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Hydrodynamic lubrication is present in the majority of machinery where load is transmitted between two contacting surfaces in relative motion. Cavitation in liquid lubricating films is common and directly affects the pressure distribution and subsequently the load-carrying capacity and friction force transmitted across the contact. By reformulating the Elrod–Adams implementation of the Jakobsson–Floberg–Olsson cavitation conditions, we developed an efficient algorithm, called Fischer-Burmeister-Newton-Schur (FBNS), for calculating the pressure distribution that combines two attractive properties. First, the system of discretized equations arising from the reformulation is continuously differentiable and unconstrained, thus allowing for the use of gradient-based methods to solve it. Second, the computational cost of solving the system is similar to that when cavitation is not considered. With the new algorithm, the transient analysis and optimisation of contacts with complex shapes becomes computationally feasible. A comparison of the FBNS with the established algorithms and an application to the transient analysis of a hydrodynamic contact with surface texturing are reported. The results show that the FBNS yields roughly two orders of magnitude reduction in computational time when compared against other algorithms.

The effect of surface roughness and topographical orientation on friction and wear has been investigated for diamond like carbon (DLC) coated and uncoated steel surfaces with three levels of surface roughness in the range of 0.004–0.11 μm Ra value and with topographical orientations at 0°, 45° and 90° angles from grinding marks. In this first part we report the experimental observations that form the basis for future computational modelling of the tribological effects and mechanisms. The surfaces were characterised by the scanning electron microscopy (SEM) and focused ion beam (FIB) method and mechanical properties were measured. In the topographical characterisation measurements included the fractal signatures, the texture aspect ratio signatures and the texture direction signatures were measured and calculated by the variance orientation transform (VOT) method. The friction and wear were measured and observed in scratch testing, micro tribological testing and linear reciprocating testing in three directions of topographical orientation, as well as in rotational pin-on-disc testing. The topographical orientation had considerable effect on both friction and wear in DLC vs DLC contacts while the effect was minor and sometimes not even observable in steel vs steel contacts. A surface strengthening effect which is higher for smooth DLC surfaces and micro-cracking and micro-delamination on asperity tips at low loads for rougher surfaces is reported. The 45° orientation resulted in higher friction and considerably higher ball wear in linear reciprocating pin-on-plate testing of DLC surfaces compared with the 0° and 90° orientations.

Wear particles can be found in any tribological system. They are the direct consequence of wear processes occurring and their morphology reflects the wear mechanisms involved in their generation. This dependence of wear particle morphology on the wear mechanisms has been exploited and widely used in machine condition monitoring. The problem with the methods currently in use is that they require a trained staff, i.e. these methods are time consuming, costly and not always reliable since they rely on the technicians’ experience. Recent efforts are therefore directed towards the development of an automated particle classification system. This is not a simple task as there are three major problems which need to be overcome first before the system can find practical industrial applications. The first problem is the establishment of the extensive and detailed database of wear particle morphologies generated under different operating conditions and with different materials used for sliding pairs. The second problem is the development of reliable and accurate description of 3D wear particle morphology, while the final problem is the development of a wear particle classification system. As such system must be robust and reliable this involves the development, selection and testing of appropriate classifiers. It is hoped that the system, when fully operational, will eliminate the need for highly trained staff, and provide more accurate and reliable diagnosis of the machinery health status. In this paper, it is shown how these problems are gradually addressed and what possible solutions are chosen. Also, the recent advances in the development of an automated wear particle classification system for the application in machine condition monitoring are presented.

A fast, new classification system for engineering surfaces has been developed and used to detect the incidence of wear. The novel feature of this system is that the classification can be performed without the need for any surface parameters. In addition, only normal working conditions data (the target class) are required to train a classifier. In this system, first, a surface to be classified is represented by a set of dissimilarity measures (e.g. differences in surface height) calculated between the unclassified surface and already pre-classified surfaces belonging to the target class. The representation set of measures is then used to assign a surface into the target class or reject as an outlier. Outliers are anomalies or faulty conditions that can be ill-defined, undersampled data or even unknown data. However, several problems still remain to be solved before the approach can be used as a fully functioning pattern recognition system for the applications in machine condition monitoring. This includes difficulties associated with selecting a right size of the representation set and building an accurate one-class classifier. These problems have been addressed in this study and analysis results for unworn and worn surfaces have been also presented. It was found that (i) skewness, correlation, principle component analysis dimensionality and boundary descriptor are well suited for selecting the representation set and (ii) a combiner of the Parzen and support vector data description (SVDD) classifiers with the median rule gives better classification results than single classifiers (i.e. Gaussian density, mixture of Gaussian densities, Parzen density and SVDD classifiers).

In this study the automated classification system, developed previously by the authors, was used to classify wear particles. Two kinds of wear particles, adhesive and abrasive, were classified. The wear particles were generated using a pin-on-disk tribometer. Various operating conditions of load, sliding time and abrasive grit size were applied to simulate adhesive and abrasive wear of different severity. SEM images of wear particles were acquired, forming a database for further analysis. The particle images were divided into eight groups or classes, each class representing different wear test conditions. All eight particle classes were first examined visually. Next, area, perimeter and elongation parameters were determined for each class and the parameters were statistically analysed. The automated classification system, based on particle surface texture, was then applied to all particle classes. The results of the automated particle classification were compared to those based on either the visual assessment of particle morphology or numerical parameter values. It was shown that the texture-based classification system was a more efficient and accurate way of distinguishing between various wear particles than classification based on size and shape of wear particles. It seems that the texture-based classification method developed has great potential to become a very useful tool in the machine condition monitoring industry.

