SCIENTIA SINICA Informationis, Volume 47 , Issue 6 : 752(2017) https://doi.org/10.1360/N112016-00235

Sparse feature competition and shapes similarity based ultrasound image sequence segmentation method

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  • ReceivedJan 30, 2017
  • AcceptedMar 1, 2017
  • PublishedMay 9, 2017


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  • Figure 1

    The flowchart of HIFU therapy

  • Figure 2

    The flowchart of the proposed method

  • Figure 3

    (Color online) Object and background feature regions


    Algorithm 1 基于K-SVD构建目标特征字典


    训练信号集${\boldsymbol A}_{\rm o}=[{\boldsymbol q}_{\rm o}^{1},\ldots,{\boldsymbol q}_{\rm o}^{M}] \in \mathbb{R}^{k^{2} \times M}$.


    (1) 随机选择$M$个样本构造初始的特征字典${\boldsymbol D}^{(0)}_{\rm o}=[{\boldsymbol a}^{(0)}_{1},\ldots,{\boldsymbol a}^{(0)}_{M}]$, 并对${\boldsymbol D}^{(0)}_{\rm o}$ 的各列减去训练集合的均值: ${\boldsymbol D}^{(0)}_{\rm o}={\boldsymbol D}^{(0)}_{\rm o}-\frac{1}{M}\sum^{M}_{i=1}{\boldsymbol q}_{\rm o}^{i}$.(2) $k=0$.




    (1) 计算稀疏编码:

    针对式(2)利用OMP算法计算系数矩阵${\boldsymbol X}_{k}$.

    (2) 字典更新阶段:

    for $j_{0}=1,\ldots,M$

    //更新${\boldsymbol D}^{k}_{\rm o}$中的第$j$ 列

    定义使用原子${\boldsymbol a}_{j}$的信号集$\Omega_{j}=\{i=1\leq i \leq M,{\boldsymbol X}_{k}[j_{0},j]\neq 0\}$.

    计算信号残差${\boldsymbol E}_{j0}:={\boldsymbol A}_{\rm o}-\sum_{j\neq j_{0}}{\boldsymbol a}_{j}{\boldsymbol x}^{\rm T}_{j}$, 其中${\boldsymbol x}_{j}$ 表示${\boldsymbol X}_{k}$的第$j$ 行.

    提取${\boldsymbol E}_{j0}$的第$i$列来构建${\boldsymbol E}^{R}_{j0}$, 其中$i\in {\boldsymbol x}_{j0}$.

    对${\boldsymbol E}^{R}_{j}={\boldsymbol U} \mathbf{\Lambda} {\boldsymbol V}^{\rm T}$ 进行SVD分解.

    更新字典原子${\boldsymbol a}_{j0}={\boldsymbol u}_{1}$, 其中${\boldsymbol u}_{1}$ 是${\boldsymbol U}$ 的第一列.

    用${\boldsymbol V} \times \mathbf{\Lambda}(1,1)$ 的第1列更新${\boldsymbol X}_{j0}^{\rm T}$ 的非零元素.

    end for

    until $\sum^{M}_{i=1} \|{\boldsymbol y}_{i}-{\boldsymbol D}{\boldsymbol x}_{i}\|^{2}_{2} \leq$ 阈值.

  • Table 1   The segmentation quantitative comparisons between the results by Lui et al.'s method and Eq. ()
    MethodMetricsTP (%)FP (%)AMED (mm)HD (mm)
    Lui et al. [45]Mean$\pm$SD 97.73$\pm$3.23 8.91$\pm$1.10 3.17$\pm$1.38 8.17$\pm$3.88
    Median$\pm$SD 95.34$\pm$4.15 6.38$\pm$1.25 2.46$\pm$1.38 9.28$\pm$2.21
    Eq. (Eq:ACM-Err) Mean$\pm$SD 97.13$\pm$2.23 6.98$\pm$0.61 2.43$\pm$1.76 5.12$\pm$2.48
    Median$\pm$SD 96.84$\pm$3.46 5.41$\pm$0.32 2.19$\pm$1.58 4.21$\pm$1.88
  • Table 2   Sample size of test sequences on different levels
    Ultrasonic echocardiography image155421
    Ultrasonic uterine fiborid image162816
    Total 318237
  • Table 3   The mean and standard deviation (SD) of TP, FP, AMED and HD measurements of the three methods on contour detection in the high, medium and low quality groups
    TP (mm) FP (%)AMED (mm)HD (mm)
    H94.35$\pm$3.92 4.15$\pm$1.43 1.93$\pm$1.14 2.84$\pm$1.65
    Li et al. [56]M92.26$\pm$5.15 5.41$\pm$1.57 3.85$\pm$1.47 4.57$\pm$1.57
    L87.24$\pm$7.19 8.27$\pm$4.08 5.12$\pm$2.03 6.54$\pm$3.04
    H96.32$\pm$1.18 3.22$\pm$0.85 1.78$\pm$0.56 2.18$\pm$1.23
    Qin et al. [57]M94.34$\pm$1.94 4.07$\pm$1.74 2.98$\pm$0.89 3.58$\pm$1.06
    L89.26$\pm$2.75 6.31$\pm$1.95 4.41$\pm$1.48 4.21$\pm$2.65
    H96.28$\pm$1.91 2.12$\pm$0.55 1.32$\pm$0.21 1.54$\pm$0.98
    OursM95.16$\pm$1.66 2.86$\pm$0.68 1.82$\pm$0.25 2.09$\pm$0.95
    L94.51$\pm$1.58 3.32$\pm$0.67 2.84$\pm$0.38 2.97$\pm$1.15
  • Table 4   Running time and iterations of the three methods
    Method Running time (s) Number of iterations
    Li et al. [56] 12.5
    Qin et al. [57] 9.3 24
    Ours 11.3 32

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