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Based on the status of the center location algorithm, firstly this paper proposed the grid space-based multi-source shortest path algorithm by the use of the network data model in grid points set space. Secondly at the basis of the algorithm P center algorithm was proposed. Finally data bottlenecks brought by the vector data in network analysis were solved. The experiment of center location regional analysis is established for the interpretation of our research.

A new fast DCT-based algorithm for accurate image arbitrary scaling and rotation is described. The algorithm is free from boundary effects characteristic for FFT-based algorithm and ensures perfect interpolation with no interpolation errors. The algorithm is compared with other available algorithms in terms of the interpolation accuracy, computational complexity and suitability for real time applications.

To solve the issue of low precision and poor real-time performance in image registration, this paper presents an algorithm for extracting and matching of image feature points based on an invariant feature algorithm of the complementation between Harris operator corner detection and SIFT algorithm. First, with Harris operator ‘s quick calculating, the algorithm extracts much corner points in the image as original feature points. Then, description goes to the feature vector of pre-selected feature points on the strike of scale-space invariant features transform (SIFT), thus obtaining descriptors of feature points. By calculating the minimum Euclidean distance of two points in vectors of different feature points described by the SIFT algorithm in the two to-be-spliced images, the accurate image matching is then achieved. Experiments demonstrate that the algorithm combines the rapid achieve performance of Harris operator and the scale-space invariance of the SIFT algorithm, which boasts good robustness for translation, whirling and scaling transformation. In the experiments of 100 images, when there occurs the translation, whirling or scaling transformation to the image, the fully consistent ratio between the coordinates of matching points and the actual coordinates with using this algorithm is over 95%. This algorithm can quickly extract with high precision feature points for matching to achieve the seamless images.

The aim of this paper is to provide the line drawing algor ithm which is accurate and eff ective in dissimilar hardware platforms and different application requirements. The most famous algorithm to draw a straightness line in a smooth fashion is Bresenham algorithm. It is advantageous that the classic Bresenham algorithm processes are all integer numeric without division and decimal frac tion. Meanwhile, it is imperfect that the algorithm generates only one pixel at a computation time. So a common inevitable phenomenon of the algorithm is its slow efficiency to some extend. Firstly, this paper fully analyzes recent researches of the Bresenham Line Drawing algorithm. Secondly, in this paper we give full attention to the initiative relation between line generation model and its linear slope, and then we present an improved algorithm which can generate pixels of a line row-major by raster graphics display device. What needs to stress, the core principle of the improved algorithm is utiliz ing the counterpart of both ends of line and the symmetry for segments. Thirdly, after discussing theory and structure, the improved algorithm implementation and simulation are given. The corresponding project, it means that the hardware acceleration in the us e of circular subtraction technology based on shift register was briefly described. Finally, results were presented to demonstrate that the new algorithm inherits the advantage of classic Bresenham algorithm without division and decimal fraction, the speed has been increased greatly, and it is eas y to implement by hardware. Keywords: Computer graphics; Bresenham algorithm; line drawing

Through the study on the existing motion estimation algorithms, for the problems existed in them, this paper improves the motion estimation algorithm. The improved algorithm reduces the complexity of the motion search algorithm through pre-judgment of motion types, dynamic selection of motion search patterns, early end of the search process and other technologies, which avoids the block matching calculation for some points with small probability, thus to achieve the purpose of reducing the complexity of the whole motion estimation algorithm, to improve the algorithm efficiency.

3D data registration algorithm based on invariant was proposed, which is sparse range image from stripe coded structured light system. The range image is uneven and its corresponding points during different views are not the same ones, but the adjacent regions. The algorithm is improved iterative closed points algorithm; invariant is added during search corresponding points such as the volume of tetrahedron. The impact of volume on noise, rigid translation, and perturbation are analyzed by means of statistics experiments, and then the search criterions are proposed. Experiments verified the validity of the data registration algorithm from the quantitative and qualitative aspects.

