Inverse Diffusion Curves using Shape Optimization

TL;DR

This paper presents a novel shape optimization method for inverse diffusion curves, enabling automatic creation of diffusion curve images that closely match user-provided color fields with improved curve quality.

Contribution

It introduces an iterative shape derivative-based algorithm for optimizing diffusion curve geometry, enhancing image approximation and user control over curve complexity.

Findings

Produces clean, well-shaped diffusion curves

Achieves close approximation to input color fields

Provides user-controlled regularization of curve complexity

Abstract

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.