The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional(3D)point processes.A point process,regard...The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional(3D)point processes.A point process,regarded as a random measure,can be expressed as a sum of Delta Dirac measures concentrated at some random points.The integration with respect to the point process leads the continuous wavelet transform of the process itself.As possible mother wavelets,we propose the application of the Mexican hat and the Morlet wavelet in order to implement the scale-angle energy density of the process,depending on the dilation parameter and on the three angles which define the direction in the Euclidean space.Such indicator proves to be a sensitive detector of any variation in the direction and it can be successfully implemented to study the isotropy or the filamentary structure in 3D point patterns.展开更多
文摘The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional(3D)point processes.A point process,regarded as a random measure,can be expressed as a sum of Delta Dirac measures concentrated at some random points.The integration with respect to the point process leads the continuous wavelet transform of the process itself.As possible mother wavelets,we propose the application of the Mexican hat and the Morlet wavelet in order to implement the scale-angle energy density of the process,depending on the dilation parameter and on the three angles which define the direction in the Euclidean space.Such indicator proves to be a sensitive detector of any variation in the direction and it can be successfully implemented to study the isotropy or the filamentary structure in 3D point patterns.
