Possibilistic clustering for shape recognition

Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required at each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from Bezdek's Fuzzy C-Means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Unfortunately, the memberships resulting from FCM and its derivatives do not correspond to the intuitive concept of degree of belonging, and moreover, the algorithms have considerable trouble in noisy environments. Recently, we cast the clustering problem into the framework of possibility theory. Our approach was radically different from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. We constructed an appropriate objective function whose minimum will characterize a good possibilistic partition of the data, and we derived the membership and prototype update equations from necessary conditions for minimization of our criterion function. In this paper, we show the ability of this approach to detect linear and quartic curves in the presence of considerable noise

A fuzzy clustering algorithm to detect planar and quadric shapes

In this paper, we introduce a new fuzzy clustering algorithm to detect an unknown number of planar and quadric shapes in noisy data. The proposed algorithm is computationally and implementationally simple, and it overcomes many of the drawbacks of the existing algorithms that have been proposed for similar tasks. Since the clustering is performed in the original image space, and since no features need to be computed, this approach is particularly suited for sparse data. The algorithm may also be used in pattern recognition applications

Robust approach to object recognition through fuzzy clustering and hough transform based methods

Object detection from two dimensional intensity images as well as three dimensional range images is considered. The emphasis is on the robust detection of shapes such as cylinders, spheres, cones, and planar surfaces, typically found in mechanical and manufacturing engineering applications. Based on the analyses of different HT methods, a novel method, called the Fast Randomized Hough Transform (FRHT) is proposed. The key idea of FRHT is to divide the original image into multiple regions and apply random sampling method to map data points in the image space into the parameter space or feature space, then obtain the parameters of true clusters. This results in the following characteristics, which are highly desirable in any method: high computation speed, low memory requirement, high result resolution and infinite parameter space. This project also considers use of fuzzy clustering techniques, such as Fuzzy C Quadric Shells (FCQS) clustering algorithm but combines the concept of noise prototype to form the Noise FCQS clustering algorithm that is robust against noise. Then a novel integrated clustering algorithm combining the advantages of FRHT and NFCQS methods is proposed. It is shown to be a robust clustering algorithm having the distinct advantages such as: the number of clusters need not be known in advance, the results are initialization independent, the detection accuracy is greatly improved, and the computation speed is very fast. Recent concepts from robust statistics, such as least trimmed squares estimation (LTS), minimum volume ellipsoid estimator (MVE) and the generalized MVE are also utilized to form a new robust algorithm called the generalized LTS for Quadric Surfaces (GLTS-QS) algorithm is developed. The experimental results indicate that the clustering method combining the FRHT and the GLTS-QS can improve clustering performance. Moreover, a new cluster validity method for circular clusters is proposed by considering the distribution of the points on the circular edge. Different methods for the computation of distance of a point from a cluster boundary, a common issue in all the range image clustering algorithms, are also discussed. The performance of all these algorithms is tested using various real and synthetic range and intensity images. The application of the robust clustering methods to the experimental granular flow research is also included

Direct Least-Squares Ellipse Fitting

Many biological and astronomical forms can be best represented by ellipses. While some more complex curves might represent the shape more accurately, ellipses have the advantage that they are easily parameterised and define the location, orientation and dimensions of the data more clearly. In this paper, we present a method of direct least-squares ellipse fitting by solving a generalised eigensystem. This is more efficient and more accurate than many alternative approaches to the ellipse-fitting problem such as fuzzy c-shells clustering and Hough transforms. This method was developed for human body modelling as part of a larger project to design a marker-free gait analysis system which is being undertaken at the National Rehabilitation Hospital, Dublin

