# Deep Representation of a Normal Map for Screen-Space Fluid Rendering
## 2 Related Work  
**Screen-space fluid rendering:** There are many methods that can be used to render a particle-based fluid simulation, with the traditional method being the isosurface-based approach [7]. However, when an isotropic kernel is used to extract isosurfaces, all the particles are represented as spheres, which causes the surface of the fluid to appear rough. To address this problem, one study used an anisotropic kernel [8] to distribute nearby particles when the physical quantity at a certain point was obtained. When the anisotropic kernel is used, particles can be expressed as ellipsoids instead of spheres, which can solve the problem of surface roughness. However, the method of extracting and rendering isosurfaces requires a considerable amount of computation because the physical quantities must be calculated for each space. Apart from creating a surface and rendering it in the world space, there are other approaches that extract and render particles in the screen space without creating a surface. Among the traditional methods, one method renders point clouds [9] and another renders fluid particles [1]. Here, a Gaussian filter [10] or a bilateral Gaussian filter is commonly used to smoothen the surface. However, when these filters are used, there is an problem in that discontinuities occur between the front and rear particles. One approach for resolving this problem uses a narrow filtering technique [2], and another, called \"screen-space mesh\" [11], combines the aforementioned two methods for rendering particles with a smooth surface. Finally, another method predicts the fluid surface using ray tracing alone [12] and generates the ray-traced image using both ray tracing and deep learning [13]. In these studies, the screen-space method has an advantage over other methods in terms of the computation time. However, the rendering quality of the screen-space method is primarily related to the quality of the normal map, and the existing filters do not achieve high-quality rendering results. Inspired by the screen-space rendering method, our study aims to generate an optimal deep learning-based filter for refining the normal map to achieve high-quality screen-space fluid rendering. **Deep learning techniques:** Deep learning has attracted considerable attention in a variety of fields and has exhibited outstanding performance in certain areas. Image classification has evolved to the point where it can outperform humans [14], and deep learning is used in many fields, such as natural language processing [15] and image processing [16,17]. Deep learning has also been used in the field of rendering. For example, path-traced images with few samples have been denoised using an autoencoder [18], and one study examined the high-quality rendering of various shading effects by learning from example images [19]. Graph neural networks (GNN) [20,21], which have strong relational properties owing to their architecture that represents relations using a graph, were studied for simulating complex physical systems (fluid, cloth, hair, etc.). In recent years, GNNs have been extended for non-particle-based simulations such as mesh-based [22] and grid-based [23] simulations. In addition, deep learning has made significant progress in creating a production model that generates data that are similar to real-life [24]. The GAN approach, a model introduced by [PERSON] et al. [6], creates a generation model using a generator to generate data and a discriminator to distinguish between the generated data and the actual data. The generator and discriminator compete to improve the overall performance of the generator. [PERSON] et al. [25] proposed a cycle-GAN method for translating two different styles of images. cGAN [5] was proposed as a method for generating data with GANs under specific conditions, and it is better suited to the image-to-image translation problem. Studies involving cGANs include research on the super-resolution problem [26,27] and the image-style transfer problem [28].