Rotation of 3D volumes by Fourier-interpolated shears

In this work, we propose a new image rotation algorithm. The main feature of our approach is the symmetric reversibility, which means that when using the same algorithm for the converse operation, then the initial data is recovered exactly. To that purpose, we decompose the lattice conversion process into three successive shear operations. The translations along the shear directions are implemented by 1-D convolutions, with new appropriate fractional delay filters. Also, the method is fast and provides high-quality resampled images.

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“…Our approach can be extended in higher dimensions, e.g. using the decomposition of 3-D rotations in 4 shears [11]. …”

Section: Resultsmentioning

confidence: 99%

Fully reversible image rotation by 1-D filtering

Condat

Ville

2008

2008 15th IEEE International Conference on Image Processing

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“…Using the FFT then provides a convenient way for exactly performing this translation in the Fourier domain. However, as already pointed out in [43], this has to be done carefully. The method simply consists in computing the FFT of , then in multiplying each FFT coefficient by a complex value of the form with appropriate value , and finally going back in the spatial domain using the inverse FFT.…”

Section: B Two Extreme Cases 1) Nearest Neighbormentioning

confidence: 98%

“…The idea of using this ideal translator in combination with a decomposition in shears was proposed in [26] and [43] for 2-D and 3-D rotations, respectively. However, the infinitely long response of sinc interpolation requires much computation time and is prone to the introduction of unwanted oscillations (ringing), due to the fact that the band-limited hypothesis is actually false for most natural images.…”

Section: B Two Extreme Cases 1) Nearest Neighbormentioning

confidence: 99%

Reversible, Fast, and High-Quality Grid Conversions

Condat

Ville

Forster-Heinlein

2008

IEEE Trans. on Image Process.

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Abstract-A new grid conversion method is proposed to resample between two 2-D periodic lattices with the same sampling density. The main feature of our approach is the symmetric reversibility, which means that when using the same algorithm for the converse operation, then the initial data is recovered exactly. To that purpose, we decompose the lattice conversion process into (at most) three successive shear operations. The translations along the shear directions are implemented by 1-D fractional delay operators, which revert to simple 1-D convolutions, with appropriate filters that yield the property of symmetric reversibility. We show that the method is fast and provides high-quality resampled images. Applications of our approach can be found in various settings, such as grid conversion between the hexagonal and the Cartesian lattice, or fast implementation of affine transformations such as rotations.

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“…Volume rotations can be performed either in real space or Fourier space. We elected to compute volume rotations in real space to avoid interpolation problems observed when performing Fourier space rotations (Welling et al, 2006). Cross-correlations can also be computed in either real space or Fourier space.…”

Section: Testsmentioning

confidence: 99%

Projection-based volume alignment

Snapp

Ruíz

et al. 2013

Journal of Structural Biology

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When heterogeneous samples of macromolecular assemblies are being examined by 3D electron microscopy (3DEM), often multiple reconstructions are obtained. For example, subtomograms of individual particles can be acquired from tomography, or volumes of multiple 2D classes can be obtained by random conical tilt reconstruction. Of these, similar volumes can be averaged to achieve higher resolution. Volume alignment is an essential step before 3D classification and averaging. Here we present a projection-based volume alignment (PBVA) algorithm. We select a set of projections to represent the reference volume and align them to a second volume. Projection alignment is achieved by maximizing the cross-correlation function with respect to rotation and translation parameters. If data are missing, the cross-correlation functions are normalized accordingly. Accurate alignments are obtained by averaging and quadratic interpolation of the cross-correlation maximum. Comparisons of the computation time between PBVA and traditional 3D cross-correlation methods demonstrate that PBVA outperforms the traditional methods. Performance tests were carried out with different signal-to-noise ratios using modeled noise and with different percentages of missing data using a cryo-EM dataset. All tests show that the algorithm is robust and highly accurate. PBVA was applied to align the reconstructions of a subcomplex of the NADH: ubiquinone oxidoreductase (Complex I) from the yeast Yarrowia lipolytica, followed by classification and averaging.

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Rotation of 3D volumes by Fourier-interpolated shears

Cited by 14 publications

References 18 publications

Fully reversible image rotation by 1-D filtering

Fully reversible image rotation by 1-D filtering

Reversible, Fast, and High-Quality Grid Conversions

Projection-based volume alignment

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