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## Book Chapter Anisotropy Estimation of Trabecular Bone in Gray-Scale: Comparison Between Cone Beam and Micro Computed Tomography Data

### Citations

378 |
KNUTSSON H.: Signal Processing For Computer Vision
- GRANLUND
- 1995
(Show Context)
Citation Context ... related to the well-known local structure tensor (ST) which has been used in the computer vision community since 1980s [4]. There are different methods for computing ST, including quadrature filters =-=[7]-=-, higher-order derivatives [15] or tensor voting [20]. However, the most used ST is given by: STσ (p) = Gσ ∗∇Ip∇IpT (6) 6 R. Moreno et al. vMF (κ = 1) HC vMF (κ = 5) vMF (κ = 10) vMF (κ = 50) Impulse ... |

205 | Extended Gaussian Images
- Horn
- 1984
(Show Context)
Citation Context ...ds The tensors were computed through the generalized MIL tensor (GMIL) and the GST. 2.3.1 GMIL tensor Basically, the GMIL tensor is computed in three steps. The mirrored extended Gaussian image (EGI) =-=[12]-=- is computed from a robust estimation of the gradient. Second, the EGI is convolved with a kernel in order to obtain an orientation distribution function (ODF). Finally, a second-order fabric tensor i... |

189 |
Computing Fourier transforms and convolutions
- Driscoll, Healy
- 1994
(Show Context)
Citation Context ...ere Ω , and C is given by: C = H ∗E, (2) Anisotropy computed on CBCT and micro-CT images 5 that is, the angular convolution (∗) of a kernel H with the mirrored EGI E. Thanks to the Funk-Hecke theorem =-=[9, 3]-=-, this convolution can be performed efficiently in the spherical harmonics domain when the kernel is positive and rotationally symmetric with respect to the north pole. One of the advantages of the GM... |

156 |
Geometric Applications of Fourier Series and Spherical Harmonics
- Groemer
- 1996
(Show Context)
Citation Context ...ere Ω , and C is given by: C = H ∗E, (2) Anisotropy computed on CBCT and micro-CT images 5 that is, the angular convolution (∗) of a kernel H with the mirrored EGI E. Thanks to the Funk-Hecke theorem =-=[9, 3]-=-, this convolution can be performed efficiently in the spherical harmonics domain when the kernel is positive and rotationally symmetric with respect to the north pole. One of the advantages of the GM... |

101 |
A feature based correspondence algorithm for image matching
- Förstner
- 1986
(Show Context)
Citation Context ...∈I ∇Ip∇ITp dI, (5) where I is the image and ∇Ip is the gradient. Notice that GST related to the well-known local structure tensor (ST) which has been used in the computer vision community since 1980s =-=[4]-=-. There are different methods for computing ST, including quadrature filters [7], higher-order derivatives [15] or tensor voting [20]. However, the most used ST is given by: STσ (p) = Gσ ∗∇Ip∇IpT (6) ... |

30 |
The relationship between the elasticity tensor and the fabric tensor
- Cowin
- 1985
(Show Context)
Citation Context ...and micro-MRI [11, 6]. Furthermore, relationships between fabric and elasticity tensors will be explored. The MIL tensor has extensively been used for predicting elasticity tensors in trabecular bone =-=[2, 27, 10]-=-. However, since the GMIL with the vMF kernel has a better performance than the MIL tensor for reproducing in vitro measurements, we want to investigate whether or not the GMIL tensor can also be used... |

29 |
A unified view of the theory of directional statistics
- Jupp, Mardia
- 1989
(Show Context)
Citation Context ...ized and the original MIL tensor. The HC is given by: H(φ) = { cos(φ) ,if φ ≤ pi/2 0 ,otherwise, (3) with φ being the polar angle in spherical coordinates. Moreover, the vMF kernel, which is given by =-=[14]-=-: H(φ) = κ 4pi sinh(κ) eκ cos(φ), (4) has been selected since it has a parameter κ that can be used to control its smoothing action. In particular, the smoothing effect is reduced as the values of κ a... |

21 |
If bone is the answer, then what is the question
- Huiskes
(Show Context)
Citation Context ...sotropy than in the orientation of trabecular bone under treatment, since osteoAnisotropy computed on CBCT and micro-CT images 3 porosis can have more effect on its anisotropy than on its orientation =-=[23, 13]-=-. Thus, the aim of the present study was to compare anisotropy measurements from different fabric tensors computed on images acquired through cone beam computed tomography (CBCT) to the same tensors c... |

11 |
Riesz-transforms versus derivatives: On the relationship between the boundary tensor and the energy tensor
- Köthe, Felsberg
(Show Context)
Citation Context ...al structure tensor (ST) which has been used in the computer vision community since 1980s [4]. There are different methods for computing ST, including quadrature filters [7], higher-order derivatives =-=[15]-=- or tensor voting [20]. However, the most used ST is given by: STσ (p) = Gσ ∗∇Ip∇IpT (6) 6 R. Moreno et al. vMF (κ = 1) HC vMF (κ = 5) vMF (κ = 10) vMF (κ = 50) Impulse Fig. 2 Graphical representation... |

