共查询到17条相似文献,搜索用时 296 毫秒
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针对一般的连续参数曲线,提出一种快速计算曲线间Hausdorff距离的方法.由于曲线的近似折线能很好的表示曲线,所以,许多软件中,采用曲线的近似折线绘制曲线.为此,证明了在任意给定误差范围下,可以将曲线间的Hausdorff距离转化为折线间的Hausdorff距离,进一步转化为点到线段间的距离进行计算,并辅之必要的剪枝策略和增量式算法以提高计算效率.该方法计算速度快,逼近度高,基本解决了参数曲线间Hausdorff距离的计算问题,在几何设计、图像匹配、图像识别等领域有广泛应用. 相似文献
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以分形理论为依据,根据分形几何描绘自然景物的基本思想,论述了一类分形曲线的递归算法和生成过程,通过参数控制,研究了如何使一条直线段生成了3种不同结构的分形曲线,运用C 编程绘出3种不同结构的分形曲线的图形;同时对Hausdorff维数理论进行了深入的研究与探讨,并且以Hausdorff维数理论为依据分析了由直线分形演绎生成的分形曲线的维数,把维数理论与实践应用相结合。本研究为分形曲线的生成和实践应用提供了理论依据。 相似文献
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讨论了度量空间上的位势空间,并利用容量的概念建立其与Hausdorff测度之间的联系. 相似文献
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分形曲线的自仿射性及其工程应用是一个重要研究课题.标度指数是刻画自仿射分形曲线的特征值,Matsushita、Nikora、Sapozhnikov等分别根据方差、测度和对数关联积分提出标度指数的算法.本文分析了上述算法的不足,使用坐标和测度建立了一个新算法.本算法符合分形原理,可较好反映曲线的自仿射性和纵横方向的不同变化特征,计算过程简单明了,便于工程应用.最后,我们应用上述四种算法计算了中国下荆江河道的标度指数,揭示了河道的自仿射性和横向摆动特征,对河道整治工程具有重要参考意义. 相似文献
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本文考虑由一类线性迭代系统产生的多分非均匀Cantor集,讨论了这类非均匀Cantor集的几何结构,获得了相关的性质,给出了这类多分非均匀Cantor集Hausdorff测度的一个充分必要条件。 相似文献
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复杂场景下的变形目标跟踪 总被引:1,自引:0,他引:1
提出一种新的针对目标变形的模板匹配跟踪方法。对于跟踪序列图像中的目标,采用均值平移方法对原图像进行滤波平滑后提取边缘;定义一种点到邻域的广义距离测度,增强了匹配的容错性,与计算 Hausdorff 距离相比计算量大为减少;采用边缘相似点的距离均值和方差作为匹配的相似测度和置信准则,进一步降低了匹配的误差;提出在 8 邻域内基于马尔可夫模型的启发式规则修正模板策略,阻止跟踪点漂移。实验结果表明,该方法能以高达 98%的正确匹配率对复杂场景序列图像中的运动目标进行稳定跟踪。 相似文献
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Bert Jüttler Pavel Chalmovianský 《Applicable Algebra in Engineering, Communication and Computing》2007,18(1-2):151-168
We describe a method to approximate a segment of the intersection curve of two implicitly defined surfaces by a rational parametric
curve. Starting from an initial solution, the method applies predictor and corrector steps in order to obtain the result.
Based on a preconditioning of the two given surfaces, the corrector step is formulated as an optimization problem, where the
objective function approximates the integral of the squared Euclidean distance of the curve to the intersection curve. An
SQP-type method is used to solve the optimization problem numerically. Two different predictor steps, which are based on simple
extrapolation and on a differential equation, are formulated. Error bounds are needed in order to certify the accuracy of
the result. In the case of the intersection of two algebraic surfaces, we show how to bound the Hausdorff distance between
the intersection curve (an algebraic space curve) and its rational approximation. 相似文献
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Length-yardstick relation was used for measurement of the fractal dimension and the length of the initiator of Koch curves. It was found that the higher the fractal dimension and then the fracture toughness, the shorter the length of the initiator of the Koch curve for the crack lines would be. 相似文献
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Bartłomiej Skorulski 《Dynamical Systems: An International Journal》2014,29(3):369-398
We prove several results establishing real analyticity of Hausdorff dimensions of limit sets of analytic families of conformal graph directed Markov systems. With this tool and with iterated function systems resulting from the existence of nice sets in the sense of Rivera-Letelier, we prove that the canonical Hausdorff measure restricted to the radial Julia set of a tame meromorphic function (can be rational) is σ-finite and that the Hausdorff dimension of the radial Julia sets for fairly general families of meromorphic functions (can be rational) is real analytic. 相似文献
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Theoretical and numerical analysis of the resonant behaviour of the Minkowski fractal dipole antenna
The resonant behaviour and the size reduction capabilities of the Minkowski fractal dipole antenna are investigated. The antenna is analysed at each resonant frequency by considering the radiation efficiency and the fractional bandwidth. Besides, a method for deriving the approximate positions of the resonant frequencies of the Minkowski dipole at each fractal iteration is proposed. The presented analysis is based on the inductive circuit model and is validated by simulations. Moreover, in order to quantify the advantages provided by the Minkowski geometry, the proposed study performs a comparison with the generalised Koch dipole in terms of fractal dimension and lacunarity. 相似文献
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Sierpinski垫片的Hausdorff测度的下界 总被引:2,自引:0,他引:2
徐士英 《中国计量学院学报》2000,11(1):8-11
本文证明 Sierpinski垫片 S的 H ausdorff测度满足 Hs(S)≥ 13 相似文献
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对由自相似压缩映射生成的递归集,引入了一种网测度α(E),证明了它与Hausdorff测度最多在一点上不相等.由此给出了这类递归集的Hausdorff维数。简化了部分分形集维数的计算,并以例子说明. 相似文献