国家自然科学基金(61772233,61876207,61772225)
广东省自然科学杰出青年基金(2014A030306050)
广东省重点领域研发计划项目(2018B010109003)
贵州省科技计划项目([2019]1164)
广州市科学技术局项目(201802010007)
广州市对外合作项目(201807010047)
贵州省教育厅青年科技人才成长项目([2016]165)
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Figure 1
An example of trimap
Figure 2
Group optimization strategy based on collaborative target feedback
Figure 3
(Color online) Alpha matting comparison between GC-CSO and CSO algorithms in GT27. (a) Original image with calibration area; (b) calibration area; (c) alpha matting with CSO algorithm; (d) alpha matting with GC-CSO algorithm
Figure 4
(Color online) Comparison of alpha matting results on high-resolution images. (a) Original image with calibration area; (b) trimap of calibration area; (c) alpha matting with GC-CSO algorithm; (d) alpha matting with CC-PSO algorithm; (e) alpha matting with CC-DE-S algorithm
//A multi-class collaborative optimization strategy based on RGB color clustering; |
Cluster the unknown region $U$ through RGB color space to generate class $C$; |
$i~\Leftarrow~1$; |
$X' \Leftarrow X' \cup $ $\left\{ {} \right.$selecting an unknown pixel ${x'_i}$$\left. {} \right\}$ from $X'$ randomly; |
$i~\Leftarrow~i~+~1$; |
According to the dimension value $\left| {X'} \right|$ of $X'$, the initial population ${P_0}$ is generated randomly; |
Operate competitive swarm optimization algorithm to optimize target $X'$; |
The optimal ${X'_{\rm best}}$ is obtained; |
//Grouping optimization strategy based on collaboration objective feedback; |
${X_{\rm~best}}~\Leftarrow~{\overrightarrow~0~_{\left(~{1~\times~\left|~U~\right|}~\right)}}$; |
$i~\Leftarrow~1$; |
${X_i} \Leftarrow {X'_{\rm best}}\left( i \right)$, where ${X'_{\rm best}}\left( i \right)$ represents the $i$th element in ${X'_{\rm best}}$; |
According to the dimension value $\left|~{{X_i}}~\right|$ of ${X_i}$, the initial population ${P_0}$ is generated randomly, and ${X'_i} \in {P_0}$; |
Operate competitive swarm optimization algorithm to optimize target ${X_i}$; |
Get the solution ${X_{i,{\rm~best}}}$ of sub-problem $i$; |
$i~\Leftarrow~i~+~1$; |
|
|
GT01 | GT02 | GT03 | GT04 | GT05 | GT06 | GT07 | GT08 | GT09 | |
Dimensions of $X$ | 1051874 | 1871217 | 1602223 | 3681622 | 879551 | 1220458 | 1182974 | 1872160 | 1309282 |
Dimensions of ${X'}$ | 367432 | 191294 | 276900 | 824993 | 141777 | 226212 | 181320 | 481223 | 243405 |
GT10 | GT11 | GT12 | GT13 | GT14 | GT15 | GT16 | GT17 | GT18 | |
Dimensions of $X$ | 1309983 | 1202842 | 768659 | 3411227 | 877021 | 994511 | 1682771 | 1146322 | 1064989 |
Dimensions of ${X'}$ | 175371 | 288977 | 234301 | 215929 | 175579 | 120159 | 298514 | 179987 | 243954 |
GT19 | GT20 | GT21 | GT22 | GT23 | GT24 | GT25 | GT26 | GT27 | |
Dimensions of $X$ | 725149 | 1167945 | 2992362 | 1285129 | 1203427 | 1318789 | 1712779 | 2573636 | 2577680 |
Dimensions of ${X'}$ | 242952 | 278184 | 472514 | 254230 | 186337 | 266761 | 407020 | 500700 | 752028 |
a $X$: the decision variable of the original high-resolution image matting problem.$X'$: the decision variable of the high-resolution image matting problem with multi-classes collaborative optimization strategy based on RGB color clustering.
Algorithm | GT01 | GT02 | GT03 | GT04 | GT05 | GT06 | GT07 | GT08 | GT09 |
GC-CSO | 8.116E$-$2 | ||||||||
CSO | 2.340E$-$2 | 3.915E$-$2 | 3.526E$-$2 | 7.835E$-$2 | 3.362E$-$2 | 6.144E$-$2 | 1.986E$-$2 | 6.899E$-$2 | |
Algorithm | GT10 | GT11 | GT12 | GT13 | GT14 | GT15 | GT16 | GT17 | GT18 |
GC-CSO | 6.887E$-$2 | 9.214E$-$3 | |||||||
CSO | 9.861E$-$2 | 1.085E$-$1 | 4.465E$-$2 | 6.030E$-$2 | 3.141E$-$1 | 2.875E$-$2 | 8.661E$-$2 | ||
Algorithm | GT19 | GT20 | GT21 | GT22 | GT23 | GT24 | GT25 | GT26 | GT27 |
GC-CSO | |||||||||
CSO | 8.433E$-$2 | 2.226E$-$2 | 7.370E$-$2 | 3.622E$-$2 | 4.230E$-$2 | 1.605E$-$1 | 2.442E$-$1 | 1.411E$-$1 | 1.966E$-$1 |
a The boldface values indicate the best results.
