An end-to-end system to automate the well-known Tanner - Whitehouse (TW3) clinical procedure to estimate the skeletal age in childhood is proposed. The system comprises the detailed analysis of the two most important bones in TW3: the radius and ulna wrist bones. First, a modified version of an adaptive clustering segmentation algorithm is presented to properly semi-automatically segment the contour of the bones. Second, up to 89 features are defined and extracted from bone contours and gray scale information inside the contour, followed by some well-founded feature selection mathematical criteria, based on the ideas of maximizing the classes{\textquoteright} separability. Third, bone age is estimated with the help of a Generalized Softmax Perceptron (GSP) neural network (NN) that, after supervised learning and optimal complexity estimation via the application of the recently developed Posterior Probability Model Selection (PPMS) algorithm, is able to accurately predict the different development stages in both radius and ulna from which and with the help of the TW3 methodology, we are able to conveniently score and estimate the bone age of a patient in years, in what can be understood as a multiple-class (multiple stages) pattern recognition approach with posterior probability estimation. Finally, numerical results are presented to evaluate the system performance in predicting the bone stages and the final patient bone age over a private hand image database, with the help of the pediatricians and the radiologists expert diagnoses. {\^A}{\textcopyright} 2006 IEEE.

}, keywords = {Age Determination by Skeleton, Aging, algorithm, Algorithms, article, Artificial Intelligence, artificial neural network, Automated, automation, Bone, bone age, Bone age assessment, bone maturation, childhood, Clustering algorithms, Computer-Assisted, Humans, instrumentation, Model selection, Neural networks, Pattern recognition, Radiographic Image Interpretation, radius, Reproducibility of Results, Sensitivity and Specificity, Skeletal maturity, ulna}, issn = {00189294}, doi = {10.1109/TBME.2008.918554}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-42249094547\&partnerID=40\&md5=2cecfea5f75a61b048611f2391b00aed}, author = {Antonio Trist{\'a}n-Vega and Juan I. Arribas} } @article {420, title = {A model selection algorithm for a posteriori probability estimation with neural networks}, journal = {IEEE Transactions on Neural Networks}, volume = {16}, year = {2005}, pages = {799-809}, abstract = {This paper proposes a novel algorithm to jointly determine the structure and the parameters of a posteriori probability model based on neural networks (NNs). It makes use of well-known ideas of pruning, splitting, and merging neural components and takes advantage of the probabilistic interpretation of these components. The algorithm, so called a posteriori probability model selection (PPMS), is applied to an NN architecture called the generalized softmax perceptron (GSP) whose outputs can be understood as probabilities although results shown can be extended to more general network architectures. Learning rules are derived from the application of the expectation-maximization algorithm to the GSP-PPMS structure. Simulation results show the advantages of the proposed algorithm with respect to other schemes. {\^A}{\textcopyright} 2005 IEEE.

}, keywords = {algorithm, Algorithms, article, artificial neural network, Automated, automated pattern recognition, Biological, biological model, Breast Neoplasms, breast tumor, classification, cluster analysis, computer analysis, Computer-Assisted, computer assisted diagnosis, Computer simulation, Computing Methodologies, decision support system, Decision Support Techniques, Diagnosis, Estimation, evaluation, Expectation-maximization, Generalized Softmax Perceptron (GSP), human, Humans, mathematical computing, Mathematical models, methodology, Models, Model selection, Neural networks, Neural Networks (Computer), Numerical Analysis, Objective function, Pattern recognition, Posterior probability, Probability, Statistical, statistical model, statistics, Stochastic Processes}, issn = {10459227}, doi = {10.1109/TNN.2005.849826}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-23044459586\&partnerID=40\&md5=f00e7d86a625cfc466373a2a938276d0}, author = {Juan I. Arribas and Jes{\'u}s Cid-Sueiro} }