H2O: Reversible Hexagonal-Orthogonal Grid Conversion by 1-D Filtering

Condat, Laurent; Forster-Heinlein, Brigitte; Ville, Dimitri Van De

doi:10.1109/icip.2007.4379095

Cited by 9 publications

(9 citation statements)

References 9 publications

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“…For instance, our choice of shears for the Cartesian to hexagonal conversion, given by (24), provides a circle with radius , which is close to the maximal value of achievable by true 2-D sinc interpolation. This value is also about 4% larger than the radius associated to the decomposition proposed in [29], which uses one diagonal shear. So according to this criterion, the decomposition in (24) is superior.…”

Section: Shuffle the Frequenciesmentioning

confidence: 82%

“…The asymmetry is low, however. With respect to this specific issue, the decomposition proposed in [29] turns out to provide more symmetrical results, but the same resampling experiments give PSNRs lower by about 1 dB in comparison with the decomposition proposed in the present work, without diagonal shear.…”

Section: A Hexagonal-to-cartesian Resamplingmentioning

confidence: 85%

“…For example, in Fig. 4(b), the decomposition that uses one diagonal shear, as proposed in [29], is shown, resulting in a more symmetrical repartition of the Nyquist region. (55) where the are the vectors along which the shears are applied.…”

Section: Shuffle the Frequenciesmentioning

confidence: 99%

“…Finally, we mention that we proposed a different decomposition for the conversion from the hexagonal to the Cartesian lattice in [29], using the three natural directions of the hexagonal lattice. This amounts to performing translations along not only the rows and columns, but also the diagonals of the image.…”

Section: B Conversion Between Cartesian and Hexagonal Latticesmentioning

confidence: 99%

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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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Section: Shuffle the Frequenciesmentioning

confidence: 82%

Section: A Hexagonal-to-cartesian Resamplingmentioning

confidence: 85%

Section: Shuffle the Frequenciesmentioning

confidence: 99%

Section: B Conversion Between Cartesian and Hexagonal Latticesmentioning

confidence: 99%

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Reversible, Fast, and High-Quality Grid Conversions

Condat

Ville

Forster-Heinlein

2008

IEEE Trans. on Image Process.

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“…With regards to the resampling procedure, there are alternative interpolation schemes and approaches. 37 However, the good agreement in presampled MTF prior to and after resampling (Fig. 10) suggests that the benefits of these alternative resampling schemes may be limited and need to be investigated.…”

Section: Discussionmentioning

confidence: 99%

Photon-counting hexagonal pixel array CdTe detector: Spatial resolution characteristics for image-guided interventional applications

et al. 2016

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Purpose: High-resolution, photon-counting, energy-resolved detector with fast-framing capability can facilitate simultaneous acquisition of precontrast and postcontrast images for subtraction angiography without pixel registration artifacts and can facilitate high-resolution real-time imaging during image-guided interventions. Hence, this study was conducted to determine the spatial resolution characteristics of a hexagonal pixel array photon-counting cadmium telluride (CdTe) detector. Methods: A 650 µm thick CdTe Schottky photon-counting detector capable of concurrently acquiring up to two energy-windowed images was operated in a single energy-window mode to include photons of 10 keV or higher. The detector had hexagonal pixels with apothem of 30 µm resulting in pixel pitch of 60 and 51.96 µm along the two orthogonal directions. The detector was characterized at IEC-RQA5 spectral conditions. Linear response of the detector was determined over the air kerma rate relevant to image-guided interventional procedures ranging from 1.3 nGy/frame to 91.4 µGy/frame. Presampled modulation transfer was determined using a tungsten edge test device. The edge-spread function and the finely sampled line spread function accounted for hexagonal sampling, from which the presampled modulation transfer function (MTF) was determined. Since detectors with hexagonal pixels require resampling to square pixels for distortion-free display, the optimal square pixel size was determined by minimizing the root-mean-squared-error of the aperture functions for the square and hexagonal pixels up to the Nyquist limit. Results: At Nyquist frequencies of 8.33 and 9.62 cycles/mm along the apothem and orthogonal to the apothem directions, the modulation factors were 0.397 and 0.228, respectively. For the corresponding axis, the limiting resolution defined as 10% MTF occurred at 13.3 and 12 cycles/mm, respectively. Evaluation of the aperture functions yielded an optimal square pixel size of 54 µm. After resampling to 54 µm square pixels using trilinear interpolation, the presampled MTF at Nyquist frequency of 9.26 cycles/mm was 0.29 and 0.24 along the orthogonal directions and the limiting resolution (10% MTF) occurred at approximately 12 cycles/mm. Visual analysis of a bar pattern image showed the ability to resolve close to 12 line-pairs/mm and qualitative evaluation of a neurovascular nitinol-stent showed the ability to visualize its struts at clinically relevant conditions. Conclusions: Hexagonal pixel array photon-counting CdTe detector provides high spatial resolution in single-photon counting mode. After resampling to optimal square pixel size for distortion-free display, the spatial resolution is preserved. The dual-energy capabilities of the detector could allow for artifact-free subtraction angiography and basis material decomposition. The proposed high-resolution photon-counting detector with energy-resolving capability can be of importance for several imageguided interventional procedures as well as for pediatric applications. C 2016 Amer...

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Assessing the quality of experience in viewing rendered decompressed light fields

Perra

2018

Multimed Tools Appl

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H2O: Reversible Hexagonal-Orthogonal Grid Conversion by 1-D Filtering

Cited by 9 publications

References 9 publications

Reversible, Fast, and High-Quality Grid Conversions

Reversible, Fast, and High-Quality Grid Conversions

Photon-counting hexagonal pixel array CdTe detector: Spatial resolution characteristics for image-guided interventional applications

Assessing the quality of experience in viewing rendered decompressed light fields

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