This work presents a new neural algorithm designed for the reconstruction of tomographic images from Cone Beam data. The main objective of this work is the search of a new reconstruction method, able to work locally, more robust in presence of noisy data and in situations with a small number of projections. This study should be intended as the first step to evaluate the potentialities of the proposed algorithm. The algorithm is iterative and based on a set of neural networks that are working locally and sequentially. All the x-rays passing through a cell of the volume to be reconstructed, give origin to a neural network which is a single-layer perceptron network. The network does not need a training set but uses the line integral of a single x-ray as ground-truth of each output neuron. The neural network uses a gradient descent algorithm in order to minimize a local cost function by varying the value of the cells to be reconstructed. The proposed strategy was first evaluated in conditions where the quality and quantity of input data varies widely, using a the Shepp-Logan Phantom. The algorithm was also compared with the iterative ART algorithm and the well known filtered backprojection method. The results show how the proposed algorithm is much more accurate even in the presence of noise and under conditions of lack of data. In situations with little noise the reconstruction, after a few iterations, is almost identical to the original.

Image registration is an important step of many practical problems, such as image fusion, image analysis and image inlaying. This paper proposes and implements an automatic image registration algorithm with high precision based on character points as well as its corresponding parallel algorithm. The algorithm applies Forstner arithmetic operator to pick up character points and for the first time uses local normalized mutual information to search their matching points. The normalized mutual information is computed using highly precise Parzen window method. Then single-point least square method is employed to search the matching points precisely, which are used together with the character points to compute the transformation parameters. Then the algorithm uses quadratic polynomial transformation to register the images. Based on the analysis of performance of the serial algorithm, the paper proposes and implements its corresponding parallel algorithm. The algorithm parallelizes each step according to its characteristic and gives the strategy of data distribution. The experimental results show that the parallel algorithm gets high efficiency and thus has good scalability and applicability.

Fuzzy C-Means (FCM) algorithm is a fuzzy pattern recognition method. Clustering precision of the algorithm is affected by its equal partition trend for data set of large discrepancy of each class samples number, and the optimal clustering result of the algorithm mightn't be a right partition in this case. In order to overcome this disadvantage, a Gaussian function Weighted Fuzzy C-Means (WFCM) algorithm is proposed, which the weighted function is produced by a Gaussian function calculating dot density of each sample. To certain extent, the WFCM algorithm has not only overcome the limitation of equal partition trend in fuzzy Cmeans algorithm, but also been favorable convergence and stability. The calculation of the weighted function and the choice of sample dot density range restriction value for the algorithm are both objective. When partially supervised information obtained from a few labeled samples is introduced to the WFCM algorithm, the classification performance of the WFCM algorithm is further enhanced and the convergent speed of objective function is further accelerated.

In this paper, we propose a maximum-entropy expectation-maximization algorithm. We use the proposed algorithm for density estimation. The maximum-entropy constraint is imposed in order to ensure smoothness of the estimated density function. The exact derivation of the maximum-entropy expectation-maximization algorithm requires determination of the covariance matrix combined with the maximum entropy likelihood function, which is difficult to solve directly. We therefore introduce a new lower-bound for the EM algorithm derived by using the Cauchy-Schwartz inequality to obtain a suboptimal solution. We use the proposed algorithm for function interpolation and image segmentation. We propose the use of the EM algorithm for image recovery from randomly sampled data and signal reconstruction from randomly scattered sensors. We further propose to use our approach to maximum-entropy expectation-maximization (MEEM) in all of these applications. Computer simulation experiments are used to demonstrate the performance of our algorithm in comparison to existing methods.

On the basis of analysis of the principle and nature of the two-dimensional Douglas-Peucker algorithm, this paper puts forward the three-dimensional Douglas-Peucker algorithm and applies this algorithm to the automated generalization of the three-dimensional discrete points or the basis of DEM. The last part of this paper introduces the verification experiments by computer programs for this new algorithm. Preliminary experiments have proved that the main geomorphologic feature points for both the general or local areas of the DEM can be correctly extracted with satisfactory computational efficiency.

