cvpr cvpr2013 cvpr2013-190 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Ning Zhu, Albert C.S. Chung
Abstract: In this paper, we propose a graph-based method for 3D vessel tree structure segmentation based on a new tubularity Markov tree model ( TMT), which works as both new energy function and graph construction method. With the help of power-watershed implementation [7], a global optimal segmentation can be obtained with low computational cost. Different with other graph-based vessel segmentation methods, the proposed method does not depend on any skeleton and ROI extraction method. The classical issues of the graph-based methods, such as shrinking bias and sensitivity to seed point location, can be solved with the proposed method thanks to vessel data fidelity obtained with TMT. The proposed method is compared with some classical graph-based image segmentation methods and two up-to-date 3D vessel segmentation methods, and is demonstrated to be more accurate than these methods for 3D vessel tree segmentation. Although the segmentation is done without ROI extraction, the computational cost for the proposed method is low (within 20 seconds for 256*256*144 image).
Reference: text
sentIndex sentText sentNum sentScore
1 hk Abstract In this paper, we propose a graph-based method for 3D vessel tree structure segmentation based on a new tubularity Markov tree model ( TMT), which works as both new energy function and graph construction method. [sent-7, score-1.518]
2 Different with other graph-based vessel segmentation methods, the proposed method does not depend on any skeleton and ROI extraction method. [sent-9, score-0.85]
3 The classical issues of the graph-based methods, such as shrinking bias and sensitivity to seed point location, can be solved with the proposed method thanks to vessel data fidelity obtained with TMT. [sent-10, score-0.989]
4 The proposed method is compared with some classical graph-based image segmentation methods and two up-to-date 3D vessel segmentation methods, and is demonstrated to be more accurate than these methods for 3D vessel tree segmentation. [sent-11, score-1.576]
5 Introduction In recent years, graph-based methods, such as graph cuts [4, 5], random walker [9], power-watershed [7] and their extensions [6, 10, 11, 17, 22, 23], have become a group of popular image segmentation methods. [sent-14, score-0.38]
6 Vessel segmentation is very useful for the diagnosis, visualization, treatment and surgery planning of vessel diseases. [sent-19, score-0.723]
7 With the advanced development ofthe medical image acquisition modalities, such as CT and MRI, many vessel segmentation methods have been developed in recent years [12, 14, 16, 18, 19, 21]. [sent-20, score-0.822]
8 However some classical segmentation methods cannot achieve good performance on some specific medical applications, such as vessel segmentation. [sent-21, score-0.845]
9 Here are some challenges for 3D vessel segmentation: a) The segmentation of elongated structures of vessels may suffer from the shrinking bias (Graph Cuts) and sensitivity of seed point locations (Random walker). [sent-22, score-1.13]
10 However, for 3D images, especially for vessel structures which spread over a large area in the image, providing enough seed points is not an easy task. [sent-24, score-0.741]
11 c) The intensity can change significantly along a vessel branch. [sent-27, score-0.664]
12 So the intensity feature which is widely used in many segmentation methods is not a good choice for vessel segmentation. [sent-28, score-0.767]
13 Also, the distal part of some vessels may be obscure (Figure 1(c)), and this may cause segmentation leakage to the background area. [sent-29, score-0.509]
14 As a result, despite of the advantages of graph-based framework, only a few methods [3, 8, 17, 20, 24], which combine graph cuts with vessel shape priors, are used for vessel segmentation. [sent-30, score-1.476]
15 Graph cuts based methods in [17, 20, 24] are used to obtain global optimal segmentation for single branches. [sent-31, score-0.244]
16 However, for the whole vessel tree segmentation, the simple combination of different branches may not be sufficient. [sent-32, score-0.727]
17 Methods in [3, 8] first detect the skeleton of vessel tree and then the graph cuts method is used for whole tree optimization. [sent-33, score-1.177]
18 All these graph cuts based methods require obtaining vessel skeleton as preprocessing and the region of interest (ROI) are then extracted accordingly. [sent-34, score-0.98]
19 As a result, the performance of these 222222111977 (a) Coronary artery on heart (b) Vessel near other object (c) Distal part of vessel Figure 1. [sent-35, score-0.736]
