This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept ...This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.展开更多
In bi-directional three-node cooperation, one regenerative strategy with network coding and power optimization is proposed for system sum-rate under a total energy constraint. In this paper, the network coding and pow...In bi-directional three-node cooperation, one regenerative strategy with network coding and power optimization is proposed for system sum-rate under a total energy constraint. In this paper, the network coding and power optimization are applied to improve system sum-rate. But max-rain optimization problem in power allocation is a NP-hard problem. In high Signal-to-Noise Ratio regime, this NP-hard problem is transformed into constrained polynomial optimization problem, which can be computed in polynomial time. Although it is a suboptimal solution, numerical simulations show that this strategy enhances the system sum-rate up to 45% as compared to a traditional four-phase strategy, and up to 13% as compared to the three-phase strategy without power optimization.展开更多
For vision-based mobile robot navigation, images of the same scene may undergo a general affine transformation in the case of significant viewpoint changes. So, a novel method for detecting affine invariant interest p...For vision-based mobile robot navigation, images of the same scene may undergo a general affine transformation in the case of significant viewpoint changes. So, a novel method for detecting affine invariant interest points is proposed to obtain the invariant local features, which is coined polynomial local orientation tensor(PLOT). The new detector is based on image local orientation tensor that is constructed from the polynomial expansion of image signal. Firstly, the properties of local orientation tensor of PLOT are analyzed, and a suitable tuning parameter of local orientation tensor is chosen so as to extract invariant features. The initial interest points are detected by local maxima search for the smaller eigenvalues of the orientation tensor. Then, an iterative procedure is used to allow the initial interest points to converge to affine invariant interest points and regions. The performances of this detector are evaluated on the repeatability criteria and recall versus 1-precision graphs, and then are compared with other existing approaches. Experimental results for PLOT show strong performance under affine transformation in the real-world conditions.展开更多
文摘This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.
基金Supported by the High Technology Research and Development Program of China (No. 2006AA01Z282 2007CB310608)
文摘In bi-directional three-node cooperation, one regenerative strategy with network coding and power optimization is proposed for system sum-rate under a total energy constraint. In this paper, the network coding and power optimization are applied to improve system sum-rate. But max-rain optimization problem in power allocation is a NP-hard problem. In high Signal-to-Noise Ratio regime, this NP-hard problem is transformed into constrained polynomial optimization problem, which can be computed in polynomial time. Although it is a suboptimal solution, numerical simulations show that this strategy enhances the system sum-rate up to 45% as compared to a traditional four-phase strategy, and up to 13% as compared to the three-phase strategy without power optimization.
基金Projects(61203332,61203208) supported by the National Natural Science Foundation of China
文摘For vision-based mobile robot navigation, images of the same scene may undergo a general affine transformation in the case of significant viewpoint changes. So, a novel method for detecting affine invariant interest points is proposed to obtain the invariant local features, which is coined polynomial local orientation tensor(PLOT). The new detector is based on image local orientation tensor that is constructed from the polynomial expansion of image signal. Firstly, the properties of local orientation tensor of PLOT are analyzed, and a suitable tuning parameter of local orientation tensor is chosen so as to extract invariant features. The initial interest points are detected by local maxima search for the smaller eigenvalues of the orientation tensor. Then, an iterative procedure is used to allow the initial interest points to converge to affine invariant interest points and regions. The performances of this detector are evaluated on the repeatability criteria and recall versus 1-precision graphs, and then are compared with other existing approaches. Experimental results for PLOT show strong performance under affine transformation in the real-world conditions.
