Laplace Beltrami eigen value based classification of normal and Alzheimer MR images using parametric and non-parametric classifiers

Automated study of brain sub-anatomic region like Corpus Callosum (CC) is challenging due to its complex topology and varying shape. The development of reliable Computer Aided Diagnosis (CAD) systems would help in the early detection of Alzheimer's Disease (AD) and to perform drug trails to palliate the effect of AD. In this work, an attempt has been made to analyse the shape changes of CC using shape based Laplace Beltrami (LB) eigen value features and machine learning techniques. CC from the normal and AD T1-weighted magnetic resonance images are segmented using Reaction Diffusion (RD) level set method and the obtained results are validated against the Ground Truth (GT) images. Ten LB eigen values are extracted from the segmented CC images. LB eigen values are positive sequence of infinite series that describe the intrinsic geometry of objects. These values capture the shape information of CC by solving the eigen value problem of LB operator on the triangular meshes. The significant features are selected based on Information Gain (IG) ranking and subjected to classification using K-Nearest Neighbour (KNN), Support Vector Machine (SVM) and Naïve Bayes (NB). The performance of LB eigen values in the AD diagnosis is evaluated using classifiers' accuracy, specificity and sensitivity measures. Results show that, RD level set is able to segment CC in normal and AD images with high percentage of similarity with GT. The extracted LB eigen values are found to show high difference in the mean values between normal and AD subjects with high statistical significance. The LB eigen modes λ2, λ7 and λ8 are identified as prominent features by IG based ranking. KNN is able to give maximum classification accuracy of 93.37% compared to linear SVM and NB classifiers. This value is observed to be high than the results obtained using geometric features. The proposed CAD system focuses solely on the geometric variations of CC extracted using LB eigen value spectrum. The extraction of eigen modes in the LB spectrum is easy to compute, does not involve too many parameters and less time consuming. Thus this CAD study seems to be clinically significant in the shape investigation of brain structures for AD diagnosis.