20 In this paper, we propose a new graph-based method for vessel tree structure segmentation based on a new tubularity Markov tree model ( TMT), which works as both new energy function and graph construction method. [sent-38, score-1.518]
21 The proposed method has four favorable properties: (i) With the new TMT model, a good data fidelity is embedded in the new objective function (Equation 2) and is evaluated to be effective on increasing the accuracy and reducing the risk of shrinking bias. [sent-39, score-0.265]
22 And (iv), the bifurcation of vessel tree structure does not require particular consideration. [sent-43, score-0.727]
23 For graph-based methods, graph construction and energy function are two major factors affecting the segmentation performance. [sent-46, score-0.296]
24 As discussed in [7], when 푝 is a small finite number, the optimization for Equation 1 can be done with graph cuts (푞 = 1) or random walker (푞 = 2). [sent-55, score-0.277]
25 Then TMT based new energy function and graph construction method for the objective function (Equation 2) will be introduced. [sent-61, score-0.224]
26 For vessel tree segmentation, we modify the unifying framework (Equation 1) from [7] to the following objective function: x = argm푥in푝l→im∞(푒푖푗∑∈퐸표푤푖푝푗∣푥푖− 푥푗∣2+푣푖∈∑푉푡푚푡푇푤푝푖∣푥푖− 1∣2) s. [sent-71, score-0.801]
27 (2) Here TMT = (퐸푡푚푡, 푉푡푚푡) is a tubularity Markov tree structure with its edge set 퐸푡푚푡 and node set 푉푡푚푡, and 푇푤푖 is the tubularity Markov response for 푣푖 ∈ 푉푡푚푡. [sent-74, score-0.979]
28 푆푉 and 푆퐵 are the vessel seeds and background s∈eed 푉s. [sent-75, score-0.686]
29 In this objective function, we delete the original region energy terms for both foreground and background and add a new data fidelity term for the nodes in the set 푉푡푚푡. [sent-76, score-0.308]
30 However, it is impossible to identify the vessel voxel from the others with only intensity since the background body organs may have similar intensity. [sent-79, score-0.755]
31 For 3D vessel segmentation, 푝 → ∞ is the best choice since this can reduce the risk of shrinking sb tiahes, abnesdt tt chihso i sc especially important fcoer t elongated structure segmentation with small number of seed points. [sent-85, score-0.981]
32 Tubularity Markov Tree and Graph Construction In this section, we propose a new graph-based optimization method for vessel segmentation. [sent-88, score-0.62]
33 A new energy function based on tubularity Markov tree model is proposed and used as vessel fidelity, and accordingly a new graph construction method is described. [sent-89, score-1.308]
34 To construct a good vessel data fidelity, the tubularity Markov tree model is proposed. [sent-90, score-1.115]
35 In this model, we make use of the tubularity shape character of vessel structure with a Markov tree representation. [sent-91, score-1.115]
36 The method for tubularity Markov tree construction is described in Algorithm 1. [sent-92, score-0.555]
37 The red lines in Figure 2 sketches the structure for the tubularity Markov tree. [sent-93, score-0.388]
38 Given a start seed node, the tubularity Markov tree is constructed by adding the nodes with the largest weighted joint tubularity score (shortened as tubularity score, 푇푠) iteratively. [sent-98, score-1.458]
39 The implementation of TMT construction is similar with the classic Prim’s minimal spanning tree in the manner of nodes spanning. [sent-99, score-0.298]
40 While in the proposed method, we aim at adding the nodes with the largest weighted joint tubularity score (푇푠) into the tree. [sent-104, score-0.471]
41 The tubularity score is calculated according to the following Algorithm 1 Tubularity Markov Tree Require: 퐼 – image voxels, 푆푉– vessel seeds, 푚푎푥푤 – maximal weight 1: INITIALIZATION: 푉푡푚푡 = 휙, 퐸푡푚푡 = 휙. [sent-105, score-1.033]
42 17: else if 푁푖 ∈ 푆푡푎푐푘푦 with current tubularity response 푇푠푖 a 푆n푡d푎 푐푇푠푘 (푁푖) > 푇푠푖 18: replace triple with (푁푖, curN, 푇푠 (푁푖)). [sent-113, score-0.45]
43 In this paper, we construct a Markov tree with the tubularity score 푇푠 based on Max-Mflux. [sent-129, score-0.52]
44 For the nodes in the vessel but deviate from the center, it may have a series of high Max-Mflux response ancestors. [sent-132, score-0.72]
45 As a result, although the response for the nodes itself may 푖 not be high, the weighted joint tubularity score considering all the ancestors may not be low. [sent-133, score-0.569]
46 And for the points with high Max-Mflux response for both the ancestors and itself, it can have a high tubularity score and as a result has a high data fidelity as foreground vessel point. [sent-134, score-1.25]
