Image partitioning into convex polygons

Abstract

The over-segmentation of images into atomic regions has become a standard and powerful tool in Vision. Traditional superpixel methods, that operate at the pixel level, cannot directly capture the geometric information disseminated into the images. We propose an alternative to these methods by operating at the level of geometric shapes. Our algorithm partitions images into convex polygons. It presents several interesting properties in terms of geometric guarantees, region compactness and scalability. The overall strategy consists in building a Voronoi diagram that conforms to preliminarily detected line-segments, before homogenizing the partition by spatial point process distributed over the image gradient. Our method is particularly adapted to images with strong geometric signatures, typically man-made objects and environments. We show the potential of our approach with experiments on large-scale images and comparisons with state-of-the-art superpixel methods.

Field‐aligned Quadrangulation for Image Vectorization

“…Image partition at pixel level requires each element is a small cluster of connected pixels with similar colors. The shape of elements should be regular, and sometimes be convex [DL15], which means that each element is a convex polygon. Unfortunately, partitioning an image into convex polygons is challenging to meet boundary adherence especially partitioning into quad-mesh.…”

“…Fig. 13(c) is the result (a) CONPOLY [DL15] (b) N-cuts [SM00] (c) Our method of image reconstruction, and it takes 0.41 seconds for a typical mesh with 1378 patches in the resolution 258*262.…”

Towards Large-Scale City Reconstruction from Satellites

“…[14] at the pixel scale gives dense and structure-free 3D models. By postprocessing a DSM with Voronoi clustering [27] or with structure-aware mesh simplification [33], we obtain more compact meshes, but the building structure cannot be not restored. Our output model is both compact and structure-aware (see the low number of principal directions in the distribution of output normals).…”

“…Our strategy is thus to couple these elevation estimates with the geometric information contained in the polygonal partitions to retrieve building contours even for partially occluded roofs. We denote by P l and P r the polygonal partitions produced by [27] for the left and the right images respectively. P l ⊂ P l represents the set of polygons in P l with elevation estimates.…”

“…We rather analyze satellite images at the scale of atomic regions, whose efficiency has been demonstrated in shape extraction [23] or stereo matching [17]. Instead of using traditional superpixel methods, we rely on a geometric algorithm that decomposes images into atomic convex polygons [27]. This algorithm is applied independently on both stereo images with a polygon size fixed to 5 pixels (average distance to polygon centroids to its edges) in our experiments.…”