How are custom styles and filters defined mathematically in ChatGPT ImageGen?

Custom styles and filters in ChatGPT ImageGen are mathematically defined through a combination of convolutional neural networks (CNNs) and mathematical operations performed on the image's pixel values or latent space representation. At the core, a CNN learns to extract and represent stylistic features from a style image. This involves learning filters that respond to specific textures, color palettes, and patterns present in the style image. These filters are essentially mathematical functions that are applied to the input image to detect and enhance these features. Once the stylistic features are extracted, they are then applied to the content image. This can be achieved through various mathematical operations, such as adjusting the color distribution of the content image to match the style image, or by applying transformations to the latent space representation of the content image based on the learned style features. For example, a filter that sharpens edges might be defined by a convolution kernel that amplifies differences in pixel values. Similarly, a color filter might be defined by a mathematical transformation that maps the original color values to new color values based on the desired style. Complex styles often involve a combination of multiple filters and transformations applied in a specific sequence. The parameters of these filters and transformations are learned during the training process, allowing the model to accurately capture and reproduce a wide range of styles. In essence, custom styles and filters are a set of mathematical instructions that are applied to an image to transform its appearance based on the learned characteristics of a specific style.