The diagnosis of worn and damaged surfaces is an important issue in machine failure analysis and condition monitoring. Of many approaches used, image classification based on feature parameters has often proven to be particularly useful. However, large image databases can be computationally costly to analyse, and the datasets are susceptible to noise. Hence, it is essential to determine which feature parameters hold the most useful information, in order to improve the classification rate and computation time. This paper presents a performance evaluation of dimension reduction techniques currently used in pattern recognition. A comparison of three methods is conducted, in order to determine which is able to produce the best results over a large range of image datasets. The methods analysed are: Non-Linear Fisher, Principal Component Analysis and kernel Principal Component Analysis. These are then tested against four different classifiers to obtain the best combination. These classifiers are: Linear Discriminant Classifier, Quadratic Discriminant Classifier, k-Nearest Neighbour and Support Vector Machine Classifiers. For further analysis, two combined dimension reduction and classification methods are tested: Minimum Classification Error and reduced feature space Support Vectors. For the comparison, four datasets of images with different scales and rotations are used, i.e. Brodatz textures, artificially generated isotropic fractal images and Talysurf images of sandblasted and abraded steel surfaces. The results showed that a combination of the Non-Linear Fisher dimension reduction technique and a Linear Support Vector Machine Classifier gave the best performance overall and are the most promising for the application in automated machine condition monitoring and expert free failure analysis. Further improvement can be achieved by performing a step-wise dimension reduction by first reducing the features using the Principal Component Analysis method, then further reduction with the Non-Linear Fisher technique.

Classification of wear particles is performed in two steps, i.e. first a particle to be classified is characterized by surface feature parameters such as roughness, directionality, homogeneity, periodicity, etc. and then, the particle is assigned to a specific class using these parameters. However, a significant limitation of this approach is that surface parameters are often not unique to a specific surface topography and their values may change significantly with scale, orientation angle and position at which the particle data was acquired. Various attempts were made to overcome this limitation by selecting a core set of parameters which ensures that wear particles are accurately classified. However, the parameter selection is usually cumbersome and requires lengthy computation. Furthermore, there is no guarantee that parameters selected are sensitive enough to separate particles belonging to different classes. Thus, a new classification technique based entirely on dissimilarity measures (e.g. Euclidean, Baddeley's distances), calculated between surface images of an unclassified particle and classified particles, was developed. The classification process is based on assigning a particle to a class of particles with the smallest dissimilarity measure. This idea arises naturally from the two facts: (i) compactness, similar objects are in close proximity to each other in their representation space, while different objects are far apart, and (ii) true representation, if objects are close to each other in their representation space they belong to the same class. In this paper, an overview of recent advances and developments in the area of particle classification based on dissimilarity measures is presented with a particular emphasis on constructing a simple and accurate classifier.

The diagnosis of worn and damaged surfaces is an important issue in machine failure analysis and condition monitoring. Of many approaches used, image classification based on feature parameters has often proven to be particularly useful. Accurate classification can, however, be limited by the fact that feature parameters vary with scale and orientation. Hence, it is essential to determine which feature parameters are both scale and rotation invariant. This paper presents a performance evaluation of feature extraction methods currently used in pattern recognition. A comparison of six methods is conducted, in order to find the method that provides the most consistent results over a large range of image sizes and rotations. The methods analysed are: co-occurrence matrix, discrete wavelet transform, combination of wavelet and co-occurrence features, Gabor filter, circular Gaussian Markov random field and local binary patterns. For the comparison, four datasets of images with different scales and rotations are used, i.e. Brodatz textures, artificially generated isotropic fractal images and Talysurf images of sandblasted and abraded steel surfaces. The performance of each method is evaluated on the datasets using k-nearest neighbours and linear based normal densities classifiers. The results showed that the combined feature extraction method produced the most robust and accurate results for each of the datasets, and appears to be suitable for the classification of tribological surfaces.

Quantitative measures are obtained from images of tribological surfaces. Based on these data, decisions are made regarding manufacturing and maintenance processes, machine-condition monitoring and failure analysis of engineering components. These decisions are often guided by an automated pattern recognition system. Components of this system are: surface topography data acquisition, surface characterization, surface classification and performance evaluation. The characterization and classification of tribological surfaces are major challenges that make the development of a reliable pattern-recognition system difficult. The reasons are that: (i) tribological surfaces often exhibit a non-stationary and multiscale nature, while most surface characterization methods currently used work well with surface data exhibiting a stationary random process, (ii) changes in topography that might occur between the interacting surfaces usually need to be known in advance, and (iii) the selection of surface parameters that separate different classes of surfaces is usually time-consuming and cumbersome. Because of these difficulties, characterization and classification methods which do not use surface parameters have been developed. In the classification methods, a measure of dissimilarity (e.g., Euclidean distance) calculated between a surface to be classified and already classified surfaces was used, instead of surface parameters. The unclassified surface was assigned to the class (of classified surfaces) with the lowest value of dissimilarity measure. The suitability of different classifiers; such as k-nearest neighbour classifier, linear-discriminant-analysis based classifiers and different dissimilarity measures; for the classification of tribological surface topographies (without the need for surface parameters) is investigated in this paper. Recent developments in this area, i.e., a fractal measure and a hybrid fractal-wavelet measure, are also discussed. The most suitable method for the classification of tribological surfaces has been selected.

