Image‐guided blended neighbor interpolation of scattered data

Hale, Dave

doi:10.1190/1.3255050

“…The biharmonic interpolant used for method 2 is very smooth compared to alternative interpolation methods, including polynomial interpolation, neighborhood-based methods, and harmonic interpolation. 31 The smoothness comes about because each dose point's force is determined in relation to radial basis functions defined for all other points, as shown in Appendix. Nonsmooth interpolants are not well suited for this application, where control points are sparse, given the size of the body phantom, since the interpolations respond to noisy dose point measurements with sudden bumps and overshoot characteristics which we do not see in our 2D dose profile.…”

Section: Discussionmentioning

confidence: 99%

Practical dose point‐based methods to characterize dose distribution in a stationary elliptical body phantom for a cone‐beam C‐arm CT system

Choi

¹

,

Constantin

²

,

Ganguly

³

et al. 2015

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Purpose: To propose new dose point measurement-based metrics to characterize the dose distributions and the mean dose from a single partial rotation of an automatic exposure control-enabled, C-armbased, wide cone angle computed tomography system over a stationary, large, body-shaped phantom. Methods: A small 0.6 cm 3 ion chamber (IC) was used to measure the radiation dose in an elliptical body-shaped phantom made of tissue-equivalent material. The IC was placed at 23 well-distributed holes in the central and peripheral regions of the phantom and dose was recorded for six acquisition protocols with different combinations of minimum kVp (109 and 125 kVp) and z-collimator aperture (full: 22.2 cm; medium: 14.0 cm; small: 8.4 cm). Monte Carlo (MC) simulations were carried out to generate complete 2D dose distributions in the central plane (z = 0). The MC model was validated at the 23 dose points against IC experimental data. The planar dose distributions were then estimated using subsets of the point dose measurements using two proposed methods: (1) the proximity-based weighting method (method 1) and (2) the dose point surface fitting method (method 2). Twenty-eight different dose point distributions with six different point number cases (4,5,6,7,14, and 23 dose points) were evaluated to determine the optimal number of dose points and their placement in the phantom. The performances of the methods were determined by comparing their results with those of the validated MC simulations. The performances of the methods in the presence of measurement uncertainties were evaluated. Results: The 5-, 6-, and 7-point cases had differences below 2%, ranging from 1.0% to 1.7% for both methods, which is a performance comparable to that of the methods with a relatively large number of points, i.e., the 14-and 23-point cases. However, with the 4-point case, the performances of the two methods decreased sharply. Among the 4-, 5-, 6-, and 7-point cases, the 7-point case (1.0% [±0.6%] difference) and the 6-point case (0.7% [±0.6%] difference) performed best for method 1 and method 2, respectively. Moreover, method 2 demonstrated high-fidelity surface reconstruction with as few as 5 points, showing pixelwise absolute differences of 3.80 mGy (±0.32 mGy). Although the performance was shown to be sensitive to the phantom displacement from the isocenter, the performance changed by less than 2% for shifts up to 2 cm in the x-and y-axes in the central phantom plane. Conclusions: With as few as five points, method 1 and method 2 were able to compute the mean dose with reasonable accuracy, demonstrating differences of 1.7% (±1.2%) and 1.3% (±1.0%), respectively. A larger number of points do not necessarily guarantee better performance of the methods; optimal choice of point placement is necessary. The performance of the methods is sensitive to the alignment of the center of the body phantom relative to the isocenter. In body applications where dose distributions are important, method 2 is a better choice than method 1, as it reconstructs the do...

