cvpr cvpr2013 cvpr2013-194 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Shihui Ying, Guorong Wu, Qian Wang, Dinggang Shen
Abstract: Recently, groupwise registration has been investigated for simultaneous alignment of all images without selecting any individual image as the template, thus avoiding the potential bias in image registration. However, none of current groupwise registration method fully utilizes the image distribution to guide the registration. Thus, the registration performance usually suffers from large inter-subject variations across individual images. To solve this issue, we propose a novel groupwise registration algorithm for large population dataset, guided by the image distribution on the manifold. Specifically, we first use a graph to model the distribution of all image data sitting on the image manifold, with each node representing an image and each edge representing the geodesic pathway between two nodes (or images). Then, the procedure of warping all images to theirpopulation center turns to the dynamic shrinking ofthe graph nodes along their graph edges until all graph nodes become close to each other. Thus, the topology ofimage distribution on the image manifold is always preserved during the groupwise registration. More importantly, by modeling , the distribution of all images via a graph, we can potentially reduce registration error since every time each image is warped only according to its nearby images with similar structures in the graph. We have evaluated our proposed groupwise registration method on both synthetic and real datasets, with comparison to the two state-of-the-art groupwise registration methods. All experimental results show that our proposed method achieves the best performance in terms of registration accuracy and robustness.
Reference: text
sentIndex sentText sentNum sentScore
1 Abstract Recently, groupwise registration has been investigated for simultaneous alignment of all images without selecting any individual image as the template, thus avoiding the potential bias in image registration. [sent-10, score-1.04]
2 However, none of current groupwise registration method fully utilizes the image distribution to guide the registration. [sent-11, score-1.043]
3 Thus, the registration performance usually suffers from large inter-subject variations across individual images. [sent-12, score-0.357]
4 To solve this issue, we propose a novel groupwise registration algorithm for large population dataset, guided by the image distribution on the manifold. [sent-13, score-1.179]
5 Specifically, we first use a graph to model the distribution of all image data sitting on the image manifold, with each node representing an image and each edge representing the geodesic pathway between two nodes (or images). [sent-14, score-0.385]
6 Then, the procedure of warping all images to theirpopulation center turns to the dynamic shrinking ofthe graph nodes along their graph edges until all graph nodes become close to each other. [sent-15, score-0.52]
7 Thus, the topology ofimage distribution on the image manifold is always preserved during the groupwise registration. [sent-16, score-0.825]
8 More importantly, by modeling , the distribution of all images via a graph, we can potentially reduce registration error since every time each image is warped only according to its nearby images with similar structures in the graph. [sent-17, score-0.443]
9 We have evaluated our proposed groupwise registration method on both synthetic and real datasets, with comparison to the two state-of-the-art groupwise registration methods. [sent-18, score-2.009]
10 All experimental results show that our proposed method achieves the best performance in terms of registration accuracy and robustness. [sent-19, score-0.335]
11 Introduction In recent years, groupwise registration emerges as a new image normalization technique to simultaneously align a number of images to the latent population center. [sent-21, score-1.178]
12 Since groupwise registration is able to avoid the bias in specifying reference image during registration, it has wide applicationqianwang@ cs . [sent-22, score-0.994]
13 Also, in many neuroscience studies, a large population of images is required to be normalized to the population center for better delineating the structural/functional difference due to brain development, aging and dementia [5, 14, 18]. [sent-28, score-0.489]
14 Although a number of groupwise registration algorithms have been proposed [4–9, 11–13, 16, 17, 19], most of exist- ing methods have the limitation of assuming only one center for a group of images, which prohibits further application on large complex population dataset. [sent-29, score-1.218]
15 For example, studies on Alzheimer’s disease usually need to register hundreds of brain images. [sent-30, score-0.156]
16 However, due to considerable inter-subject variations, the group mean by simple average [12] is usually very fuzzy (due to the loss of anatomical details), especially when all images are far from being well registered. [sent-31, score-0.156]
