cvpr cvpr2013 cvpr2013-139 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Jing Yuan, Wu Qiu, Eranga Ukwatta, Martin Rajchl, Xue-Cheng Tai, Aaron Fenster
Abstract: Segmenting 3D endfiring transrectal ultrasound (TRUS) prostate images efficiently and accurately is of utmost importance for the planning and guiding 3D TRUS guided prostate biopsy. Poor image quality and imaging artifacts of 3D TRUS images often introduce a challenging task in computation to directly extract the 3D prostate surface. In this work, we propose a novel global optimization approach to delineate 3D prostate boundaries using its rotational resliced images around a specified axis, which properly enforces the inherent rotational symmetry of prostate shapes to jointly adjust a series of 2D slicewise segmentations in the global 3D sense. We show that the introduced challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. In this regard, we propose a novel coupled continuous max-flow model, which not only provides a powerful mathematical tool to analyze the proposed optimization problem but also amounts to a new and efficient duality-basedalgorithm. Ex- tensive experiments demonstrate that the proposed method significantly outperforms the state-of-art methods in terms ofefficiency, accuracy, reliability and less user-interactions, and reduces the execution time by a factor of 100.
Reference: text
sentIndex sentText sentNum sentScore
1 ca Abstract Segmenting 3D endfiring transrectal ultrasound (TRUS) prostate images efficiently and accurately is of utmost importance for the planning and guiding 3D TRUS guided prostate biopsy. [sent-5, score-1.663]
2 Poor image quality and imaging artifacts of 3D TRUS images often introduce a challenging task in computation to directly extract the 3D prostate surface. [sent-6, score-0.735]
3 We show that the introduced challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. [sent-8, score-0.152]
4 In this regard, we propose a novel coupled continuous max-flow model, which not only provides a powerful mathematical tool to analyze the proposed optimization problem but also amounts to a new and efficient duality-basedalgorithm. [sent-9, score-0.247]
5 Currently, 3D endfiring transrectal ultrasound (TRUS) is the most commonly used imaging modality for image-guided biopsy of PCa due to its real-time imaging capability, low cost and simplicity [15]. [sent-13, score-0.363]
6 However, poor TRUS image quality, such as US speckle, shadowing by calcifications, missing edges or texture similarities between the inner and outer regions of the prostate [22] etc, makes it challenging to implement an automated or semiautomated 3D prostate TRUS segmentation in practice. [sent-16, score-1.536]
7 Previous Approaches In general, the proposed automated or semi-automated approaches to 3D TRUS prostate segmentation can be summarized by two categories: the direct 3D segmentation methods and 3D resliced segmentation methods. [sent-19, score-1.146]
8 Essentially, most direct 3D segmentation methods [10, 17, 13, 9] propose to evolve an initialized 3D surface to the correct prostate boundaries, with or without optimized shape deformations, which worked well for the reported applications. [sent-20, score-0.803]
9 However, direct computation over the large 3D TRUS data volumes makes them significantly time-consuming; moreover, intensive user interactions are required to initialize and conduct such direct 3D segmentation approaches. [sent-21, score-0.095]
10 Especially, the rotational-resliced segmentation approaches, recently proposed in [8, 14], sever the input 3D TRUS image into n slices with equal angular spacing about the specified rotational scan axis, as illustrated in Fig. [sent-24, score-0.397]
11 1(a), and make use of the approximate rotational symmetry of prostate shapes around the given axis to assist the 3D prostate segmentation. [sent-25, score-1.631]
12 The 3D prostate surface is, therefore, reconstructed from all the extracted 2D contours. [sent-28, score-0.708]
13 We show that the introduced challenging combinatorial optimization problem can be globally optimized by means ofconvexrelaxation. [sent-33, score-0.103]
14 In addition, we introduce the novel coupled continuous maxflow model as the dual formulation of the given convex relaxed optimization problem. [sent-34, score-0.295]
15 With help of the new coupled continuous max-flow model, we prove the proposed combinatorial optimization problem can be solved globally and exactly. [sent-35, score-0.328]
16 Hence, the globally optimal segmentation of the n 2D slices w. [sent-36, score-0.325]