47 The new tubularity score is robust for the seed node position. [sent-135, score-0.571]
48 Take a perfect tube for example, the Max-Mflux response is the same on centerline no matter where the seed point is located. [sent-136, score-0.227]
49 Since the weights in 푇푠 is summed to 1, the tubularity scores for all centerline points are the same, regardless whatever 휆 is. [sent-137, score-0.481]
50 The proposed new model is named as tubularity Markov tree model, here the “tree” represents the spanning structure, and the relationship between a particular node and its ancestors is more likely a Markov chain. [sent-142, score-0.678]
51 The spanning of the tree is based on the new weighted joint tubularity score. [sent-143, score-0.568]
52 After obtaining the tree and tubularity response, the graph is constructed according to Algorithm 2, which is the main framework for the proposed method. [sent-145, score-0.59]
53 Similarly, 푒(푣푝, 푆푣) represents all the edges connecting 푣푝 and the vessel seed points. [sent-149, score-0.743]
54 Algorithm 2 TMT-based vessel segmentation 1:INPUT: 퐼 image voxels, 푆푉 vessel seeds, 푆퐵 background seeds. [sent-154, score-1.37]
55 In this section, a new model named TMT is proposed, and new data fidelity and graph construction method based on the model is also introduced. [sent-174, score-0.256]
56 Based on the new weighted joint tubularity score in Equation 3, and the tree spanning method described in Algorithm 1, the TMT model provides good data fidelity, and perform preliminary graph construction. [sent-175, score-0.688]
57 Algorithm 2 is then used to construct the whole graph for energy optimization of the new singular object segmentation objective function (Equation 2). [sent-176, score-0.267]
58 Experiments For method evaluation, we have compared the proposed method with some other segmentation methods on both synthetic images and clinical CTA images. [sent-178, score-0.233]
59 As stated in Section 1, two important challenges for vessel segmentation are: a) the vessels are surrounded by human organs with similar intensity (Figure 1(b)), b) the distal part of vessel may be obscure (Figure 1(c)). [sent-180, score-1.783]
60 Similar with real vessels, the radius of the synthetic vessel is also decreased gradually. [sent-184, score-0.722]
61 In the second synthetic image (Figure 4(a)), the intensity of synthetic vessel and nearby objects are set to 1200 and that of background is set to 800. [sent-186, score-0.855]
62 The proposed method was compared with powerwatershed method [7], graph cuts [4] on the two groups of synthetic images, and to be fair, we also conduct the comparison with the graph cuts method by providing the same graph constructed with the proposed method. [sent-189, score-0.696]
63 34269 021 603 % part dark and when the noise level increases, the leakage to the background for both graph cut methods and watershed method may happen. [sent-203, score-0.248]
64 The segmentation result then shrink to the background seeds points and all the other voxels in the image are labeled as foreground object. [sent-204, score-0.252]
65 The accuracy of the graph cuts method with TMT graph drops later than the other two methods, which means with TMT, a better performance on noisy images is obtained for the graph cuts method. [sent-208, score-0.584]
66 By providing reasonable data fidelity which can reduce the shrinking risk, the proposed method can have good performance on noisy images. [sent-210, score-0.239]
67 Different with the graph cuts method with TMT, our method emphasizes more on the weights by 푝 → ∞ and dmoeetsh noodt e smufpfhera sfrizoems mtheo shrinking wbieaisg. [sent-211, score-0.378]
68 h In all experiments, the weight for calculating the tubularity score was set to 0. [sent-212, score-0.413]
69 The TMT construction is the reason that the proposed methods and the Graph Cuts method with TMT require more the computation time than watershed and graph cuts method respectively. [sent-225, score-0.385]
70 Actually, although it takes a few seconds to obtain TMT and the graph can be a little larger than that in watershed and graph cuts method, the optimization procedure for the proposed method and graph cuts with TMT may be accelerated with the help of TMT construction. [sent-226, score-0.678]
71 In Figure 3(c), a slice of distal part of the synthetic vessel is also presented. [sent-230, score-0.849]
72 The experiments was also carried out on clinical images for coronary artery segmentation. [sent-234, score-0.272]
