Abstract: Density estimation based visual object counting (DE-VOC) methods estimate the counts of an image by integrating over its predicted density map. They perform effectively but inefficiently. This paper proposes a fast DE-VOC method but maintains its effectiveness. Essentially, the feature space of image patches from VOC can be clustered into subspaces, and the examples of each subspace can be collected to learn its embedding. Also, it is assumed that the neighborhood embeddings of image patches and their corresponding density maps generated from training images are similar. With these principles, a closed form DE-VOC algorithm is derived, where the embedding and centroid of each neighborhood are precomputed by the training samples. Consequently, the density map of a given patch is estimated by simple classification and mapping. Experimental results show that our proposed method is comparable with mainstream ones on counting accuracy while running much faster in testing phase.

Abstract: This research recognizes the leaf shape using Centroid Contour Distance (CCD) as shape descriptor. CCD is an algorithm of shape representation contour-based approach which only exploits boundary information. CCD calculates the distance between the midpoint and the points on the edge corresponding to interval angle. Leaf shapes that included in this study are ellips, cordate, ovate, and lanceolate. We analyzed 200 leaf images of tropical plant. Each class consists of 50 images. The best accuracy is obtained by 96.67%. We used Probabilistic Neural Network to classify the leaf shape. Experimental results demonstrated the effectiveness of the proposed approach for shape recognition with high accuracy.

Abstract: Depth scans acquired from different views may contain nuisances such as noise, occlusion, and varying point density. We propose a novel Signature of Geometric Centroids descriptor, supporting direct shape matching on the scans, without requiring any preprocessing such as scan denoising or converting into a mesh. First, we construct the descriptor by voxelizing the local shape within a uniquely defined local reference frame and concatenating geometric centroid and point density features extracted from each voxel. Second, we compare two descriptors by employing only corresponding voxels that are both non-empty, thus supporting matching incomplete local shape such as those close to scan boundary. Third, we propose a descriptor saliency measure and compute it from a descriptor-graph to improve shape matching performance. We demonstrate the descriptor’s robustness and effectiveness for shape matching by comparing it with three state-of-the-art descriptors, and applying it to object/scene reconstruction and 3D object recognition.

Abstract: Spacecraft's attitude information plays an important role in celestial navigation The attitude is mainly determined by matching the star's centroid in the obtained image with its corresponding information in star catalog Generally, the star image can be regarded as a spot with a diameter <5 pixels Therefore, it is very difficult to extract the star centroid with sub-pixel accuracy, especially in the hardware system, such as FPGAs The existing spot centroid extraction methods with high accuracy require plenty of pixels to realize the complex computations Limited to the star's diameter and hardware requirements, such methods are not suitable for star centroid extraction in hardware system To solve the problem, a two-step extraction method for star centroid with sub-pixel accuracy is proposed The maximum pixel-level center can be located through zero crossing of the first derivative in a small region Taking the pixel-level center as the middle of the window with fixed size, the sub-pixel offsets to the sub-pixel center can be calculated using fixed window weighted centroid method The sub-pixel center of the star is then obtained by adding the offsets to the pixel-level center This method can be implemented in hardware to increase processing speed, using Verilog hardware description languages A simulation is performed on computer and FPGA Experimental results show the excellent performance in accuracy and processing speed of two-step method In addition, two-step method has strong ability of resisting noise and good robustness compared to other methods

Abstract: Particle‐based CFD methods are powerful approaches to investigate free surface, multiphase flows, and fluid structure interaction problems because of their ability of tracking moving fluid interface even with huge deformations or fragmentation and merging. However, many fluid interface particle detection techniques are simple to implement but with low accuracy or provide relatively good detection results at complicated implementation cost or higher computational time. In case of incompressible flow simulation methods solving the Poisson equation of pressure, such as the moving particle semi‐implicit method, boundary particles detection techniques' accuracy affects precision and stability of pressure computation and interaction between fluid phases. In the present work, a new fluid interface particle detection technique is proposed to improve the accuracy of the boundary particles detection and keep the implementation easy. Denominated as the neighborhood particles centroid deviation technique, it is a two‐criteria technique based on the particle number density and the neighborhood particles weighted geometric center deviation. Compared with other techniques, the proposed neighborhood particles centroid deviation technique shows the best results by eliminating false interface particles inside the fluid domain and keeping the interface particles layer thin and regular. As a result, relatively stable pressure time histories and more consistent pressure and velocity fields are achieved. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Abstract: Clustering of objects according to shapes is of key importance in many scientific fields. In this paper we focus on the case where the shape of an object is represented by a configuration matrix of landmarks. It is well known that this shape space has a finite-dimensional Riemannian manifold structure (non-Euclidean) which makes it difficult to work with. Papers about clustering on this space are scarce in the literature. The basic foundation of the $$k$$k-means algorithm is the fact that the sample mean is the value that minimizes the Euclidean distance from each point to the centroid of the cluster to which it belongs, so, our idea is integrating the Procrustes type distances and Procrustes mean into the $$k$$k-means algorithm to adapt it to the shape analysis context. As far as we know, there have been just two attempts in that way. In this paper we propose to adapt the classical $$k$$k-means Lloyd algorithm to the context of Shape Analysis, focusing on the three dimensional case. We present a study comparing its performance with the Hartigan-Wong $$k$$k-means algorithm, one that was previously adapted to the field of Statistical Shape Analysis. We demonstrate the better performance of the Lloyd version and, finally, we propose to add a trimmed procedure. We apply both to a 3D database obtained from an anthropometric survey of the Spanish female population conducted in this country in 2006. The algorithms presented in this paper are available in the Anthropometry R package, whose most current version is always available from the Comprehensive R Archive Network.

