SCIENTIA SINICA Informationis, Volume 47 , Issue 12 : 1674-1693(2017) https://doi.org/10.1360/N112016-00156

Hierarchical complexity measures for effective shape-based image retrieval

Bin WANG 1,2,*
More info
  • ReceivedDec 31, 2016
  • AcceptedMar 13, 2017
  • PublishedAug 30, 2017


Funded by





江苏高校优势学科建设工程(PA- PD)


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  • Figure 1

    (a) Five samples from the MPEG-7 CE-1 contour shape database and (b) the edge points extracted from them

  • Figure 2

    (a) Five samples from the MPEG-7 CE-2 region shape database and (b) the edge points extracted from them

  • Figure 3

    Classification of shape descriptors

  • Figure 4

    (a) A shape image distorted by salt pepper noise and (b) the contour extracted from it

  • Figure 5

    An example of hierarchical description framework. In the figure, a shape being rotated by angle $\theta$ counterclockwise is partitioned into five levels of blocks ($k=0,1,2,3,4$) by four iterative cuts, where the cut line is marked by grey color and the centroid of the current region block is marked by white dot

  • Figure 6

    An example of the complexity measures for a shape region block. Left figure: the measured shape region block (the grey line is the cut line crossing the centre of the shape region block and the rectangle shown in dash line is the bounding box of the shape region block; Right figure (upper): measuring the rectangle degree (Eq. (11)); Right figure (bottom): measuring the balance degree (Eq. (12)), the numbers (right-most) are the values of the complexities of the region blocks

  • Figure 7

    MPEG-7 CE-1 image dataset. (a) Samples from the dataset; (b) 20 samples from a class in the dataset

  • Figure 8

    MPEG-7 CE-2 image dataset. (a) Samples from the dataset; (b) 21 samples from a class in the dataset, where the shape images shown from row 2 to row 5 are the rotated, scaled and perspective transformed versions of the sample shown in the first row, respectively

  • Figure 9

    (a) 20 object samples from the COIL-20 database; (b) the binary images derived from the images shown in (a)

  • Figure 10

    (a) Example views of one object from the COIL-20 database; (b) the binary images derived from the images shown in (a)

  • Figure 11

    The curve of the recogniton error rate $E$ vs. the number $M$ of the uniformly selected views per object for training using the COIL-20 database

  • Figure 12

    An original shape sample (the left figure) and its versions distorted by salt and pepper noise (the right four figures with noise intensity of 0.2, 0.4, 0.6 and 0.8, respectively)

  • Table 1   Retrieval rates on the MPEG-7 CE-1 shape dataset $^{\rm~a)}$
    Algorithm Bulls-eye test score (%)
    Curve based Shape Tree [8] 87.70$^{\dag}$
    Locally affine invariant descriptors [14] 89.62$^{\dag}$
    Shape Contexts [23] 76.51$^{\dag}$
    Point-set based Distance Set [24] 78.38$^{\dag}$
    Shape L$$${\rm~\hat{A}}$ne Rouge [26] 85.25$^{\dag}$
    Unordered point-set description(UPSD) [25] 78.18
    Zernike Moments [29] 68.90
    Generic Fourier descriptors (GFD) [33] 67.60
    Region based Radon composite features (RCF) [37] 67.30
    Adaptive hierarchical density histogram (AHDH) [39] 63.95$^{\dag}$
    Polar harmonic transforms (PHTs) [31] 70.92
    The proposed HCMD 86.36
    a) The scores marked by $\dag$ are directly cited from the published results.

    Algorithm 1 Calculating hierarchical complexity measures descriptor (HCMD)

    Require: $(f_{x,y})_{G\times~H}$: the matrix of binary shape image; $K$: the number of hierarchical levels; $T$: the number of sampling angles from range $[0,2\pi]$;

    Output: $(\xi_{k,t})_{K\times~T}$, $(\zeta_{k,t})_{K\times~T}$, $(\eta_{k,t})_{K\times~T}$, $(\mu_{k,t})_{K\times~T}$: HCMD of shape $f$;

    Initialize $(\xi_{k,t})_{K\times~T}\leftarrow~0$ and $(\zeta_{k,t})_{K\times~T}\leftarrow~0$;



    $\overline{x}\leftarrow\frac{1}{S}\sum\nolimits_{(x,y)\in~B}x$; $\overline{y}\leftarrow\frac{1}{S}\sum\nolimits_{(x,y)\in~B}y$;



    for $t=1$ to $T$


    for $k=1$ to $K$

    if $S>0$ then


    $x_r\leftarrow\max(D_x)$; $x_l\leftarrow\min(D_x)$; $y_r\leftarrow\max(D_y)$; $y_l\leftarrow\min(D_y)$;








    $D\leftarrow~D_c$; $S\leftarrow~S_L$;



    end if

    end for


    end for

    for $k=1$ to $K$



    end for

    Return $(\xi_{k,t})_{K\times~T}$, $(\zeta_{k,t})_{K\times~T}$, $(\eta_{k,t})_{K\times~T}$ and $(\mu_{k,t})_{K\times~T}$;

  • Table 2   Retrieval rates on MPEG-7 CE-2 shape dataset
    Algorithm Bulls-eye test score (%)
    Point-set based Shape Contexts [23] 70.98
    Unordered point-set description (UPSD) [25] 84.13
    Zernike Moments [29] 80.20
    Generic Fourier descriptors (GFD) [33] 81.20
    Region based Radon composite features (RCF) [37] 67.40
    Adaptive hierarchical density histogram (AHDH) [39] 49.94
    Polar harmonic transforms (PHTs) [31] 64.13
    The proposed HCMD 94.52