Vectorization of Line Drawings via Polyvector Fields

Abstract

Input imageFrame eld Final result Fig. 1. Given a possibly noisy grayscale bitmap image, we compute a frame field aligned with the directions on the image, superimposing multiple directions around sharp corners as well as X-and T-junctions. We then use this frame field to extract the drawing topology and create the final vectorization with the computed topology. Frame field computation (shown for a subset of pixels in the upper zoom and the full field in the lower one) is the key component of the system. The frame field disambiguates X-and T-junctions even in the noisy areas, allowing tracing to be straightforward and robust. Input images are from www.easy-drawings-and-sketches.com, ©Ivan Huska.Image tracing is a foundational component of the work ow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean line drawings, modern algorithms o en fail to faithfully vectorize junctions, or points at which curves meet; this produces vector drawings with incorrect connectivity. is subtle issue undermines the practical application of vectorization tools and accounts for hesitance among artists and engineers to use automatic vectorization so ware. To address this issue, we propose a novel image vectorization method based on state-of-the-art mathematical algorithms for frame eld processing. Our algorithm is tailored speci cally to disambiguate junctions without sacri cing quality.

Inertia‐based Fast Vectorization of Line Drawings

“…in the case of the cat nose in Figure 10. Some weaknesses of our method compared to Bessmeltsev et al [BS18] can be seen at the jagged lines like animal hair in the images. This weakness is caused by the grid line that does not intersect with these small elements; however, our method reproduces these details but with the lack of some connections between them.…”

Learning to Approximate Directional Fields Defined Over 2D Planes

“…Thus, we obtain an intuitive interpretation of field components {u, v}; the PolyVector structure allows us to express the directionality of curves. A similar parameterization is adopted in [2].…”

“…To become independent to the order of primitives and the chosen sign of a tangent, we follow a well-known workaround and perform variable substitution c 0 = u 2 v 2 , c 2 = −(u 2 + v 2 ), which determines two vectors u and v up to relabeling and sign [2]. The final vector field representation has four parameters: two complex coordinates for each of the variables c 0 and c 2 .…”

“…In the area of 2D and 3D computer graphics and geometry processing, directional fields have been utilized for a vast number of applications, such as mesh generation using distinct 3D data modalities [4,6], texture mapping [16], and image-based tracing of line drawings [2], to name a few. Appearing datasets [10] open more possibilities for this setup with various problems to solve.…”

“…However, obtaining a robust approximation of a directional field from raw input data is a challenging problem in many instances. Current approaches to computing directional fields require optimization of non-trivial targets with custom optimizers (e.g., ADMM, L-BFGS, and their versions), which may be computationally demanding and may yield unstable solutions, where significant noise, occlusions, or gaps exist in the data [2].…”