Identification of fingers on the basis of Hamiltonian cycles of local features

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引用次数: 1

Abstract

The problem of finding the lengths of Hamiltonian cycles on complex graphs is considered. The task has such practical applications as determining the optimal routes (salesman's task), identifying graph structures (recognizing the characteristics of local features of biometric objects), etc. When solving the task of verification of biometric samples, the problems of addition or disappearance of reference points, deformation of the distances between them, the appearance of linear and angular displacements of the whole sample emerges. Using the method described in the article, the problem of displacements can be eliminated, as the solution is stable when shuffling of the points is present. Moreover, it is possible to obtain reference plans with the same stability. Obtaining them requires less computational complexity and provides greater recognition accuracy. A detailed description of the problem solution based on the application of the method of branches and boundaries for symmetric matrices of graphs, which describe the distribution of local features in the images of fingerprints, has been proposed. It is known that a guaranteed solution for finding the length of the Hamiltonian cycle for an arbitrary graph of the planar distribution of points is possible only by using an exhaustive search. However, the computational complexity of such a search is not acceptable. The method of branches and boundaries, like all existing methods of directional search, does not guarantee finding a solution with an arbitrarily large dimension of the graph. Therefore, a method of decomposing graphs is proposed, which allows reducing a complex problem to a set of simpler ones. That allows for a significant reduction in computational complexity. The relative invariance of the metrics of Hamiltonian cycles to probabilistic shifts, which are characteristic of biometric pattern recognition problems, has been shown.
基于局部特征哈密顿循环的手指识别
研究了复图上哈密顿环长度的求解问题。该任务具有确定最优路线(推销员任务)、识别图结构(识别生物特征物体的局部特征)等实际应用。在解决生物特征样品的验证任务时,会出现参考点的增加或消失、参考点之间距离的变形、整个样品的线位移和角位移的出现等问题。使用文中描述的方法,可以消除位移问题,因为当存在点的洗牌时解是稳定的。此外,还可以获得具有相同稳定性的参考方案。获得它们需要较少的计算复杂度,并提供更高的识别精度。基于描述指纹图像局部特征分布的对称图矩阵的分支和边界方法,给出了问题求解的详细描述。已知对于任意平面点分布的哈密顿循环长度的保证解只有用穷举搜索才有可能。然而,这种搜索的计算复杂度是不可接受的。分支和边界的方法,像所有现有的定向搜索方法一样,不能保证找到任意大维图的解。因此,提出了一种分解图的方法,可以将一个复杂的问题简化为一组更简单的问题。这样可以显著降低计算复杂度。哈密顿循环的度量对概率位移的相对不变性,这是生物特征模式识别问题的特征,已经被证明。
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