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Vector graphics has been employed in a wide variety of applications due to its scalability and editability. Editability is a high priority for artists and designers who wish to produce vector-based graphical content with user interaction. In this paper, we introduce a new vector image representation based on piecewise smooth subdivision surfaces, which is a simple, unified and flexible framework that supports a variety of operations, including shape editing, color editing, image stylization, and vector image processing. These operations effectively create novel vector graphics by reusing and altering existing image vectorization results. Because image vectorization yields an abstraction of the original raster image, controlling the level of detail of this abstraction is highly desirable. To this end, we design a feature-oriented vector image pyramid that offers multiple levels of abstraction simultaneously. Our new vector image representation can be rasterized efficiently using GPU-accelerated subdivision. Experiments indicate that our vector image representation achieves high visual quality and better supports editing operations than existing representations.