## Extension of the ICP algorithm to nonrigid intensity-based registration of 3D volumes (1997)

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Venue: | COMPUT. VIS. IMAGE UNDERSTANDING |

Citations: | 32 - 5 self |

### BibTeX

@ARTICLE{Feldmar97extensionof,

author = {J. Feldmar and J. Declerck and G. Malandain and N. Ayache},

title = {Extension of the ICP algorithm to nonrigid intensity-based registration of 3D volumes},

journal = {COMPUT. VIS. IMAGE UNDERSTANDING},

year = {1997},

pages = {193--206}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present in this paper a new registration and gain correction algorithm for 3D medical images. It is intensity based. The basic idea is to represent images by 4D points (xj;yj;zj;ij) and to define a global energy function based on this representation. For minimisation, we propose a technique which does not require computing the derivatives of this criterion with respect to the parameters. It can be understood as an extension of the Iterative Closest Point algorithm [5, 56] or as an application of the formalism proposed in [13]. Two parameters enable us to develop a coarse-to-fine strategy both for resolution and for deformation. Our technique presents the advantage of minimising a well-defined global criterion, to deal with various classes of transformations (for example rigid, affine, volume spline and radial basis functions), to be simple to implement, and to be efficient in practice. Results on real brain and heart 3D images are presented to demonstrate the validity of our approach. We also explain how one can compute basic statistics on the deformation parameters to constrain the set of possible deformations by learning and to discriminate between different groups.

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Citation Context ...we propose a technique which does not require computing the derivatives of this criterion with respect to the parameters. It can be understood as an extension of the Iterative Closest Point algorithm =-=[5, 56]-=- or as an application of the formalism proposed in [13]. Two parameters enable us to develop a coarse-to- ne strategy both for resolution and for deformation. Our technique presents the advantage of m... |

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Citation Context ...8, 23, 52]. The registration method presented in this paper is related to intensity based techniques. Most such methods were developed for 3D-3D rigid registration and try to maximise the correlation =-=[30, 55]-=- or the mutual information [15, 46, 53]between the two images. We explore alowlevel method because high or middle level representations can be di cult to compute, either be3cause of the image acquisi... |

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Citation Context ...e group for the patients. Based on the parameters of the deformations, we could perform an Hottelling T 2 test to validate or invalidate the null hypothesis that the means of the two groups are equal =-=[10, 32]-=-. This would enable us to answer the question: is there a signi cant di erence in shape between the two groups . If this is the case, then one should consider Fisher's linear discrimant [10, 32]. Inde... |

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Citation Context ...l minimum. 12example a tumor). It is important to deal explicitly with this occlusion problem to get an accurate transformation. One might adopt a robust criterion (in the sense of statistics) as in =-=[14, 29]-=- for rigid surface registration. But then stage 2 of the algorithm would not be a linear system resolution and the algorithm would be far less e cient. We prefer the approach proposed in [56] for 3D-3... |

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Citation Context ... a MR image of a new patientinto anatomical regions based on knowledge of voxel-to-voxel correspondence. Previous research has aimed to compute such a match based on crest lines, surfaces or contours =-=[19, 23, 31, 45, 47, 49, 51]-=- or based directly on the intensities in the images [4, 12, 16, 25, 27, 39, 50]. The algorithm presented in this paper aims to compute a global geometric transformation that minimises an explicit glob... |

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Citation Context ... be worth doing it for the algorithm presented in this paper. Indeed, time sequences of 3D images will probably be more and more common and we believe that analysis of such images presents achallenge =-=[38, 1, 36, 41]-=-. The last problem concerns the validation of non-rigid registration. How is it possible to say that one algorithm is better than another ? The easiest way of doing it is maybe to ask a radiologist or... |

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Citation Context ...rmediate level (surfaces, contours) or low level. We do not present a review here of the numerous registration methods based on high and middle level representations; complete reviews can be found in =-=[3, 8, 23, 52]-=-. The registration method presented in this paper is related to intensity based techniques. Most such methods were developed for 3D-3D rigid registration and try to maximise the correlation [30, 55] o... |

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Citation Context ...l signi cance to determine the best deformation space and to describe it with as few parameters as possible. One approach is to determine this set by learning. This has been investigated in [17, 48], =-=[40]-=- and [48] respectively for displacement elds, modal analysis and Fourier analysis. Similary to [17], we could compute the set of possible values of the control points on a database and then perform Pr... |

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Citation Context ...sponding energy tends to minimise this di erence between the two sets of points describing the images. This way of using the gradient information is similar to the use of surface normals presented in =-=[24]-=- for rigid surface registration: it gave satisfactory results though a precise theoretical approach would be necessary, as exposed in [42]. (2) 3 Minimisation technique To minimise the energy function... |

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Citation Context ...use it is not easy to extract features of the organs in the images. Brain images are a good example of images that are di cult to segment. A lot of research has been done to try to solve this problem =-=[33, 35, 54]-=-. However, matching two MR brain images from two di erent patients is important in practice. Indeed, we have access to a brain image which has been manually segmented (or labelled) (courtesy of Ron Ki... |

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Citation Context ...rmediate level (surfaces, contours) or low level. We do not present a review here of the numerous registration methods based on high and middle level representations; complete reviews can be found in =-=[3, 8, 23, 52]-=-. The registration method presented in this paper is related to intensity based techniques. Most such methods were developed for 3D-3D rigid registration and try to maximise the correlation [30, 55] o... |

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Citation Context ... presented in this paper is related to intensity based techniques. Most such methods were developed for 3D-3D rigid registration and try to maximise the correlation [30, 55] or the mutual information =-=[15, 46, 53]-=-between the two images. We explore alowlevel method because high or middle level representations can be di cult to compute, either be3cause of the image acquisition modality or because it is not easy... |

