## 2 Related Work  
The process of image stylization consists of mapping a content image and a specific style to an output image. This problem has been a significant field of research within Visual Computing for more than two decades, beginning with non-photorealistic rendering (NPR) [7] and continuing with NST and even more recently with DST. Figure 1: “The Persistence of Memory” by [PERSON]. Non-photorealistic rendering includes image synthesis from 3D objects, media, and substrate emulation, but we choose to focus on NPR [7] from images. Early algorithms aimed to map patches of pixels into brush strokes [7]. Later, the mapping targeted more notable regions. Although less common, higher forms of abstraction have been tackled using ad hoc approaches that emulate movements such as Cubism [8] and artists such as [PERSON] [9]. Early style transfer techniques were based on algorithmic feature generation [7]. [PERSON] et al. [1] introduced the notion of NST, bringing a remarkable improvement to the state-of-the-art by weighing the features of a Convolutional Neural Network (CNN) trained for object recognition. In his work, [PERSON] represented the style using the Gram matrix of the extracted feature tensors from shallow layers of the network and the content by a feature vector extracted from a deeper layer. With respect to these variables, an output image would be created by simultaneously minimizing loss functions for both the style and the content representations. Subsequent works brought improvements by including spatial [10] or semantic [11] constraints, MRF priors [12], or by replacing the style or content representations [13]. Current state-of-the-art NST [1, 12, 13, 14] techniques have become increasingly more adept at faithfully reproducing low-context features such as brush strokes and color palettes. However, their general inability to recreate high-context information such as object deformations and projective changes severely limits the quality of the reimagined artworks. This observation has prompted researchers to explore novel style transfer methods which incorporate geometric deformations. While the body of literature regarding geometric NST is substantially more limited, recent publications have demonstrated the efficacy of this approach by consistently outperforming texture-based NST. Some of the first methods have been optimized for specific types of content such as faces [2] and text [3]. Recent works [4, 15, 16] have focused on developing general-purpose methods that are domain/class agnostic. Judging by the results presented in [16], this increased flexibility does not incur significant decreases in quality. In DST, in Ref. [4], a novel optimization-based geometric style transfer technique was presented. This approach leverages NBB to find cross-domain correspondences between the provided content and the style images. Low-quality matches are further filtered using a heuristic based on NBB activation strength. This sparse set of displacements is extended to a full displacement field via Thin Plate Spline interpolation (TPS). The Style Transfer by Relaxed Optimal Transport and Self-Similarity (STROTSS) [13] texture style transfer loss is augmented with an additional warping term. This enables joint optimization of both style and geometric deformations. It should be noted that, while this approach can produce high-quality results, it is also computationally expensive. The approaches described in [15, 16] attempt to address the shortcomings of DST. In both cases, a general-purpose model is used to obtain a mapping from a 4D function of distance measurements to a 2D warp field. This approach is significantly faster in practice, because the mapping is learned offline. The main difference between the two lies in how the warp field is represented. The first uses a parametric warp function based on affine and bi-quadratic wraps, while the latter provides a more flexible implementation allowing arbitrary deformations as in DST.