17 Meanwhile, we derive a new and efficient coupled continuous max-flow based algorithm by the modern convex optimization theory, which can be directly im- plemented on GPU for a substantial speed-up in computation. [sent-40, score-0.272]
18 Global Optimization to 3D Prostate TRUS Segmentation Let V be the input 3D prostate endfiring transrectal ultrasound (TRUS) image, which is resliced rotationally around a given axis to n 2D images S1 . [sent-45, score-1.135]
19 The ellipsoid-like shape of the prostate allows to specify the resliced rotation axis, such that the extracted prostate regions on every two adjacent slices are spatially consistent, namely the rotational symmetry prior. [sent-49, score-1.986]
20 In this section, we propose a novel and efficient global optimization approach to simultaneously extract the n prostate contours of the input slices S1 . [sent-50, score-0.919]
21 We show the proposed combinatorial optimization problem can be exactly and globally solved by convex relaxation; for which we introduce a new spatially continuous max-flow model and prove its equivalence to the convex relaxed optimization formulation under the perspective of primal and dual. [sent-54, score-0.363]
22 We demonstrate that the new spatially continuous max-flow model carries great advantages to the proposed 3D prostate TRUS segmentation approach in both optimization analysis and algorithmic scheme. [sent-55, score-0.939]
23 n, denote the prostate region of the 2D slice Si, and ui (x), i = 1. [sent-61, score-1.024]
24 n, be the labeling function of the prostate 222222111200 Figure 1. [sent-64, score-0.708]
25 n, can be formulated as the spatially continuous min-cut problem which minimizes the following energy function Ei(ui) := ? [sent-74, score-0.112]
26 n, two cost functions Cis (x) and Cit (x) are defined, which evaluate the costs to label the pixel x ∈ Si as the prostate region and background respectively; the weighted total-variation function measures the length of each region indicated ui(x) ∈ {0, 1}. [sent-83, score-0.708]
27 Rotational Symmetry Prior In this work, the n slices S1 . [sent-84, score-0.187]
28 Sn are simply aligned along the resliced rotation axis, such that the rotation axis vertically bisects each slice (see the white dot line in Fig. [sent-87, score-0.42]
29 We propose to enforce the rotational symmetry prior ofthe segmented prostate regions Ri, i = 1. [sent-89, score-0.888]
30 n, by penalizing the spatial inconsistence of the extracted regions within two neightbour slices (see Fig. [sent-92, score-0.187]
31 Specifically, we penalize the area difference of two adjacent prostate regions, i. [sent-99, score-0.739]
32 n − 1, (2) and the area difference of Rn and R1 within the last and first slices defined as πn(u) :=? [sent-105, score-0.187]
33 Optimization Formulation Now we propose to extract the 3D prostate surface from the input 3D image by segmenting the n 2D image slices while incorporating their rotational symmetry prior. [sent-108, score-1.115]
34 Convex Relaxation and Coupled Continuous Max-Flow Model In this study, we show that the proposed optimization problem (4) can be globally and exactly solved by its convex relaxation n n u1. [sent-117, score-0.167]
35 n (x) ∈ {0, 1} in (4) is replaced by its convex relaxation u1. [sent-124, score-0.1]
36 Hence, (5) amounts to a convex optimization problem for which a global optimum exists. [sent-128, score-0.134]
37 We now study the convex relaxation problem (5) under the primal and dual perspective of convex optimization. [sent-129, score-0.172]
38 We introduce the novel coupled continuous max-flow model and demonstrate that it is dual or equivalent to the studied convex minimization problem (5). [sent-130, score-0.271]
39 With help of the introduced coupled continuous max-flow model, we prove the computed global optimum of the convex relaxation problem (5) also solve its original combinatorial optimization problem (4) globally and exactly. [sent-131, score-0.465]
40 In addition, the coupled continuous max-flow model derives a new and efficient algorithm to (5) without directly tackling its challenging nonsmooth function terms, i. [sent-132, score-0.226]
41 Coupled Continuous Max-Flow Model We first introduce the new spatially continuous configuration of flows (as illustrated in Fig. [sent-137, score-0.178]
42 2 (a) and (b)), such that • For each image slice Si, i = 1. [sent-138, score-0.232]
43 • Between two adjacent slices Si and Si+1, i= 1. [sent-142, score-0.218]
44 n 1, we link x ∈ Si to the same pixel x ∈ Si+1 and there is a flow ri (x) streaming in both directions. [sent-145, score-0.139]
45 Between the last slice Sn and the first slice S1, we link the pixel x := (x1, x2) ∈ S1 to the pixel (L x1, x2) ∈ Sn and there is a flow rn (x) streaming in both directions. [sent-146, score-0.575]
