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Volume Enhancement-Anisotropic Invariant Wavelet Transform
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In
the tomography volume, the microtubule features are so weak locally that any
general averaging de-noising technique will easily smooth out the
microtubules completely. The wavelet with anisotropic basis is more
advantageous than the wavelet with isotropic basis in preserving the
elongated tubular features while removing the noise and the isotropic
features. A translation and rotation invariant transform is also desired to
improve the wavelet filtering for low SNR images.
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Anisotropic basis functions are constructed by the tensor
product of the 1-D basis functions.
Therefore, they have more combinations of different
scales/frequencies along horizontal and vertical directions. The figures
here illustrate the difference between 2D anisotropic basis
(left) and isotropic basis (right).
This makes the anisotropic basis suitable for
capturing objects with different scales along different directions.
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Anisotropic basis captures elongated object more efficiently. In
the below histograms of transform coefficients of an elongated object, the
isotropic transform (left) produces a large number of small
coefficients, close to the coefficients of noise, while the anisotropic
transform (right) produces a large number of large coefficients. Therefore
thresholding and inverse transform with anisotropic transform
better preserves elongated features and diminish noise.
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Effect of Wavelet Filtering. (left) an original slice. (right)
processed with anisotropic invariant wavelet transform, with background
structures removed and microtubules enhanced.
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