11 |
A review of morphology–elasticity relationships in human trabecular bone: theories and experiments
- Zysset
(Show Context)
Citation Context ...and micro-MRI [11, 6]. Furthermore, relationships between fabric and elasticity tensors will be explored. The MIL tensor has extensively been used for predicting elasticity tensors in trabecular bone =-=[2, 27, 10]-=-. However, since the GMIL with the vMF kernel has a better performance than the MIL tensor for reproducing in vitro measurements, we want to investigate whether or not the GMIL tensor can also be used... |

7 |
A Global Relationship between Trabecular Bone Morphology and Homogenized Elastic Properties
- Zysset, Goulet, et al.
- 1998
(Show Context)
Citation Context ...he other tensors. Finally, unlike GST, both HC and vMF generate tensors that are close to be orthotropic, that is, E2≈ E3. This is in line with the common assumption of orthotropy for trabecular bone =-=[28]-=-. Figures 4-6 show Bland-Altman plots for the generalized MIL tensor with the HC and vMF (with κ=10) kernels and the GST. As seen in these figures, GST yields wider limits of agreement, i.e., larger d... |

6 |
B.: Trabecular bone morphology from micromagnetic resonance imaging
- Hipp, Jansujwicz, et al.
- 1996
(Show Context)
Citation Context ...he images. Ongoing research includes performing comparisons in different skeletal sites, different degrees of osteoporosis and comparing the results with images acquired through HR-pQCT and micro-MRI =-=[11, 6]-=-. Furthermore, relationships between fabric and elasticity tensors will be explored. The MIL tensor has extensively been used for predicting elasticity tensors in trabecular bone [2, 27, 10]. However,... |

6 |
Quantifying anisotropy of trabecular bone from gray-level images, Bone 40
- Tabor, Rokita
- 2007
(Show Context)
Citation Context ...chosen in this study our previously proposed generalized mean intercept length (MIL) tensor [17] (GMIL) with different kernels and, due to its simplicity, the global gray-scale structure tensor (GST) =-=[26]-=-. This chapter is an extended version of the work in [18]. The chapter is organized as follows. Section 2 presents the material and methods used in this study. Section 3 shows comparisons between usin... |

4 |
High-resolution computed tomography for clinical imaging of bone microarchitecture
- Burghardt, Link, et al.
- 2011
(Show Context)
Citation Context ...lution with this technique is worse compared to the one obtained through CT in vivo [8]. Regarding CT modalities, cone beam CT (CBCT) [16, 22] and high-resolution peripheral quantitative CT (HR-pQCT) =-=[1, 5]-=- are two promising CT techniques for in vivo imaging. Although these techniques are not appropriate to all skeletal sites, their use is appealing since they can attain higher resolutions and lower dos... |

4 | Generalizing the mean intercept length tensor for gray-level images
- Moreno, Borga, et al.
(Show Context)
Citation Context ...s computed on images acquired through micro computed tomography (micro-CT). Due to its flexibility, we have chosen in this study our previously proposed generalized mean intercept length (MIL) tensor =-=[17]-=- (GMIL) with different kernels and, due to its simplicity, the global gray-scale structure tensor (GST) [26]. This chapter is an extended version of the work in [18]. The chapter is organized as follo... |

3 |
Ö.: Techniques for computing fabric tensors: a review
- Moreno, Borga, et al.
- 2014
(Show Context)
Citation Context ...ntation and anisotropy of trabecular bone. Many methods have been proposed for computing fabric tensors from segmented images, including boundary-, volume-, texture-based and alternative methods (cf. =-=[19]-=- for a complete review). However, due to large bias generated by partial volume effects, these methods are usually not applicable to images acquired in vivo, where the resolution of the images is in t... |

2 |
H.: New advances in imaging osteoporosis and its complications. Endocrine 42
- Griffith, Genant
- 2012
(Show Context)
Citation Context ... that it requires long acquisition times that can easily lead to motion-related artifacts and that the obtained resolution with this technique is worse compared to the one obtained through CT in vivo =-=[8]-=-. Regarding CT modalities, cone beam CT (CBCT) [16, 22] and high-resolution peripheral quantitative CT (HR-pQCT) [1, 5] are two promising CT techniques for in vivo imaging. Although these techniques a... |

2 |
P.: Morphology-elasticity relationships using decreasing fabric information of human trabecular bone from three major anatomical locations. Biomechanics and Modeling in Mechanobiology 12(4
- Gross, Pahr, et al.
- 2013
(Show Context)
Citation Context ...and micro-MRI [11, 6]. Furthermore, relationships between fabric and elasticity tensors will be explored. The MIL tensor has extensively been used for predicting elasticity tensors in trabecular bone =-=[2, 27, 10]-=-. However, since the GMIL with the vMF kernel has a better performance than the MIL tensor for reproducing in vitro measurements, we want to investigate whether or not the GMIL tensor can also be used... |

