameters to separate signal information from noise

A population model is presented that accounts for spatial structure within habitat patches. It is designed for social species of wildlife that form social group home ranges that are much smaller than patch size. The model represents social group home ranges by Voronoi regions that tessellate a patch to form a Voronoi diagram. Neighbouring social groups are linked with habitat-confined shortest paths and form a dispersal network. The model simulates population dynamics and makes use of Voronoi diagrams and dispersal networks as a spatial component. It then produces density maps as outputs. These are maps that show predicted animal densities across the patches of a landscape. A construction procedure for the particular Voronoi diagram type used by the model is described. As a test case, the model is run for the squirrel glider (Petaurus norfolcensis), a small arboreal marsupial native to Australia. A time series of density maps are produced that show squirrel glider density changing across a landscape through time.

We describe in this paper a highly structured numerical method that allows for an important speedup in the calculations. The method is implemented in a bi-dimensional binary tree (quadtree or octree) structure in a partition of unity framework. The partition of unity is constructed by using natural neighbour interpolation. Data can be easily obtained from voxel or pixel-based images, as well as STL files or other CAD descriptions. The method described here possesses linear completeness at least and essential boundary conditions are implemented through the characteristic function method, by employing a special class of functions called R-functions. After the theoretical description of the method, some examples of its performance are presented and analysed.

We describe in this paper a highly structured numerical method that allows for an important speedup in the calculations. The method is implemented in a bi-dimensional binary tree (quadtree or octree) structure in a partition of unity framework. The partition of unity is constructed by using natural neighbour interpolation. Data can be easily obtained from voxel or pixel-based images, as well as STL files or other CAD descriptions. The method described here possesses linear completeness at least and essential boundary conditions are implemented through the characteristic function method, by employing a special class of functions called R-functions. After the theoretical description of the method, some examples of its performance are presented and analysed.

Since different regions of a color image generally exhibit different spectral characteristics, the energy compaction of applying a single spectral transform to all regions is largely inefficient from a compression perspective. Thus, it is proposed that different subsets of wavelet coefficients of a color image be subjected to different spectral transforms before the resultant coefficients are coded by an efficient wavelet coefficient coding scheme such as that used in JPEG2000 or color set partitioning in hierarchical trees (CSPIHT). A quadtree represents the spatial partitioning of the set of high frequency coefficients of the color planes into spatially oriented subsets which may be further partitioned into smaller directionally oriented subsets. The partitioning decisions and decisions to employ fixed or signal-dependent bases for each subset are rate-distortion (R-D) optimized by employing a known analytical R-D model for these coefficient coding schemes. A compression system of asymmetric complexity, that integrates the proposed adaptive spectral transform with the CSPIHT coefficient coding scheme yields average coding gains of 0.3 dB and 0.9 dB in the Y component at 1.0 b/p and 2.5 b/p, respectively, and 0.9 dB and 1.35 dB in the U and V components at 1.0 b/p and 2.5 b/p, respectively, over a reference compression system that integrates the single spectral transform derived from the entire image with the CSPIHT coefficient coding scheme.

This paper presents novel coding algorithms based on tree structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one dimensional (1-D) case, our scheme is based on binary tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments.

This paper presents a new hybrid scheme for image data compression using quadtree decomposition and parametric line fitting. In the first phase of encoding, the input image is partitioned into quadrants using quadtree decomposition. To prevent from very ...

The context of this study is 3D video. Starting from a sequence of multi-view video plus depth (MVD) data, the proposed quad-based representation takes into account, in a unified manner, different issues such as compactness, compression, and intermediate view synthesis. The representation is obtained into two steps. Firstly, a set of 3D quads is extracted by using a quadtree decomposition of the depth maps. Secondly, a selective elimination of the quads is performed in order to reduce interview redundancies and thus provide a compact representation. Experiments on two real sequences show good quality results at the rendering stage and a small data overload compared to mono-view video.

A generalized multidimensional Wiener filter for denoising is adapted to hyperspectral images (HSIs). Commonly, multidimensional data filtering is based on data vectorization or matricization. Few new approaches have been proposed to deal with multidimensional data. Multidimensional Wiener filtering (MWF) is one of these techniques. It considers a multidimensional data set as a third-order tensor. It also relies on the separability between a signal subspace and a noise subspace. Using multilinear algebra, MWF needs to flatten the tensor. However, flattening is always orthogonally performed, which may not be adapted to data. In fact, as a Tucker-based filtering, MWF only considers the useful signal subspace. When the signal subspace and the noise subspace are very close, it is difficult to extract all the useful information. This may lead to artifacts and loss of spatial resolution in the restored HSI. Our proposed method estimates the relevant directions of tensor flattening that may not be parallel either to rows or columns. When rearranging data so that flattening can be performed in the estimated directions, the signal subspace dimension is reduced, and the signal-to-noise ratio is improved. We adapt the bidimensional straight-line detection algorithm that estimates the HSI main directions, which are used to flatten the HSI tensor. We also generalize the quadtree partitioning to tensors in order to adapt the filtering to the image discontinuities. Comparative studies with MWF, wavelet thresholding, and channel-by-channel Wiener filtering show that our algorithm provides better performance while restoring impaired HYDICE HSIs.

Foundational work for 3D user interface creation, implementation, and research using hardware accelerated GPU methodologies in the form of a software framework, approach, and techniques that are modelled after successful traits of successful and scientifically sound 2D user interface technology and foundations.  For the thesis, a colour selection in 3D was created and used to conduct a user study, which thoroughly proved that 3D user interfaces can be just as successful as 2D user interfaces.  A state of the art 2D color selector was used for comparison.