The reliable and accurate 3-D characterization and classification of tribological surfaces is still a challenging problem. Many tribological surfaces exhibit topographical features over a wide range of scales; ranging from nano-scales (atomic or molecular scales) to micro-scales (up to hundred micrometer scales). There are several surface topography characterization methods that exist today. However, due to the non-stationary and multi-scale nature of tribological surfaces even for the moderately complicated topography of a tribological surface, these methods provide a limited description. Recently a new method, based on fractal modelling, has been developed and applied to the characterization of tribological surfaces. The method involves construction of a mathematical model, called a partition iterated function system (PIFS), for surface data. This model encapsulates complete information about the surface 3-D data. Iterative application of this model into any initial image results in a sequence of images converging to the original surface image. Based on this method a pattern recognition system has been developed and applied to the classification of tribological surfaces. Recently, the work has been conducted on the improvement of the PIFS method. An attempt was made to apply both fractals and wavelets to analyze surface topography data. It was thought that since the fractal method allows the characterization of surface topography over the widest achievable range of scales and the wavelet method provides the characterization of surface topography at individual scales a combination of these two methods could provide the most accurate results. The hybrid fractal-wavelet method has recently been developed and applied to the characterization of tribological surfaces. In this paper it is demonstrated that it is possible to both characterize and classify tribological surfaces without the need for any surface parameters, with unique precision and accuracy. Also a short overview of recent advances and developments in the characterization and classification of tribological surfaces is presented.

Classification of the topography of freshly machined, worn and damaged surfaces (e.g. damaged by adhesion, scoring, abrasion, pitting) is still a problem in machine failure analysis. Tribological surfaces often exhibit both a multiscale nature (i.e. different length scales of surface features) and a non-stationary nature (i.e. features which are superimposed on each other and located at different positions on a surface). The most widely used approaches to surface classification are based on the Fourier transform or statistical functions and parameters. Often these approaches are inadequate and provide incorrect classification of the tribological surfaces. The main reason is that these techniques fail to simultaneously capture the multiscale nature and the non-stationary nature of the surface data. A new method, called a hybrid fractal-wavelet method, has recently been developed for the characterization of tribological surfaces in a multiscale and non-stationary manner. In contrast to other methods, this method combines both the wavelets’ inherent ability to characterize surfaces at each individual scale and the fractals’ inherent ability to characterize surfaces in a scale-invariant manner. The application of this method to the classification of artificially generated fractal and tribological surfaces (e.g. worn surfaces) is presented in this paper. The newly developed method has been further modified to better suit tribological surface data, including a new measure of differences between initial and decoded images. The accuracy of this method in the classification of surfaces was assessed.

Many numerical surface topography analysis methods exist today. However, even for the moderately complicated topography of a tribological surface these methods can provide only limited information. The reason is that tribological surfaces often exhibit a non-stationary and multi-scale nature while the numerical methods currently used work well with surface data exhibiting a stationary random process and provide surface descriptors closely related to a scale at which surface data were acquired. The suitability of different methods, including Fourier transform, windowed Fourier transform, Cohen's class distributions (especially the Wigner-Ville distribution), wavelet transform, fractal methods and a hybrid fractal-wavelet method, for the analysis of tribological surface topographies is investigated in this paper. The method best suited to this purpose has been selected.

Many types of tribological surfaces have been observed to exhibit a multiscale nature, i.e. topographical features over different scales ranging from nanometers to hundreds of micrometers. Consequently, recent developments in the characterization of tribological surfaces have concentrated on wavelet transformation and fractal-based methods. The wavelet methods are used due to their ability to decompose surface data into different scale components and to characterize surface data at each individual scale. On the other hand, fractal methods are used due to their ability to characterize surface data in a scale-invariant manner. It has been shown that these two capabilities of (i) decomposition of surface data and (ii) scale-invariant analysis are essential in the characterization of 3-D surface topography. Thus, it is apparent that a characterization method which exhibits both of these capabilities would yield the best results. Developing such a method is not an easy task. This problem in the characterization of tribological surfaces is addressed in our paper. A new method, called a hybrid fractal-wavelet method, is proposed. This method is a combination of a partition iterated function system (PIFS) and a symmetric wavelet transform (SWT). The PIFS is used to scale-invariantly characterize the surface topography over a wide range of different scales, while the SWT is used to characterize the surface topography at each individual scale. This multiscale characterization ability of the newly developed method is demonstrated on a tribological surface example.

Wear particles and surfaces are three-dimensional (3-D) objects and their numerical characterization and classification is still largely an unresolved problem. Usually a set of various parameters is employed to describe the surface topography. These parameters are of limited use, especially when dealing with anisotropic surfaces. To solve this problem a modified Hurst orientation transform (HOT) method has been developed and applied to characterize the surface anisotropy. However, despite the apparent success this method does not yet provide a full description of the surface topography. It is known that complex structures observed in nature can be described and modeled by a combination of simple mathematical rules. It is therefore reasonable to assume that, in principle, it should also be possible to describe any surface by a set of such rules. The problem is in finding those rules. For this purpose, a modified partitioned iterated function system (PIFS) was developed and applied to encode the 3-D surface topography information, i.e. to obtain full description of surface topography of wear particles and surfaces. Importantly, PIFS information gained from individual wear particles or surfaces allows to classify them in groups which are characteristic to a particular failure type. This, in turn, allows to ascribe an ‘unclassified’ particle or surface to a particular group/category which is characteristic to a specific failure type or wear mechanism. This forms the basis of a system, which when fully developed, would allow an automated recognition of particles and surface morphologies without the need for experts. The system then can be developed further to include diagnosis of the type of failure. In this paper an overview of recent advances and developments in the characterization, classification and recognition of wear particles and surfaces is presented.

