## Unifying Maximum Likelihood Approaches in Medical Image Registration (1999)

Citations: | 77 - 21 self |

### BibTeX

@MISC{Roche99unifyingmaximum,

author = {Alexis Roche and Grégoire Malandain and Nicholas Ayache},

title = {Unifying Maximum Likelihood Approaches in Medical Image Registration},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

While intensity-based similarity measures are increasingly used for medical image registration, they often rely on implicit assumptions regarding the imaging physics. The motivation of this paper is to clarify the assumptions on which a number of popular similarity measures rely. After formalizing registration based on general image acquisition models, we show that the search for an optimal measure can be cast into a maximum likelihood estimation problem. We then derive similarity measures corresponding to different modeling assumptions and retrieve some well-known measures (correlation coefficient, correlation ratio, mutual information). Finally, we present results of rigid registration between several image modalities to illustrate the importance of choosing an appropriate similarity measure.

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Citation Context .... Statistical relationship. Finally, assuming a functional relationship is sometimes too restrictive. Then, it is more appropriate to use information theoretic measures, from which mutual information =-=[9, 23]-=- is today probably the most popular: I (I ; J) = X i X j log p(i; j) p(i) p(j) ; (3) where p(i; j) is the intensity joint probability distribution of the images, and p(i) and p(j) the corresponding ma... |

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Citation Context ...is that when matched the images are identical. This includes a number of popular measures: the sum of squared intensity dioeerences (SSD), the sum of absolute intensity dioeerences, cross-correlation =-=[3]-=-, entropy of the dioeerence image [4], etc. Although these measures are not equivalent in terms of robustness and accuracy, none of them is able to cope with relative intensity changes from one image ... |

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Citation Context .... Statistical relationship. Finally, assuming a functional relationship is sometimes too restrictive. Then, it is more appropriate to use information theoretic measures, from which mutual information =-=[9, 23]-=- is today probably the most popular: I (I ; J) = X i X j log p(i; j) p(i) p(j) ; (3) where p(i; j) is the intensity joint probability distribution of the images, and p(i) and p(j) the corresponding ma... |

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Citation Context ...ad, this latter point may be assigned an arbitrary intensity j . by the registration criterion, which necessitates some heuristic normalization to avoid nasty eoeects such as disconnecting the images =-=[21, 23, 19]-=-. Here, to keep consistent with the maximum likelihood framework, we denitely cannot ignore them: doing so, we would no longer maximize the image likelihood, P (I jJ; T ), but the likelihood of a part... |

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Citation Context ...) ; (2) where OE(J) is the least square optimal non-linear approximation of I in terms of J [13]. The correlation ratio is closely related to a very popular measure previously proposed by Woods et al =-=[26]-=-, and generalized using robust metrics in [12]. Statistical relationship. Finally, assuming a functional relationship is sometimes too restrictive. Then, it is more appropriate to use information theo... |

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Citation Context ...egistration methods were written by van den Elsen et al [22], Lavall#e [7], and Maintz [10]. Quite recently, a comparison of algorithms based on a retrospective evaluation was published by West et al =-=[25]-=-. Registration methods are usually classied as being either feature-based or intensity-based. Methods from the former class proceed in two sequential steps. The rst is to extract homologous geometrica... |

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Citation Context ...ities, and thus it has not provided convincing results in multimodal registration. Functional relationship. For multimodal images, more complex relationships are involved. The approach we proposed in =-=[19]-=- was to assume that, at the registration position, one image could be approximated in terms of the other by applying some intensity function, IsOE(J). Making no assumption regarding the nature of the ... |

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Citation Context ...ed from dioeerent patients, e.g. to build statistical anatomical atlases. Non-rigid registration is then always used. Reviews of medical image registration methods were written by van den Elsen et al =-=[22]-=-, Lavall#e [7], and Maintz [10]. Quite recently, a comparison of algorithms based on a retrospective evaluation was published by West et al [25]. Registration methods are usually classied as being eit... |

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Citation Context ... to the head volume. Thus, ffl represents the error one can expect in the region of interest. We also computed the intrinsic rotation error, \Delta `, and translation error, \Delta t, as described in =-=[14]-=-. Table 1 shows RMS of ffl, \Delta `, and \Delta t over the ten patients, for each modality combination. These have to be compared to the image resolution, which is quite poor here (4 mm in the z-axis... |

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Citation Context ...transformation T appears as a parameter of this joint probability function, and it is natural to invoke the maximum likelihood principle to formulate registration, as already proposed for instance in =-=[23, 8, 1, 11, 5]-=-. It simply states that the most likely transformation between I and J is the one that maximizes the joint probability of (I ; J),sT = arg max T P (I ; J jT ) = arg max T P (I jJ; T ); the last equiva... |

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Citation Context ...s. Much effort in this area has been devoted to the geometrical modeling of anatomical variations from one subject to another. In general, interpatient registration involves nonrigid transformations (=-=Toga, 1999-=-). Reviews of medical image registration methods were written by van den Elsen et al. (1993), Lavallee (1995), and Maintz and Viergever (1998). Quite recently, a comparison of algorithms based on a re... |

