## 3 Experimental Results  
We evaluate our proposed model on CT datasets provided for CSI spine and verteb segmentation at the 2 nd MICCAI workshop and corresponding ground truth obtained from trauma center during the daily medical examination. The CT scan comprises all thoracic (T1-T12) and lumbar (L1-L5) vertebrae with 1 mm of slice thickness, and the data resolution ranges from 0.31 mm to 0.45 mm for in-plane resolution. These datasets are obtained from the patient's age group between 16 to 35 years old [45]. The proposed work is implemented in MATLAB 2017a as backend and trained on Dell desktop with a 3.6 GHz Intel(R) i7 CPU, 32 GB RAM, and Windows 7 ultimate operating system.  
The training process evolves for binary segmentation of verteb where all the vertebrae have the same labels, and the model distinguishes between verteb and background in which features are learned in an unsupervised manner called pretraining. The activation conditional probability over hidden and visible units is given by the logistic function and is used as an activation function for the sigmoid function. Each RBM is trained by contrastive divergence (CD) algorithm [31]. The input image  
Figure 5: The structure of the proposed PaDBN Model.  
patch of visible layer x constructs RBM1 with the first hidden layer h1, and h1 is treated as a visible layer for constituting RBM2 with the second hidden layer h2. In our training procedure, we use two RBMs to train our model. The parameters of RBM1 (W, b, c) are obtained using CD algorithm. By fixing this layer parameter and training RBM2 from CD algorithm, the DBN global parameters are obtained as shown in Figure 6. A sparse penalty factor [31], which conducts the RBM sparsity by creating a connection of weight and hidden unit bias, is proposed on the basis of cross entropy. Cross entropy is used to distinguish between verteb and nonvertebra using two small probability distributions to prevent the phenomenon of verteb homogeneity during training. The 1024 raw dimension features are given as input to the network. The dataset is split into training 70% (training80%-validation20%) and testing 30%; seven CT images are used for training (training-validation) and three for testing.  
The training data samples comprise the matrix with 538,624 \(\times\) 1024 dimensions and validation samples having a matrix with 179,200 \(\times\) 1024 dimensions. Five-hundred-and-thirty-eight-thousand-six-hundred-and-twenty-four samples were randomly chosen for training, and 179,200 samples were randomly chosen for validation. To achieve efficient training, the mini batch size was set to 128. The training samples were divided into 4028 mini batches, and validation samples were divided into 1400 mini batches. The architecture of PaDBN was selected as 1024-100-100-2, where the number of input nodes is 1024. The number of epochs in unsupervised pretraining is 50 to fully train every RBM of PaDBN. The 3000 epochs are used in fine-tuning. The model is trained to minimize the mean square error (MSE) between the predicted map and the ground truth. The output layer is used as a sigmoid layer to show the probability map of verteb or nonvertebra objects. Our trained model can assess the labels of the arbitrarily sized image. Given a test image, we extract the overlapping patches of size 32  
Figure 6: The learning curve of the model.  
\(\times\) 32 and feed them to the trained model to generate prediction probability maps. For the overlapped image patch, the final probability maps will be the average probability map of overlapping patches that can be used to realize verteb segmentation. Thus, the generalization and stability of the trained model can be guaranteed.