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## Abstract Multi-modal image set registration and atlas formation (2005)

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12155 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...y). Let p(cj), q(cj) be two probability mass functions on the set C. Then DKL(piq) P 0 with equality if and only if p(cj) = q(cj) for all cj 2 C. Proof. By an application of JensenÕs inequality, see (=-=Cover and Thomas, 1991-=-). h In our setting, we use the Kullback–Leibler divergence as a measure of dissimilarity between the two probability mass functions pX and pi at spatial location x 2 X, DKLðpXðxÞkpiðxÞÞ X pXðcjðxÞÞ... |

2142 |
On information and sufficiency
- Kullback, Leibler
- 1951
(Show Context)
Citation Context ...dissimilarity between two class posteriors, we use Kullback–Leibler divergence (relative entropy). Definition 1. Let p and q be probability mass functions on a set C. The Kullback–Leibler divergence (=-=Kullback and Leibler, 1951-=-) between p and q is defined as DKLðpkqÞ X cj2C pðcjÞ log pðcjÞ qðcjÞ . The Information Inequality theorem provides the basic properties of DKL(piq): P. Lorenzen et al. / Medical Image Analysis 10 (... |

436 |
An overlap invariant entropy measure of 3D medical image alignment
- Studholme, Hill, et al.
- 1999
(Show Context)
Citation Context ...s not constrained by an initial class labeling. Although inter-subject high-dimensional image registration has received much attention (Rueckert et al., 1998; Miller et al., 1999; Gaens et al., 1998; =-=Studholme et al., 1999-=-), to our knowledge, little attention has been given to the use of multi-modal image sets in image registration. The foundation for the work presented in this paper have been proposed in (Lorenzen and... |

349 |
Deformable templates using large deformation kinematics
- Christensen, Rabbitt, et al.
- 1996
(Show Context)
Citation Context ... ordering of the N image sets and increases linearly as image sets are added, thus, making the algorithm scalable. 2.5. Implementation We use ChristensenÕs greedy algorithm for propagating templates (=-=Christensen et al., 1996-=-). In the atlas formation setting, the velocity v n i for each iteration n is computed as follows. First, compute the updated atlas estimate (i.e. the normalized geometric mean) ^p n ðcjðxÞÞ P ck2C ... |

319 |
An invariant form for the prior probability in estimation problems
- Jeffreys
- 1946
(Show Context)
Citation Context ...(error) which is maximized when DKL(Æ) is minimized. 2.3.2. Bounds on P(error) for our two-hypothesis problem One of the first divergence measures involving density ratios is the Jeffreys divergence (=-=Jeffreys, 1946-=-), Jðq1kq2ÞDKLðq1kq2ÞþDKLðq2kq1Þ. As will be described in Section 3.2, this symmetric form of Kullback–Leibler divergence will be used as the distance measure to drive the registration. Using inequal... |

275 |
The divergence and Bhattacharyya distance measures in signal selection
- Kailath
- 1967
(Show Context)
Citation Context ...ivergence will be used as the distance measure to drive the registration. Using inequalities derived in (Hoeffding and Wolfowitz, 1958) a lower bound on P(error) in terms of J(q1iq2) is presented in (=-=Kailath, 1967-=-) and (Toussaint, 1972), 1 4 e J 2 6 PðerrorÞ. Thus, a reduction in DKL(Æ) leads to an increase in the lower bound of P(error). It should be noted, that while we have defined Jeffreys divergence in te... |

211 | Unbiased diffeomorphic atlas construction for computational anatomy
- Joshi, Davis, et al.
- 2004
(Show Context)
Citation Context ...f anatomical labels. Common techniques for creating atlases often include the choice of a template image, which inherently produces a bias. Motivated by the atlas construction framework presented in (=-=Joshi et al., 2004-=-), we propose the construction of an unbiased multi-class atlas from a population of anatomical class posteriors using large deformation diffeomorphic registration. When applied to two image sets, thi... |