A new scale-invariant pattern recognition method has been developed for the characterization of wear particle surface morphology. The method is based on a partition-iterated function system (PIFS) constructed for a wear particle image. A database containing PIFSs constructed for different classes of wear particles was built. Each class is a set of wear particles exhibiting a similar morphology. The objective of pattern recognition is to assign a new wear particle, which is not yet classified, into one of these particle classes. For the classification, PIFSs taken from the database are decoded with the unclassified particle image used as an initial image. Decoded images obtained from PIFSs are then individually compared with the new particle image. If the difference calculated between these images is less than a threshold value, the new particle is assigned to a class. Problems associated with the use of the pattern recognition method, such as rotational- and translation-invariance, comparison between two images and computer implementation, are addressed in this paper. The effects of image resolution, tilt angle, noise, gain variations and defocusing were also investigated. Results obtained for computer-generated images of fractal surfaces and microscopic images of wear particles are demonstrated.

The importance of wear particle characterization is continuously growing, as the need for prediction and monitoring of wear increases. Accurate analysis of wear particles can, however, be limited by problems associated with particle characterization, especially of the wear particles' surface morphology. Since the shape and surface topography of wear particles often exhibit a fractal nature, fractal (scale-invariant) methods are, therefore, used in their characterization. However, the methods used to date ignore the fact that all fractal objects can be described by a small set of mathematical rules; although finding those rules which describe a particular fractal image is a difficult problem. No general solution exists to date and this paper attempts to redress this problem. A new analysis method, ‘scale-invariant analysis’, which is based on a partitioned iterated function system (PIFS), is proposed for the characterization of wear particle morphology. PIFS is a collection of contractive affine transformations. Each affine transformation transforms one part of a wear particle image onto another part of the same image. PIFSs were constructed for both computer generated and SEM images of wear particles. Results obtained in this study clearly demonstrate that the morphology of wear particles can effectively be characterized using the PIFS method.

Fractal-based methods have been used in surface characterization with increasing success over the past years. These methods have been employed to characterize isotropic surfaces but, as yet, little quantitative consideration has been given to the characterization of anisotropic surfaces. In this work, the Hurst orientation transform (HOT) is used to characterize the surface anisotropy and directionality. The calculation of the HOT involves searching all pairs of pixels in a circular region to build a table of maximum differences. From this table, the Hurst coefficients are calculated in many directions and plotted as a function of orientation to reveal surface anisotropy. In this work, two new surface texture parameters, i.e. texture aspect ratio and texture direction, obtained from rose plots of the Hurst coefficients were used in the characterization of surface anisotropy and directionality. Applications of the HOT method to stereo and interferometric images of wear particles and X-ray images of healthy and osteoarthritic joints are also demonstrated.

Significant advances have recently been made in the numerical characterization of particle boundaries. However, progress in the numerical characterization of particle surfaces is slow. There are two fundamental issues associated with this problem; i.e., the acquisition of reliable three-dimensional (3-D) surface data and numerical description of the 3-D surface features. In this paper, the first issue is addressed while the second issue will be addressed in our next papers. Pairs of field emission scanning electron microscope (FESEM) stereo images of wear particles found in synovial joints have been acquired. A specially developed stereoscopy method was applied to the acquired FESEM images in order to obtain 3-D surface topography data of wear particles. The surface topography data obtained from the wear particles was then processed to produce: the range image, the contour map and the shaded image of a particle surface. The surface topography of wear particles was also shown in the colour stereo images. The results obtained in this study have clearly demonstrated that 3-D surface topography data of wear particles is very helpful in particle visualization and it can be used in numerical description of the surface.

Wear particles are three-dimensional objects. Recent advances, accelerated by the application of computer technology, allow numerical characterization of particle shape in two dimensions. However, three-dimensional (3D) characterization of wear particle surface topography is still largely an unresolved problem. There are two issues associated with this problem, i.e., the acquisition of accurate wear particle surface topography data and the numerical description of 3D surface features. The usually small size of wear particles restricts the techniques that could be used to acquire accurate data from the particle surface. Surface profilometers, e.g., Talysurf, the instruments traditionally used in surface topography imaging, cannot be used because of the small size of particles. The limitation of an atomic force microscope is its relatively small vertical range, while the horizontal resolution of laser confocal or interferometric microscopes is too low to obtain accurate particle surface topography data. The application of a combination of SEM and stereoscopy techniques seems to alleviate this problem. 3D surface topography data obtained using this technique can be processed and presented in many different ways. The usefulness of various methods of surface data representation in visualization and numerical characterization of wear particle surfaces is discussed. One of the major difficulties associated with the characterization of surface topographies is the accurate description of surface spatial properties, i.e., their anisotropy and directionality. Recently, a specially modified Hurst Orientation Transform (HOT), to suit wear particle surface data, has been developed and applied to characterize the surface topography of particles. The Hurst coefficients are related to fractal dimensions and are a measure of surface roughness, i.e., a rougher surface is represented by lower Hurst coefficients. It was found that the modified HOT can be applied to reveal the surface anisotropy of wear particles. Although none of the other methods developed so far allow such a thorough characterization of wear particle surfaces as does the modified HOT, this method still does not provide a full description of the surface topography. Therefore, it appears that a totally different approach is needed in order to make a fundamental breakthrough in the characterization of wear particle surfaces. Since many of the complex structures observed in nature can be described and modelled by a combination of simple mathematical rules, it may be possible to describe the surface of a particle by a set of such rules. In our first attempt, a Partitioned Iterated Function System (PIFS) was applied to encode the wear particle surface topography information. This information can then be used to calculate the relevant surface descriptors. In this paper, an overview of recent advances and developments in the numerical characterization of wear particle surfaces is presented.

