Background
Methods
Study design
Method overview
Unsupervised component
Step 1): Lesion hemisphere detection and enantiomorphic Normalization
Step 2): Initial estimation of LPM
α
|
λ
| Accuracy | Precision | Recall | Dice |
---|---|---|---|---|---|
0.2 | 1 | 0.953±0.012 | 0.321±0.195 | 0.784±0.165 | 0.430±0.166 |
3 | 0.959±0.012 | 0.392±0.198 | 0.726±0.164 | 0.478±0.168 | |
5 | 0.961±0.011 | 0.427±0.199 | 0.694±0.156 | 0.497±0.165 | |
7 | 0.963±0.011 | 0.446±0.199 | 0.673±0.158 | 0.508±0.164 | |
0.4 | 1 | 0.965±0.011 | 0.502±0.199 | 0.639±0.154 | 0.532±0.170 |
3 | 0.968±0.012 | 0.552±0.198 | 0.582±0.153 | 0.547±0.169 | |
5 | 0.964±0.012 | 0.555±0.196 | 0.589±0.151 | 0.548±0.168 | |
7 | 0.940±0.011 | 0.553±0.201 | 0.601±0.151 | 0.547±0.168 | |
0.6 | 1 | 0.967±0.012 | 0.547±0.198 | 0.596±0.155 | 0.545±0.170 |
3 | 0.954±0.012 | 0.553±0.200 | 0.591±0.154 | 0.547±0.174 | |
5 | 0.940±0.011 | 0.559±0.203 | 0.592±0.159 | 0.546±0.169 | |
7 | 0.941±0.011 | 0.572±0.203 | 0.574±0.158 | 0.541±0.165 | |
0.8 | 1 | 0.967±0.011 | 0.549±0.207 | 0.593±0.154 | 0.546±0.169 |
3 | 0.940±0.011 | 0.559±0.204 | 0.596±0.155 | 0.546±0.173 | |
5 | 0.941±0.011 | 0.584±0.201 | 0.557±0.151 | 0.543±0.172 | |
7 | 0.941±0.012 | 0.623±0.198 | 0.500±0.151 | 0.503±0.168 |
Step 3): Amendment to normalization-segmentation template tissue maps
Step 4): LPM refinement
Supervised component
Step 5): Feature extraction
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Zero-order features: At each voxel, the corresponding 5×5×5 block provides a 125-dimensional feature vector in each of the five maps, where each dimension takes the value (intensity in the T1 image and probability value in the other four maps) of the corresponding voxel in the block. In this block, we further calculate 13 Haar-like features [49] as shown in Fig. 5, where each feature dimension is the average voxel-value difference between the black and white regions within the 5×5×5 sliding block. By concatenating voxel features and Haar-like features from all five maps, the zero-order features have a total dimension of (125+13)×5=690 and we denote it as f0(x,y,z).×
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1st-order feature: At voxel (x,y,z),we extract its 1st-order features as$$\begin{array}{@{}rcl@{}} {}\textbf{f}_{1}(x,y,z)=\frac{1}{27}\sum\limits_{i=-1}^{1}\sum\limits_{j=-1}^{1}\sum\limits_{k=-1}^{1}\textbf{f}_{0}(x+i,y+j,z+k). \end{array} $$(5)The 1st-order feature is also a 690-dimensional feature vector.