46 2 (a) and (b)), we introduce the new coupled continuous max-flow model, which maximizes the total amount of flows streaming from the n sources s1 . [sent-148, score-0.307]
47 n ; (8) • Capacity constraints on coupled flows: |ri (x) | ≤ α , i = 1. [sent-159, score-0.106]
48 n ; (9) Flow conservation constraints: all the flows at each pixel of every slice are balanced, i. [sent-162, score-0.327]
49 (11) Primal and Dual Formulations Introduce the multiplier functions ui (x), i = 1. [sent-175, score-0.084]
50 the flow conservation conditions, we then have the equivalent primal-dual model of (6) such that • u1m. [sent-181, score-0.076]
51 The proposed coupled continuous max-flow model (6) is dual or equivalent to the convex relaxation problem (5), and also the primal-dual model (12), i. [sent-190, score-0.322]
52 Global and Exact Optimization of (4) With help of the coupled continuous max-flow model (6), we can prove Proposition 2. [sent-195, score-0.225]
53 un∗ (x)) ∈ [0, 1] be the global optimum of the convex relaxation problem (5), the thresholds uiγ (x) ∈ {0, 1}, i= 1. [sent-199, score-0.137]
54 2, we see that the global optimum of the challenging combinatorial optimization problem (4) can be achieved by thresholding the optimum of its convex relaxation (5) with any parameter γ ∈ [0, 1). [sent-212, score-0.234]
55 1, it is also easy to see that the optimum of such convex relaxation problem (5) is just given by the optimal multipliers to the corresponding flow conservation conditions (10)-(1 1). [sent-214, score-0.213]
56 Especially, we will see the new coupled continuous max-flow algorithm is efficient and successfully avoids directly tackling the non-smooth function terms of (5). [sent-219, score-0.199]
57 By means of the augmented Lagrangian algorithm, we propose the coupled continuous max-flow algorithm such that, at each k-th iteration, 1. [sent-229, score-0.199]
58 Maximize Lc(u, ps,t, q, r) over the source flows pis (x) Cis (x), i = 1. [sent-240, score-0.12]
59 Maximize Lc(u1,2, ps1,2 , , q1,2 , r) over the coupled flow field |r(x) | ≤ β by fixing (q1,2 ,ps1,2, and (u1,2)k, which gives rk+1 pt1,2)k+1 := a|rrg(xm)|≤aβx−2c? [sent-261, score-0.175]
60 Experiments and Results Settings: Twenty 3D endfiring TRUS prostate images were used to validate the proposed method. [sent-278, score-0.819]
61 These images were acquired with a rotational scanning 3D TRUSguided prostate biopsy system, which made use of a commercially available end-firing TRUS transducer (Philips, Bothell WA). [sent-279, score-0.914]
62 19 mm3, and was resliced rotationally to 30 2D slices with a reslicing step angle of 6◦. [sent-283, score-0.361]
63 1 (b)) was used to initialize the segmentation of the first slice by visually coinciding its center (red dot in Fig. [sent-285, score-0.327]
64 The mean shape was learned from twenty manually segmented 2D prostate transverse images, which were not used in the validation procedure. [sent-287, score-0.797]
65 Our segmentation method was evaluated using the following metrics by comparing our computation results to × manual segmentations: Dice similarity coefficient (DSC), the mean absolute surface distance (MAD) and maximum absolute surface distance (MAXD) [9]. [sent-288, score-0.127]
66 The proposed method, denoted by MGO, was also compared to other rotational-resliced segmentation methods: active contour based method (MAC) [8] and level set based method (MLS) [14]. [sent-289, score-0.141]
67 Shape Priors: In this study, a 2D statistical shape model, learned by principal component analysis (PCA) [7, 16, 18, 19] over a dataset with Nd samples, was introduced to facilitate segmenting the first slice, hence all the slices in turn. [sent-292, score-0.227]
68 foreground and background, estimated by sampled pixels in one slice or learned through the training data. [sent-303, score-0.232]
69 For the first slice S1, its two cost functions are updated as: ? [sent-304, score-0.232]
70 C˜t1(C˜x1s)(x =) C =1t C(xs1)( +x) w +1( w11 − u˜1˜ u(x1()xα)iT)αΣiTk1Σαk1iαi (20) where w1 > 0 is constant and u˜1 (x) is the labeling function of the segmentation of S1 from the previous iteration. [sent-305, score-0.095]
71 Accuracy: Careful initializations were required by the MAC and MLS methods, where four to eight points on the prostate boundary in the first slice were selected to construct the initial contour by the cardinal splines [8]. [sent-306, score-1.01]
72 3D prostate segmentation (green contour) by the proposed MGO method and manual segmentation (red contour): (a) transverse view; (b) sagittal view; (c) coronal view; (d) orthogonal view overlapped with the manual segmentation surface. [sent-323, score-1.241]
