## 1 Introduction
### Related Work
Unlike feature representation by the convolutional neural network (CNN) that comprises convolutional and subsampling tasks in learning a set of locally connected nodes through the locally receptive field for features extraction, our proposed PaDBN model is a full connection method for high-level feature learning. Unsupervised feature learning is implemented by the CD algorithm which trains the stacked RBMs to obtain the initial weight and supervised learning is implemented by the back-propagation algorithm to fine-tune the whole network and can optimize the deep-learned features for certain tasks, such as segmentation. While CNN is a partially connected approach that stresses the importance of locality while PaDBN is a fully connected approach which gets learning a single global weight matrix for features representation. The size of overlapping patches was set to 32 \(\times\) 32 pixels. Therefore, we choose PaDBN instead of CNN in our work. The objective we purse is to achieve the segmentation of vertebrae from CT images. In the present study, we propose based on our preliminary work [44], a new hierarchical deep learning feature representation PaDBN method for vertebrae segmentation. We adapted square and rectangular ROI extraction from input CT image for overlapping patch generation and used balance classes in training set to get high classification accuracy that was not done in our preliminary work [44]. Note, no matter what the proportion of samples in testing set, smaller and compact deep belief network architecture is adopted to minimize resources with better accuracy than our previous architecture. Our preliminary work describes a proof-of-concept strategy for improving vertebrae segmentation and result suggests that a fast correction method improves the segmentation and has potential to be incorporated as an additional implement into clinical usage. These preliminary results further motivated us to perform a full evaluation of PaDBN model for vertebrae segmentation accuracy. Moreover, this work also reported known limitation of the previous version and proposed a variation of the method to circumvent them. Our proposed model is an unsupervised learning of input feature statistics from CT images. We transfer the obtained network weight matrix to back-propagation neural network with the same structure to start the supervised learning step. In supervised learning step, conjugate gradient is tested for back-propagation neural network learning. These learned features are further integrated into the patch matching framework to find patches for label propagation. Then, a deformable model is adopted for the verteb segmentation by the verteb likelihood mapping driven from patch matching. Finally, the postprocessing stage improves the segmentation by removing the overflow portion by different morphological operations. The output of the postprocessing step is the final verteb segmentation. The proposed method is extensively evaluated on CT datasets from the 2014 MICCAI workshop on the spine (CSI 2014) [45]; these datasets are available on SpineWeb [46]. The experimental results show that the deep learning features of PaDBN achieve excellent segmentation accuracy. Compared with state-of-the-art verteb segmentation methods, our algorithm obtains competitive segmentation accuracy.