We introduce and study the problem MUTUAL PLANAR DUALITY, which asks for two planar graphs G1 and G2 whether G1 can be embedded such that its dual is isomorphic to G2. Our algorithmic main result is an NP-completeness proof for the general case and a linear-time algorithm for biconnected graphs. To shed light onto the combinatorial structure of the duals of a planar graph, we consider the commo...

In present PET/CT scanners, PET attenuation correction is performed by relying on the information given by CT scan. In the CT-based attenuation correction methods, dual-energy technique (DECT) is the most accurate approach, which has been limited due to the increasing patient dose. In this feasibility study, we have introduced a new method that can implement dual-energy technique with only a si...

A classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter. Since the paper of Hammons et al., there is a lot of interest in codes over rings, especially in codes over Z4 and their (usually non-linear) binary Gray map images. We show that Delsarte’s observation extends to codes over arbitr...

We investigate the First-Order Primal-Dual (FPD) algorithm of Chambolle and Pock [1] in connection with MAP inference for general discrete graphical models. We provide a tight analytical upper bound of the stepsize parameter as a function of the underlying graphical structure (number of states, graph connectivity) and thus insight into the dependency of the convergence rate on the problem struc...

We develop an efficient algorithm for the construction of common tangents between a set of Bezier curves. Common tangents are important in visibility, lighting, robot motion, and convex hulls. Common tangency is reduced to the intersection of parametric curves in a dual space, rather than the traditional intersection of implicit curves. We show how to represent the tangent space of a plane Bezi...

background: photon attenuation as an inevitable physical phenomenon influences on the diagnostic information of spect images and results to errors in accuracy of quantitative measurements. this can be corrected via different physical or mathematical approaches. as the correction equation in mathematical approaches is nonlinear, in this study a new method of linearization called ‘piece wise line...

Space is continuous. But the communities of researchers that study the cognitive map in non-humans are strangely divided, with debate over its existence found among behaviorists but not neuroscientists. To reconcile this and other debates within the field of navigation, we return to the concept of the parallel map theory, derived from data on hippocampal function in laboratory rodents. Here the...

Abstract To obtain more semantic information with small samples for medical image segmentation, this paper proposes a simple and efficient dual-rotation network (DR-Net) that strengthens the quality of both local global feature maps. The key steps DR-Net algorithm are as follows (as shown in Fig. 1). First, number channels each layer is divided into four equal portions. Then, different rotation...