Fast Hough transform for automated detection of spheres in three-dimensional point clouds

Coggrave, C. R.

doi:10.1117/1.2739011

Cited by 17 publications

(8 citation statements)

References 15 publications

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“…It has been shown by Ogundana et al 1 that the bin size and the global votes threshold affect the accuracy of parameter estimation in Hough space. Therefore, the discussion in this section will focus on the HT's plane detection capability when applied to simulated and experimental 3-D datasets of planes.…”

Section: Experimental and Simulation Resultsmentioning

confidence: 99%

“…4.2. 1 where the method was adopted for the automated detection of spheres. However, unlike sphere detection where the radius is supplied to the detection algorithm, no a priori knowledge of any of the plane's parameters is required.…”

Section: Finding Lines Using the Hough Transformmentioning

confidence: 99%

“…Increasing the size of Hough space bins has been shown to reduce the problems associated with noisy 3-D datasets. 1 As surface normals are estimated by least squares fitting of a plane to the coordinates of the point and its nearest neighbors, another solution is to increase the kernel size used for this process.…”

Section: Finding Lines Using the Hough Transformmentioning

confidence: 99%

“…It can be observed that the value of W k increases roughly in proportion to σ , and also that the W k values are significantly larger than those obtained from spheres for the same noise level. 1 Furthermore, a known drawback of the FON parameterization is that errors in the FON position depend on the distance from the origin. 7 This is demonstrated in Table 2, which shows how W k changes when the centroid of the plane is simply translated along the x axis.…”

Section: Simulated Datamentioning

confidence: 99%

“…In addition, a summary of the adaptation of the 3-D HT to plane detection is given. 1 Plane detection using both the 1-D and 3-D HT is described in Sec. 4.…”

Section: Introductionmentioning

confidence: 99%

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Automated detection of planes in 3-D point clouds using fast Hough transforms

Ogundana

Coggrave²,

Burguete

et al. 2011

Opt. Eng

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Calibration of 3-D optical sensors often involves the use of calibration artifacts consisting of geometric features, such as 2 or more planes or spheres of known separation. In order to reduce data processing time and minimize user input during calibration, the respective features of the calibration artifact need to be automatically detected and labeled from the measured point clouds. The Hough transform (HT), which is a well-known method for line detection based on foot-of-normal parameterization, has been extended to plane detection in 3-D space. However, the typically sparse intermediate 3-D Hough accumulator space leads to excessive memory storage requirements. A 3-D HT method based on voting in an optimized sparse 3-D matrix model and efficient peak detection in Hough space is described. An alternative 1-D HT is also investigated for rapid detection of nominally parallel planes. Examples of the performance of these methods using simulated and experimental shape data are presented. C 2011 Society of Photo-Optical Instrumentation Engineers (SPIE).

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Section: Experimental and Simulation Resultsmentioning

confidence: 99%

Section: Finding Lines Using the Hough Transformmentioning

confidence: 99%

Section: Finding Lines Using the Hough Transformmentioning

confidence: 99%

Section: Simulated Datamentioning

confidence: 99%

“…In addition, a summary of the adaptation of the 3-D HT to plane detection is given. 1 Plane detection using both the 1-D and 3-D HT is described in Sec. 4.…”

Section: Introductionmentioning

confidence: 99%

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Automated detection of planes in 3-D point clouds using fast Hough transforms

Ogundana

Coggrave²,

Burguete

et al. 2011

Opt. Eng

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Location and direction dependence in the 3D MTF for a high‐resolution CT system

