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## Unbiased diffeomorphic atlas construction for computational anatomy (2004)

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Venue: | NEUROIMAGE |

Citations: | 211 - 24 self |

### Citations

259 | Shape manifolds, Procrustean metrics, and complex projective spaces
- Kendall
- 1984
(Show Context)
Citation Context ...N anatomical images N {Ii}i = is 1 depicted in Fig. 2. Throughout this paper, we use the squared error dissimilarity metric but other metrics such as the Kullback–Leibler divergence can also be used (=-=Kendall, 1984-=-). Under the squared error dissimilarity measure, the template estimation problem becomes X ˆhi; ÎI argmin hi;I N Z ðIiðhiðÞ x Þ IðÞ x Þ i 1 X 2 dx Z 1 Z þ jjLviðx; tÞjj 0 X 2 dxdt: ð5Þ This minim... |

258 |
General Pattern Theory
- Grenander
- 1993
(Show Context)
Citation Context ...ler and Younes, 2001; Rohlfing et al., 2003b; Thompson and Toga, 2002) that can map and transform a single brain atlas on to a population. In this paradigm, the atlas serves as a deformable template (=-=Grenander, 1994-=-). The deformable template can project detailed atlas data such as structural, biochemical, functional as well as vascular information on to the individual or an entire population of brain images. The... |

187 | Morphometric Tools for Landmark Data - BOOKSTEIN - 1999 |

185 | Computational anatomy: An emerging discipline - Grenander, Miller - 1998 |

147 | Variational problems on flows of diffeomorphisms for image matching
- Dupuis, Grenander, et al.
- 1998
(Show Context)
Citation Context ...res the least deformation represented by diffeomorphisms hi(x), to best match each of the input images. This framework is depicted in Fig. 2. We apply the theory of large deformation diffeomorphisms (=-=Dupuis et al., 1997-=-; Joshi et al., 2003; Miller and Younes, 2001)to generate deformations hi aH that are solutions to the Lagrangian ODEs d dt hiðx; tÞ = vi(hi(x, t), t), t a [0, 1]. The transformations hi are generated... |

143 |
On the metrics and Euler-Lagrange equations of computational anatomy
- Miller, Trouve, et al.
(Show Context)
Citation Context ...for understanding anatomical geometry. These groups vary in dimensionality from simple global translations (R 3 ) and rigid rotations (SO(3)) to the infinite dimensional group of diffeomorphisms (H) (=-=Miller et al., 2002-=-). In this paper, we address the problem of anatomical template construction as the joint estimation of the most representative image and the associated anatomical geometry given a database of brain i... |

135 |
Hippocampal morphometry in schizophrenia by high dimensional brain mapping
- Csernansky, Joshi, et al.
- 1998
(Show Context)
Citation Context ...lation of brain images. The transformations encode the variability of the population under study. A statistical analysis of the transformations can also be used to characterize different populations (=-=Csernansky et al., 1998-=-; Hohne et al., 1992; Talairach et al., 1988). For a detailed review of deformable atlas mapping and the general framework for computational anatomy, see Grenander and Miller (1998) and Thompson and T... |

131 |
Automated image registration: II. intersubject validation of linear and nonlinear models,
- Woods
- 1998
(Show Context)
Citation Context ...lassifiers was substantially better than an individual classifier (Miller et al., 1999). Combination of the deformed label images was done using an extension of the STAPLE (Shen and Davatzikos, 2002; =-=Woods et al., 1998-=-) algorithm. This classification method requires multiple high-dimensional deformations to be applied to each new individual, which poses a computational problem if applied to large clinical studies. ... |

129 | Group Actions, Homeomorphisms, and Matching: A General Framework , Intl
- Miller, Younes
(Show Context)
Citation Context ...tomy cannot faithfully represent the complex structural variability between individuals. A major focus of computational anatomy has been the development of image mapping algorithms (Gee et al., 1993; =-=Miller and Younes, 2001-=-; Rohlfing et al., 2003b; Thompson and Toga, 2002) that can map and transform a single brain atlas on to a population. In this paradigm, the atlas serves as a deformable template (Grenander, 1994). Th... |

116 | Les éléments aléatoires de nature quelconque dans un espace distancié - Fréchet - 1948 |

96 | VALMET: A new validation tool for assessing and improving 3D object segmentation
- Gerig, Jomier, et al.
(Show Context)
Citation Context ...tions (three repeated segmentations by two raters). This allows to compare not only binary segmentations but also probabilistic segmentations. We use a previously developed validation package VALMET (=-=Gerig et al., 2001-=-) that includes a probabilistic overlap measure between two fuzzy segmentations. This metric is derived from the normalized L1 distance between two probability distributions POV ðA; BÞ 1 R j PA PB j... |