The original algorithm of phase reconstruction is proposed and its characteristics are estimated. This algorithm requires detection of dislocation coordinates so it should be used together with the algorithm of dislocation localization. In the paper the comparison is performed of the proposed algorithm with the well known Fried's algorithm. After that the phase reconstruction technique is included into the model of a typical adaptive optics system.

This paper presents a novel fast and high-accurate 3-D registration algorithm. The ICP (Iterative Closest Point) algorithm converges all the 3-D data points of two data sets to the best matching points with minimum evaluation values. This algorithm is broadly used, because it has good availability to many applications. But, it needs many computational costs and it is very sensible to error values. Because, it uses whole data points of two data sets and least mean square optimization. We had proposed the M-ICP algorithm, which is an extension of the ICP algorithm based on modified M-estimation for realization of robustness against outlying gross noise. The proposed algorithm named HM-ICP (Hierarchical M-ICP) is an extension of the M-ICP with selecting region for matching and hierarchical searching of selected regions. In this algorithm, we select regions using evaluation of variance for distance values in the target region and homogeneous topological mapping. Some fundamental experiments utilizing real data sets of 3-D measurement show effectiveness of the proposed method. We achieved more than 4-digits number reduction of computational costs and confirmed less than 0.1% error to the measurement distance.

We propose a new three-step phase-shifting algorithm, which is much faster than the traditional three-step algorithm. We achieve the speed advantage by using a simple intensity ratio function to replace the arctangent function in the traditional algorithm. The phase error caused by this new algorithm is compensated for by use of a look-up-table (LUT). Our experimental results show that both the new algorithm and the traditional algorithm generate similar results, but the new algorithm is 3.4 times faster. By implementing this new algorithm in a high-resolution, real-time 3D shape measurement system, we were able to achieve a measurement speed of 40 frames per second (fps) at a resolution of 532 × 500 pixels, all with an ordinary personal computer.

We propose a new implicit surface polygonalization algorithm based on front propagation. The algorithm starts from a simple seed (e.g. a triangle) that can be automatically initialized, and always enlarges its boundary contour outwards along its tangent direction suggested by the underlying volume data. Our algorithm can conduct mesh optimization and Laplacian smoothing on-the-fly and generate meshes of much higher quality than the Marching-cubes algorithm. Experimental results on both real and synthetic volumetric datasets are shown to demonstrate the robustness and effectiveness of the new algorithm.

Conventionally, the FDK algorithm is used to reconstruct images from cone-beam projections in many imaging systems. One advantage of this algorithm is its shift-invariant feature in the filtering process. In this paper, a new cone-beam reconstruction algorithm is derived for a single arc source trajectory. Examples of the arc trajectory include the full circular scan mode, a short-scan mode and a super-short-scan mode depending upon the angular range of the scanning path. Since the single arc does not satisfy Tuy's data sufficiency condition, there is no mathematically exact algorithm. However, one advantage of this reconstruction is that the shift-invariance property has been preserved despite the lack of a mathematically complete data set. The new algorithm includes backprojections from three adjacent segments of the arc defined by T1(vector x), T2(vector x) and T3(vector x). Each backprojection step consists of a weighted combination of 1D Hilbert filtering of the modified cone-beam data along horizontal and non-horizontal directions. The non-horizontal filtering is a new feature of this FBP algorithm. For the full circle scanning path, this algorithm reduces to the conventional FDK algorithm plus a term involving a first order derivative filter. Numerical simulations have been performed to validate the algorithm.

In this paper we discuss image reconstruction algorithms in super-short-scan fan-beam and cone-beam computed tomography (CT). We propose a new fan-beam filtered back-projection algorithm which can obtain exact region of interest (ROI) reconstruction if and only if every projecting line passing through the ROI intersects the source trajectory, even if the scanning range is smaller than the half-scan. And we prove the algorithm is approximate when the projections are truncated. Furthermore, we expand the algorithm to cone-beam reconstruction. Then we simulate the algorithm on the computer and evaluate the noise properties of the new algorithm and the other algorithms. Numerical results in our work suggest that the new algorithm is generally less susceptible to data noise and less artifacts than the before algorithms. In particular, the new algorithm is easily and successfully expanded to cone-beam tomography when the source trajectory is a short-arc on the single circle or on the helical trajectory.

