Locality-Preserving Free-Form Deformation

TL;DR

lp-FFD addresses the challenge of preserving local detail when deforming meshes via free-form deformation by simultaneously optimizing grid-handle locations and embedding the input mesh's local characteristics into the grid. It formulates a single linear optimization that combines mesh distortion, vertex constraints, grid-handle constraints, and grid regularization using $E_{ml}$, $E_{mp}$, $E_{gp}$, and $E_{gr}$ with weights $\lambda_{ml}, \lambda_{mp}, \lambda_{gp}, \lambda_{gr}$, leveraging a Laplacian $L$, a weight matrix $W$, and a transformation matrix $T$. Through iterative updates and LU-based solutions, lp-FFD achieves a favorable balance between angular and area distortions compared to direct and inverse FFD baselines, while enabling interactive direct and indirect manipulations and easy export of deformation grids. The approach also demonstrates smoother image deformations and practical applications such as screen-space editing and deformation transfer, with a user study indicating higher perceived naturalness and usability. Limitations include reduced rotational invariance and partial-stretch artifacts when manipulating with few handles, guiding future work to incorporate rotation and grid-resizing strategies and extend to broader deformation contexts.

Abstract

This paper proposes a method to estimate the locations of grid handles in free-form deformation (FFD) while preserving the local shape characteristics of the 2D/3D input model embedded into the grid, named locality-preserving FFD (lp-FFD). Users first specify some vertex locations in the input model and grid handle locations. The system then optimizes all locations of grid handles by minimizing the distortion of the input model's mesh elements. The proposed method is fast and stable, allowing the user to directly and indirectly make the deformed shape of mesh model and grid. This paper shows some examples of deformation results to demonstrate the robustness of our lp-FFD. In addition, we conducted a user study and confirm our lp-FFD's efficiency and effectiveness in shape deformation is higher than those of existing methods used in commercial software.

Figures (9)

• Figure 3: The comparison of regularization methods. The deformed results were obtained (a) without any regularization, (b) with Noh et al. noh2021inverse, and (c) with $E_{gr}$ ($\#P = 10\!\times\!10$). The angular and area distortions are computed by wang2016arap++. The model is designed with reference to Girl from sykora2009rigid.
• Figure 4: Examples of deforming 2D layered models with lp-FFD ($\#P = 10\!\times\!10$). The models are from fukusato2022vdf and fukusato2023slider respectively.
• Figure 5: Examples of deforming the Stanford Bunny ($\#V = 502$) and the Stanford Armadillo ($\#V = 1502$) with lp-FFD ($\#P = 5\!\times\!5\!\times\!5$).
• Figure 6: Comparing a deformed model and grid ($\#P = 10\!\times\!10$) using (a) Hsu et al. hsu1992ffd, (b) Schaefer et al. schaefer2006image, (c) DGP sorkine2007asap + inverse FFD noh2021inverse, and (d) lp-FFD. The model was designed with reference to Ginger Man from igarashi2005rigid.
• Figure 7: Deforming a flag image with DGP (with linear texture mapping) and lp-FFD. The number of mesh vertices $\#V$ and grid handles $\#P$ is $21$ and $25 (= 5\!\times\!5)$ respectively, and eight vertex handles (yellow points) are attached.