-
2nd-order feature: At voxel (x,y,z), we extract its 2nd-order features as$$\begin{array}{@{}rcl@{}} {}\textbf{f}_{2}(x,y,z)&=&\left(\textbf{f}_{0}(x,y,z)-\textbf{f}_{1}(x,y,z)\right)\\&&\times\left(\textbf{f}_{0}(x,y,z)-\textbf{f}_{1}(x,y,z)\right)^{T}, \end{array} $$(6)
Step 6): Individual SVM classifiers
Accuracy | Precision | Recall | Dice | |
---|---|---|---|---|
Initial LPM | 0.964±0.012 | 0.555±0.196 | 0.589±0.151 | 0.548±0.168 |
Unsupervised classification | 0.981±0.012 | 0.665±0.183 | 0.671±0.140 | 0.663±0.161 |
Only zero-order features | 0.983±0.011 | 0.747±0.151 | 0.646±0.145 | 0.681±0.143 |
Only 1st-order features | 0.983±0.011 | 0.754±0.149 | 0.649±0.142 | 0.687±0.144 |
Only 2nd-order Features | 0.970±0.012 | 0.526±0.170 | 0.641±0.152 | 0.547±0.160 |
Combine zero- & 1st-order features | 0.983±0.011 | 0.755±0.147 | 0.649±0.140 | 0.694±0.126 |
Combined classification (all 3 features) | 0.983±0.011 | 0.783±0.143 | 0.685±0.131 | 0.731±0.106 |
Unsupervised classification | |||||
---|---|---|---|---|---|
Accuracy | Precision | Recall | Dice | ||
0.981±0.012 | 0.665±0.183 | 0.671±0.140 | 0.663±0.161 | ||
Supervised classification | |||||
Inputs | Classifiers | Accuracy | Precision | Recall | Dice |
T1 MRI | zero-order | 0.952±0.015 | 0.150±0.313 | 0.402±0.203 | 0.202±0.302 |
1st-order | 0.957±0.014 | 0.162±0.306 | 0.389±0.241 | 0.214±0.301 | |
2nd-order | 0.954±0.015 | 0.144±0.347 | 0.377±0.272 | 0.193±0.342 | |
All combined | 0.956±0.014 | 0.187±0.291 | 0.421±0.198 | 0.258±0.291 | |
Prob. maps | zero-order | 0.981±0.012 | 0.696±0.178 | 0.637±0.146 | 0.665±0.164 |
of WM, GM | 1st-order | 0.981±0.012 | 0.702±0.177 | 0.621±0.157 | 0.659±0.166 |
external CSF, LPM | 2nd-order | 0.968±0.013 | 0.503±0.192 | 0.609±0.159 | 0.551±0.173 |
All combined | 0.983±0.012 | 0.781±0.144 | 0.681±0.142 | 0.728±0.112 | |
T1 MRI & prob. | zero-order | 0.983±0.011 | 0.747±0.151 | 0.646±0.145 | 0.681±0.143 |
maps of WM, GM, | 1st-order | 0.983±0.011 | 0.754±0.149 | 0.649±0.142 | 0.687±0.144 |
external CSF, LPM | 2nd-order | 0.970±0.012 | 0.526±0.170 | 0.641±0.152 | 0.547±0.160 |
All combined | 0.983±0.011 | 0.783±0.143 | 0.685±0.131 | 0.731±0.106 |
Step 7): Combined classification
ω
1
|
ω
2
|
ω
3
| Accuracy | Precision | Recall | Dice |
---|---|---|---|---|---|---|
0.1 | 0.1 | 0.8 | 0.982±0.012 | 0.785±0.139 | 0.669±0.138 | 0.722±0.118 |
0.1 | 0.2 | 0.7 | 0.983±0.011 | 0.780±0.144 | 0.684±0.136 | 0.728±0.112 |
0.1 | 0.3 | 0.6 | 0.983±0.011 | 0.783±0.143 | 0.685±0.131 | 0.731±0.106 |
0.1 | 0.4 | 0.5 | 0.983±0.011 | 0.789±0.138 | 0.680±0.133 | 0.730±0.111 |
0.1 | 0.5 | 0.4 | 0.983±0.011 | 0.792±0.137 | 0.675±0.135 | 0.729±0.112 |