The presented reconstruction algorithm is based on merging the fast multipole method (FMM) for the forward solver with the rapidly convergent descent method for the cost function minimization algorithm (by Fletcher and Powell 1964 and 1970). Parametric results are presented showing the potential of the proposed computational algorithm.

In order to achieve high video coding efficiency, a new motion estimation and compensation algorithm is proposed based on Genetic Algorithm. This algorithm exploits the uniformity and correlation in the properties of the cluster of blocks called Super-Block. These Super-Blocks have adaptive boundaries that are used to partially generate initial population for fast convergence to global minimum. Rest of the population is generated using pure Random Number Generator (RNG). This population then generates offspring which then competes within itself by the virtue of it’s fitness to survive into the next generation. The fitness value in each generation is calculated by comparing the reference frame with the predicted frame. The algorithm stops after convergence or when maximum generations are reached. This algorithm compares well against conventional algorithms like FSA (Full Search Algorithm), One-Step Method or N-Step Method in terms of number of searches, complexity, robustness and scalability.

Classification of images requires extraction of optimal set of features. In this paper, a method that uses genetic algorithm creating texture descriptors on features computed from a feature extraction method is presented. A feature extraction algorithm is applied to a database of images and a training feature matrix is created. This matrix is updated by a dynamic algorithm, which finds the vectors most close to the real solution in the Euclidean norm. This set forms the texture descriptor which can be further used for classification of unknown samples. A weighted fitness function that selects best parents in each generation has been implemented. Examples of classification are presented with the features computed from a classification algorithm. Results show that the classification performance of the features improved after applying the genetic algorithm. The algorithm is cost efficient. This algorithm is also compared with that of the Learning Vector Quantization method which quantizes the training vectors to an optimal set of codebook vectors.

Applications in scientific visualization often involve extensive data sets, which represent scalar or vector valued functions resulting from experimental measurements. Ray Casting (RC) is a well-known approach for visualizing a multi-dimensional volume data. It casts a large number of rays from the viewer into the volume and then computes the progressive attenuation along each ray in the volume. It is known that the ray-casting algorithm requires extensive computation time. In this study, we propose two techniques to speed up the ray-casting process. First, we derive an estimation of ray step sizes during its progressive re-sampling without invocating viewing transformation operations. Hence lengthy computations of trigonometric functions and matrix multiplications can be avoided. Furthermore, by exploring the ray coherence property, we propose a scan-line algorithm so that ray/volume intersections can be found efficiently. The proposed algorithm is implemented and compared with the conventional RC algorithm. Experimental results show that the proposed algorithm performs three to four times faster than the conventional RC algorithm.

The traditional training algorithm for vector quantization such as the LBG algorithm uses the convergence of distortion sequence as the condition of the end of algorithm. We presented a novel training algorithm for vector quantization in this paper. The convergence of the entropy sequence of each region sequence is employed as the condition of the end of the algorithm. Compared with the famous LBG algorithm, it is simple, fast and easy to be comprehended and controlled. We test the performance of the algorithm by typical test image Lena and Barb. The result shows that the PSNR difference between the algorithm and LBG is less than 0.1dB, but the running time of it is at most one second of LBG.

