## 3 Proposed Personalized HRTF Estimation Method  
### Neural Network Architecture  
This section proposes a method for estimating the personalized HRTF using ear images and anthropometric measurements. Since the measured anthropometric data may potentially be missing information that may have been used to estimate HRTFs, it is difficult to take the ear measurements represented in Figure 3b in practice. Thus, instead of measuring the anthropometric parameters of a physical ear, the proposed method directly uses an image of the ear.  
Figure 4 illustrates a block diagram of the proposed HRTF personalized method, including the architecture of a DNN for the proposed personalized HRTF estimation, where both anthropometric measurements and ear images are used as input features, and HRTFs are used as target features. As shown in the figure, the proposed neural network is composed of three sub-networks. The first sub-network of the proposed neural network is a DNN that uses anthropometric measurements as input features to represent the information on the relationship between anthropometric measurements and HRTFs, which is referred to as \"Sub-network A\". The second sub-network is a feature representation network based on CNN from ear images and referred to as \"Sub-network B\". The two sub-networks are combined together using another DNN to estimate personalized HRTFs, referred to as \"Sub-network C\".  
Sub-network A is composed of an input layer, two hidden layers, and an output layer, as illustrated in the left-upper corner in Figure 4. Compared to the input features of the DNN in Section 2, only 17 features (height and circumference measurements) are used here as input features for Sub-network A. The pinna measurements of both ears can be modeled by Sub-network B, as will be described in the next paragraph. In addition, the number of each hidden layer's nodes is set to 32, and the output layer consists of eight nodes and becomes a part of the input layer for Sub-network C. As an activation function, the ReLU is applied to the hidden layers and the output layer.  
Figure 4: Block diagram of the proposed personalized HRTF estimation method using anthropometric measurements and ear images.  
Sub-network B is composed of an input layer, two convolution layers, two max-pooling layers, a fully connected layer, and an output layer. The 32 \(\times\) 32 edge-detected ear images are used for the input features of this sub-network. A detailed explanation is given in Section 3.2. Each convolution layer consists of 3 \(\times\) 3 kernels where the number of the kernels is 16. The max-pooling layer is followed by each convolution layer of 2 \(\times\) 2 size. A fully connected layer converts a 2-D shape output to a 1-D shape from the last max-pooling layer. The output layer of Sub-network B consists of eight nodes and is also used as a part of the input layer of Sub-network C. Similar to Sub-network A, the ReLU activation function is applied for two convolution layers, the fully connected layer, and the output layer.  
Lastly, Sub-network C consists of an integrated input layer with 16 nodes and three hidden layers with 32 nodes each. The output layer has 200 nodes that correspond to the length of HRTFs in the CIPIC database, as described in Section 2. In addition, the ReLU activation function is applied for both the hidden layers and the output layer.