17 Then, taking the fuzzy group mean as the reference to guide the entire groupwise registration with clear individual images will eventually undermine the overall registration accuracy. [sent-32, score-1.564]
18 , geometric mean [6] and sharp mean [17], have been proposed to address this issue, however, each image is independently registered to the population center without coordinating with its neighboring images on the image manifold. [sent-35, score-0.343]
19 In CVPR 2010, two groupwise registration papers [11, 19] proposed the similar idea to register all images by considering nearest neighboring images. [sent-37, score-1.07]
20 To deal with groupwise registration on large population dataset [5, 7], Wang et al. [sent-44, score-1.154]
21 proposed a hierarchical registration framework to cluster images into a pyramid of classes [16]. [sent-45, score-0.359]
22 Then, intra-class registration is performed to register all (similar) images within each class for generating the representative center image. [sent-46, score-0.452]
23 The center images of all classes are further registered from the bottom to the top in the pyramid, until all images are registered. [sent-47, score-0.165]
24 Therefore, this groupwise registration framework can efficiently register a large image data set with relatively better registration performance by addressing the challenges of registering two images with large anatomical differences. [sent-48, score-1.485]
25 Inspired by this ideal of hierarchical pyramid, we introduce the concept of graph into the groupwise registration, and then formulate the procedure of agglomerating all images into the common space as a dynamic evolution of graph shrinkage. [sent-49, score-0.946]
26 Specifically, we consider each image as a node in the graph with each edge representing the geodesic pathway between the two nodes. [sent-50, score-0.302]
27 During graph shrinking, each image (or node in graph) is driven by the average velocities from its connected images (or nodes) in the graph, and warped along the geodesic on the image manifold. [sent-52, score-0.297]
28 On the contrary, we address this limitation by employing diffeomorphism in our graph shrinkage procedure. [sent-64, score-0.198]
29 In the groupwise registration method proposed by Joshi eMt a. [sent-70, score-0.994]
30 I n[1 t2he], gthroeu population ctreanttieonr i ms emthooddel pedro as tsehed Kbya rJcohsehri mean Ic under an H1 (Sobolev) metric, as described below: ? [sent-72, score-0.181]
31 =1d2(Ii,I), (1) where d(·, ·) is the geodesic distance between two images on Mere. [sent-74, score-0.146]
32 For any pair of images Ii, Ij ∈ M, their geodesic distance d(Ii, Ij) is given as: d(Ii,Ij) =? [sent-84, score-0.146]
33 ds, (2) where vis,j is the velocity vector (or tangent vector in [10]) on the geodesic γij (s), with γij (0) = Ii and γij (1) = Ij . [sent-90, score-0.268]
34 According to the definition in [10], geodesic on manifold is a curve parameterized with constant velocity, i. [sent-92, score-0.202]
35 This indicates that the magnitude of the geodesic pathway from Ii to Ij eventually equals the length of the velocity vector at the initial point Ii (s = 0). [sent-104, score-0.364]
36 For convenience, in the following, we omit the superscript ‘0’ in vi0,j and use vi,j to represent the constant velocity vector of the geodesic from Ii to Ij . [sent-105, score-0.285]
37 Energy Function of Graph Shrinkage Model The goal of groupwise registration is to simultaneously register all subject images to the population center. [sent-108, score-1.23]
38 , in the end of groupwise registration), the overall distance F(t) between all pairs of the deformed images should be as small as possible: = ? [sent-113, score-0.741]
39 In general, deformable image registration will be performed to estimate each velocity vector vi,j (t) and further calculate the deformation pathway between Ii(t) and Ij (t) by exp(vi,j (t)), where exp is the exponential map [10]. [sent-126, score-0.646]
40 Since it is challenging to register two images with large anatomical differences, minimizing F(t) by considering the registration of all possible pairs of images might undermine the overall registration performance. [sent-127, score-0.851]
41 Inspired by the ABSORB method, it is reasonable to consider the registration only between the two images with similar anatomical structures. [sent-128, score-0.408]
42 Therefore, we introduce the variable eij to indicate whether images Ii(t) and Ij (t) are similar enough (eij = 1) or not (eij = 0). [sent-129, score-0.192]
43 = 1 Next, we use a graph defined on the image manifold to interpret F(t) in Eq. [sent-139, score-0.18]
44 eij }= b e1 represents a link between Ii(t) and Ij (t). [sent-143, score-0.168]
45 Demonstration of our proposed groupwise registration by graph shrinkage. [sent-160, score-1.094]
