## 3 The Proposed Method
### Character Image Feature Recognition Methods  
In a convolutional neural network, the extraction of features from the data relies heavily on a convolutional layer, and it is the key layer in the overall CNN network structure. The pre-processed character image data is convolved with the input data using a two-dimensional convolution layer and a pooling layer to convolve the convolution kernel. The character images are processed by the convolutional layer with the convolution formula:  
\[S(i,j)=(I*K)(i,j)=\sum_{m}\sum_{n}I(m,n)K(i-m,j-n) \tag{1}\]  
where \(S(i,j)\) is the character feature after convolution, and \(K\) is the sequence of convolution kernel functions. The process of CNN processing character images is mainly as follows: input normalized Tibetan character image \(I\) can extract the feature sequence of different Tibetan characters, using the kernel function sequence \(K\) to do convolution operation with \(I\). The pooling layer reduces the dimensionality of the data, and the fully-connected layer prevents the loss of feature information after data training. The classification layer, on the other hand, classifies the feature data into categories. Using the Relu function as the excitation function, the expression is:  
\[y=max(0,x) \tag{2}\]  
Figure 8: Sliced images of ancient Tibetan characters.  
Figure 7: Sample processing process for Tibetan antiquarian documents.  
The computational process for the classification layer uses the Softmax layer and is computed as follows:  
\[softmax(a_{i})=\frac{exp(a_{i})}{\sum_{k=1}^{k\sum(a_{1})}exp} \tag{3}\]  
where \(k\) is the number of types classified. The output of the classification layer indicates the probability of the character being classified to the corresponding type. Stochastic Gradient Descent (SGD) is used as the training method for CNN.  
In this paper, we use a 15-layer CNN structure: the first layer is the image input layer (32 \(\times\) 64 \(\times\) 1), the second layer is the convolutional layer (16 3 \(\times\) 3 convolutional kernels), the third layer is the batch normalization layer, the fourth layer is the ReLU layer, the fifth layer is the maximum pooling layer (2 \(\times\) 2), the sixth layer is the convolutional layer (32 \(\times\) 3 convolutional kernels), the seventh layer is the batch normalization layer, the eighth layer is the ReLU layer, the ninth layer is the maximum pooling layer (2 \(\times\) 2), the tenth layer is a convolutional layer (64 3 \(\times\) 3 convolutional kernels), the eleventh layer is a batch normalization layer, the twelfth layer is a ReLU layer, the thirteenth layer is a fully connected layer, the fourteenth layer is a Softmax layer, and the fifteenth layer is the output layer of classification results. The classified samples are sorted from largest to smallest according to the probability of the classified Softmax layer.  
By processing the sample dataset and convolutional neural network model for feature extraction, Up-CNN and Down-CNN recognition models are built for above-baseline samples and below-baseline samples and trained and optimized for above-baseline samples and below-baseline samples, respectively, to achieve classification and recognition of unmarked characters in images of Tibetan ancient documents. The input layer of the Up-CNN is 64 \(\times\) 32 \(\times\) 1. The output of the thirteenth to fifteenth layers are all 13-dimensional, corresponding to the 13 classes of the upper vowel category, and the rest of the layer structure is similar to the aforementioned 15-layer CNN structure; The output of the thirteenth to fifteenth layers of the Down-CNN are all 273-dimensional, corresponding to the 273 classes of the below-baseline category, and the rest of the layer structure is the same as the aforementioned 15-layer CNN structure.