2 |
H.: Comparison between microcomputed tomography and cone-beam computed tomography radiologic bone to assess atrophic posterior maxilla density and microarchitecture
- Monje, Monje, et al.
- 2013
(Show Context)
Citation Context ...easily lead to motion-related artifacts and that the obtained resolution with this technique is worse compared to the one obtained through CT in vivo [8]. Regarding CT modalities, cone beam CT (CBCT) =-=[16, 22]-=- and high-resolution peripheral quantitative CT (HR-pQCT) [1, 5] are two promising CT techniques for in vivo imaging. Although these techniques are not appropriate to all skeletal sites, their use is ... |

2 |
Ö.: Correlations between fabric tensors computed on cone beam and micro computed tomography images
- Moreno, Borga, et al.
- 2013
(Show Context)
Citation Context ...mean intercept length (MIL) tensor [17] (GMIL) with different kernels and, due to its simplicity, the global gray-scale structure tensor (GST) [26]. This chapter is an extended version of the work in =-=[18]-=-. The chapter is organized as follows. Section 2 presents the material and methods used in this study. Section 3 shows comparisons between using GMIL and GST in both CBCT and micro-CT data. Finally, S... |

2 |
Novel algorithm detecting trabecular termini in µCT and MRI images
- Tabor
- 2005
(Show Context)
Citation Context ... increase the accuracy of the MIL tensor for predicting the elastic properties of trabecular bone. In the same line, we have recently hypothesized that trabecular termini (i.e., free ended trabeculae =-=[24]-=-) should not be considered for computing fabric tensors since contribution of termini to the mechanical competence of trabecular bone is rather limited [21]. Thus, it is worthwhile to assess the power... |

2 |
The potential of multi-slice computed tomography based quantification of the structural anisotropy of vertebral trabecular bone. Med Eng Phys 35:7–15
- Tabor, Petryniak, et al.
- 2013
(Show Context)
Citation Context ...l by a more appropriate one, as it was shown in this chapter for the vMF kernel. A poor performance of the GST has also been reported in images acquired through multi-slice computed tomography (MSCT) =-=[25]-=-. The authors of that study hypothesized that such a bad performance could be due to voxel anisotropy obtained from MSCT. However, the results from the current study suggest that the problems of the G... |

1 |
High-resolution in vivo imaging of bone and joints: a window to microarchitecture. Nature Reviews Rheumatology
- Geusens, Chapurlat, et al.
- 2014
(Show Context)
Citation Context ...lution with this technique is worse compared to the one obtained through CT in vivo [8]. Regarding CT modalities, cone beam CT (CBCT) [16, 22] and high-resolution peripheral quantitative CT (HR-pQCT) =-=[1, 5]-=- are two promising CT techniques for in vivo imaging. Although these techniques are not appropriate to all skeletal sites, their use is appealing since they can attain higher resolutions and lower dos... |

1 |
A.: Reproducibility and error sources of -mri-based trabecular bone structural parameters of the distal radius and tibia
- Gomberg, Wehrli, et al.
- 2004
(Show Context)
Citation Context ...he images. Ongoing research includes performing comparisons in different skeletal sites, different degrees of osteoporosis and comparing the results with images acquired through HR-pQCT and micro-MRI =-=[11, 6]-=-. Furthermore, relationships between fabric and elasticity tensors will be explored. The MIL tensor has extensively been used for predicting elasticity tensors in trabecular bone [2, 27, 10]. However,... |

1 | Ö.: Volume-based fabric tensors through lattice-Boltzmann simulations
- Moreno, Smedby
- 2014
(Show Context)
Citation Context ...ecular termini (i.e., free ended trabeculae [24]) should not be considered for computing fabric tensors since contribution of termini to the mechanical competence of trabecular bone is rather limited =-=[21]-=-. Thus, it is worthwhile to assess the power of fabric tensors that disregard termini for predicting elasticity. Acknowledgements We thank Andres Laib from SCANCO Medical AG for providing the microCT ... |

1 |
K.: Determination of vertebral and femoral trabecular morphology and stiffness using a flat-panel C-arm-based CT approach
- Mulder, Rietbergen, et al.
- 2012
(Show Context)
Citation Context ...easily lead to motion-related artifacts and that the obtained resolution with this technique is worse compared to the one obtained through CT in vivo [8]. Regarding CT modalities, cone beam CT (CBCT) =-=[16, 22]-=- and high-resolution peripheral quantitative CT (HR-pQCT) [1, 5] are two promising CT techniques for in vivo imaging. Although these techniques are not appropriate to all skeletal sites, their use is ... |