46 Then, the topology of their distribution can be described by a graph, where the graph edges denote the local connections between graph nodes. [sent-165, score-0.286]
47 Specifically, the velocity vector vi,j (t) is associated with each graph edge, where the integration along vi,j (t) forms the geodesic distance from Ii(t) to Ij (t). [sent-166, score-0.384]
48 Thus, the minimization of F(t) can be regarded as a dynamic graph shrinkage procedure, which deforms each image from Ii(t) to Ii(t + Δt) with the decreased overall geodesic distance, while keeping the topology of the entire graph. [sent-167, score-0.457]
49 2, all the images (in blue dots) at time t are the nodes in the graph where the graph edges are denoted by the red solid curves. [sent-169, score-0.257]
50 The graph G(t + Δt) (in purple dots and green curves) keeps the same topology )w (iitnh pGu(rtp)l (ei dno o btslu aen ddo gtsr aennd c ruerdv ecsu)rv keese)p. [sent-171, score-0.198]
51 sA thse et simame te itonpcoreloasgeys, w ailtlh hI iG ((tt))s are supposed ntod m reedet c uatr vthese) population center in the end of groupwise registration. [sent-172, score-0.86]
52 Obviously, the key steps in our method are (1) constructing the graph on the image manifold and (2) deforming image Ii(t) toward the hidden population center at time t. [sent-173, score-0.41]
53 The na¨ ıve solution for graph construction is to set a threshold h and then remove elements with geodesic distances higher than the threshold h, i. [sent-178, score-0.238]
54 Specifically, two criteria are used to construct the graph: (C1) for any two nodes in the graph, there should be at least one path connecting these two nodes; (C2) the number of graph edges should be as low as possible, for saving the computational cost during the groupwise registration. [sent-182, score-0.792]
55 Given the geodesic distance between any two images Ii(0) and Ij (0), we set the search range within the low bound bL = 0 and the upper bound bH = maxi,j d(Ii (0) , Ij (0)). [sent-184, score-0.206]
56 ∈Th (e0n,, 1if) the tentatively constructed graph satisfies the criterion (C1), the upper bound bH will be decreased to h; otherwise, the low bound bL will be increased to h. [sent-186, score-0.212]
57 (6) to guide the groupwise registration as described below. [sent-189, score-1.018]
58 Graph Shrinkage As we formulate the problem of groupwise registration as the dynamic shrinkage of graph, it is critical to determine the deformation of each image Ii(t) at time t, which 222333222533 can consistently minimize F(t) in Eq. [sent-192, score-1.108]
59 It is natural to move Ii(t) along the average velocity direction on the manifold according to its connected images in the graph G(t). [sent-196, score-0.366]
60 The geodesic from Ii(t) to Ij (t) can be calculated by the exponential mapping from the vector space of stationary velocity field to diffeomorphism, i. [sent-203, score-0.284]
61 Given a time increment Δt, image Ii(t) is deformed to Ii(t + Δt) along the geodesic exp( vˆi (t) · Δt), where the velocity direction is steered by vˆi (t) (Eq. [sent-206, score-0.367]
62 theorem to prove that F(t) is a monotonously decreasing function of time t along the velocity direction defined in Eq. [sent-222, score-0.246]
63 Theorem 1 The velocity fields defined in (7) make the objective function F(t) strictly and monotonously decreasing. [sent-224, score-0.194]
64 Numerical Implementation By Theorem 1, it is clear that the velocity vector defined by Eq. [sent-392, score-0.163]
65 i N veexc-t, along these velocity vectors, a stepsize Δq. [sent-400, score-0.185]
66 Summary In our groupwise registration method, we first use graph to model the distribution of all images on the manifold. [sent-453, score-1.143]
67 Then, the groupwise registration is formulated as the graph shrinking procedure, where each image in the graph deforms along the graph edge on the manifold. [sent-454, score-1.409]
68 Output: TNhe a dfinefeo arlmiganteiodn pathway Ifr}om Ii to the population center Iˆc. [sent-458, score-0.281]
69 Then, Update the warped image Iik+1; End k ⇐ k + 1; Until: Convergence a knd + output the deformation field from each Ii to the population center by exp(Δtk vˆik) ◦ · · · ◦ exp(Δt0 vˆi0). [sent-463, score-0.266]
70 Experimental Results In this section, we evaluate the registration performance of our proposed groupwise registration method on both synthetic and real datasets of infant brain images. [sent-465, score-1.626]
71 For the sake of comparison, we also apply the group-mean registration method [12] and the ABSORB method [11] in our experiments2. [sent-466, score-0.335]
72 After performing the groupwise registration with the group-mean method, ABSORB and our proposed method, we can obtain the final distributions of all registered images in the projected PCA space. [sent-489, score-1.094]
73 It is clear that our method achieves the best performance in terms of less registration errors. [sent-506, score-0.352]