Abstract: Some problems of partitioning a finite set of points of Euclidean space into two clusters are considered. In these problems, the following criteria are minimized: (1) the sum over both clusters of the sums of squared pairwise distances between the elements of the cluster and (2) the sum of the (multiplied by the cardinalities of the clusters) sums of squared distances from the elements of the cluster to its geometric center, where the geometric center (or centroid) of a cluster is defined as the mean value of the elements in that cluster. Additionally, another problem close to (2) is considered, where the desired center of one of the clusters is given as input, while the center of the other cluster is unknown (is the variable to be optimized) as in problem (2). Two variants of the problems are analyzed, in which the cardinalities of the clusters are (1) parts of the input or (2) optimization variables. It is proved that all the considered problems are strongly NP-hard and that, in general, there is no fully polynomial-time approximation scheme for them (unless P = NP).

Abstract: A planet centroid is an important observable object in autonomous optical navigation. A high-accuracy algorithm is presented to extract the planet centroid from its raw image. First, we proposed a planet segmentation algorithm to segment the planet image block to eliminate noise and to reduce the computation load. Second, we developed an effective algorithm based on Prewitt-Zernike moments to detect sub-pixel real edges by determining possible edges with the Prewitt operator, removing pseudo-edges in backlit shady areas, and relocating real edges to a sub-pixel accuracy in the Zernike moments. Third, we proposed an elliptical model to fit sub-pixel edge points. Finally, we verified the performance of this algorithm against real images from the Cassini-Huygens mission and against synthetic simulated images. Simulation results showed that the accuracy of the planet centroid is up to 0·3 pixels and that of the line-of-sight vector is at 2·1 × 10−5 rad.

Abstract: This paper investigates the weighted centroid formation tracking control for multi-agent systems. First, a class of novel distributed observers is developed for each agent to infer the formation's weighted centroid in finite time. Then, the distance-based control law is proposed based on the estimations, such that the weighted centroid of the formation is driven to track the assigned time-varying reference, meanwhile maintaining the prescribed formation shape. Moreover, the formation stabilization error is shown to converge to zero using the proposed observer-controller scheme utilizing the finite-time Lyapunov stability of the observers. Finally, all the theoretical results are further validated through numerical simulations.

Abstract: Wireless sensor network (WSN) is a basic component of internet and it plays an important role in many application areas, such as military surveillance, environmental monitoring and medical treatment. Node localization is one of the interesting issues in the field of WSN. Now, most of the existing node localization algorithms can be divided into two categories. One is range-based measurement and the other is range-free measurement. The localization algorithm of range-based measurement can achieve better location accuracy than the localization algorithm of range-free measurement. However, they are generally very energy consuming. Therefore, the range-free measurements are most widely used in practical applications. According to the application of localization algorithm in WSN by range-free measurements, an improved centroid localization algorithm based on iterative computation for wireless sensor network is proposed. In this algorithm, the position relationship of the closed area surrounded by the anchor nodes inside the unknown node's communication range and the unknown node is obtained by approximate point-in-triangulation test at first. Different position relationships determine different stopping criteria for iteration. Then, the centroid coordinates of the closed area surrounded by the anchor nodes inside the unknown node's communication range and the received signal strength (RSSI) between the centroid node and the unknown node are calculated. The anchor node with the weakest RSSI would be replaced by the centroid node. By this method, the closed area surrounded by the anchor nodes inside the unknown node's communication range is reduced. The location accuracy is increased by the cyclic iterative method. With the change of the anchor node ratio, the communication radius of the unknown node and the effect of RSSI error, the algorithm performance is investigated by using simulated data. The simulation results validate that although the improved centroid localization algorithm performance will be lost when the number of the anchor nodes inside the unknown node communication range decreases, the new approach can achieve good performance under the condition of few anchor nodes inside the unknown node communication range and this method is of strong robusticity against RSSI error disturbance.