Evaluation of collision properties of spheres using high-speed video analysis

Experimental evaluation of the collision properties of spheres is performed using video image analysis techniques. A high-speed Kodak EktaPro1000 video camera is utilized to record a collision sequence between two spheres at 1000 frames/sec, and then the images are analyzed to calculate three dimensional translation and rotation before and after the collision. These quantities are used to compute the collision properties for a pair of one inch nylon spheres, i.e. the coefficient of friction, and the coefficients of normal and tangential restitution. The focus of the thesis is on image analysis techniques that provide high accuracy results even though the image resolution is very low, i.e. 240x192 pixels. The procedure developed here can be extended to smaller size spheres and can also be applicable to other motion analysis expenments involving low resolution images

Fuzzy Set Methods for Object Recognition in Space Applications

Progress on the following four tasks is described: (1) fuzzy set based decision methodologies; (2) membership calculation; (3) clustering methods (including derivation of pose estimation parameters), and (4) acquisition of images and testing of algorithms

A New Measure of Cluster Validity Using Line Symmetry

[[abstract]]Many real-world and man-made objects are symmetry, therefore, it is reasonable to assume that some kind of symmetry may exist in data clusters. In this paper a new cluster validity measure which adopts a non-metric distance measure based on the idea of "line symmetry" is presented. The proposed validity measure can be applied in finding the number of clusters of different geometrical structures. Several data sets are used to illustrate the performance of the proposed measure.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]TW

Multiple ellipse fitting by center-based clustering

This paper deals with the multiple ellipse fitting problem based on a given set of data points in a plane. The presumption is that all data points are derived from k ellipses that should be fitted. The problem is solved by means of center-based clustering, where cluster centers are ellipses. If the Mahalanobis distance-like function is introduced in each cluster, then the cluster center is represented by the corresponding Mahalanobis circle-center. The distance from a point a∈R^2 to the Mahalanobis circle is based on the algebraic criterion. The well-known k-means algorithm has been adapted to search for a locally optimal partition of the Mahalanobis circle-centers. Several numerical examples are used to illustrate the proposed algorithm

Spatio-temporal dimension of lightning flashes based on three-dimensional Lightning Mapping Array

3D mapping system like the LMA - Lightning Mapping Array - are a leap forward in lightning observation. LMA measurements has lead to an improvement on the analysis of the fine structure of lightning, allowing to characterize the duration and maximum extension of the cloud fraction of a lightning flash. During several years of operation, the first LMA deployed in Europe has been providing a large amount of data which now allows a statistical approach to compute the full duration and horizontal extension of the in-cloud phase of a lightning flash. The “Ebro Lightning Mapping Array” (ELMA) is used in the present study. Summer and winter lighting were analyzed for seasonal periods (Dec–Feb and Jun–Aug). A simple method based on an ellipse fitting technique (EFT) has been used to characterize the spatio-temporal dimensions from a set of about 29,000 lightning flashes including both summer and winter events. Results show an average lightning flash duration of 440 ms (450 ms in winter) and a horizontal maximum length of 15.0 km (18.4 km in winter). The uncertainties for summer lightning lengths were about ± 1.2 km and ± 0.7 km for the mean and median values respectively. In case of winter lightning, the level of uncertainty reaches up to 1 km and 0.7 km of mean and median value. The results of the successful correlation of CG discharges with the EFT method, represent 6.9% and 35.5% of the total LMA flashes detected in summer and winter respectively. Additionally, the median value of lightning lengths calculated through this correlative method was approximately 17 km for both seasons. On the other hand, the highest median ratios of lightning length to CG discharges in both summer and winter were reported for positive CG discharges.Peer ReviewedPreprin

Proceedings of the Third International Workshop on Neural Networks and Fuzzy Logic, volume 2

Papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by the National Aeronautics and Space Administration and cosponsored by the University of Houston, Clear Lake, held 1-3 Jun. 1992 at the Lyndon B. Johnson Space Center in Houston, Texas are included. During the three days approximately 50 papers were presented. Technical topics addressed included adaptive systems; learning algorithms; network architectures; vision; robotics; neurobiological connections; speech recognition and synthesis; fuzzy set theory and application, control and dynamics processing; space applications; fuzzy logic and neural network computers; approximate reasoning; and multiobject decision making