210 | Automated model-based tissue classification of MR images of the brain - Leemput, Maes, et al. - 1999 |

185 |
Computational anatomy: An emerging discipline
- Grenander, Miller
- 1998
(Show Context)
Citation Context ...m in computational anatomy is the construction of an exemplar atlas from a population of medical images. This atlas represents the anatomical variation present in the population (Miller et al., 1997; =-=Grenander and Miller, 1998-=-; Thompson et al., 2000). Many images are mapped into a common coordinate system to study intra-population variability and interpopulation differences, to provide voxel-wise mapping of functional site... |

174 |
Landmark matching via large deformation diffeomorphisms
- Joshi, Miller
(Show Context)
Citation Context ...e e is the identity transformation. In this paper, we focus on the infinite dimensional group of diffeomorphisms H where we apply the theory of large deformation diffeomorphisms (Miller et al., 1999; =-=Joshi and Miller, 2000-=-) to generate deformations hi that are solutions to the Lagrangian ODEs d dt hiðx; tÞ viðhðx; tÞ; tÞ; t 20; 1Š. The transformations hi are generated by integrating velocity fields forward in time an... |

129 | Group Actions, Homeomorphisms, and Matching: A General Framework , Intl
- Miller, Younes
(Show Context)
Citation Context ...xÞ x þ Z 1 0 vðhðx; tÞ; tÞ dt. The distance between any two diffeomorphisms is defined by Dðh1; h2Þ Dðe; h 1 1 h2Þ. The construction of h and h 1 , as well as the properties of D, are described in (=-=Miller and Younes, 2001-=-) and (Miller et al., 2002). Having defined a metric on the space of diffeomorphism and a regularization operator L, the energy minimization problem described in Eq. (1) is formulated as f^ X hi; ^pg ... |

88 |
Variational Methods for Multimodal Image Matching
- Hermosillo
- 2002
(Show Context)
Citation Context ...t of mutual information and other dissimilarity measures has been studied extensively. A thorough investigation of these dissimilarity measures in high-dimensional image registration is presented in (=-=Hermosillo, 2002-=-). Mutual information is, equivalently, the Kullback–Leibler divergence between the joint distribution and product of marginal distributions of two random variables. A multi-modal free-form registrati... |

74 |
A brain tumor segmentation framework based on outlier detection
- Prastawa, Bullitt, et al.
- 2004
(Show Context)
Citation Context ...teriors, the parameters l j and R j are updated by their expected values. We are currently investigating the use of kernel density estimation as a replacement for the Gaussian models as described in (=-=Prastawa et al., 2004-=-). 3.2. Registration At a given spatial location x 2 X, the dissimilarity between image sets I 1ðxÞ and I 2ðxÞ is measured by the dissimilarity between the posterior mass functions modeling them, p1(x... |

68 | A viscous fluid model for multimodal non-rigid image registration using mutual information - D'Agostino, Maes, et al. - 2003 |

47 | Consistent groupwise non-rigid registration for atlas construction
- Bhatia, Hajnal, et al.
- 2004
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Citation Context ...tion can be extended to multiple random variables, its extension to registration involving three or more images is problematic in that it requires maintaining an impractical number of histogram bins (=-=Bhatia et al., 2004-=-). Consider a multi-modal image set registration involving four twelve-bit DICOM images, an example of which is provided in Section 5.2. Using mutual information would require the construction of a 2 ... |

47 |
Non-rigid multimodal image registration using mutual information
- Gaens, Maes, et al.
- 1998
(Show Context)
Citation Context ...itrary number, and is not constrained by an initial class labeling. Although inter-subject high-dimensional image registration has received much attention (Rueckert et al., 1998; Miller et al., 1999; =-=Gaens et al., 1998-=-; Studholme et al., 1999), to our knowledge, little attention has been given to the use of multi-modal image sets in image registration. The foundation for the work presented in this paper have been p... |

