32860736
Nonrigid motion recovery for 3D surfaces
We present a spline-based nonrigid motion and point correspondence recovery method for 3D surfaces. This method is based on differential geometry. Shape information is used to recover the point correspondences. In contrast to the majority of shape-based methods, which assume that shape (unit normal, curvature) changes are minimum after motion, our method focuses on the nonrigid relationship between before-motion and after-motion shapes. This nonrigid shape relationship is described by modeling the underlying nonrigid motion; we model it as a spline transformation, which has global control over the entire motion field along with the local deformation integrated within. This provides our method certain advantages over some pure differential geometric methods, which also utilize the nonrigid shape relationship but only work on local areas without a global control. For example, motion regularity is hard to implement in these pure differential geometric methods but is not a problem when the motion field is controlled by a spline transformation. The orthogonal parameterization requirement of the nonrigid shape relationship has to be approximated in these previous methods but is easy to meet in our method. Furthermore, the small deformation constraint introduced by the previous works is relaxed in our method. Experiments on both synthetic and real motions have been conducted. The quantitative and qualitative evaluations of our method are presented. The application of our method to the human tongue motion analysis is also presented in this paper.
33110840
A Level Set Approach for Shape Recovery of Open Contours
In this paper, a geometric deformable model for shape recovery of open contours in noisy images is presented. We use two level set functions to model the open contour and find the end points of the open contour as the intersection of the two level set functions. The evolutions of both level set functions do not depend on the gradient of the images, as in the classical geometric deformable models, but are decided by a region-based band velocity. The band velocity is different from region information introduced by other deformable models which can only be used to find the closed contours in images, it is designed for evolutions of both closed and open contours and particularly unique for contours which are open and do not enclose any region. Prior shape information is also integrated into the contour evolution process, which prevents two level set functions from intersecting at other places than at the contour end points. With the described method open contours can be recovered from noisy images. Successful experiments on several data sets are presented in this paper.
3605809
Performance evaluation for energy efficient topologic control in ad hoc wireless networks
Minimizing total energy to keep an ad hoc wireless network symmetrically connected is an NP-hard problem. Recently, several greedy approximations have been proposed, based on k-restricted decompositions of the network. Their performance ratios are established through estimations of the least upper bound ρk for the ratio between total powers of best possible k-restricted decomposition and the optimal solution. In this paper, we determine the exact value of ρk for all k.
8308439
From Gene Trees to Species Trees
This paper studies various algorithmic issues in reconstructing a species tree from gene trees under the duplication and the mutation cost model. This is a fundamental problem in computational molecular biology. Our main results are as follows. 
A linear time algorithm is presented for computing all the losses in duplications associated with the least common ancestor mapping from a gene tree to a species tree. This answers a problem raised recently by Eulenstein, Mirkin, and Vingron [J. Comput. Bio., 5 (1998), pp. 135--148]. The complexity of finding an optimal species tree from gene trees is studied. The problem is proved to be NP-hard for the duplication cost and for the mutation cost. Further, the concept of reconciled trees was introduced by Goodman et al. and formalized by Page for visualizing the relationship between gene and species trees. We show that constructing an optimal reconciled tree for gene trees is also NP-hard. Finally, we consider a general reconstruction problem and show it to be NP-hard even for the well-known nearest neighbor interchange distance. A new and efficiently computable metric is defined based on the duplication cost. We show that the problem of finding an optimal species tree from gene trees is NP-hard under this new metric but it can be approximated within factor 2 in polynomial time. Using this approximation result, we propose a heuristic method for finding a species tree from gene trees with uniquely labeled leaves under the duplication cost. Our experimental tests demonstrate that when the number of species is larger than 15 and gene trees are close to each other, our heuristic method is significantly better than the existing program in Page's GeneTree 1.0 that starts the search from a random tree.
6156793
Optimum Robot Control for 3D Virtual Fixture in Constrained ENT Surgery
In ENT surgery, the operating volume is very limited. This is especially true in sinus surgery, when the instrument passes through the sinus cavity to reach the pathological area. The sinus bones impose geometric constraints on the work volume. During the surgery, the surgeon needs to take care of the motion of the instrument tip to accomplish some delicate procedure; meanwhile he/she needs to avoid hitting anatomic constraints. In this paper, we present a method to assist the path following task in a constrained area. We project instrument tip motion, boundary information on the joint displacement via robot kinematics, and then use a constrained quadratic optimization algorithm to compute the optimal set of corresponding joint displacements. In the preliminary study, we show that the optimization constrained control can avoid collision with geometric constraints on the work volume, while keeping the precision of the tool motion.
43310555
Twist-Rotation Transformations of Binary Trees and Arithmetic Expressions
The paper studies the computational complexity and efficient algorithms for the twist?rotation transformations of binary trees, which is equivalent to the transformation of arithmetic expressions over an associative and commutative binary operation. The main results are (1) a full binary tree with n labeled leaves can be transformed into any other in at most 3nlogn+2n twist and rotation operations, (2) deciding the twist?rotation distance between two binary trees is NP-complete, and (3) the twist?rotation transformation can be approximated with ratio 6logn+4 in polynomial time for full binary trees with n uniquely labeled leaves.
15861046
A Survey on Topology issues in Wireless Sensor Network
Topology issues have received more and more attentions in Wireless Sensor Networks (WSN). While WSN applications are normally optimized by the given underlying network topology, another trend is to optimize WSN by means of topology control. A number of approaches have been invested in this area, such as topology directed routing, cooperating schemes, sensor coverage based topology control and network connectivity based topology control. Most of the schemes have proven to be able to provide a better network monitoring and communication performance with prolonged system lifetime. In this survey paper, we provide a full view of the studies in this area. By summarizing previous achievements and analyzing existed problems, we also point out possible research directions for future work .