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Citation Context ...ed. This algorithm has numerous applications. Indeed, it should enable us to perform registration when contour (or higher level feature) extraction is di cult. It is an extension of the ICP algorithm =-=[5,9,11,37, 56]-=-. Our technique has several advantages: minimising a well-de ned global criterion, to deal with various, well-de ned classes of transformations (for example rigid, a ne and volume spline or radial bas... |

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Citation Context ... presented in this paper is related to intensity based techniques. Most such methods were developed for 3D-3D rigid registration and try to maximise the correlation [30, 55] or the mutual information =-=[15, 46, 53]-=-between the two images. We explore alowlevel method because high or middle level representations can be di cult to compute, either be3cause of the image acquisition modality or because it is not easy... |

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Citation Context ...to-voxel correspondence. Previous research has aimed to compute such a match based on crest lines, surfaces or contours [19, 23, 31, 45, 47, 49, 51] or based directly on the intensities in the images =-=[4, 12, 16, 25, 27, 39, 50]-=-. The algorithm presented in this paper aims to compute a global geometric transformation that minimises an explicit global criterion and uses a coarse to ne strategy to try to avoid local minima. The... |

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Citation Context ...to-voxel correspondence. Previous research has aimed to compute such a match based on crest lines, surfaces or contours [19, 23, 31, 45, 47, 49, 51] or based directly on the intensities in the images =-=[4, 12, 16, 25, 27, 39, 50]-=-. The algorithm presented in this paper aims to compute a global geometric transformation that minimises an explicit global criterion and uses a coarse to ne strategy to try to avoid local minima. The... |

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Citation Context ...e question should depend on the goal of the registration. For example, we are interested in detecting blobs of activation in f-MRI data. After non-rigid registration, we use the software described in =-=[26]-=- to detect such blobs. The software tells us, for each blob, the probability of observing it by chance. It seems to be reasonable (even if it is debatable) to say, since registration and blobs detecti... |

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Citation Context ... anatomical signi cance to determine the best deformation space and to describe it with as few parameters as possible. One approach is to determine this set by learning. This has been investigated in =-=[17, 48]-=-, [40] and [48] respectively for displacement elds, modal analysis and Fourier analysis. Similary to [17], we could compute the set of possible values of the control points on a database and then perf... |

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Citation Context ... be worth doing it for the algorithm presented in this paper. Indeed, time sequences of 3D images will probably be more and more common and we believe that analysis of such images presents achallenge =-=[38, 1, 36, 41]-=-. The last problem concerns the validation of non-rigid registration. How is it possible to say that one algorithm is better than another ? The easiest way of doing it is maybe to ask a radiologist or... |

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Citation Context ... a MR image of a new patientinto anatomical regions based on knowledge of voxel-to-voxel correspondence. Previous research has aimed to compute such a match based on crest lines, surfaces or contours =-=[19, 23, 31, 45, 47, 49, 51]-=- or based directly on the intensities in the images [4, 12, 16, 25, 27, 39, 50]. The algorithm presented in this paper aims to compute a global geometric transformation that minimises an explicit glob... |

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Citation Context ...e group for the patients. Based on the parameters of the deformations, we could perform an Hottelling T 2 test to validate or invalidate the null hypothesis that the means of the two groups are equal =-=[10, 32]-=-. This would enable us to answer the question: is there a signi cant di erence in shape between the two groups . If this is the case, then one should consider Fisher's linear discrimant [10, 32]. Inde... |

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Citation Context ...-rest pairs. The results are visually very good. In order to give a more quantitative quality measure, we would have to do the same experiements as we did in [28] for 3D-3D non rigid surface matching =-=[21]-=-. Note that it is important for this problem to deal explicitly with occlusion, because ischemia appears as occlusion in the images (it corresponds to holes present in one image and not in the other o... |

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Citation Context ...use it is not easy to extract features of the organs in the images. Brain images are a good example of images that are di cult to segment. A lot of research has been done to try to solve this problem =-=[33, 35, 54]-=-. However, matching two MR brain images from two di erent patients is important in practice. Indeed, we have access to a brain image which has been manually segmented (or labelled) (courtesy of Ron Ki... |

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Citation Context ... be worth doing it for the algorithm presented in this paper. Indeed, time sequences of 3D images will probably be more and more common and we believe that analysis of such images presents achallenge =-=[38, 1, 36, 41]-=-. The last problem concerns the validation of non-rigid registration. How is it possible to say that one algorithm is better than another ? The easiest way of doing it is maybe to ask a radiologist or... |

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Citation Context ...t squares estimation turns out to be the resolution of a linear system as explained in appendix A. Note from a very practical point of view that the code necessary for this estimation is available in =-=[44]-=- and there is almost no programming to be done. 11It is straightforward to show that this algorithm minimises the de ned energy and that it converges 2 . Let us de ne the energy function E 0 : E 0 (f... |

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Citation Context ...e derivatives of this criterion with respect to the parameters. It can be understood as an extension of the Iterative Closest Point algorithm [5, 56] or as an application of the formalism proposed in =-=[13]-=-. Two parameters enable us to develop a coarse-to- ne strategy both for resolution and for deformation. Our technique presents the advantage of minimising a well-de ned global criterion, to deal with ... |

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Citation Context ...rmediate level (surfaces, contours) or low level. We do not present a review here of the numerous registration methods based on high and middle level representations; complete reviews can be found in =-=[3, 8, 23, 52]-=-. The registration method presented in this paper is related to intensity based techniques. Most such methods were developed for 3D-3D rigid registration and try to maximise the correlation [30, 55] o... |