Abstract: In order to locate source signal more accurately in authorized frequency bands, a novel primary user localization algorithm based on compressive sensing (PU-CSL) in cognitive radio networks (CRNs) is proposed in this paper. In comparison to existing centroid locating algorithms, PU-CSL shows higher locating accuracy for integrally exploring correlation between source signal and secondary users (SUs). Energy detection is first adopted for collecting the energy fingerprint of source signal at each SU, then degree of correlation between source signal and SUs is reconstructed based on compressive sensing (CS), which determines weights of centroid coordinates. A weighted centroid scheme is finally utilized to estimate source position. Simulation results show that PU-CSL has smaller maximum error of positioning and root-mean-square error. Moreover, the proposed PU-CSL algorithm possess excellent location accuracy and strong anti-noise performance.

Abstract: We consider the strongly NP-hard problem of partitioning a set of Euclidean points into two clusters so as to minimize the sum (over both clusters) of the weighted sum of the squared intracluster distances from the elements of the clusters to their centers. The weights of sums are the cardinalities of the clusters. The center of one of the clusters is given as input, while the center of the other cluster is unknown and determined as the geometric center (centroid), i.e. the average value over all points in the cluster. We analyze the variant of the problem with cardinality constraints. We present an approximation algorithm for the problem and prove that it is a fully polynomial-time approximation scheme when the space dimension is bounded by a constant.

Abstract: An important problem in computer vision is object recognition, which has received considerable attention in the literature. The performance of any object recognition system depends on the shape representation used and on the matching algorithm applied. In this paper, we propose a novel circle views (CVs) shape signature for recognizing 2-D object silhouettes. Many views from one circular orbit (or more) centered at the shape centroid are defined based on the distances from each viewing point on the circular orbit to a fixed number of sampled shape contour points. One compact and robust shape descriptor is obtained by applying the Fourier transform to the proposed signature. The obtained descriptor is translation, rotation, and scale invariant. Two popular shape benchmarks have been used for testing: 1) MPEG-7 and 2) Kimia’s-99 databases. The proposed CVs signature provides a promising retrieval rate (83.71% on MPEG-7 database). A further increase in the retrieval rate (90.35%) has been achieved by applying a shape context learning technique. A slight modification to the learning technique has been proposed that reduces its computational cost significantly. An attractive feature of the proposed CVs signature is its simplicity and computational efficiency, which makes the CVs signature more practical for different application areas.

Abstract: A selection of data types is defined from available log data for an evaluation of events associated with an entity. One or more evaluations associated with the entity are defined and reference data is generated from the selection of data types based on the one or more defined evaluations. The one or more evaluations are grouped into a pattern. A three dimensional (3D) score diversity diagram visualization is initialized for display in a graphical user interface, where a point representing the entity in the visualization is localized in 3D space at a coordinate based on two-dimensional (2D) coordinates in a 2D coordinate system of a centroid of the calculated area of a polygon placed to into the 2D coordinate system and defined by the values of each evaluation associated with the entity.

Abstract: Missing values in data are common in real world applications. In this research we developed a new version of the well-known k-means clustering algorithm that deals with such incomplete datasets. The k-means algorithm has two basic steps, performed at each iteration: it associates each point with its closest centroid and then it computes the new centroids. So, to run it we need a distance function and a mean computation formula. To measure the similarity between two incomplete points, we use the distribution of the incomplete attributes. We propose several directions for computing the centroids. In the first, incomplete points are dealt with as one point and the centroid is computed according to the developed formula derived in this research. In the second and the third, each incomplete point is replaced with a large number of points according to the data distribution and from these points the centroid is computed. Even so, the runtime complexity of the suggested k-means is the same as the standard k-means over complete datasets. We experimented on six standard numerical datasets from different fields and compared the performance of our proposed k-means to other basic methods. Our experiments show that our suggested k-means algorithms outperform previously published methods.

