Recursive analysis and estimation for the discrete Boolean random set model

Random sets provide a powerful class of models for images containing randomly placed objects of random shapes and orientation. Those pixels within the foreground are members of a random set realization. The discrete Boolean model is the simplest general random set model in which a Bernoulli point process (called a germ process) is coupled with an independent shape or grain process. A typical realization consists of many overlapping shapes. Estimation in these models is difficult owing to the fact that many outcomes of the process obscure other outcomes. The directional one-dimensional (ID) model, in which random- length line segments emanate to the right from germs on the line, is analyzed via recursive expressions to provide a complete characterization of these discrete models in terms of the distributions of their black and white runlengths. An analytic representation is given for the optimal windowed filter for the signalunion- noise process, where both signal and noise are Boolean models. Several of these results are extended to the nondirectional case where segments can emanate to the left and right. Sufficient conditions are presented for a two-dimensional (2D) discrete Boolean model to induce a one dimensional Boolean model on an intersecting line. When inducement holds, the likelihood of runlength observations of the two-dimensional model is used to provide maximum-likelihood estimation of parameters of the 2D model. The ID directional discrete Boolean model is equivalent to the discrete-time infinite-server queue. Analysis for the Boolean model is extended to provide densities for many random variables of interest in queueing theory

Image analysis tool for the characterisation of bone turnover in the appendicular skeleton

Osteoporosis is a disease characterised by reduced bone mass and altered microarchitecture leading to an increased risk of fracture. The consequences of osteoporosis include reduced quality of life and pain, associated with fractures. Its financial burden on health services are significant. Characterisation of osteoporosis using imaging techniques is therefore important. Peripheral Quantitative Computed Tomography (pQCT) is a cross-sectional imaging method which is used to scan bones in the appendicular skeleton. pQCT imaging may be particularly useful in clinical groups where changes in bone mineral density (BMD) and structure are known to occur in the limbs. Two such groups are patients following spinal cord injury (SCI) or anterior cruciate ligament (ACL) injury. Aims. This project aimed to develop analysis techniques to characterise bone in pQCT images. Their purpose was to describe localised changes within pQCT images of the bone, as opposed to the standard global measurements. Methods. Fully automated segmentation and registration software was developed and tested followed by two independent processing algorithms. The first generates spatial maps to characterise local changes in BMD. This is achieved using both quadrant analysis software and a voxel-based approach, the latter comparing pairs of images and generating a voxel-by-voxel ΔBMD map of changes in BMD. The second processing algorithm uses morphological granulometries to investigate the bone microarchitecture. Results. Evaluation of these image analysis methods was carried out using two clinical studies. The first investigates acute longitudinal changes in the distal tibia (DT) and distal femur (DF) post-motor-complete-SCI using pQCT. Images from 15 subjects (13M, 2F) with a mean age of 36y±19y, were acquired at 4-monthly intervals during the first year post-injury. The second comprises of ACL injury subjects, with imaging of the injured and contralateral proximal tibia (PT) and distal femur before (n=19, 18M 1F, 30y±9y of age) and after (n=8, 8M 0F, 31y±9y of age) surgical ACL reconstruction. The software developed to automatically segment bone from surrounding structures was successful: 98% success rate for epiphyseal tibial regions, 67% success rate for the distal femur. Registration of images was then performed and the spatial analysis methods to automatically produce quadrants of trabecular bone were applied, displaying individual results graphically. The voxel based analysis method was developed, tested and applied to produce ΔBMD maps, utilising statistical inference and corrections for multiple comparisons using a false-discovery rate technique. These maps characterised localised changes in BMD between pairs of both longitudinal and contralateral images. Software was also developed to apply morphological granulometries to pQCT images, calculating global and local pattern spectrum moments. On application of the analysis methods to the longitudinal SCI images, the BMD and microarchitecture findings were observed to be disparate amongst subjects, with large variations in bone characteristics both globally and regionally. The quadrant and voxel based analysis methods provided information on longitudinal regional changes in each subject, indicating individual patterns of change. Structural analysis of bone microarchitecture using granulometries was demonstrated to have potential as a useful adjunct to BMD in identifying SCI subjects more susceptible to rapid bone loss. The analysis methods were also successfully applied to the ACL injury subjects. Following segmentation and registration, the total and trabecular BMD in the injured knee was observed to be significantly lower than that of the contralateral control knee pre-operatively for both the PT and DF (p<0.05). Post-operatively the total and trabecular BMD in the injured DF remained significantly low (p<0.05), however the PT demonstrated significantly lower BMD in the injured leg for the trabecular bone only (p<0.05). Reduced BMD in the PT post-operatively in humans is a novel observation, and indicates a benefit afforded by segmenting trabecular from cortical bone. Regional analysis using quadrants indicated some anatomical variation in bone loss within the injured limb, although it is acknowledged that these are preliminary findings which would require to be confirmed in larger studies. The voxel ΔBMD maps generally indicated global losses across the bones of the ACL injured leg both pre-operatively and post-operatively. No consistent patterns were obtained in the ΔBMD maps for these subjects, suggesting individual patterns of response to ACL injury. The structural information provided by granulometric analysis was limited for the ACL study. Conclusions. Automated software has been developed to characterise bone in pQCT images of the appendicular skeleton. It has been successfully applied to two clinical studies, facilitating localised changes in bone density to be demonstrated and descriptions of microarchitecture to be provided. The SCI subjects appear to have individualistic responses to injury, with a wide range of changes in bone density and microarchitecture observed. ACL injury patients all lost bone mass, but patterns of change were variable. The analysis methods developed to permit characterisation of bones in individual subjects, are proposed to be of value in both clinical and research domains exploring bone mass and microarchitecture, with the ultimate goals being the prediction of fracture risk and tailoring therapy for the individual

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version

Colour morphological sieves for scale-space image processing

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Factories of the Future

Engineering; Industrial engineering; Production engineerin