74 Groupwise Registration on Longitudinal Infant Brains The infant data used in this paper is a part of a large ongoing study of early brain development in normal children where T1-weighted MR brain images were collected by using a 3T SIEMENS scanner. [sent-509, score-0.404]
75 Totally 7 longitudinal infant brains are used in this experiment, each with 6 time points (0, 3, 6, 9, 12 and 18 months of ages). [sent-513, score-0.338]
76 222333222866 Two longitudinal infant brains of two subjects at 6 different times are displayed in Fig. [sent-515, score-0.338]
77 Representative longitudinal infant brains of 2 subjects at different times The 3D renderings of the average images of all registered infant brain images by the conventional group-mean method, ABSORB, and our groupwise registration method are shown in Fig. [sent-518, score-1.732]
78 6, it is difficult, especially in the beginning of groupwise registration, to find a representative group-mean image that well represents all infant brains. [sent-521, score-0.831]
79 Therefore, the convention- al group-mean method failed to align infant brains onto the common space, as indicated by very fuzzy average image shown in Fig. [sent-522, score-0.277]
80 Both ABSORB and our groupwise registration methods achieve more reasonable registration results than the convention group-mean method, since these two methods take the advantages of detected data manifold and consider registering only the similar images during the iterative registration procedure. [sent-524, score-1.799]
81 On the other hand, by comparing the groupwise registration results of ABSORB in Fig. [sent-525, score-0.994]
82 To quantitatively evaluate the registration accuracy, we use the Dice ratio to measure the overlap degree between ROI A and ROI B, given as: Dice(A,B) = 2 ×||AA| + ∩ | BB||, (24) where | · | means the volume of the particular ROI. [sent-528, score-0.36]
83 Since no template image sis t hseel evcotleudm as a r tehfee preanrcteic fuolra groupwise registration, we will construct a labeled image in the common space by majority voting on ROIs of all registered images, in order to use the Dice ratio to evaluate the registration performance. [sent-529, score-1.11]
84 It is clear that our method achieves the highest Dice ratio compared to the other two groupwise registration Table 1. [sent-532, score-1.036]
85 Dice ratios of three brain tissues by three methods WM GM CSF Overall Group-mean method71. [sent-533, score-0.159]
86 Moreover, the iterative evolution of the Dice ratio on GM, WM, and CSF during the groupwise registration is shown in Fig. [sent-548, score-1.06]
87 Instead, in ABSORB, each individual image only considers its neighboring similar images when deforming to the estimated population center, which is not sufficient to preserve the topology of the entire image distribution during the groupwise registration. [sent-552, score-0.997]
88 Therefore, it is difficult to guarantee that all the tentatively deformed images converge to the population center, which also explains why the curves of the Dice ratio by ABSORB is not smooth as shown in Fig. [sent-553, score-0.294]
89 Conclusion In this paper, we have developed a novel groupwise registration by first introducing a concept of graph to model the entire image distribution. [sent-556, score-1.111]
90 Then, the procedure of groupwise registration is formulated as the dynamic shrinkage of graph on the manifold, which brings the advantage of preserving the topology of the image distribution during the groupwise registration. [sent-557, score-1.923]
91 Our proposed method has been evaluated on both synthetic data and real longitudinal infant brain data, where our method achieves the best registration result in comparison with the group-mean method and ABSORB. [sent-558, score-0.732]
92 Mean images by the three methods on longitudinal infant dataset. [sent-578, score-0.296]
93 RhtmBoadn4mehtIordain6Number8102 (a) Evolution of Dice ratio on white matter (b) Evolution of Dice ratio on gray matter (c) Evolution of Dice ratio on CSF Figure 8. [sent-582, score-0.167]
94 Evolution of Dice ratios of three brain tissues during the groupwise registration by three methods on longitudinal infant dataset. [sent-583, score-1.425]
95 Efficient large deformation registration via geodesics on a learned manifold of images. [sent-635, score-0.466]
96 An efficient incremental strategy for constrained groupwise registration based on symmetric pairwise registration. [sent-663, score-1.012]
97 Groupwise registration based on hierarchical image clustering and atlas synthesis. [sent-688, score-0.401]
98 Sharpmean: groupwise registration guided by sharp mean image and tree-based registration. [sent-695, score-1.015]
99 Registration of longitudinal brain image sequences with implicit template and spatial-temporal heuristics. [sent-701, score-0.219]
100 Image atlas construction via intrinsic averaging on the manifold of images. [sent-707, score-0.162]
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