1. The document proposes a method called optimized gradient meshes to vectorize raster images. Gradient meshes represent images using rectangular Ferguson patches with control points and derivatives that define color and geometry. 2. An optimization process minimizes an energy function to fit the gradient mesh to the input image, making the mesh smoother and adhering it to user-guided lines and boundaries. This is posed as a non-linear least squares problem solved using Levenberg-Marquardt. 3. Results show optimized gradient meshes can reconstruct images with high fidelity while remaining compact and scalable representations that are easy to edit compared to the input raster images.