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“…When solving the above anisotropic eikonal equation for the minimal-distance map tðxÞ, it is straightforward to simultaneously obtain the nearest neighbor interpolant (Hale, 2009). A known sample x k is nearest to a point x only if the non-Euclidean distance tðxÞ is less than that for any other known sample point.…”

Section: Dtwmentioning

confidence: 99%

“…One way to check for possible errors in wellseismic ties is to extend the well-log measurements along seismic reflectors to compute an image-guided nearest neighbor interpolation (Hale, 2010b) of the measurements. In this method, assuming that we have a set of k known well-log values V ¼ fv 1 ; v 2 ; : : : ; v k g (v k ∈ R) that are spatially scattered at corresponding k known locations X ¼ fx 1 ; x 2 ; : : : ; x k g, we then compute an image-guided nearest neighbor interpolation of the known values by solving the following anisotropic eikonal equation (Hale, 2009): ∇tðxÞ · DðxÞ∇tðxÞ ¼ 1; x ∈ = X ; tðxÞ ¼ 0;…”

Section: Dtwmentioning

confidence: 99%

Simultaneous multiple well-seismic ties using flattened synthetic and real seismograms

Wu

¹

,

Caumon²

2016

SEG Technical Program Expanded Abstracts 2016

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Well-seismic ties allow rock properties measured at well locations to be compared with seismic data and are therefore useful for seismic interpretation. Numerous methods have been proposed to compute well-seismic ties by correlating real seismograms with synthetic seismograms computed from velocity and density logs. However, most methods tie multiple wells to seismic data one by one; hence, they do not guarantee lateral consistency among multiple well ties. We therefore propose a method to simultaneously tie multiple wells to seismic data. In this method, we first flatten synthetic and corresponding real seismograms so that all seismic reflectors are horizontally aligned. By doing this, we turn multiple wellseismic tying into a 1D correlation problem. We then compute only vertically variant but laterally constant shifts to correlate these horizontally aligned (flattened) synthetic and real seismograms. This two-step correlation method maintains lateral consistency among multiple well ties by computing a laterally and vertically optimized correlation of all synthetic and real seismograms. We applied our method to a 3D real seismic image with multiple wells and obtained laterally consistent well-seismic ties.

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“…where x ¼ ðx 1 ; x 2 ; x 3 Þ represent the 3D spatial coordinates within the 3D seismic image ( Figure 1a) and tðxÞ is a map of non-Euclidean distance (Hale, 2009) from x to the nearest known sample x k . When solving the above anisotropic eikonal equation for the minimal-distance map tðxÞ, it is straightforward to simultaneously obtain the nearest neighbor interpolant (Hale, 2009).…”

Section: Dtwmentioning

confidence: 99%

Simultaneous multiple well-seismic ties using flattened synthetic and real seismograms

Wu

¹

,

Caumon

²

2017

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Well-seismic ties allow rock properties measured at well locations to be compared with seismic data and are therefore useful for seismic interpretation. Numerous methods have been proposed to compute well-seismic ties by correlating real seismograms with synthetic seismograms computed from velocity and density logs. However, most methods tie multiple wells to seismic data one by one; hence, they do not guarantee lateral consistency among multiple well ties. We therefore propose a method to simultaneously tie multiple wells to seismic data. In this method, we first flatten synthetic and corresponding real seismograms so that all seismic reflectors are horizontally aligned. By doing this, we turn multiple wellseismic tying into a 1D correlation problem. We then compute only vertically variant but laterally constant shifts to correlate these horizontally aligned (flattened) synthetic and real seismograms. This two-step correlation method maintains lateral consistency among multiple well ties by computing a laterally and vertically optimized correlation of all synthetic and real seismograms. We applied our method to a 3D real seismic image with multiple wells and obtained laterally consistent well-seismic ties.

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Image‐guided blended neighbor interpolation of scattered data

Cited by 64 publications

References 12 publications

Practical dose point‐based methods to characterize dose distribution in a stationary elliptical body phantom for a cone‐beam C‐arm CT system

Practical dose point‐based methods to characterize dose distribution in a stationary elliptical body phantom for a cone‐beam C‐arm CT system

Simultaneous multiple well-seismic ties using flattened synthetic and real seismograms

Simultaneous multiple well-seismic ties using flattened synthetic and real seismograms

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