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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

Abstract


Funded by

国家自然科学基金(61303215)

湖北省教育厅青年人才项目(Q20154404)

  • 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

    Require:

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

    初始化.

    (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) $k=0$.

    Output:

    repeat

    $k+1$.

    (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$1.88
  • Table 2   Sample size of test sequences on different levels
    ImageHighMediumLow
    Ultrasonic echocardiography image155421
    Ultrasonic uterine fiborid image162816
    Total 318237
  • Table 3   The mean and standard deviation (SD) of TP, FP, AMED and HD measurements of the three methods on contour detection in the high, medium and low quality groups
    MethodLevelMean$\pm$SD
    TP (mm) FP (%)AMED (mm)HD (mm)
    H94.35$\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