Hernandez

Mahesh

et al. 2021

Medical Physics

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Purpose The purpose of this study was to quantify location and direction‐dependent variations in the 3D modulation transfer function (MTF) of a high‐resolution CT scanner with selectable focal spot sizes and resolution modes. Methods The Aquilion Precision CT scanner (Canon Medical Systems) has selectable 0.25 mm or 0.5 mm detectors (by binning) in both the axial (x‐y) and detector array width (z) directions. For the x‐y and z orientations, detectors are configured (x–y) = 0.5 mm/(z) = 0.5 mm for normal resolution (NR), 0.25/0.5 mm for high resolution (HR), and 0.25/0.25 mm for super high resolution (SHR). Six focal spots (FS1‐FS6) range in size from 0.4 (x‐y) × 0.5 mm (z) for FS1 to 1.6 × 1.4 mm for FS6. Phantoms fabricated from spherical objects were positioned at radial distances of 0, 4.0, 7.5, 11.0, 14.5, and 18.5 cm. Axial and helical acquisitions were utilized and reconstructed using filtered back projection with the FC18 “Body,” FC30 “Bone,” and FC81 “Bone Sharp” kernels. The reconstructions were used to measure a 1D slice of the 3D MTF by oversampling the 3D ESF in the axial plane [MTF(fr); φ = 0°)], 45° out of the axial plane [MTF(fr); φ = 45°)], in the longitudinal direction [MTF(fr); φ = 80°)], and along the radial and azimuthal directions within the axial plane. Results The MTF(fr); φ = 45°) drops to 10% (f10) at 1.20, 1.45, and 2.06 mm−1 for NR, HR, and SHR, respectively, for a helical acquisition with FS1, FC30, and r = 4 cm from the isocenter. The MTF(fr); φ = 45°) includes contributions of both the axial‐plane MTF (f10 = 1.10, 2.04, and 2.01 mm−1) and the longitudinal MTF (f10 = 1.17, 1.18, and 1.82 mm−1) for the NR, HR, and SHR modes, respectively. For SHR, the axial scan mode showed a 15–25% improvement over helical mode in the longitudinal resolution. Helical pitch, ranging from 0.569 to 1.381, did not appreciably affect the 3D resolution (<2%). The radial MTFs across the axial field of view (FOV) showed dependencies on the focal spot length in z; for example, for SHR with FS2 (0.6 × 0.6 mm), f10 at r = 11 cm was within 17% of the value at r = 4 cm, but for SHR with FS3 (0.6 × 1.3), the reduction in f10 was 46% from 4 to 11 cm from the isocenter. The azimuthal MTF also decreased as r increased but less so for longer gantry rotation times and smaller focal spot dimensions in the axial plane. The longitudinal MTF was minimally affected (<11%) by position in the FOV and was principally affected by the focal spot length in the z‐dimension. Conclusions The 3D MTF was measured throughout the FOV of a high‐resolution CT scanner, quantifying the advantages of different resolution modes and focal spot sizes on the axial‐plane and longitudinal MTF. Reconstruction kernels were shown to impact axial‐plane resolution, imparting non‐isotropic 3D resolution characteristics. Focal spot size (both in x‐y and in z) and gantry rotation time play important roles in preserving the high‐resolution characteristics throughout the field of view for this new high‐resolution CT scanner technology.

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Theory, method, and test tools for determination of 3D MTF characteristics in cone‐beam CT

Wu¹,

Boone

Hernandez

et al. 2021

Medical Physics

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Purpose The modulation transfer function (MTF) is widely used as an objective metric of spatial resolution of medical imaging systems. Despite advances in capability for three‐dimensional (3D) isotropic spatial resolution in computed tomography (CT) and cone‐beam CT (CBCT), MTF evaluation for such systems is typically reported only in the axial plane, and practical methodology for assessment of fully 3D spatial resolution characteristics is lacking. This work reviews fundamental theoretical relationships of two‐dimensional (2D) and 3D spread functions and reports practical methods and test tools for analysis of 3D MTF in CBCT. Methods Fundamental aspects of 2D and 3D MTF measurement are reviewed within a common notational framework, and three MTF test tools with analysis code are reported and made available online (https://istar.jhu.edu/downloads/): (a) a multi‐wire tool for measurement of the axial plane MTF [denoted as MTF(fr;φ=0∘), where φis the measurement angle out of the axial plane] as a function of position in the axial plane; (b) a wedge tool for measurement of the MTF in any direction in the 3D Fourier domain [e.g., φ = 45°, denoted as MTF(fr;φ=45∘)]; and (c) a sphere tool for measurement of the MTF in any or all directions in the 3D Fourier domain. Experiments were performed on a mobile C‐arm with CBCT capability, showing that MTF(fr;φ=45∘) yields an informative one‐dimensional (1D) representation of the overall 3D spatial resolution characteristics, capturing important characteristics of the 3D MTF that might be missed in conventional analysis. The effects of anisotropic filters and detector readout mode were investigated, and the extent to which a system can be said to provide “isotropic” resolution was evaluated by quantitative comparison of MTF at various φ. Results All three test tools provided consistent measurement of MTF(fr;φ=0∘), and the wedge and sphere tools demonstrated how measurement of the MTF in directions outside the axial plane (φ>0∘) can reveal spatial resolution characteristics to which conventional axial MTF measurement is blind. The wedge tool was shown to reduce statistical measurement error compared to the sphere tool due to improved sampling, and the sphere tool was shown to provide a basis for measurement of the MTF in any or all directions (outside the null cone) from a single scan. The C‐arm system exhibited non‐isotropic spatial resolution with conventional non‐isotropic 1D apodization filters (i.e., frequency cutoff filters) — which is common in CBCT — and implementation of isotropic 2D apodization yielded quantifiably isotropic MTF. Asymmetric pixel binning modes were similarly shown to impart non‐isotropic effects on the 3D MTF, and the overall 3D MTF characteristics were evident in each case with a single, 1D measurement of the 1D MTF(fr;φ=45∘). Conclusion Three test tools and corresponding MTF analysis methods were presented within a consistent framework for analysis of 3D spatial resolution characteristics in a manner amenable to routine, practical measurements. Exper...

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Fast Hough transform for automated detection of spheres in three-dimensional point clouds

Cited by 17 publications

References 15 publications

Automated detection of planes in 3-D point clouds using fast Hough transforms

Automated detection of planes in 3-D point clouds using fast Hough transforms

Location and direction dependence in the 3D MTF for a high‐resolution CT system

Theory, method, and test tools for determination of 3D MTF characteristics in cone‐beam CT

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