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

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

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

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

Robust fuzzyclustering for object recognition and classification of relational data

Prototype based fuzzy clustering algorithms have unique ability to partition the data while detecting multiple clusters simultaneously. However since real data is often contaminated with noise, the clustering methods need to be made robust to be useful in practice. This dissertation focuses on robust detection of multiple clusters from noisy range images for object recognition. Dave\u27s noise clustering (NC) method has been shown to make prototype-based fuzzy clustering techniques robust. In this work, NC is generalized and the new NC membership is shown to be a product of fuzzy c-means (FCM) membership and robust M-estimator weight (or possibilistic membership). Thus the generalized NC approach is shown to have the partitioning ability of FCM and robustness of M-estimators. Since the NC (or FCM) algorithms are based on fixed-point iteration technique, they suffer from the problem of initializations. To overcome this problem, the sampling based robust LMS algorithm is considered by extending it to fuzzy c-LMS algorithm for detecting multiple clusters. The concept of repeated evidence has been incorporated to increase the speed of the new approach. The main problem with the LMS approach is the need for ordering the distance data. To eliminate this problem, a novel sampling based robust algorithm is proposed following the NC principle, called the NLS method, that directly searches for clusters in the maximum density region of the range data without requiring the specification of number of clusters. The NC concept is also introduced to several fuzzy methods for robust classification of relational data for pattern recognition. This is also extended to non-Euclidean relational data. The resulting algorithms are used for object recognition from range images as well as for identification of bottleneck parts while creating desegregated cells of machine/ components in cellular manufacturing and group technology (GT) applications

