# Image Interpolation Based on Spiking Neural Network Model
## 1 Introduction
In 1998, an approach to pattern analysis that calculates synaptic potentials in a network of neurons was developed [22]. An approach based on the leaky integrate-and-fire (LIF) neuron model for the segmentation of gray-level images was presented in 2005 [23]. It has been observed that SNNs, which process information with the help of spikes generated by connected neurons, are quite successful in HVS-based image processing [24]. For edge detection, the first SNN-based approach was proposed by [PERSON] et al. [25]. The researchers developed a network model in which the gray-level values of pixels are transmitted to neurons in the intermediate layer with the help of excitatory and inhibitory synaptic connections from the receptor layer. The spikes generated in the neurons in the intermediate layer are transmitted to the corresponding neuron in the output layer by excitatory synaptic connections. Similar to the network model in the approach of [PERSON] et al., different receptor and intermediate layers with different matrices and window sizes have been used in many studies [26; 27; 28; 29; 30; 31; 32]. In 2017 [33], an SNN model for edge detection was designed using the Hodgkin and Huxley (HH) [34] neuron model. The HH model, which is much more complex and has a high computational cost was also used by [PERSON] [35] for edge detection in 2020. However, in [PERSON]'s study, the values of some parameters in the HH neuron model were assumed as 0 and it was seen that the conductance-based integrate and fire (CIF) neuron model was used. An SNN design based on the CIF neuron model for edge detection was also used to calculate the diffusion function of the anisotropic diffusion filter (ADF) in 2022 [36]. Spiking neural network (SNN)-based approaches developed to simulate HVS detect edges more successfully than gradient-based techniques [25; 33; 35]. The most important reason for this success is that SNN-based approaches detect edges in the image by mod  
Figure 1: Responses of a retinal ganglion cell. eling neurons in HVS instead of linear differences between the gray-level values of the pixels. Additionally, thanks to models and analytical solutions that have been developed, calculations with SNNs can be performed very quickly [35; 36]. This study mainly focuses on increasing image interpolation success. Therefore, to increase the success of interpolation, a new SNN-based edge detection approach is proposed instead of gradient, which is highly sensitive to noise. Additionally, a new SNN model is developed for edge detection. Edge detection approaches based on conductance-based integrate and fire neuron models generally use 5 \(\times\) 5 receptor fields [25; 28; 35]. Furthermore, the use of the HH neuron model increases the computational cost considerably [33]. It is seen that the edge directions can also be determined as different angles (30 and 60 degrees) [26; 27; 29; 33]. Apart from these, additional filters such as the Gabor filter are also used in the model [35]. The proposed SNN model reduces the computational cost by using 3 \(\times\) 3 neighborhoods. It also does not include additional filters or additional parameters of the HH model. For these reasons, a new model, which is faster and simpler than other existing SNN models, is proposed. Moreover, instead of calculating the differences between the center pixel and each of its neighbors individually in the 3 \(\times\) 3 receptor area [36], the proposed model tries to identify edges in 4 different directions. The success of the proposed method is tested by using the 12 images that are most frequently used in interpolation studies. After the edge detection process with the proposed SNN model, all pixels are first divided into two groups as edge and non-edge pixels. For pixels detected as edges, the 1D interpolation method is used according to the directions of the edges, whereas the bicubic interpolation technique, which is one of the most known methods, is used for non-edge pixels. The proposed method is compared to various edge-based interpolation techniques.