Pen Trace Reconstruction with Skeleton Representation of a Handwritten Text Image

This paper presents a new approach for the pen trace reconstruction task in handwritten text images. The proposed approach is based on the skeleton representation of a binary image which provides sufficient information about the pen movement trajectory during the writing. As such, the initial problem can be viewed as a problem of constructing a specific walk in the skeleton graph covering all its edges. The proposed approach consists of splitting the graph into structural elements and estimating the pen movement direction in each of them with the resulting trace being composed of the traces of these elements.

Revisiting Leighton’s theorem with the Haar measure

Leighton’s graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton’s theorem that allows generalisations; we prove the corresponding result for graphs with fins. As a corollary we obtain pattern rigidity for free groups with line patterns, building on the work of Cashen–Macura and Hagen–Touikan. To illustrate the potential for future applications, we give a quasi-isometric rigidity result for a family of cyclic doubles of free groups.

Graph-Covering-Based Architectural Synthesis for Programmable Digital Microfluidic Biochips

Digital microfluidic technology has been extensively applied in various biomedical fields. Different from application-specific biochips, a programmable design has several advantages such as dynamic reconfigurability and general applicability. Basically, a programmable biochip divides the chip into several virtual modules. However, in the previous design, a virtual module can execute only one operation at a time. In this paper, the authors propose a new multi-functional module for programmable digital microfluidic biochips, which can execute two operations simultaneously. Moreover, they also propose a binding and scheduling algorithm for programmable biochips, which is motivated from a graph-covering problem. Experiment demonstrates that their algorithm can reduce the completion time of the applications compared with the previous approaches.