SUMMARY Objective. To analyse and compare the shape of wear particles found in healthy and osteoarthritic human knee joints for monitoring the progress of osteoarthritis, the long-term prognosis and to evaluate therapeutic regimens. Method. Joint particles from seven patients with normal cartilage in all compartments of the knee joint, 12 patients with fibrillation of less than half the cartilage thickness (grade 1), seven patients with fibrillation of more than half the cartilage thickness (grade 2) and four patients with erosions down to bone (grade 3) were analysed. A total of 565 particles were extracted from synovial fluid samples by ferrography and analysed in a scanning electron microscope. A number of numerical descriptors, i.e. boundary fractal dimension, shape factor, convexity and elongation, were calculated for each particle image and correlated to the degree of osteoarthritis using non-parametric tests. Results. Experiments demonstrated that there were significant diVerences between the numerical descriptors calculated for wear particles from healthy and osteoarthritic knee joints (P< 0.01), suggesting that the particle shape can be used as an indicator of the joint condition. In particular, the fractal dimension of the particle boundary was shown to correlate directly with the degree of osteoarthritis. Conclusion. Numerical analysis of the shape of wear particles found in human knee joints may provide a reliable means for the assessment of cartilage repair after surgical or conservative treatment of osteoarthritis. Several studies revealed that radiological features do of ferrography to the analysis of wear particles present in synovial fluid. This early analysis of particles, hownot permit a confident prediction of the status of articular cartilage. Plain radiographs, in general, signi- ever, was based on a subjective visual classification. Recently, fractal methods have been applied to characficantly underestimate the extent of cartilage damage [1‐3]. The osteoarthritic deterioration of the joint terize the complexity of wear particles generated in synovial joints [9‐11]. In the present study, the hypocartilage begins long before a radiological diagnosis can be made. Our inability to diagnose the disease thesis that numerical descriptions of wear particles can be used to detect early osteoarthritic changes and to

Of the many approaches used to characterize the complex nature of wear particle boundaries, the boundary fractal dimension has often been shown to be particularly useful. Accurate calculation of the fractal dimension can, however, be limited by a problem of variation in step length, the difficulties associated with line fitting into the Richardson plot and the fact that the dimension is sensitive to image noise and focusing. In this paper, the performance of three boundary fractal methods; i.e., the exact ‘hand and dividers’, the fractal analysis by estimation-normalized approach, and the fast Hamblin-Stachowiak method; was evaluated on artificial shapes and wear particle images. The most accurate method for calculating the fractal dimension from a particle boundary was selected. The sensitivity of these methods to image noise and focusing was also examined.

A modified Hurst orientation transform (HOT) method for characterization of wear particle surfaces is proposed and described in this paper. The method involves the calculation of self-affine Hurst coefficients in all directions and displays the calculated coefficient values in a form of rose plot. The calculation of individual Hurst coefficients, H, is based on the rescale range (r/s) analysis (r(d)/s∼ d H ). The rose plot is then used to obtain three texture surface parameters, i.e.: texture aspect ratio, texture minor axis and texture direction. The effectiveness of this modified HOT and resulting surface texture parameters was evaluated. The method was first applied to computer-generated images of isotropic and anisotropic particle fractal surfaces and then to field emission scanning electron microscope images of wear particles found in synovial joints. The ability of the surface parameters to reveal surface isotropy or anisotropy, measure roughness and determine the dominant direction of surface texture was assessed. The effects of measurement conditions such as noise, gain variations and focusing on the surface parameters were also investigated. The results demonstrate that the HOT and surface texture parameters developed can successfully be used in the characterization of wear particle surface topography.

Wear processes occur in synovial joints and as a result wear particles are produced. Preliminary work has shown that the shape of these particles might be related to joint diseases. Samples of knee joint synovial fluid were collected from thirty patients and analysed for wear particles. The condition of the patients' joints selected for the study ranged from healthy to severely osteoarthritic. Populations of particles were extracted from synovial fluid samples by ferrography and analysed in a scanning electron microscope (SEM). The SEM particle images were then processed by a computer and analysed numerically. Numerical particle shape descriptors, such as the boundary fractal dimension, shape factor, convexity and elongation were calculated. A non-parametric Mann-Whitney-Wilcoxon rank test and multiple comparison test performed on the knee joint particle populations demonstrated that there are clear differences in the particle slope between these populations, i.e. that there is a direct relationship between wear particle shape and joint condition. The results obtained indicate that the particle shape can be used as an indicator of the synovial joint condition, i.e. in the diagnosis and prognosis of joint diseases.

