  Vector image representation is a popular choice when editability and
flexibility in resolution are desired. However, most images are only available
in raster form, making raster-to-vector image conversion (vectorization) an
important task. Classical methods for vectorization are either domain-specific
or yield an abundance of shapes which limits editability and interpretability.
Learning-based methods, that use differentiable rendering, have revolutionized
vectorization, at the cost of poor generalization to out-of-training
distribution domains, and optimization-based counterparts are either slow or
produce non-editable and redundant shapes. In this work, we propose Optimize &
Reduce (O&R), a top-down approach to vectorization that is both fast and
domain-agnostic. O&R aims to attain a compact representation of input images by
iteratively optimizing B\'ezier curve parameters and significantly reducing the
number of shapes, using a devised importance measure. We contribute a benchmark
of five datasets comprising images from a broad spectrum of image complexities
- from emojis to natural-like images. Through extensive experiments on hundreds
of images, we demonstrate that our method is domain agnostic and outperforms
existing works in both reconstruction and perceptual quality for a fixed number
of shapes. Moreover, we show that our algorithm is $\times 10$ faster than the
state-of-the-art optimization-based method.
