We present an improved version of the Simple Linear Iterative Clustering (SLIC) superpixel segmentation. Unlike SLIC, our algorithm is non-iterative, enforces connectivity from the start, requires lesser memory, and is faster. Relying on the superpixel boundaries obtained using our algorithm, we also present a polygonal partitioning algorithm. We demonstrate that our superpixels as well as the polygonal partitioning are superior to the respective state-of-the-art algorithms on quantitative benchmarks.