Image processing and data analysis: the multiscale approach
Image processing and data analysis: the multiscale approach
Astronomical Image and Data Analysis (Astronomy and Astrophysics Library)
Astronomical Image and Data Analysis (Astronomy and Astrophysics Library)
The curvelet transform for image denoising
IEEE Transactions on Image Processing
A sampling theory for compact sets in Euclidean space
Proceedings of the twenty-second annual symposium on Computational geometry
Wavelet and curvelet moments for image classification: Application to aggregate mixture grading
Pattern Recognition Letters
Combining local filtering and multiscale analysis for edge, ridge, and curvilinear objects detection
IEEE Transactions on Image Processing
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Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy distribution and discriminate the different cosmological models. We present in this paper multiscale geometric transforms sensitive to clusters, sheets, and walls: the 3D isotropic undecimated wavelet transform, the 3D ridgelet transform, and the 3D beamlet transform. We show that statistical properties of transform coefficients measure in a coherent and statistically reliable way, the degree of clustering, filamentarity, sheetedness, and voidedness of a data set.