Abstract We present a fully automated technique that segments raster images into smooth shaded regions and reconstructs them using an optimal mix of solid fills, linear gradients, and radial gradients. Our method leverages a novel discontinuity‐aware segmentation strategy and gradient reconstruction algorithm to accurately capture intricate shading details and produce compact Bézier curve representations. Extensive evaluations on both designer‐created art and generative images demonstrate that our approach achieves high visual fidelity with minimal geometric complexity and fast processing times. This work offers a robust and versatile solution for converting detailed raster images into scalable vector graphics, addressing the evolving needs of modern design workflows.

This paper shows that the satisfiability problems for a bounded fragment of probabilistic CTL (called bounded PCTL) and an extension of the modal μ-calculus with probabilistic quantification over next-modalities (called PμTL) are decidable. For bounded PCTL we provide an NEXPTIME-algorithm for the satisfiability problem and show that the logic has a small model property where the model size is independent from the probability bounds in the formula. We show that the satisfiability problem of a simple sub-logic of bounded PCTL is PSPACE-complete. We prove that PμTL has a small model property and that a decision procedure using 2 player parity games can be employed for the satisfiability problem of PμTL. These results imply that PμTL and qualitative PCTL formulas with only thresholds >0 and =1---are incomparable. We also establish that---in contrast to PCTL---every satisfiable PμTL-formula has a rational model, a model with rational probabilities only.