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Citation Context ...). The intensity function f is nothing but a least-square t of the image I in terms of the reference J : it is in fact the same tting function as in the denition of the correlation ratio (equation 2) =-=[19, 18]-=-, and we see that the registration energy U(T ) is related to the correlation ratio j 2 (I jJ # ) by: j 2 (I jJ # ) = 1 \Gamma 1 k e U(T) N ; with k = p 2 e Var(I): In the original version of the corr... |

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Citation Context ...nt patients, e.g. to build statistical anatomical atlases. Non-rigid registration is then always used. Reviews of medical image registration methods were written by van den Elsen et al [22], Lavall#e =-=[7]-=-, and Maintz [10]. Quite recently, a comparison of algorithms based on a retrospective evaluation was published by West et al [25]. Registration methods are usually classied as being either feature-ba... |

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Citation Context ...t to variations with respect to this ideal situation. A number of comparison studies have shown that similarity measures yield dioeerent performances depending on the considered modality combinations =-=[25, 2, 15, 12, 19]-=-. There is probably no universal measure and, for a specic problem, the point is rather to choose the one that is best adapted to the nature of the images. Up to now, the link between explicit modelin... |

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Citation Context ...t to variations with respect to this ideal situation. A number of comparison studies have shown that similarity measures yield dioeerent performances depending on the considered modality combinations =-=[25, 2, 15, 12, 19]-=-. There is probably no universal measure and, for a specic problem, the point is rather to choose the one that is best adapted to the nature of the images. Up to now, the link between explicit modelin... |

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Citation Context ...suggested the analogy of this approach with registration based on information theory. Notably, other teams had motivated information-theoretical measures using different arguments (Maes et al., 1997; =-=Studholme et al., 1996-=-). In Section 2, we propose to formulate image registration as a general maximum likelihood estimation problem, examining carefully the assumptions that are required. In Section 3, deriving optimal si... |

7 |
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Citation Context ...ather to choose the one that is best adapted to the nature of the images. Up to now, the link between explicit modeling assumptions and similarity measures has not been made clear. After some authors =-=[11, 5]-=- proposed that image registration could be seen as a maximum likelihood estimation problem, Viola et al [23, 24] suggested the analogy of this approach with registration using information theory. Rema... |

6 | The EM Algorithm: A Guided Tour
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Citation Context ...ion-Maximization (EM) algorithm is a powerful method that is typically adapted to this situation. The interested reader will nd an excellent introduction to the EM algorithm and several references in =-=[6]-=-. Applying the EM algorithm to our problem, the parameters are updated iteratively until convergence according to the following reestimation formulae: f (n+1) p = X k w (n) pk i k , X k w (n) pk ; g (... |

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Citation Context ...l non-linear approximation of I in terms of J [13]. The correlation ratio is closely related to a very popular measure previously proposed by Woods et al [26], and generalized using robust metrics in =-=[12]-=-. Statistical relationship. Finally, assuming a functional relationship is sometimes too restrictive. Then, it is more appropriate to use information theoretic measures, from which mutual information ... |

5 |
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Citation Context ...dentical. This includes a number of popular measures: the sum of squared intensity dioeerences (SSD), the sum of absolute intensity dioeerences, cross-correlation [3], entropy of the dioeerence image =-=[4]-=-, etc. Although these measures are not equivalent in terms of robustness and accuracy, none of them is able to cope with relative intensity changes from one image to the other. AOEne relationship. The... |

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Citation Context ...transformation T appears as a parameter of this joint probability function, and it is natural to invoke the maximum likelihood principle to formulate registration, as already proposed for instance in =-=[23, 8, 1, 11, 5]-=-. It simply states that the most likely transformation between I and J is the one that maximizes the joint probability of (I ; J),sT = arg max T P (I ; J jT ) = arg max T P (I jJ; T ); the last equiva... |

4 | Mutual information matching and interpolation artefacts
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Citation Context ...ved in practice by oversampling the image J using fast interpolation techniques such as trilinear or partial volume interpolation (Maes et al., 1997; Sarrut and Miguet, 1999; Sarut and Feschet, 1999; =-=Pluim et al., 1999-=-). Notice that for evaluating the registration criterion Eq. (8), we do not actually have to interpolate every point in space, but only, for a given transformation, the points that are put into corres... |

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Citation Context ...l as the computer working precision. This is achieved in practice by oversampling the image J using fast interpolation techniques such as trilinear or partial volume interpolation (Maes et al., 1997; =-=Sarrut and Miguet, 1999-=-; Sarut and Feschet, 1999; Pluim et al., 1999). Notice that for evaluating the registration criterion Eq. (8), we do not actually have to interpolate every point in space, but only, for a given transf... |

2 | A Maximum-Likelihood Approach to PET Emission/Attenuation Image Registration
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Citation Context ...ather to choose the one that is best adapted to the nature of the images. Up to now, the link between explicit modeling assumptions and similarity measures has not been made clear. After some authors =-=[11, 5]-=- proposed that image registration could be seen as a maximum likelihood estimation problem, Viola et al [23, 24] suggested the analogy of this approach with registration using information theory. Rema... |

1 | The Partial Intensity Dierence interpolation - Sarrut, Feschet - 1999 |

1 | A novel approach for the registration of 2D portal and 3D CT images for treatment setup verification - Duncan - 1998 |