//RGB clustering part; |
$i~\Leftarrow~1$; $j~\Leftarrow~1$; |
|
|
${X_i}~\Leftarrow~{X_i}~\cup~\left\{~{{x_j}}~\right\}$; |
|
|
$X' \Leftarrow X' \cup $ $\left\{ {} \right.$selecting an unknown pixel ${x'_i}$$\left. {} \right\}$ from $X'$ randomly; |
$i~\Leftarrow~i~+~1$; |
//The initial population ${P_0}$ is generated randomly with the population size of $n$; |
|
$x_{i,j}^F~\Leftarrow~1~+~\left(~{\left|~{{{\cal~P}_F}}~\right|~-~1}~\right)~\cdot~{\rm~rand}\left(~{}~\right)$; |
$x_{i,j}^B~\Leftarrow~1~+~\left(~{\left|~{{{\cal~P}_B}}~\right|~-~1}~\right)~\cdot~{\rm~rand}\left(~{}~\right)$; |
${X'_i} \Leftarrow {X'_i} \cup ( {x_{i,j}^F,x_{i,j}^B} )$; |
|
${P_0} \Leftarrow {P_0} \cup {X'_i}$; |
//Collaborative optimization part; |
Evaluate all individuals in ${P_t}$ with formula ( |
$P' \Leftarrow {P_t}$; ${P_{t + 1}} \Leftarrow \emptyset $; |
|
Two individuals $X_{r1}^t$ and $X_{r2}^t$ are selected randomly from ${P_t}$; |
|
$X_w^t~\Leftarrow~X_{r1}^t;~X_l^t~\Leftarrow~X_{r2}^t$; |
|
$X_w^t~\Leftarrow~X_{r2}^t;~X_l^t~\Leftarrow~X_{r1}^t$; |
|
$V_l^{t~+~1}~\Leftarrow~R_1^t~\cdot~V_l^t~+~R_2^t~\cdot~\left(~{X_w^t~-~X_l^t}~\right)~+~\varphi~~\cdot~R_3^t~\cdot~(~{\overline~{{X^t}}~~-~X_l^t}~)$; |
$X_l^{t~+~1}~\Leftarrow~X_l^t~+~V_l^{t~+~1}$; |
|
$x_{l,j}^F~\Leftarrow~\min~(~{x_{l,j}^F,\left|~{{{\cal~P}_F}}~\right|}~)$; $x_{l,j}^F~\Leftarrow~\max~(~{x_{l,j}^F,1}~)$; |
$x_{l,j}^B~\Leftarrow~\min~(~{x_{l,j}^F,\left|~{{{\cal~P}_B}}~\right|}~)$; $x_{l,j}^B~\Leftarrow~\max~(~{x_{l,j}^B,1}~)$; |
|
Add $X_l^{t + 1}$ and $X_w^t$ to the new generation population ${P_{t + 1}}$ and remove $X_{r1}^t$ and $X_{r2}^t$ from $P'$; |
|
$t~\Leftarrow~t~+~1$; |
Algorithm | GT01 | GT02 | GT03 | GT04 | GT05 | GT06 | GT07 | GT08 | GT09 |
GC-CSO | 2.251E$-$2 | 3.350E$-$2 | 5.971E$-$2 | ||||||
CC-PSO | 1.959E$-$2 | 4.012E$-$2 | 7.591E$-$2 | 4.326E$-$2 | 6.458E$-$2 | 2.593E$-$2 | 8.714E$-$2 | 6.830E$-$2 | |
CC-DE-S | 3.881E$-$2 | 3.659E$-$2 | 7.944E$-$2 | 4.190E$-$2 | 2.981E$-$2 | 9.418E$-$2 | 7.406E$-$2 | ||
Algorithm | GT10 | GT11 | GT12 | GT13 | GT14 | GT15 | GT16 | GT17 | GT18 |
GC-CSO | 6.887E$-$2 | 9.514E-02 | 2.946E$-$1 | ||||||
CC-PSO | 7.179E$-$2 | 1.227E$-$1 | 1.411E$-$2 | 9.281E$-$2 | 5.564E$-$2 | 6.538E$-$2 | 3.035E$-$1 | 5.206E$-$2 | 8.427E$-$2 |
CC-DE-S | 9.844E$-$2 | 1.819E$-$2 | 5.055E$-$2 | 6.113E$-$2 | 4.423E$-$2 | 8.695E$-$2 | |||
Algorithm | GT19 | GT20 | GT21 | GT22 | GT23 | GT24 | GT25 | GT26 | GT27 |
GC-CSO | 8.385E$-$2 | 7.367E$-$2 | 4.167E$-$2 | 2.254E$-$1 | 1.938E$-$1 | ||||
CC-PSO | 2.315E$-$2 | 7.085E$-$2 | 3.898E$-$2 | 6.251E$-$2 | 1.577E$-$1 | 2.084E$-$1 | 1.577E$-$1 | 2.060E$-$1 | |
CC-DE-S | 8.414E$-$2 | 2.189E$-$2 | 3.835E$-$2 | 8.465E$-$1 | 1.400E$-$1 |
a The boldface values indicate the best results.