89 | On the geometry and shape of brain submanifolds
- Joshi, Grenander, et al.
- 1997
(Show Context)
Citation Context ...e of the differential operator L to the force function, that is, vi k (x) =L 1 Fi k (x), where L = aj 2 + hjj + g is the Navier–Stokes operator. This computation is carried out in the Fourier domain (=-=Joshi et al., 1997-=-). For each iteration the dominating computation is the Fast Fourier Transform. Thus, the order of the algorithm is MNn log n where M is the number of iterations, N is the number of images to be regis... |

86 | Geodesic estimation for large deformation anatomical shape averaging and interpolation - Avants, Gee - 2004 |

69 | set evolution with region competition: automatic 3-D segmentation of brain tumors
- Ho, Bullit, et al.
- 2002
(Show Context)
Citation Context ...ging techniques intense research has been directed toward the development of digital three-dimensional atlases of the brain. Most digital brain atlases so far are based on a single subject’s anatomy (=-=Ho et al., 2002-=-; Warfield et al., 2002). Although these atlases provide a standard coordinate system, they * Corresponding author. Department of Radiation Oncology, University of North Carolina. Fax: +1 919 962 1799... |

60 |
Statistics of shape via principal geodesic analysis on lie groups
- Fletcher, Lu, et al.
- 2003
(Show Context)
Citation Context ...n for a collection of data points xi can be defined as the minimizer of the sum-of-squared distances to each of the data points. That is l argmin x a M X N i 1 dx; ð xiÞ 2 : In our previous work (=-=Fletcher et al., 2003a-=-,b), we have used these concepts to extend first and second order statistical analysis to finite dimensional Riemannian Manifolds for statistical analysis of medial representations of objects. In this... |

60 | Average brain models: A convergence study
- Guimond, Meunier, et al.
- 2000
(Show Context)
Citation Context ...erence image can bias the result of the registration. Inverse consistent registration is desired when there is no a priori reason to choose one image over another as a reference image. Previous work (=-=Guimond et al., 2000-=-; Magnotta et al., 2003) has introduced methods for computing approximate inverse consistent registrations by applying inverse consistency constraints on intermediate incremental transformations. For ... |

54 | Detection, visualization and animation of abnormal anatomic structure with a deformable probabilistic brain atlas based on random vector eld transformation - TOGA - 1996 |

47 | Consistent groupwise non-rigid registration for atlas construction
- Bhatia, Hajnal, et al.
- 2004
(Show Context)
Citation Context ...re recent and related work, Avants and Gee (2004) developed an algorithm in the large deformation diffeomorphic setting for template estimation by averaging velocity fields. Most other previous work (=-=Bhatia et al., 2004-=-) in atlas formation has focused on the small deformation setting in which arithmetic averaging of displacement fields is well defined. Guimond et al. (2000) develop an iterative averaging algorithm t... |

47 | Toga, "A framework for computational anatomy
- Thompson, W
- 2002
(Show Context)
Citation Context ...ctural variability between individuals. A major focus of computational anatomy has been the development of image mapping algorithms (Gee et al., 1993; Miller and Younes, 2001; Rohlfing et al., 2003b; =-=Thompson and Toga, 2002-=-) that can map and transform a single brain atlas on to a population. In this paradigm, the atlas serves as a deformable template (Grenander, 1994). The deformable template can project detailed atlas ... |

44 | Co-planar stereotaxis atlas of the human brain - Talairach, Tournoux - 1988 |

44 | An introduction to brain warping
- Toga, Thompson
- 1999
(Show Context)
Citation Context ...n, the log is the matrix log which for a rotation matrix can be easily calculated using the Rodriguez formula. A straightforward extension of the well known Procrustes method minimizes Eq. (2) above (=-=Toga, 1999-=-).sAlthough the above methodology has been extensively studied for rigid transformations, the concept can be readily extended to general transformations. Given a metric on a group of transformations, ... |

35 | Gaussian distributions on Lie groups and their application to statistical shape analysis - Fletcher, Joshi, et al. - 2003 |