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

Human perception-oriented segmentation for triangle meshes

A segmentação de malhas é um tópico importante de investigação em computação gráfica, em particular em modelação geométrica. Isto deve-se ao facto de as técnicas de segmentaçãodemalhasteremváriasaplicações,nomeadamentenaproduçãodefilmes, animaçãoporcomputador, realidadevirtual, compressãodemalhas, assimcomoemjogosdigitais. Emconcreto, asmalhastriangularessãoamplamenteusadasemaplicações interativas, visto que sua segmentação em partes significativas (também designada por segmentação significativa, segmentação perceptiva ou segmentação perceptualmente significativa ) é muitas vezes vista como uma forma de acelerar a interação com o utilizador ou a deteção de colisões entre esses objetos 3D definidos por uma malha, bem como animar uma ou mais partes significativas (por exemplo, a cabeça de uma personagem) de um dado objeto, independentemente das restantes partes. Acontece que não se conhece nenhuma técnica capaz de segmentar correctamente malhas arbitrárias −ainda que restritas aos domínios de formas livres e não-livres− em partes significativas. Algumas técnicas são mais adequadas para objetos de forma não-livre (por exemplo, peças mecânicas definidas geometricamente por quádricas), enquanto outras são mais talhadas para o domínio dos objectos de forma livre. Só na literatura recente surgem umas poucas técnicas que se aplicam a todo o universo de objetos de forma livre e não-livre. Pior ainda é o facto de que a maioria das técnicas de segmentação não serem totalmente automáticas, no sentido de que quase todas elas exigem algum tipo de pré-requisitos e assistência do utilizador. Resumindo, estes três desafios relacionados com a proximidade perceptual, generalidade e automação estão no cerne do trabalho descrito nesta tese. Para enfrentar estes desafios, esta tese introduz o primeiro algoritmo de segmentação baseada nos contornos ou fronteiras dos segmentos, cuja técnica se inspira nas técnicas de segmentação baseada em arestas, tão comuns em análise e processamento de imagem,porcontraposiçãoàstécnicasesegmentaçãobaseadaemregiões. Aideiaprincipal é a de encontrar em primeiro lugar a fronteira de cada região para, em seguida, identificar e agrupar todos os seus triângulos internos. As regiões da malha encontradas correspondem a saliências e reentrâncias, que não precisam de ser estritamente convexas, nem estritamente côncavas, respectivamente. Estas regiões, designadas regiões relaxadamenteconvexas(ousaliências)eregiõesrelaxadamentecôncavas(oureentrâncias), produzem segmentações que são menos sensíveis ao ruído e, ao mesmo tempo, são mais intuitivas do ponto de vista da perceção humana; por isso, é designada por segmentação orientada à perceção humana (ou, human perception- oriented (HPO), do inglês). Além disso, e ao contrário do atual estado-da-arte da segmentação de malhas, a existência destas regiões relaxadas torna o algoritmo capaz de segmentar de maneira bastante plausível tanto objectos de forma não-livre como objectos de forma livre. Nesta tese, enfrentou-se também um quarto desafio, que está relacionado com a fusão de segmentação e multi-resolução de malhas. Em boa verdade, já existe na literatura uma variedade grande de técnicas de segmentação, bem como um número significativo de técnicas de multi-resolução, para malhas triangulares. No entanto, não é assim tão comum encontrar estruturas de dados e algoritmos que façam a fusão ou a simbiose destes dois conceitos, multi-resolução e segmentação, num único esquema multi-resolução que sirva os propósitos das aplicações que lidam com malhas simples e segmentadas, sendo que neste contexto se entende que uma malha simples é uma malha com um único segmento. Sendo assim, nesta tese descreve-se um novo esquema (entenda-seestruturasdedadosealgoritmos)demulti-resoluçãoesegmentação,designado por extended Ghost Cell (xGC). Este esquema preserva a forma das malhas, tanto em termos globais como locais, ou seja, os segmentos da malha e as suas fronteiras, bem como os seus vincos e ápices são preservados, não importa o nível de resolução que usamos durante a/o simplificação/refinamento da malha. Além disso, ao contrário de outros esquemas de segmentação, tornou-se possível ter segmentos adjacentes com dois ou mais níveis de resolução de diferença. Isto é particularmente útil em animação por computador, compressão e transmissão de malhas, operações de modelação geométrica, visualização científica e computação gráfica. Em suma, esta tese apresenta um esquema genérico, automático, e orientado à percepção humana, que torna possível a simbiose dos conceitos de segmentação e multiresolução de malhas trianguladas que sejam representativas de objectos 3D.The mesh segmentation is an important topic in computer graphics, in particular in geometric computing. This is so because mesh segmentation techniques find many applications in movies, computer animation, virtual reality, mesh compression, and games. Infact, trianglemeshesarewidelyusedininteractiveapplications, sothattheir segmentation in meaningful parts (i.e., human-perceptually segmentation, perceptive segmentationormeaningfulsegmentation)isoftenseenasawayofspeedinguptheuser interaction, detecting collisions between these mesh-covered objects in a 3D scene, as well as animating one or more meaningful parts (e.g., the head of a humanoid) independently of the other parts of a given object. It happens that there is no known technique capable of correctly segmenting any mesh into meaningful parts. Some techniques are more adequate for non-freeform objects (e.g., quadricmechanicalparts), whileothersperformbetterinthedomainoffreeform objects. Only recently, some techniques have been developed for the entire universe of objects and shapes. Even worse it is the fact that most segmentation techniques are not entirely automated in the sense that almost all techniques require some sort of pre-requisites and user assistance. Summing up, these three challenges related to perceptual proximity, generality and automation are at the core of the work described in this thesis. In order to face these challenges, we have developed the first contour-based mesh segmentation algorithm that we may find in the literature, which is inspired in the edgebased segmentation techniques used in image analysis, as opposite to region-based segmentation techniques. Its leading idea is to firstly find the contour of each region, and then to identify and collect all of its inner triangles. The encountered mesh regions correspond to ups and downs, which do not need to be strictly convex nor strictly concave, respectively. These regions, called relaxedly convex regions (or saliences) and relaxedly concave regions (or recesses), produce segmentations that are less-sensitive to noise and, at the same time, are more intuitive from the human point of view; hence it is called human perception- oriented (HPO) segmentation. Besides, and unlike the current state-of-the-art in mesh segmentation, the existence of these relaxed regions makes the algorithm suited to both non-freeform and freeform objects. In this thesis, we have also tackled a fourth challenge, which is related with the fusion of mesh segmentation and multi-resolution. Truly speaking, a plethora of segmentation techniques, as well as a number of multiresolution techniques, for triangle meshes already exist in the literature. However, it is not so common to find algorithms and data structures that fuse these two concepts, multiresolution and segmentation, into a symbiotic multi-resolution scheme for both plain and segmented meshes, in which a plainmeshisunderstoodasameshwithasinglesegment. So, weintroducesuchanovel multiresolution segmentation scheme, called extended Ghost Cell (xGC) scheme. This scheme preserves the shape of the meshes in both global and local terms, i.e., mesh segments and their boundaries, as well as creases and apices are preserved, no matter the level of resolution we use for simplification/refinement of the mesh. Moreover, unlike other segmentation schemes, it was made possible to have adjacent segments with two or more resolution levels of difference. This is particularly useful in computer animation, mesh compression and transmission, geometric computing, scientific visualization, and computer graphics. In short, this thesis presents a fully automatic, general, and human perception-oriented scheme that symbiotically integrates the concepts of mesh segmentation and multiresolution

A framework for hull form reverse engineering and geometry integration into numerical simulations

The thesis presents a ship hull form specific reverse engineering and CAD integration framework. The reverse engineering part proposes three alternative suitable reconstruction approaches namely curves network, direct surface fitting, and triangulated surface reconstruction. The CAD integration part includes surface healing, region identification, and domain preparation strategies which used to adapt the CAD model to downstream application requirements. In general, the developed framework bridges a point cloud and a CAD model obtained from IGES and STL file into downstream applications