43 | Automatic brain tumor segmentation by subject specific modification of atlas priors - Prastawa, Bullitt, et al. - 2003 |

35 | Symmetrization of the Non-Rigid Registration Problem using Inversion-Invariant Energies: Application to Multiple Sclerosis
- Cachier, Rey
- 2000
(Show Context)
Citation Context ...tion energy cost functions. In traditional techniques for image registration, solutions may be systematically biased with respect to expanding and contracting regions in the estimated transformation (=-=Cachier and Rey, 2000-=-). Inverse consistent registrations442 P. Lorenzen et al. / Medical Image Analysis 10 (2006) 440–451 is desired when there is no preference, or believability, for one image over another. Existing meth... |

27 | Non-rigid registration of breast MR images using mutual information
- Rueckert, Hayes, et al.
- 1998
(Show Context)
Citation Context ...ation is performed on sets of images, of arbitrary number, and is not constrained by an initial class labeling. Although inter-subject high-dimensional image registration has received much attention (=-=Rueckert et al., 1998-=-; Miller et al., 1999; Gaens et al., 1998; Studholme et al., 1999), to our knowledge, little attention has been given to the use of multi-modal image sets in image registration. The foundation for the... |

25 |
Large deformation fluid diffeomorphisms for landmark and image matching
- Miller, Joshi, et al.
- 1999
(Show Context)
Citation Context ...ets of images, of arbitrary number, and is not constrained by an initial class labeling. Although inter-subject high-dimensional image registration has received much attention (Rueckert et al., 1998; =-=Miller et al., 1999-=-; Gaens et al., 1998; Studholme et al., 1999), to our knowledge, little attention has been given to the use of multi-modal image sets in image registration. The foundation for the work presented in th... |

17 |
Distinguishabiloity of sets of distributions
- Hoeding, Wolfowitz
- 1958
(Show Context)
Citation Context ...kq2ÞþDKLðq2kq1Þ. As will be described in Section 3.2, this symmetric form of Kullback–Leibler divergence will be used as the distance measure to drive the registration. Using inequalities derived in (=-=Hoeffding and Wolfowitz, 1958-=-) a lower bound on P(error) in terms of J(q1iq2) is presented in (Kailath, 1967) and (Toussaint, 1972), 1 4 e J 2 6 PðerrorÞ. Thus, a reduction in DKL(Æ) leads to an increase in the lower bound of P(e... |

14 | Multi-modal image registration by minimizing Kullback-Leibler distance
- Chung, Norbash, et al.
(Show Context)
Citation Context ..., 2003a,b). This method only finds correspondences between two scalar images. A method that minimizes Kullback–Leibler divergence between expected and observed joint class histograms is presented in (=-=Chan et al., 2003-=-). This technique, however, estimates class labels as a preprocessing step and is used only for rigid registration between scalar images. The method presented in this paper is more general in that reg... |

14 |
Suetens, "An information theoretic approach for non-rigid image registration using voxel class probabilities
- D'Agostino, Vandermeulen, et al.
(Show Context)
Citation Context ...free-form registration algorithm that matches voxel class labels, rather than intensities, via minimizing Kullback–Leibler divergence, another information theoretic distance measure, is presented in (=-=DÕAgostino et al., 2003a-=-,b). This method only finds correspondences between two scalar images. A method that minimizes Kullback–Leibler divergence between expected and observed joint class histograms is presented in (Chan et... |

14 |
Large deformation minimum mean squared error template estimation for computational anatomy
- Davis, Lorenzen, et al.
- 2004
(Show Context)
Citation Context ...has been given to the use of multi-modal image sets in image registration. The foundation for the work presented in this paper have been proposed in (Lorenzen and Joshi, 2003; Lorenzen et al., 2004a; =-=Davis et al., 2004-=-; Lorenzen et al., 2004b). 1.1. Model-based multi-modal image set registration Across image sets, the number of constituent images may vary, thus registration based on an intensity similarity measure ... |