The matching process between the input data of real hand's characteristic marks and postulated positions of the model is needed while using model-based methods in gesture recognition. This fitting process can be regarded as a procedure of optimization based on a certain hand alignment measure. In this paper, an improved algorithm for the model fitting process is proposed to substitute conventional searching algorithm. The algorithm is the combination of Genetic Algorithm (GA) and classical Line Searching Algorithm (LSA). The new algorithm guarantees the fitting solution to be the global optimal and the operation near to be real time implementable. The experimental results show that the proposed algorithm is capable of searching optimal internal model positions with high speed and precision.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Pricing of derivatives is one of the central problems in Computational Finance. Since the theory of derivative pricing is highly mathematical, numerical techniques such as lattice approach, finite-difference and finite-element techniques among others have been resorted in the past. Recently Fast Fourier Transform (FFT) have been used for such applications as derivative pricing. In the current work, we develop a parallel algorithm for FFT and implement it to price options. Our main aim is to study the performance of this algorithm. For a data size of N and P processors, a blocked data distribution for the algorithm in general produces log(N) - log(P) iterations of local communications and log(P) iterations of remote communications. Therefore, the algorithm is divided into two parts: local and remote. In the local algorithm, the processors perform the computations on their locally partitioned data elements without any communications. In the case of remote algorithm, the processors perform the computation on the local data elements with remote communications. In this paper we focus on the remote communication and computation aspect of the algorithm. We discuss the performance of our algorithm and the results (in general terms) from FFT algorithm and binomial tree algorithm developed and implemented for the same/similar problem. We make some general observation on these two algorithms.

An adaptive algorithm based on a direction set method for solving unconstrained minimization problems without using derivatives is developed for spectral estimation with the presence of noise. It is a fast algorithm since it requires O(N) multiplications for each system update where N is the number of parameters used in the system design. Computer simulations have shown that the algorithm is stable and very efficient for spectral estimation. The frequency estimates obtained by this algorithm often are smoother than those generated using a conjugate gradient based algorithm which has a computational complexity of O(N 2 ). A detailed study of the algorithm for adaptive spectral estimation including its computational complexity, computer simulations and its convergence comparing with other known methods, is given in this paper.

The ordered subsets (OS) algorithm1 has enjoyed considerable interest for accelerating the well-known EM reconstruction algorithm for emission tomography and has recently found widespread use in clinical practice. This is primarily due to the fact that, while retaining the advantages of EM, the OS-EM algorithm can be easily implemented by slightly modifying the existing EM algorithm. The OS algorithm has also been applied1 with the one-step-late (OSL) algorithm,2 which provides maximum a posteriori estimation based on Gibbs priors. Unfortunately, however, the OSL approach is known to be unstable when the smoothing parameter that weights the prior relative to the likelihood is relatively large. In this work, we note that the OS principle can be applied to any algorithm that involves calculation of a sum over project indices, and show that it can also be applied to a generalized EM algorithm with useful quadratic priors. In this case, the algorithm is given in the form of iterated conditional modes (ICM), which is essentially a coordinate-wise descent method, and provides a number of important advantages. We also show that, by scaling the smoothing parameter in a principled way, the degree of smoothness is reconstructed images, which appears to vary depending on the number of subsets, can be efficiently matched for different numbers of subsets. Our experimental results indicate that the OS-ICM algorithm along with the method of scaling the smoothing parameter provides robust results as well as a substantial acceleration.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Motion estimation has been widely used by various video coding standards. Full Search is the most straightforward and optimal block matching algorithm but its huge computational complexity is the major drawback. To overcome this problem several fast block matching motion estimation algorithms have been reported. In this paper a fast four step search algorithm based on the strict application of Unimodal Error Surface Assumption has been proposed. Quadrant Selection Approach has been adopted to reduce the computational complexity. The algorithm is adaptive in the sense that it can be stopped at the second or third step depending on the motion content of the block based on the Half Stop Technique. Simulation results show that the number of search points in our algorithm are almost half as compared to the conventional four step search algorithm. The total number of search points varies from 7 to 17 in our proposed algorithm. The worst case computational requirement is only 17 block matches. Our algorithm is robust, as the performance is independent of the motion of the image sequences. It also possesses regularity and simplicity of hardware oriented features.