Abstract: In video processing, face detection and tracking has a wide scope for research. Although existing algorithms serve the purpose of face detection and tracking in video sequences, tremendous development in video technologies is posing more challenges while processing such videos. In this paper, we propose a new face tracking method based on fusion of corner measure algorithm and KLT tracker. Initially, Viola-Jones algorithm detect the face present in the first frame of the video sequence, detected portion of the face is extracted and Harris corner measure algorithm applied. Once corner points are computed, centroid is calculated. The resulting corner points which are in the form of an array are converted into matrix. KLT is a point tracking algorithm, works based on Eigen values and its result is in the form of matrix. The matrix generated from corner measure and centroid computation is concatenated with the matrix obtained using KLT face tracking algorithm. If the corner measure algorithm fails to track the facial region then KLT tracker performs its work and the reverse is also true. The proposed algorithm achieves accuracy better than KLT algorithm alone. The results at the end of this paper clearly indicate the practical achievement of theoretical assumption made.

Abstract: In the light of regularized dynamic time warping kernels, this paper re-considers the concept of time elastic centroid for a setof time series. We derive a new algorithm based on a probabilistic interpretation of kernel alignment matrices. This algorithm expressesthe averaging process in terms of a stochastic alignment automata. It uses an iterative agglomerative heuristic method for averagingthe aligned samples, while also averaging the times of occurrence of the aligned samples. By comparing classification accuracies for45 heterogeneous time series datasets obtained by first nearest centroid/medoid classifiers we show that: i) centroid-basedapproaches significantly outperform medoid-based approaches, ii) for the considered datasets, our algorithm that combines averagingin the sample space and along the time axes, emerges as the most significantly robust model for time-elastic averaging with apromising noise reduction capability. We also demonstrate its benefit in an isolated gesture recognition experiment and its ability tosignificantly reduce the size of training instance sets. Finally we highlight its denoising capability using demonstrative synthetic data:we show that it is possible to retrieve, from few noisy instances, a signal whose components are scattered in a wide spectral band.

Abstract: This letter introduces a new robust estimation method for the central value of a set of $N$ covariance matrices. This estimator, called Huber's centroid, is described starting from the expression of two well-known methods that are the center of mass and the median. In addition, a computation algorithm based on the gradient descent is proposed. Moreover, Huber's centroid performances are analyzed on simulated data to identify the impact of outliers on the estimation process. In the end, the algorithm is applied to brain decoding, based on magnetoencephalography data. For both simulated and real data, the covariance matrices are considered as realizations of Riemannian Gaussian distributions and the results are compared to those given by the center of mass and the median.

Abstract: The Molodensky-Badekas model is one of the similarity transformation models used in Ghana for transferring Global Positioning System (GPS) coordinates from the geocentric World Geodetic System 1984 (WGS 84) ellipsoid to the local non-geocentric coordinate system, and vice versa. The objective of the Molodensky-Badekas model is to introduce a centroid to cater for the correlation that exists between the parameters when used over a small portion on the earth surface. However, the Molodensky-Badekas model performance depends on a particular centroid method adopted and the adjustment technique used. By virtue of literature covered, it was realised that the arithmetic mean centroid has been the most widely used. In view of this, the present study developed and tested two new hybrid centroid techniques known as the harmonic-quadratic mean and arithmetic-quadratic mean centroids. The proposed hybrid approaches were compared with the geometric mean, harmonic mean, median, quadratic mean and arithmetic mean. In addition, the Total Least Squares (TLS) technique was used to compute the transformation parameters with varying centroid techniques to investigate and assess their accuracies in precise GPS datum transformation parameters estimation within the Ghana Geodetic Reference Network. Statistical indicators such as Mean Error (ME), Mean Squared Error (MSE), Standard Deviation (SD), and Mean Horizontal Position Error (MHPE) were used to assess the centroid techniques performance. The results attained show that the Harmonic-Quadratic Mean produced reliable coordinate transformation results within the Ghana geodetic reference network and thus could serve as practical alternative technique to the frequently used arithmetic mean. Keywords: Coordinate transformation, Molodensky-Badekas model, Centroid, Total Least Squares

Abstract: This paper proposes a new method for partitioning data clustering using PSO. The Proposed methods LPSOC designed for hard clusters. LPSOC alleviate some of the drawbacks of traditional algorithms and the state-of-the-art PSO clustering algorithm. Population-based algorithms such as PSO is less sensitive to initial condition than other algorithms such as K-means since search starts from multiple positions. The proposed algorithm LPSOC is less susceptible to local minima than K-means or even gbest version of PSO. In gbest PSO, all centroids are encoded in a single particle. Thus, the global best particle is a complete solution to the problem because its encoding contains the best position found for the centroids of all clusters. We used the local version of PSO in LPOSC. LPSOC uses a neighborhood of particles for optimizing the position of each cluster centroid. The whole swarm represents a solution to the clustering problem. This representation is far less computationally expensive than standard gbest version. The LPSOC is tested using six datasets from different domains to measure its performance fairly. LPOSC is compared with standard PSO for clustering and K-means. The results assure that the proposed method is very promising.