13 |
Structural and radiometric asymmetry in brain images. Medical Image Analysis
- Joshi, Lorenzen, et al.
- 2003
(Show Context)
Citation Context ...n i is computed at each iteration by applying the inverse of the differential operator L to the body force function, i.e. vn i ðxÞ L 1 F n i ðxÞ. This computation is performed in the Fourier domain (=-=Joshi et al., 2003-=-). The forward and inverse integration is described as follows. At time t the transformations hi are described as .shiðx; t þ dÞ hiðx; tÞþ Z tþd t hiðx; tÞþdviðhiðx; tÞ; tÞ viðhiðx; sÞ; sÞ ds for sma... |

10 | Multi-class posterior atlas formation via unbiased kullback-leibler template estimation
- Lorenzen, Davis, et al.
- 2004
(Show Context)
Citation Context ...e use of multi-modal image sets in image registration. The foundation for the work presented in this paper have been proposed in (Lorenzen and Joshi, 2003; Lorenzen et al., 2004a; Davis et al., 2004; =-=Lorenzen et al., 2004b-=-). 1.1. Model-based multi-modal image set registration Across image sets, the number of constituent images may vary, thus registration based on an intensity similarity measure is not possible in this ... |

9 |
Mathematical and computational challenges in creating deformable and probabilistic atlases of the human
- THOMPSON
(Show Context)
Citation Context ...s the construction of an exemplar atlas from a population of medical images. This atlas represents the anatomical variation present in the population (Miller et al., 1997; Grenander and Miller, 1998; =-=Thompson et al., 2000-=-). Many images are mapped into a common coordinate system to study intra-population variability and interpopulation differences, to provide voxel-wise mapping of functional sites, and facilitate tissu... |

6 | Large Deformation Inverse Consistent Elastic Image Registration
- He, Christensen
- 2003
(Show Context)
Citation Context ...or approaching this problem, involving an algorithm that estimates incremental transformations while approximating inverse consistency constraints on each incremental transformation, is presented in (=-=He and Christensen, 2003-=-). The approach presented in this paper is intrinsically inverse consistent as the registration problem is formulated symmetrically. Therefore, no correction penalty for consistency is required. The r... |

4 |
Comments on ‘The divergence and Bhattacharyya distance measures in signal selection
- Toussaint
- 1972
(Show Context)
Citation Context ...ed as the distance measure to drive the registration. Using inequalities derived in (Hoeffding and Wolfowitz, 1958) a lower bound on P(error) in terms of J(q1iq2) is presented in (Kailath, 1967) and (=-=Toussaint, 1972-=-), 1 4 e J 2 6 PðerrorÞ. Thus, a reduction in DKL(Æ) leads to an increase in the lower bound of P(error). It should be noted, that while we have defined Jeffreys divergence in terms of symmetric Kullb... |

3 |
High-dimensional multi-modal image registration
- Lorenzen, Joshi
- 2003
(Show Context)
Citation Context ...et al., 1999), to our knowledge, little attention has been given to the use of multi-modal image sets in image registration. The foundation for the work presented in this paper have been proposed in (=-=Lorenzen and Joshi, 2003-=-; Lorenzen et al., 2004a; Davis et al., 2004; Lorenzen et al., 2004b). 1.1. Model-based multi-modal image set registration Across image sets, the number of constituent images may vary, thus registrati... |

1 |
Model based symmetric information theorectic large deformation multi-modal image registsration
- Lorenzen, Davis, et al.
(Show Context)
Citation Context ...ledge, little attention has been given to the use of multi-modal image sets in image registration. The foundation for the work presented in this paper have been proposed in (Lorenzen and Joshi, 2003; =-=Lorenzen et al., 2004a-=-; Davis et al., 2004; Lorenzen et al., 2004b). 1.1. Model-based multi-modal image set registration Across image sets, the number of constituent images may vary, thus registration based on an intensity... |

1 | et al. / Medical Image Analysis 10 (2006) 440–451 451 - Lorenzen - 2002 |