In this paper we present an iterative algorithm computing a global optimum for a large system of linear equations enforcing the so-called integrability condition for a given noisy non-integrable vector field. The algorithm will be applied to Photometric Stereo shape reconstruction. The scheme in question (a 2-D Leap-Frog Algorithm) relies neither on a prior knowledge of boundary conditions nor on other global constraints imposed on the so-far derived gradient integration techniques for noise-contaminated data. The proposed algorithm is an improvement of the recently developed Lawn-Mowing Algorithm, which computes a suboptimal solution to the above mentioned problem. The backbone of the proposed algorithm is a generalization of the 1-D Leap-Frog Algorithm derived for finding geodesic joining two points on a Riemannian manifold. The discussion is supplemented by examples illustrating the performance of the 2-D Leap-Frog Algorithm.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We propose a new Gibbs sampling algorithm, the soft- criterion acceptance algorithm, and use it for the texture synthesis. The new algorithm combines the advantages of the ICM algorithm in computations and of the algorithm of simulated annealing (SA) in global convergence. As a result, it is computationally efficient in comparison with the Gibbs sampler by S. Geman and D. Geman. The key idea is that the difference of the maximum and minimum of the energy functions is used to construct a soft criterion for updating each pixel value in a probabilistic acceptance fashion that is similar to the SA. The algorithm is verified by computational experiments.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Many phase-stepping algorithms have been developed for last decade. Some of them may be more attractive to practical measurement because of the insensitivity to phase-stepping errors. But it should be noticed that all existing phase- stepping algorithm need to know or calculate the phase steps. Why cannot we extract the measured phase without knowing or calculating phase steps. A new phase-stepping algorithm is proposed by our group. The algorithm can be implemented without knowing or calculating the phase steps. Actually, the new algorithm gives important improvements for the algorithms developed by C.T. Farrell and M.A. Player. Based on using Lissajous figures and ellipse fitting, the new algorithm introduces a simple transform for the intensity of the interferograms. New phase extraction expressions are derived. The simulating results indicate that the new algorithm is insensitive to phase-stepping errors and the accuracy of the new algorithm is only limited by the computation truncation errors.

A fuzzy logic clustering algorithm to classify a given image into targets and backgrounds is presented. The algorithm forms clusters and is trained without supervision. The clustering is done on the basis of the statistical properties of the set of inputs. The algorithm features an adaptive mechanism for selecting the number of clusters, and it features an adaptive threshold. The problem of threshold selection is considered and the convergence of the algorithm is shown. The algorithm also does not require the number of clusters been known a priori. An example is given to illustrate the application of the algorithm.

Motion compensation is a key operation in video compression to remove the temporal redundancy in a video sequence. One of the application examples is the MPEG video compression standard. The most commonly used motion estimation algorithm is the block matching algorithm due to its regularity. Full search is the most straight forward block matching algorithm which can always locate the optimal motion vector. However, its computational complexity makes it impractical in real time applications. Fast algorithm required less computation but the obtained motion vector is suboptimal. In this paper, a hybrid block matching algorithm is proposed. In this algorithm, average intensities of groups of pixels are used to roughly estimate the motion first. Then, the fast search algorithm is applied in a reduced search region centered around the result of the first pass. Experimental results show that the performance of the estimation accuracy is quite close to that of the full search algorithm while the computational complexity is only slightly increased with respect to those fast algorithms.

A self-organizing k-means algorithm to classify the inputs (data) into classes is presented. This algorithm provides solutions to the problems that the k-means classification algorithm faces. The k-means classification algorithm has the problem of selecting the threshold(s). It also requires that the number of classes be known a priori. This algorithm forms clusters, removes noise, and is trained without supervision. The clustering is done on the basis of the statistical properties of the set of input data. The algorithm consists of two phases. The first phase is similar to the Carpenter/Grossberg classifier, and the second phase is a modified version of the k-means algorithm. An example is given to illustrate the application of this algorithm and to compare this algorithm with the k-means algorithm.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A new method is introduced whereby the shape of a finite set of points in the plane is computed. The shape is approximated by a sequence of sets named k-connected hulls. We present an efficient algorithm for constructing the shape of a set of points. This algorithm is based on the relationship between the k-connected hulls sets an the Voronoi diagram.