73 Reliability: It should be noted that the segmentation accuracy of the methods MAC and MLS relies on the segmentation accuracy of the first slice. [sent-325, score-0.19]
74 Segmentation errors appearing in one slice will be introduced to the segmentation of the next slice and so on, thereby larger errors can be accumulated to affect the segmentation of the 3D TRUS image. [sent-326, score-0.654]
75 In the experiments of MAC and MLS, the first slice and its initial contour should be carefully determined by the user in order to decrease the associated segmentation errors as much as possible. [sent-327, score-0.373]
76 However, due to poor image quality, it is still challenging to locate the correct prostate boundary in some cases based only on the information of a single slice, even incorporating some high-level interaction (initial boundary points). [sent-328, score-0.781]
77 For examples, when it appears that the overlapped area between the prostate and urethral entrance (the arrow shown in Fig. [sent-329, score-0.794]
78 4 (b)), it is hard to distinguish the correct prostate boundary even for radiologists without the image information about its neighboring slices. [sent-331, score-0.732]
79 4 shows the segmentation results of MAC and MLS with poor initialization: their segmentations of the first slice with the same initialization are illustrated in Fig. [sent-333, score-0.394]
80 With the result for the first slice, the segmentation accuracy for all slices, computed by MAC, decreases greatly with the progress of the propagation (blue curve in Fig. [sent-338, score-0.095]
81 In contrast, the proposed MGO approach makes use of the global rotational correlation between all adjacent slices, which jointly adjusts the segmentation of each slice in a global way, hence performs much more reliably with the poor image quality and initialization (green curves in Fig. [sent-342, score-0.498]
82 A prostate segmentation result from a 3D MR image. [sent-365, score-0.803]
83 Green boundary: algorithmic result, red boundary: manual segmentation result. [sent-366, score-0.127]
84 (a) transverse view; (b) sagittal view; (c) coronal view; (d) orthogonal view overlapped with the segmented surface. [sent-367, score-0.184]
85 1, the shortest computation time was required by the proposed method: the mean segmentation time was 0. [sent-373, score-0.095]
86 Application in 3D Prostate MRIs: We also applied the proposed method to segment 2 3D T2-weighted MR prostate images using a body coil, which were acquired at a size of 291 341 38 voxels with a voxel size of 0. [sent-381, score-0.729]
87 For simplicity, the rotational axis and first slice were manually determined in the transverse view. [sent-385, score-0.444]
88 5 shows that the segmentation boundary agrees well with the manual segmentation, even in the sagittal view (Fig. [sent-390, score-0.214]
89 Conclusions In this paper, we propose a novel global optimized resliced approach to the computationally challenging 3D endfiring TRUS prostate images by enforcing the inherent rotational symmetry of prostate shapes, which jointly seg- ments a series of 2D reslices in a global sense. [sent-394, score-1.86]
90 1 1 we proposed a novel coupled continuous max-flow model, which not only provides a powerful mathematical tool to analyze the proposed optimization problem but also directly derives a new and efficient duality-based algorithm in numerical practices. [sent-430, score-0.25]
91 A study on continuous max-flow and min-cut approaches part ii: Multiple lin- [3] [4] [5] [6] [7] [8] [9] [10] [11] early ordered labels. [sent-451, score-0.093]
92 MR imaging-guided prostate biopsy with a closed MR unit at 1. [sent-480, score-0.799]
93 Fast prostate segmentation in 3D TRUS images based on continuity constraint using an autoregressive model. [sent-504, score-0.803]
94 Design of a novel MRI compatible manipulator for image guided prostate interventions. [sent-550, score-0.737]
95 Evaluation of visualization of the prostate gland in vibro-elastography images. [sent-562, score-0.708]
96 Rotational-slice-based prostate segmentation using level set with shape constraint for 3d end-firing trus guided biopsy. [sent-571, score-1.153]
97 A shape-based approach to the segmentation of medical imagery using level sets. [sent-587, score-0.095]
98 Semiautomatic 3D prostate segmentation from TRUS images using spherical harmonics. [sent-601, score-0.803]
99 3d image segmentation of deformable objects with joint shape-intensity prior models using level sets. [sent-609, score-0.095]
100 Neighbor-constrained segmentation with level set based 3-d deformable models. [sent-617, score-0.095]
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