73 As can be seen in Figure 5, the proposed method is compared with classic region growing [2] (Figure 5(a)), graph cuts [4] (Figure 5(b)), graph cuts with TMT graph (Figure 5(c)) and power watershed method [7] (Figure 5(d)) on a 256*256* 144 clinical image. [sent-235, score-0.764]
74 As shown in these figures, region growing and graph cuts methods suffer a lot from leakage since the distal parts of the vessel are obscure and have no clear boundary. [sent-236, score-1.11]
75 Given a seed point (red point in Figure 5(a)), the region growing method grows to the whole heart area and also spread to some other vessels nearby. [sent-237, score-0.325]
76 And the tracking of real objective coronary artery (green part in Figure 5(a)) stops earlier so the distal parts are missing. [sent-238, score-0.402]
77 Since the distal parts of the real vessels are not clear, the obtained results of graph cuts methods leak to other organs and vessels near the coronary arteries. [sent-239, score-0.872]
78 As for the power watershed method, although it emphasizes more on weights which may reduce the risk of shrinking, the unpredictable intensity changes along the vessels makes it difficult to track the distal parts. [sent-240, score-0.532]
79 For the proposed method, with the vessel fidelity from TMT, the 222222222422 (a)RegionGrowing (b) Graph Cuts[4] (c)GraphCutswithTMT (d)PowerWatershed[7] (e)ProposedMethod (a)Prop sedmethod (b)Surfaceobtainedwith[3] (c)Surfaceobtainedwith[8] Figure 5. [sent-242, score-0.721]
80 The proposed method was also compared with two graph-based vessel segmentation methods [8, 3]. [sent-247, score-0.723]
81 In these two methods, the skeletons are first detected and the graph cuts methods are applied on the region of interest. [sent-248, score-0.274]
82 So in this group of experiments, we first detect the centerline of the vessels with the method in [25] and find the region of interest according to the associated radius obtained. [sent-249, score-0.253]
83 However, without the help of regional energy, the method in [3] suffers from shrinking problem, which makes some distal parts thinner than the real segmentation. [sent-252, score-0.251]
84 However, they require the skeleton of the vessels as premise. [sent-254, score-0.267]
85 As a result, the performance of these methods depends on the accuracy of the skeleton detection for the vessel structures. [sent-255, score-0.727]
86 Conclusion In this paper, we propose a graph-based method for 3D vessel tree structure segmentation based on a new tubularity Markov tree model ( TMT), which works as both new energy function and graph construction method. [sent-261, score-1.518]
87 Different with all other graph-based vessel segmen222222222533 tation methods, the proposed method does not depend on any skeleton and ROI extraction method. [sent-263, score-0.747]
88 The classical issues of the graph-based method, such as shrinking bias and sensitivity to seed point position, can be solved with the proposed method thanks to the TMT model as vessel data fidelity in the graph-based unifying framework. [sent-264, score-1.032]
89 The proposed method is compared with some classical graph-based image segmentation methods and two up-to-date 3D vessel segmentation methods. [sent-265, score-0.849]
90 The experiments show that the proposed method is more accurate than these methods for 3D vessel tree segmentation. [sent-266, score-0.727]
91 The computational time for the whole tree segmentation is within 20 seconds although the whole 3D image is included in the algorithm. [sent-267, score-0.232]
92 Segmentation of interwoven 3d tubular tree structures utilizing shape priors and graph cuts. [sent-280, score-0.234]
93 Interactive graph cuts for optimal boundary & region segmentation of objects in nd images. [sent-290, score-0.356]
94 Liver vessels segmentation using a hybrid geometrical moments/graph cuts method. [sent-307, score-0.404]
95 3-d graph cut segmentation with riemannian metrics to avoid the shrinking problem. [sent-327, score-0.302]
96 A review of 3D vessel lumen segmentation techniques: Models, features and extraction schemes. [sent-347, score-0.768]
97 Bayesian maximal paths for coronary artery segmentation from 3D CT angiograms. [sent-352, score-0.327]
98 Coronary lumen segmentation using graph cuts and robust kernel regression. [sent-382, score-0.364]
99 Robust shape regression for [22] [23] [24] [25] supervised vessel segmentation and its application to coronary segmentation in cta. [sent-392, score-0.96]
100 Minimum average-cost path for real time 3d coronary artery segmentation of ct images. [sent-413, score-0.327]
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