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Style Transfer for Taotie Pattern Using Convolutional Neural Networks

Style transfer refers to the process of transferring the style of an image $\overrightarrow{a}$$\overrightarrow{a}$ to another image $\overrightarrow{p}$$\overrightarrow{p}$, resulting in $\overrightarrow{p}$$\overrightarrow{p}$ having a visually similar style to $\overrightarrow{a}$$\overrightarrow{a}$. Addressing the problem of transferring the taotie pattern style, we propose an artistic style transfer algorithm based on Convolutional Neural Networks (CNN). This algorithm utilizes the feature responses and Gram matrices of each layer in a CNN to map content and style to independent feature spaces. The task of style transfer is achieved efficiently and flexibly by minimizing the content and style loss functions through gradient descent.

Specifically, for a VGG19 network pre-trained on object recognition tasks, we represent the content of layer $l\in L$$l \in L$ by the feature response $F^l\in {\mathbb{R}}^{N_{l}imes{M}_l}$$F^l \in \mathbb{R}^{N_l imes M_l}$, and the style by the Gram matrix $G_{ij}^l=\sum _k{F}_{ik}^l{F}_{jk}^l$$G_{ij}^l = \sum_k F_{ik}^l F_{jk}^l$. Here, $i\in N_l$$i \in N_l$ denotes the convolutional filters in layer $l$$l$, $j\in M_l$$j \in M_l$ denotes the feature responses corresponding to the convolutional filter $i$$i$ in layer $l$$l$, and the Gram matrix $G_{ij}^l$$G_{ij}^l$ is the correlation matrix of different feature responses in layer $l$$l$. For the content image $\overrightarrow{p}$$\overrightarrow{p}$, style image $\overrightarrow{a}$$\overrightarrow{a}$, and a random noise image $\overrightarrow{x}$$\overrightarrow{x}$, the style transfer loss function is defined as:

The content loss function is given by:

The style loss function is:

In these equations, $F_{ij}^l$$F_{ij}^l$ and $P_{ij}^l$$P_{ij}^l$ represent the content features of $\overrightarrow{p}$$\overrightarrow{p}$ and $\overrightarrow{x}$$\overrightarrow{x}$, respectively, while $G_{ij}^l$$G_{ij}^l$ and $A_{ij}^l$$A_{ij}^l$ represent the style features of $\overrightarrow{a}$$\overrightarrow{a}$ and $\overrightarrow{x}$$\overrightarrow{x}$, respectively. By minimizing the style transfer loss function ${\mathcal{L}}_{transfer}(\overrightarrow{p},\overrightarrow{a},\overrightarrow{x})$$\mathcal{L}_{transfer}(\overrightarrow{p}, \overrightarrow{a}, \overrightarrow{x})$ using gradient descent, the random noise image $\overrightarrow{x}$$\overrightarrow{x}$ is transformed into the final style-transferred image.

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