This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one-dimensional case, our scheme is based on binary-tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying R-D behavior (D(R)∼c02-c1R), thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of O(NlogN). We then show the extension of this scheme to the two-dimensional case using a quadtree. This quadtree-coding scheme also achieves an exponentially decaying R-D behavior, for the polygonal image model composed of a white polygon-shaped object against a uniform black background, with low computational cost of O(NlogN). Again, the key is an R-D optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree-coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp.

Splatting is an object-order volume rendering algorithm that produces images of high quality, and for which several optimization techniques have been proposed. This paper presents new techniques that accelerate splatting algorithms by exploiting both object-space and image-space coherence. In particular, we propose two visibility test methods suitable for octree-based splatting. The first method, based on dynamic image-space range trees, offers an accurate occlusion test and does not trade off image quality. The second method, based on image-space quadtrees, uses an approximate occlusion test that is faster than the first algorithm. Although the approximate visibility test may produce visual artifacts in rendering, the introduced error is usually not found very often. Tests with several datasets of useful sizes and complexities showed considerable speedups with respect to the splatting algorithm enhanced with octree only. Considering that they are very easy to implement, and need little additional memory, our techniques will be used as very effective splatting methods.

In previous research with the focus on mobile and web mapping, we introduced a set of object-directed, real-time generalisation algorithms for point data, providing solutions for the major generalisation operators – selection, simplification, aggregation and displacement. This paper presented the quantitative cartographic analysis of these algorithms applied in a set of experiments to the SwissLichens database featuring close to 87,000 lichen observations reported in Switzerland to date.

Image segmentation is an essential complementary process in digital image processing and computer vision, but mostly utilizes simple segmentation techniques, such as fixed partitioning scheme and global thresholding techniques due to their simplicity and popularity, in spite of their inefficiency. This paper introduces a new split-merge segmentation process for a quadtree scheme of colour images, based on exploiting the spatial and spectral information embedded within the bands and between bands, respectively. The results show that this technique is efficient in terms of quality of segmentation and time, which can be used in standard techniques as alternative to a fixed partitioning scheme.

We propose a new classification method for vectorvalued images, based on: 1) a causal Markovian model, defined on the hierarchy of a multiscale region adjacency tree (MRAT), and 2) a set of nonparametric dissimilarity measures that express the data likelihoods. The image classification is treated as a hierarchical labeling of the MRAT, using a finite set of interpretation labels (e.g., land cover classes). This is accomplished via a noniterative estimation of the modes of posterior marginals (MPM), inspired from existing approaches for Bayesian inference on the quadtree. The paper describes the main principles of our method and illustrates classification results on a set of artificial and remote sensing images, together with qualitative and quantitative comparisons with a variety of pixel-based techniques that follow the Bayesian-Markovian framework either on hierarchical structures or the original image lattice.

This paper presents novel coding algorithms based on tree structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one dimensional (1-D) case, our scheme is based on binary tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments.

A comparison is made between K-trees, (i.e. quadtrces and octrees,) which are regular decompositions of volumes, and new, irregular decompositions called R-trees. This comparison is made within the context of the representation problems that might be associated with a robotic system. The results show that the irregular decomposition is independent of object position and can provide a more efficient encoding for certain shapes. However, detecting intersections between R-trees requires an algorithm of greater complexity than that of interference detection for octrees due to the irregularity of the R-tree decomposition. Object representation Image encoding Quadtree Hierarchical data structures Recursive Decomposition

The massive quantities of geographic information that are collected by modern sensing technologies are difficult to use and understand without data reduction methods that summarize distributions and report salient trends. Statistical analyses, therefore, are increasingly being used to analyze large geographic data sets over a broad spectrum of spatial and temporal scales. Computational Grids coordinate the use of distributed computational resources to form a large virtual supercomputer that can be applied to solve computationally intensive problems in science, engineering, and commerce. This paper presents a solution to computing a spatial statistic, G * i (d) using Grids. Our approach is based on a quadtree-based domain decomposition that uses task-scheduling algorithms based on GridShell and Condor. Computational experiments carried out on the TeraGrid were designed to evaluate the performance of solution processes. The Grid-based approach to computing values for G * i (d) shows improved performance over the sequential algorithm while also solving larger problem sizes. The solution demonstrated not only advances knowledge about the application of the Grid in spatial statistics applications but also provides insights into the design of Grid middleware for other computationally intensive applications.

Based on a compressed linear quadtree, a data structure is proposed which is more than a structure to compress a gray-level or color image, but a structure, which can be applied to retrieve a block image. This compressed linear quadtree may directly extract a detailed block image without decompressing the compressed data of the original image.

Emerging database applications require the use of new indexing structures beyond B-trees and R-trees. Examples are the k-D tree, the trie, the quadtree, and their variants. They are often proposed as supporting structures in data mining, GIS, and CAD/CAM applications. A common feature of all these indexes is that they recursively divide the space into partitions. A new extensible index structure, termed SP-GiST, is presented that supports this class of data structures, mainly the class of space partitioning unbalanced trees. Simple method implementations are provided that demonstrate how SP-GiST can behave as a k-D tree, a trie, a quadtree, or any of their variants. Issues related to clustering tree nodes into pages as well as concurrency control for SP-GiST are addressed. A dynamic minimum-height clustering technique is applied to minimize disk accesses and to make using such trees in database systems possible and efficient. A prototype implementation of SP-GiST is presented as well as performance studies of the various SP-GiST's tuning parameters.

This article describes a new automatic quadtree-/octree-based and scale-dependent generalization algorithm for point selection. The benefit toward existing point selection methods is that it preserves global as well as local characteristics of the spatial point distribution and of the spatial point density. It can be applied not only to points in 2D space but also to points in 3D space. In this article, an evaluation of the new point selection method is also provided.