In this sequel to [3] we try to give a comprehensive account of the “connected components” G00 and G000 as well as the various quotients G/G00, G/G000, G00/G000, for G a group definable in a (saturated) ominimal expansion of a real closed field. Key themes are the structure of G00/G000 and the problem of “exactness” of the G 7→ G00 functor. We prove that the examples produced in [3] are typical...

Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. Persistence barcode is a graphical representation of such information. A filtration might be determined by time in a set of spatiotemporal data, but classical methods for computing persistent homology do not respect the fact that we can not move backwards in time. In this paper,...

We present an algorithm for extracting the perimeter resolution cells of 8-connected components as chain-encoded sequences.

We propose an efficient method for labeling connected components in bi-level images. The proposed algorithm uses a Deterministic Finite Automaton to obtain chain codes and label component boundaries, and use a tracing technique that is simpler than existing methods. Experiments on various types of images show that the proposed method improves contour tracing efficiency.

In this paper we consider the problem of computing the 2-vertex-connected components (2-vccs) of directed graphs. We present two new algorithms for solving this problem. The first algorithm runs in O(mn) time, the second in O(nm) time. Furthermore, we show that the old algorithm of Erusalimskii and Svetlov runs inO(nm) time. In this paper, we investigate the relationship between 2-vccs and domi...

We consider a family of random graphs with a given expected degree sequence. Each edge is chosen independently with probability proportional to the product of the expected degrees of its endpoints. We examine the distribution of the sizes/volumes of the connected components which turns out depending primarily on the average degree d and the secondorder average degree d̃. Here d̃ denotes the weigh...

Segmentation is an important step in many perception tasks, such as object detection and recognition. We present an approach to organized point cloud segmentation and its application to plane segmentation, and euclidean clustering for tabletop object detection. The proposed approach is efficient and enables real-time plane segmentation for VGA resolution RGB-D data. Timing results are provided ...