A method of characterizing the surface topography of wear particles by the application of computer image analysis to scanning electron microscope (SEM) stereoscopic pairs of images is proposed and described in this paper. The image analysis consists of noise reduction, edge detection, thresholding, stereoscopic matching, calculation of elevation points and interpolation. An improved automatic stereoscopic matching algorithm has been developed. The algorithm was initially applied to computer-generated images of a polished marble sphere and a polished marble cube and later to SEM images of wear particles found in artificial and synovial joints. The results demonstrate that SEM stereoscopy can successfully be used in the characterization and measurements of wear particle surface topography.

Pair of sheep knee joints were used in the experiments. One of the joints was worn in a simulator over different periods of time under carefully simulated physiological forces and kinematic cycles while the other, 'control joint', was kept intact for comparison. Wear particles were extracted from a synovial fluid from both the worn and unworn sheep joints by a ferrography technique and then examined in a scanning electron microscope (SEM). The shape of the particles was characterized by boundary fractal dimension, shape factor and convexity. The shape parameters obtained for particle populations were statistically compared using a Wilcoxon rank test. It has been found that subtle changes in the shape of the particle boundary occur during the wear process. Studying the changes in wear particle boundaries provides important information about the cause and progression of wear in synovial joints.

Hitherto, all the existing techniques for controlling nonlinear systems required at least one of the following assumptions: the system is affine, is SISO, has a known nonlinear structure parametrized linearly by unknown parameters, and full state feedback is possible. This paper proposes a technique for the control of general nonlinear systems with unknown structure, which requires none of the above assumptions. The dynamic control law is based on the implicit function theorem, where the underlying unknown implicit function is emulated by a feedforward neural network. The controller can either be trained offline or adaptively trained in a direct adaptive control mode. Simulation examples are presented to illustrate the effectiveness of the proposed technique.

There is a growing need for classification systems that can accurately detect and predict knee osteoarthritis (OA) from plain radiographs. For this purpose, a system based on a support vector machine (SVM) classifier and distances measured between trabecular bone (TB) texture images was developed and tested in previous work. Unlike other systems, it allows an image classification without the calculation and selection of numerous texture features, and it is invariant to a range of imaging conditions encountered in a routine X-ray screening of knees. Although the system exhibited 85.4% classification accuracy in OA detection, which was higher than those obtained from other systems, its performance could be further improved. To achieve this, a dissimilarity-based multiple classifier (DMC) system is developed in this study. The system measures distances between TB texture images and generates a diverse ensemble of classifiers using prototype selection, bootstrapping of training set and heterogeneous classifiers. A measure of competence is used to select accurate (i.e. better-than-random) classifiers from the ensemble, which are then combined through the majority voting rule. To evaluate the newly developed system in OA detection (prediction of OA progression), TB texture images selected on standardised radiographs of healthy and OA (non-progressive and progressive OA) knees were used. The results obtained showed that the DMC system has higher classification accuracies for the detection (90.51% with 87.65% specificity and 93.33% sensitivity) and prediction (80% with 82.00% specificity and 77.97% sensitivity) than other systems, indicating its potential as a decision-support tool for the assessment of radiographic knee OA.

The objective of this work is to evaluate differences in trabecular bone (TB) texture between subjects with and without tibiofemoral cartilage defects using a variance orientation transform (VOT) method. A case-control study was performed in subjects without radiographic knee osteoarthritis (OA) (KL grade2) matched on sex, BMI, age, knee compartment, and meniscectomy where cases (n = 28) had cartilage defects (grade ≥2) and controls (n = 28) had no cartilage defects (grade2). Cartilage defects were assessed from MRI using validated methods. The VOT was applied to TB regions selected on medial and lateral compartments in knee X-rays and fractal signatures (FS) in the horizontal (FS(H) ) and vertical (FS(V) ) directions, and along the roughest part of TB (FS(Sta) ) and texture aspect ratio signatures (StrS), at different trabecular image sizes (0.30-0.70 mm) were calculated. Compared with controls, FS(V) for cases were higher (p 0.011) at image sizes 0.30-0.40 mm and 0.45-0.55 mm in the medial compartment. In the lateral compartment, FS(H) and FS(Sta) for cases were higher (p 0.028) than those for controls at 0.30-0.40 mm and 0.45-0.55 mm, while FS(V) was higher (p 0.02) at 0.30-0.40 mm. TB texture roughness was greater in subjects with cartilage defects than in subjects without, suggesting thinning and fenestration of TB occur early in OA and that the VOT identifies changes in TB in knees with early cartilage damage. No differences in StrS (p 0.05) were found.

Objective: To evaluate differences in tibial trabecular bone (TB) texture between subjects with and without radiographic knee osteoarthritis (OA) using a variance orientation transform (VOT) method. Design: Subjects with knee OA (Kellgren & Lawrence grade >= 2) and controls without OA (both n = 26, seven women) were matched by sex, age, body mass index and compartment. The VOT method was applied to TB X-ray images and fractal signature and dimension in horizontal (FSH, FDH) and vertical (FSV, FDV) directions and along the roughest part of TB (FSSta, FDSta), texture aspect ratio (Str) and signature (StrS), and mean FD (FDMEAN) were calculated. The VOT method was compared against an augmented Hurst orientation transform (HOT) method using paired t tests, intraclass correlation coefficients (ICCs) and coefficients of variation (CVs%). Longitudinal sensitivity to OA bone changes was not assessed. Results: For the reproducibility of texture parameters, ICCs were >0.75 and CVs% were

We investigated spatiotemporal data, joint kinematics, and joint kinetics during gait in a group of subjects who had recently undergone arthroscopic partial meniscectomy and compared the results to those of healthy controls. Gait analysis was performed on 105 pain-free meniscectomy patients and 47 controls, walking at a self-selected speed. The meniscectomy population was comparable to controls in spatiotemporal parameters and knee kinematics. However, they had reduced range of motion (ROM) and lower peak moments in the sagittal plane on the operated limb compared to the nonoperated limb. Compared to controls, the meniscectomy patients had significantly larger knee adduction moments over stance, even after accounting for their greater body weight. These differences likely increase articular loads on the medial compartment of the tibiofemoral joint and may contribute to the high risk of knee osteoarthritis following arthroscopic meniscal surgery.