A fast algorithm to detect rectangles in aerial images is suggested. A contour image is used as an input for the algorithm. the primitive lines are extracted in the contour image and joined into line segments by cluster analysis method. the line-merging algorithm is developed, and an algorithm to detect rectangles from the extracted straight lines is suggested. The developed algorithm allows a good relation between computational time and line quality.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Color vector quantization is a very important technique to display a color image with N2, typically N equals 256, colors in a personal computer and workstation or print a color image with K, typically K equals 256, colors without too much color degradation. The LBG algorithm is a popular suboptimal algorithm to solve the color vector quantization. However, it is very slow. Several fast algorithms such as the popularity algorithm, the median cut algorithm have been proposed. In this paper, we propose a new fast algorithm for color vector quantization. The proposed algorithm has been implemented in a tree structure. Assume that n is the number of pixels in the image and m is the dimension of the color space. In the tree structure, there is n leaves in the tree in the worst case, where n is the total pixel numbers in the original color image. The storage complexity of the proposed algorithm is O(n) and the time complexity if O(n log2 N). It is much faster than the median cut algorithm. In the same space complexity O(mn) our algorithm has time complexity O(n log2 K) while the median cut algorithm requires O(m log2 Kn log2 n), where m equals 3 is the dimensionality of the color space. Also, our algorithm finds the centroid of a compact cube instead of a rectangular shape in the median cut algorithm. Therefore, it produces better color images after vector quantization.

A new data clustering algorithm using a self organizing method is presented. This algorithm forms clusters and is trained without supervision. The clustering is done on the basis of the statistical properties of the set of data. This algorithm differs from the K-means algorithm and other clustering algorithms in that the number of desired clusters is not required to be known a priori. It also removes noise and is fast. The convergence of the algorithm is shown. An example is given to show the application of the algorithm to clustering data and to compare the results obtained using this algorithm with those obtained using the K-means algorithm.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The principle of shape recognition by using granulometries, is to transform a binary planar shape into a curve which is translation, rotation and scale invariant by a family of morphological transformations depending on the size of the structuring element. This paper presents a fast algorithm for the computation of the anti-granulometry by closings which avoids boundary effects. This algorithm is based on a simple geometric transformation called the `Steiner Inverse Transform', on which original theoretical results are given.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A new algorithm is proposed for determining the interpolation points for an Iterated Function System (IFS) model for one-dimensional data. The algorithm quickly selects points which are shown to provide favorable results when compared to an exhaustive search of all possible points. The algorithm is based on a recent proof which relates the fixed points of the IFS maps to the extremum points of the attractor of the IFS. The resulting algorithm greatly reduces the search time for the best interpolation points, and results are given comparing the proposed algorithm to exhaustive searches for a small number of maps on a series of test files.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

This paper presents a methodology for the classifying problem based upon a pseudo k-means algorithm. Both supervised and unsupervised classifying algorithms are presented here to show the flexibility of the pseudo k-means algorithm. The supervised algorithm is computationally efficient compared with the k-nn algorithm. The unsupervised algorithm avoids the error and time consuming problem due to the improper selection of initial class centers in the k-means algorithm. The pseudo k-means algorithm is easy to extend to the high dimension situation. Examples are presented to illustrate the effectiveness of the approach.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A clustering algorithm for the design of efficient vector quantizers to be followed by entropy coding is proposed. The algorithm generates a sequence of quantizers whith rates close to theoretical ratedistortion bound. A fast version of this algorithm can be used as an alternative to the entropy-constrained vector quantizer technique proposed by Chou Lookabaugh and Gray.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We report on the development of a new class of parallel computation algorithm for low-level scene analysis. The algorithm is a high resolution, high speed estimator for boundary extraction of simple objects imaged under noisy conditions. We explain the algorithm structure and underlying physical models; we then present demonstrative pictorial examples of application to synthetic test imagery. We next introduce a generalization of the algorithm wherein a hierarchical variable resolution search is employed to gain major improvements in algorithm convergence speed and robustness. We discuss the importance of making the algorithm adaptive to local image statistics and show that the algorithm parallel-window topology is consonant with this goal. We present further experimental results that depict the generalized algorithm applied to real data bases; these results demonstrate that even simple adaptation models can substantially improve algorithm convergence accuracy.