# BrushGaussian: Brushstroke-Based Stylization for 3D Gaussian Splatting
## 2 Related Works
### Three-Dimensional Representation and Style Transfer  
Three-dimensional style transfer originates from 2D image style transfer and aims to stylize objects or scenes in 3D space. Compared to 2D style transfer, 3D style transfer is a relatively new and challenging task. In addition to balancing content and style, it must ensure view-consistent stylization across different perspectives. This additional requirement makes 3D style transfer inherently more complex and less explored than its 2D counterpart. To address these challenges, researchers have explored various 3D representations, including polygon meshes, point clouds, neural radiance fields (NeRFs), and 3D Gaussian Splatting, to enable view-consistent 3D style transfer. A polygon mesh is a structured representation of a 3D object composed of vertices, edges, and faces that define its geometric shape. Mesh-based representations naturally separate shape (polygon structure) and color (UV map or texture), making them an intuitive choice for 3D style transfer. Early research primarily focused on texture stylization, leveraging UV mapping to transfer style-related color information onto 3D objects. For example, [PERSON] et al. [65] incorporated physical reflectance effects to achieve realistic style transfer, while [PERSON] et al. [3] applied style transfer to mesh-based indoor scene reconstructions. Additionally, [PERSON] et al. [66] introduced a text-guided approach for texture generation, editing, and transfer on meshes. However, researchers sought not only to stylize texture but also to alter geometric shape. To address this, [PERSON] et al. [67] introduced a differentiable rasterizer, allowing users to edit 3D surfaces using off-the-shelf image processing filters. Similarly, [PERSON] et al. [68] proposed a method to automatically deform triangle meshes based on text descriptions. Despite these advancements, mesh-based methods suffer from a fundamental limitation--they rely on strictly connected polygon structures. Large deformations can introduce topological inconsistencies, leading to holes or distortions in the mesh. This constraint prevents mesh-based approaches from achieving sophisticated, stroke-based rendering, limiting their flexibility in artistic style transfer. A point cloud is a discrete set of data points in 3D space, representing object geometry without explicit connectivity. Similarly to meshes, point clouds contain both spatial (position) and color attributes, making them a promising 3D style transfer representation. [PERSON] et al. [9] introduced a neural style transfer method for colored point clouds, enabling both geometry and color stylization. [PERSON] et al. [6] further refined this approach by modulating style features via linear transformation matrices, capturing finer stylistic details. [PERSON] et al. [7] extended point cloud stylization to single-image inputs, using depth estimation to infer 3D-aware content features and generate stylized novel views. Unlike meshes, point clouds do not require connectivity, making them less prone to topological issues. Consequently, point cloud-based methods often achieve better visual quality than mesh-based approaches. However, they remain sensitive to geometric reconstruction errors, particularly in complex real-world scenes, and suffer from high memory consumption and slow processing speeds. These limitations hinder their application in detailed and high-resolution stylization. A neural radiance field (NeRF) [69] is an implicit 3D representation that encodes volumetric radiance and density into a deep neural network, allowing for photo-realistic rendering from novel viewpoints. Unlike mesh-based approaches, which rely on UV maps, NeRF stores learned volumetric features, which are then mapped to RGB values during rendering. Several works have demonstrated the potential of NeRF-based style transfer [12; 13; 14; 15; 70; 71; 16; 17], [PERSON] et al. [13] introduced a nearest-neighbor feature matching approach, surpassing previous methods in both visual quality and style preservation. [PERSON] et al.