Abstract: The invention discloses a centroid frequency and spectral ratio integrated borehole seismic quality factor inversion method, and the method comprises the steps: building a reversion equation for calculating a stratum attenuation coefficient through a spectral ratio; building a reversion equation between the movement amount of the centroid frequency and the stratum attenuation coefficient; building a combined reversion equation among the spectral ratio, the centroid frequency and the stratum attenuation coefficient; and solving a target function of combined inversion through employing a damping LSQR algorithm. The method maintains the stability of the results of a spectral ratio method, and the impact on the method from non-stratum factor amplitude attenuation is small. The method integrates the advantages of high calculation precision of a centroid frequency calculation method and the sensitive reflection of attenuation abnormity, makes the most of the frequency changes of attenuation of seismic waves, and builds the combined reversion equation for solving the attenuation coefficient through the centroid frequency and the spectral ratio for combined reversion. The method employs better spectral ratio information for the constraint reversion of the centroid frequency method, improves the reversion effect, effectively reduces the noises and other interference, and improves the stability of absorption attenuation parameter reversion results.

Abstract: This paper presents an improved methodology for evaluating the position and orientation errors of airfoil sections of a manufactured aero-engine blade. The existing method estimates these errors by finding rigid-body transformations with translational and rotational parameters altogether to best match the inspection data points onto the design airfoil profiles. Such transformations lead to unreliable evaluation results due to combining the position and orientation errors with each other. This paper proposes to decouple the position and orientation errors in their evaluation in order to avoid the combining effect. To isolate the position error from the orientation error, an important location tolerance evaluation feature, the centroid of a manufactured airfoil section, must be correctly identified from the sectional inspection data points. Identifying the centroid location directly from discrete data points is subject to an error caused by biased area calculations on the pressure and suction sides of an airfoil. This work proposes to reconstruct a valid airfoil profile from the inspection data points for each airfoil section to overcome the area bias problem and to maintain consistency in identifying the centroid. With the centroid of each inspected airfoil section identified, the position error and the orientation error can then be evaluated in sequence. A series of case studies has been performed to demonstrate the effectiveness of the proposed methodology and how it is able to prevent wrongful rejection/acceptance of geometrically acceptable/unacceptable blades as well as incorrect modification of the related manufacturing processes.

Abstract: Many signal and image processing applications, including texture analysis, radar detection or EEG signal classification, require the computation of a centroid from a set of covariance matrices. The most popular approach consists in considering the center of mass. While efficient, this estimator is not robust to outliers arising from the inherent variability of the data or from faulty measurements. To overcome this, some authors have proposed to use the median as a more robust estimator. Here, we propose an estimator which takes advantage of both efficiency and robustness by combining the concepts of Riemannian center of mass and median. Based on the theory of M-estimators, this robust centroid estimator is issued from the so-called Huber's function. We present a gradient descent algorithm to estimate it. In addition, an experiment on both simulated and real data is carried out to evaluate the influence of outliers on the estimation and classification performances.

Abstract: The invention provides a light stripe center rapid extraction method based on a gray centroid method, belongs to the field of computer vision measurement, and relates to feature information effective acquisition in vision measurement when left and right video camera view fields and photographing angles are inconsistent. According to the method, laser light stripes of a surface to be measured are photographed by a binocular video camera, center point crude extraction is performed in each line of pixels of the light stripes by utilizing the conventional gray centroid method, and a boundary recognition threshold is set so as to determine the effective measurement area of the light stripes. Then light stripe direction pixel coordinates are linearly split by utilizing determination of the number of left and right image information so that the sub-pixel coordinates of light stripe centers in the direction can be obtained. Light stripe center accurate extraction is performed by utilizing boundary point information and the split result so that effective light stripe center point coordinates are obtained. According to the method, equivalent, rapid and high-precision extraction of the light stripe center points of the object surface to be measured is realized so that various problems existing in subsequent matching can be effectively reduced on the basis of meeting the real-time requirement of measurement, and thus binocular vision measurement subsequent reconstruction precision can be enhanced.

Abstract: Centroid index is the only measure that evaluates cluster level differences between two clustering results. It outputs an integer value of how many clusters are differently allocated. In this paper, we apply this index to other clustering models that do not use centroid as prototype. We apply it to centroid model, Gaussian mixture model, and arbitrary-shape clusters.