It is shown that the depth of the last node inserted in a random quad tree constructed from independent uniform [Q, 11d random vectors is in probability asymptotic to (2/d) log n, where log denotes the natural logarithm. In addition, for d =2, exact values are obtained for all the moments of the depth of the last node .

We propose a large scale terrain adaptive compression method with high compression rate in this paper by using integer wavelet transform combined with restricted quadtree triangulation based on the terrain variation characteristic. By taking advantage of the efficient computing and multi-resolution attributes of our algorithm, we can decompress the wavelet coefficients which indicate the terrai...

A novel image coding scheme using wavelet transform is presented. The developed coding scheme prevents undesirable classifications of wavelet coefficients which arise from conventional quadtree based image coding. This is accomplished by pre-processing the wavelet coefficients. This pre-processing is based statistical distributions of the wavelet coefficients in subbands and the human visual sy...

Mean shape-gain vector quantization (MSGVQ) is extended to include negative gains and square isometries. Square isometries together with a classi cation technique based on average block intensities enable us to enlarge the MSGVQ codebook size without any additional storage requirements while keeping the complexity of both the codebook generation and the encoding manageable. Variable rate codes ...

Dynamic attributes are attributes that change continuously over time making it impractical to issue explicit updates for every change. In this paper, we adapt a variant of the quadtree structure to solve the problem of indexing dynamic attributes. The approach is based on the key idea of using a linear function of time for each dynamic attribute that allows us to predict its value in the future...

Given a compressed image in the restricted quadtree and shading format, this paper presents a fast algorithm for computing 2D discrete cosine transform (DCT) on the compressed grey image directly without the need to decompress the compressed image. The proposed new DCT algorithm takes O(K2 logK + N2) time where the decompressed image is of size N × N and K denotes the number of nodes in the res...

Data-parallel primitives for performing operations on the PM1 quadtree, bucket PMR quadtree, and R-tree spatial data structures are presented using the scan model. Algorithms are described for building these three data structures that make use of these primitives. The data-parallel algorithms are assumed to be main memory resident. The algorithms were implemented on a minimally con gured Thinki...

The Support Vector Classification (SVC) is a powerful machine learning technique for pattern recognition purposes, whose efficiency depends significantly on its parameters selection. This paper proposes an algorithm that integrates the quadtree data structure with the grid search to select the optimal (C,) SVC parameters. The goal is to reduce computational operations and processing time from ...

In this paper, we present a method for synthesizing photorealistic visual speech using a parametric model based on quadtree splines. In an image-based visual speech synthesis system, visemes are used for generating an arbitrary new image sequence. The images between visemes are usually synthesized using a certain mapping. Such a mapping can be characterized by motion parameters estimated from t...

In this paper, a path planner is proposed for a fixed wing micro air vehicle (MAV), in the framework of fuzzy quadtrees. It is shown that a fuzzy version of the quadtree planner is apt for micro air vehicle applications with severe space, power and budgetary constraints. The algorithm can significantly reduce both space and time complexity and still yield an optimal and safe path for the vehicl...