Summary Objective Arthroscopic partial medial meniscectomy (APMM) is a common procedure to treat a medial meniscal tear. Individuals who undergo APMM have a heightened risk of developing tibio-femoral osteoarthritis (OA). Cartilage defects scored from magnetic resonance imaging (MRI) scans predict cartilage loss over time. It is not known whether cartilage defects in the early years following APMM are more common or of greater severity than in age-matched controls. This study compared the prevalence and severity of tibio-femoral cartilage defects in patients 3–5 years post-APMM with that of age-matched controls. Methods Twenty-five individuals who had undergone APMM in the previous 46.9±5.0 months and 24 age-matched controls participated in this study. Sagittal plane knee MRI scans were acquired from the operated knees of patients and from randomly assigned knees of the controls and graded (0–4) for tibio-femoral cartilage defects. Defect prevalence (score of ≥2 for any compartment) and severity of the cartilage from both tibio-femoral compartments were compared between the groups. Results The APMM group had greater prevalence (77 vs 42%, P =0.012) and severity (4.1±1.9 vs 2.8±1.1, P =0.005) of tibio-femoral cartilage defects than controls. Age was positively associated with tibio-femoral cartilage defect severity for APMM, r =0.523, P =0.007, but not for controls, r =0.045, P =0.834. Conclusion Tibio-femoral joint cartilage defects are more prevalent and of greater severity in individuals who had undergone APMM ∼44 months earlier than in age-matched controls.

In this study the automated classification system previously developed by the authors was used to classify articular cartilage surfaces with different degrees of wear. This automated system classifies surfaces based on their texture. Plug samples of sheep cartilage (pins) were run on stainless steel discs under various conditions using a pin-on-disc tribometer. Testing conditions were specifically designed to produce different severities of cartilage damage due to wear. Environmental scanning electron microscope (SEM) (ESEM) images of cartilage surfaces, that formed a database for pattern recognition analysis, were acquired. The ESEM images of cartilage were divided into five groups (classes), each class representing different wear conditions or wear severity. Each class was first examined and assessed visually. Next, the automated classification system (pattern recognition) was applied to all classes. The results of the automated surface texture classification were compared to those based on visual assessment of surface morphology. It was shown that the texture-based automated classification system was an efficient and accurate method of distinguishing between various cartilage surfaces generated under different wear conditions. It appears that the texture-based classification method has potential to become a useful tool in medical diagnostics.

cartilage volume loss was stronger for the tibiae than for the femoral cartilages. Conclusions: We find greater progression of cartilage loss in the mechanically stressed compartment of varus and valgus knees than in the non-stressed compartment and than in knees with neutral alignment. Progression in persons with neutral alignment appears to be predominantly characterized by a reduction in cartilage thickness (rather than by reduction in cartilaginous area). An increase in denuded area, however, appears to be an important contributor to cartilage loss in the stressed compartments of persons with valgus and varus OA.

There is a growing need for noninvasive and inexpensive methods that can effectively be used on a large scale, to detect an onset of early osteoarthritis in human knee joints. Of many possible options, fractal analysis of two-dimensional projection x-ray images of trabecular bone (TB) texture, appears as one of the best approaches. However, there are some problems associated with the characterization of the roughness and anisotropy of the bone texture. To resolve these problems, a modified Hurst orientation transform (HOT) method, previously developed by the authors, has been used in this study. The advantages of the HOT method over other techniques used to analyze bone texture, are that it calculates a two-dimensional fractal dimension in all possible directions and also provides a measure of anisotropy for both surfaces exhibiting strong anisotropy and surfaces exhibiting weak anisotropy. In this study, the accuracy of the HOT method in measuring the bone texture roughness and anisotropy; together with the effects of image noise, blur, exposure, magnification, and projection angle on its performance were investigated. Computer-generated images of fractal surfaces and x-ray images obtained for a human tibia head were used. Results obtained show that the HOT method can effectively be used to characterize the roughness and anisotropy (isotropy) of TB texture.

Purpose: To develop directional fractal signature methods for the analysis of trabecular bone (TB) texture in hand radiographs. Problems associated with the small size of hand bones and the orientation of fingers were addressed. Methods: An augmented variance orientation transform (AVOT) and a quadrant rotating grid (QRG) methods were developed. The methods calculate fractal signatures (FSs) in different directions. Unlike other methods they have the search region adjusted according to the size of bone region of interest (ROI) to be analyzed and they produce FSs defined with respect to any chosen reference direction, i.e., they work for arbitrary orientation of fingers. Five parameters at scales ranging from 2 to 14 pixels (depending on image size and method) were derived from rose plots of Hurst coefficients, i.e., FS in dominating roughness (FS{sub Sta}), vertical (FS{sub V}) and horizontal (FS{sub H}) directions, aspect ratio (StrS), and direction signatures (StdS), respectively. The accuracy in measuring surface roughness and isotropy/anisotropy was evaluated using 3600 isotropic and 800 anisotropic fractal surface images of sizes between 20 × 20 and 64 × 64 pixels. The isotropic surfaces had FDs ranging from 2.1 to 2.9 in steps of 0.1, and the anisotropic surfaces had two dominating directionsmore » of 30° and 120°. The methods were used to find differences in hand TB textures between 20 matched pairs of subjects with (cases: approximate Kellgren-Lawrence (KL) grade ≥2) and without (controls: approximate KL grade

