Active appearance pyramids for object parametrisation and fitting

Object class representation is one of the key problems in various medical image analysis tasks. We propose a part-based parametric appearance model we refer to as an Active Appearance Pyramid (AAP). The parts are delineated by multi-scale Local Feature Pyramids (LFPs) for superior spatial specificity and distinctiveness. An AAP models the variability within a population with local translations of multi-scale parts and linear appearance variations of the assembly of the parts. It can fit and represent new instances by adjusting the shape and appearance parameters. The fitting process uses a two-step iterative strategy: local landmark searching followed by shape regularisation. We present a simultaneous local feature searching and appearance fitting algorithm based on the weighted Lucas and Kanade method. A shape regulariser is derived to calculate the maximum likelihood shape with respect to the prior and multiple landmark candidates from multi-scale LFPs, with a compact closed-form solution. We apply the 2D AAP on the modelling of variability in patients with lumbar spinal stenosis (LSS) and validate its performance on 200 studies consisting of routine axial and sagittal MRI scans. Intervertebral sagittal and parasagittal cross-sections are typically used for the diagnosis of LSS, we therefore build three AAPs on L3/4, L4/5 and L5/S1 axial cross-sections and three on parasagittal slices. Experiments show significant improvement in convergence range, robustness to local minima and segmentation precision compared with Constrained Local Models (CLMs), Active Shape Models (ASMs) and Active Appearance Models (AAMs), as well as superior performance in appearance reconstruction compared with AAMs. We also validate the performance on 3D CT volumes of hip joints from 38 studies. Compared to AAMs, AAPs achieve a higher segmentation and reconstruction precision. Moreover, AAPs have a significant improvement in efficiency, consuming about half the memory and less than 10% of the training time and 15% of the testing time.