Persistence-based resolution-independent meshes of superpixels

The over-segmentation problem is to split a pixel-based image into a smaller number of superpixels that can be treated as indecompasable regions to speed up higher level image processing such as segmentation or object detection. A traditional superpixel is a potentially disconnected union of square pixels, which can have complicated topology (with holes) and geometry (highly zigzag boundaries). This paper contributes to new resolution-independent superpixels modeled as convex polygons with straight-line edges and vertices with real coordinates not restricted to a fixed pixel grid. Any such convex polygon can be rendered at any resolution higher than in original images, hence superpixels are resolution-independent. The key difficulty in obtaining resolution-independent superpixels is to find continuous straight-line edges, while classical edge detection focuses on extracting only discrete edge pixels. The recent Persistent Line Segment Detector (PLSD) avoids intersections and small angles between line segments, which are hard to fix before a proper polygonal mesh can be constructed. The key novelty is an automatic selection of strongest straight-line segments by using the concept of persistence from Topological Data Analysis, which allows to rank segments by their strength. The PLSD performed well in comparison with the only past Line Segment Detector Algorithm (LSDA) on the Berkeley Segmentation Database of 500 real-life images. The PLSD is now extended to the Persistent Resolution-Independent Mesh (PRIM)