A new method, called a pattern recognition by partition iterated function system (PR-PIFS), has recently been developed and successfully applied to classify wear particles. The method is based on the fact that the surface topography of 3-D objects can be described by a small set of mathematical rules. Since the PR-PIFS method is fully automated, it eliminates the need for specialists and reliance on human visual inspection techniques. Also, the method is rotationally- and scale-invariant and no vector of various surface parameters is needed. The application of this method to the classification of artificially generated fractal and tribological surfaces (e.g. worn surfaces) is presented in this paper. For this purpose, the PR-PIFS method has been specially modified to suit tribological surface data. The accuracy of this method in the classification of surfaces rotated by various angles and scaled to different sizes was assessed.

Surface topography affects wear and lubrication mechanisms occurring between two interacting surfaces. Despite its importance, there is no reliable method fully describing 3-D surface topography features and the results provided by currently used methods are not satisfactory. This is because traditional methods, used to characterize surfaces, such as Fourier transforms, statistical functions and parameters are not able to fully describe intrinsic properties of surfaces, especially those that exist over many different scales. Fractal methods have, therefore, been adapted and applied to overcome these difficulties. In this paper, a partition iterated function system (PIFS) method, recently developed by the authors, is briefly described and applied to 3-D surface topography images of artificial orthopaedic implant surfaces and surfaces of wear particles. This method utilises the ability of fractal geometry to describe complex objects such as clouds, trees and mountains by a few mathematical equations. The complex objects can then be reconstructed back from these equations. When the PIFS method is applied to surface information on 3-D surface topography, it is encoded into a set of affine contractive transformations which fully describe details of the surface topography over different scales. The PIFS method developed appears to be superior to other fractal methods used so far to characterize surface topography. It works well with a wide range of fractal surfaces and it can simultaneously be used to mathematically model the surface topography, calculate the fractal dimension and recognise patterns.

Summary Objective To examine the association between trabecular bone texture and knee joint replacement (KJR) measured using a variance orientation transform (VOT) method. Methods The association of trabecular bone texture and KJR was examined prospectively over 6 years in 123 subjects with symptomatic knee osteoarthritis (OA): data regarding KJR was available for 114 (93%). At baseline, weight-bearing anteroposterior tibio-femoral radiographs were acquired. Trabecular bone texture regions were selected from the medial and lateral subchondral tibia. The VOT method was applied to each region and five fractal bone texture parameters, i.e., mean fractal dimension (FD MEAN ), fractal dimensions in the horizontal (FD H ) and vertical (FD V ) directions, and along the roughest part of trabecular bone (FD Sta ), and texture aspect ratio (Str) were calculated. The association between groups with increasing baseline fractal parameters (defined using tertiles) with risk of JR was examined using logistic regression. Results 28 (25%) participants' study knees underwent KJR over 6 years. Participants with KJR had lower medial FD MEAN and FD H parameters ( P = 0.02 for difference). With increasing FD MEAN , adjusted for age, gender, body mass index (BMI), osteophyte grade, joint space narrowing (JSN) grade and WOMAC pain score, the odds of KJR was reduced ( P = 0.04 for trend). Conclusion This study suggests that the texture of medial tibial trabecular bone measured from plain radiographs is related to the risk of KJR: with increasing FD MEAN (the overall measure of bone texture roughness) the risk of KJR was reduced, independent of other clinical predictors of joint replacement. Tibial trabecular bone texture may be a useful marker of disease progression and a target of therapy in OA.

SummaryObjectiveTo develop an accurate method for quantifying differences in the trabecular structure in the tibial bone between subjects with and without knee osteoarthritis (OA).MethodsStandard knee radiographs were taken from 26 subjects (seven women) with meniscectomy and radiographic OA Kellgren & Lawrence grade 2 or worse in the medial compartment. Each case knee was individually matched by sex, age, body mass index and medial or lateral compartment with a control knee.A newly developed augmented Hurst orientation transform (HOT) method was used to calculate texture parameters for regions selected in X-ray images of non-OA and OA tibial bones. This method produces a mean value of fractal dimensions (FDMEAN), FDs in the vertical (FDV) and horizontal (FDH) directions and along a direction of the roughest part of the tibial bone (FDSta), fractal signatures and a texture aspect ratio (Str). The ratio determines a degree of the bone texture anisotropy. Reproducibility was calculated using an intraclass correlation coefficient (ICC). Comparisons between cases and controls were made with paired t tests. The performance of the HOT method was evaluated against a benchmark fractal signature analysis (FSA) method.ResultsCompared with controls, trabecular bone in OA knees showed significantly lower FDMEAN, FDV, FDH and FDSta and higher Str at trabecular image sizes 0.2–1.1mm (P0.8). In the medial compartment, fractal signatures calculated for OA horizontal and vertical trabeculae were significantly lower at sizes 0.3–0.55mm (P