35 | Validation of Image Segmentation and Expert Quality with an Expectation-Maximization Algorithm, volume 2488
- Warfield, Zou, et al.
- 2002
(Show Context)
Citation Context ...ntense research has been directed toward the development of digital three-dimensional atlases of the brain. Most digital brain atlases so far are based on a single subject’s anatomy (Ho et al., 2002; =-=Warfield et al., 2002-=-). Although these atlases provide a standard coordinate system, they * Corresponding author. Department of Radiation Oncology, University of North Carolina. Fax: +1 919 962 1799. E-mail address: joshi... |

26 |
A 3d anatomical atlas based on a volume model
- HÖHNE, BOMANS, et al.
- 1992
(Show Context)
Citation Context ...he transformations encode the variability of the population under study. A statistical analysis of the transformations can also be used to characterize different populations (Csernansky et al., 1998; =-=Hohne et al., 1992-=-; Talairach et al., 1988). For a detailed review of deformable atlas mapping and the general framework for computational anatomy, see Grenander and Miller (1998) and Thompson and Toga (1997). One of t... |

25 |
Large deformation fluid diffeomorphisms for landmark and image matching
- Miller, Joshi, et al.
- 1999
(Show Context)
Citation Context ...ventricles and basal ganglia. Atlas construction is based on eight infant MRI. and showed that the combination of these independent classifiers was substantially better than an individual classifier (=-=Miller et al., 1999-=-). Combination of the deformed label images was done using an extension of the STAPLE (Shen and Davatzikos, 2002; Woods et al., 1998) algorithm. This classification method requires multiple high-dimen... |

24 | Expectation maximization strategies for multi-atlas multi-label segmentation - Rohlfing, Russakoff, et al. - 2003 |

21 |
Elastically deforming an atlas to match anatomical brain images
- Gee, Reivich, et al.
- 1993
(Show Context)
Citation Context ...cause a single anatomy cannot faithfully represent the complex structural variability between individuals. A major focus of computational anatomy has been the development of image mapping algorithms (=-=Gee et al., 1993-=-; Miller and Younes, 2001; Rohlfing et al., 2003b; Thompson and Toga, 2002) that can map and transform a single brain atlas on to a population. In this paradigm, the atlas serves as a deformable templ... |

13 |
Structural and radiometric asymmetry in brain images. Medical Image Analysis
- Joshi, Lorenzen, et al.
- 2003
(Show Context)
Citation Context ...tion represented by diffeomorphisms hi(x), to best match each of the input images. This framework is depicted in Fig. 2. We apply the theory of large deformation diffeomorphisms (Dupuis et al., 1997; =-=Joshi et al., 2003-=-; Miller and Younes, 2001)to generate deformations hi aH that are solutions to the Lagrangian ODEs d dt hiðx; tÞ = vi(hi(x, t), t), t a [0, 1]. The transformations hi are generated by integrating velo... |

6 | Large Deformation Inverse Consistent Elastic Image Registration - He, Christensen - 2003 |

5 | Extraction and application of expert priors to combine multiple segmentations of human brain tissue
- Rohlfing, Russakoff, et al.
(Show Context)
Citation Context ...present the complex structural variability between individuals. A major focus of computational anatomy has been the development of image mapping algorithms (Gee et al., 1993; Miller and Younes, 2001; =-=Rohlfing et al., 2003b-=-; Thompson and Toga, 2002) that can map and transform a single brain atlas on to a population. In this paradigm, the atlas serves as a deformable template (Grenander, 1994). The deformable template ca... |

3 |
High-dimensional multi-modal image registration
- Lorenzen, Joshi
- 2003
(Show Context)
Citation Context ...2 dxdt subject to hx ðÞxt Z 1 0 vhx; ð ð tÞ; tÞdt: The distance between any two diffeomorphisms is defined by Dh1; ð h2Þ De; h 1 1 B h2 : This distance satisfies all of the properties of a metric (=-=Lorenzen and Joshi, 2003-=-). Namely it is nonnegative, symmetric, and satisfies the triangle inequality. D is trivially nonnegative. Symmetry follows from the fact that h 1 is generated by integrating backward in time the nega... |

2 | magnetic resonance based consistent brain image registration - Magnotta, Bockholt, et al. |

1 |
Hammer: hierarchical S. Joshi et al. / NeuroImage 23 (2004) S151–S160 attribute matching mechanism for elastic registration
- Shen, Davatzikos
- 2002
(Show Context)
Citation Context ...tion of these independent classifiers was substantially better than an individual classifier (Miller et al., 1999). Combination of the deformed label images was done using an extension of the STAPLE (=-=Shen and Davatzikos, 2002-=-; Woods et al., 1998) algorithm. This classification method requires multiple high-dimensional deformations to be applied to each new individual, which poses a computational problem if applied to larg... |