Neural Image Abstraction Using Long Smoothing B-Splines

TL;DR

This work integrates smoothing uniform B-splines into a differentiable vector graphics pipeline (DiffVG) to produce long, smooth strokes with analytic derivative-based control, including variable stroke width and support for open or closed curves. By linearly converting B-splines to cubic Bézier segments, the method remains compatible with DiffVG while enabling high-order smoothness through a tractable smoothing cost based on derivatives, e.g., $\mathcal{L}_{\mathrm{smooth}}^{d} = \frac{1}{T} \int \|\mathbf{x}^{(d)}(u)\|^2 du = \mathbf{c}^{\top} \bar{\mathbf{G}} \mathbf{c}$. The approach supports end-to-end gradient-based optimization guided by image-space losses, CLIP or diffusion priors, and a variety of stylization objectives, enabling applications such as area fillings, single-stroke abstractions, area-based vectorizations with color quantization, and text/calligram stylization. The resulting framework offers a flexible, continuous, and computationally efficient pathway to generate expressive vector graphics suited for creative design, image abstraction, and robotic reproduction, while highlighting avenues for future work in non-uniform parameterizations and broader stylistic controls.

Abstract

We integrate smoothing B-splines into a standard differentiable vector graphics (DiffVG) pipeline through linear mapping, and show how this can be used to generate smooth and arbitrarily long paths within image-based deep learning systems. We take advantage of derivative-based smoothing costs for parametric control of fidelity vs. simplicity tradeoffs, while also enabling stylization control in geometric and image spaces. The proposed pipeline is compatible with recent vector graphics generation and vectorization methods. We demonstrate the versatility of our approach with four applications aimed at the generation of stylized vector graphics: stylized space-filling path generation, stroke-based image abstraction, closed-area image abstraction, and stylized text generation.

Figures (22)

• Figure 1: Flow chart of our pipeline, all operations are differentiable.
• Figure 2: Optimization procedure. From left to right: input image with an initial spline (quintic with multiplicity $3$ on all keypoints) and subsequent optimization steps $10, 150, 300$.
• Figure 3: Comparison of different spline degrees $p$ (rows), smoothing derivative orders $d$ and smoothing weight $\lambda_{\text{smooth}}$ (columns). In each row, we let the smooting derivative to $p-1$. We quantify smoothness using the dimensionless jerk measure Hogan2009dim. Lower is smoother. We use the stylized area fill method in Section \ref{['sec:AreaFilling']} using the style image in Fig. \ref{['fig:more-s']}, left.
• Figure 4: Text combining areas generated with our stylized area filling method. Each letter is generated separately.
• Figure 5: Examples of stylized area filling for a letter "S". The images on the lower left are used to guide stylization.