0.1 | 0.6 | 0.3 | 0.983±0.011 | 0.787±0.140 | 0.675±0.134 | 0.727±0.113 |
0.1 | 0.7 | 0.2 | 0.982±0.011 | 0.787±0.139 | 0.672±0.135 | 0.725±0.112 |
0.1 | 0.8 | 0.1 | 0.983±0.011 | 0.787±0.141 | 0.665±0.147 | 0.721±0.114 |
0.2 | 0.1 | 0.7 | 0.982±0.011 | 0.776±0.149 | 0.685±0.133 | 0.728±0.112 |
0.2 | 0.2 | 0.6 | 0.983±0.011 | 0.783±0.141 | 0.684±0.133 | 0.730±0.112 |
0.2 | 0.3 | 0.5 | 0.983±0.011 | 0.788±0.138 | 0.679±0.133 | 0.729±0.112 |
0.2 | 0.4 | 0.4 | 0.983±0.011 | 0.792±0.136 | 0.673±0.134 | 0.728±0.112 |
0.2 | 0.5 | 0.3 | 0.983±0.011 | 0.788±0.137 | 0.674±0.134 | 0.727±0.113 |
0.2 | 0.6 | 0.2 | 0.983±0.011 | 0.787±0.137 | 0.669±0.139 | 0.723±0.113 |
0.2 | 0.7 | 0.1 | 0.983±0.011 | 0.785±0.139 | 0.666±0.148 | 0.721±0.114 |
0.3 | 0.1 | 0.6 | 0.983±0.011 | 0.782±0.140 | 0.684±0.135 | 0.730±0.112 |
0.3 | 0.2 | 0.5 | 0.983±0.011 | 0.788±0.136 | 0.677±0.134 | 0.728±0.112 |
0.3 | 0.3 | 0.4 | 0.983±0.011 | 0.790±0.135 | 0.673±0.135 | 0.727±0.112 |
0.3 | 0.4 | 0.3 | 0.982±0.011 | 0.787±0.136 | 0.673±0.137 | 0.726±0.113 |
0.3 | 0.5 | 0.2 | 0.983±0.011 | 0.787±0.135 | 0.668±0.141 | 0.723±0.114 |
0.3 | 0.6 | 0.1 | 0.982±0.011 | 0.784±0.138 | 0.665±0.137 | 0.720±0.114 |
0.4 | 0.1 | 0.5 | 0.983±0.011 | 0.786±0.137 | 0.678±0.133 | 0.728±0.111 |
0.4 | 0.2 | 0.4 | 0.983±0.011 | 0.787±0.137 | 0.675±0.134 | 0.727±0.112 |
0.4 | 0.3 | 0.3 | 0.983±0.011 | 0.787±0.139 | 0.672±0.134 | 0.725±0.112 |
0.4 | 0.4 | 0.2 | 0.983±0.011 | 0.786±0.139 | 0.668±0.141 | 0.722±0.114 |
0.4 | 0.5 | 0.1 | 0.983±0.011 | 0.783±0.140 | 0.664±0.143 | 0.719±0.114 |
0.5 | 0.1 | 0.4 | 0.983±0.011 | 0.787±0.139 | 0.674±0.136 | 0.726±0.113 |
0.5 | 0.2 | 0.3 | 0.983±0.011 | 0.785±0.140 | 0.672±0.137 | 0.724±0.112 |
0.5 | 0.3 | 0.2 | 0.983±0.011 | 0.784±0.141 | 0.668±0.143 | 0.721±0.114 |
0.5 | 0.4 | 0.1 | 0.983±0.011 | 0.783±0.143 | 0.662±0.145 | 0.717±0.117 |
0.6 | 0.1 | 0.3 | 0.983±0.011 | 0.783±0.142 | 0.672±0.137 | 0.723±0.112 |
0.6 | 0.2 | 0.2 | 0.983±0.011 | 0.782±0.142 | 0.668±0.144 | 0.721±0.114 |
0.6 | 0.3 | 0.1 | 0.983±0.011 | 0.782±0.142 | 0.662±0.146 | 0.717±0.120 |
0.7 | 0.1 | 0.2 | 0.983±0.011 | 0.781±0.144 | 0.668±0.142 | 0.720±0.113 |
0.7 | 0.2 | 0.1 | 0.983±0.011 | 0.782±0.144 | 0.661±0.150 | 0.716±0.123 |
0.8 | 0.1 | 0.1 | 0.983±0.011 | 0.781±0.146 | 0.660±0.153 | 0.715±0.129 |
Results
Experiment data and setting
Evaluation metrics
Experiment results on in-house dataset and analysis
γ
| Accuracy | Precision | Recall | Dice |
---|---|---|---|---|
\(\frac {1}{6}\)
| 0.976±0.012 | 0.470±0.197 | 0.611±0.154 | 0.516±0.178 |
\(\frac {2}{6}\)
| 0.978±0.012 | 0.510±0.194 | 0.624±0.151 | 0.550±0.174 |
\(\frac {3}{6}\)
| 0.979±0.011 | 0.550±0.189 | 0.631±0.148 | 0.582±0.169 |
\(\frac {4}{6}\)
| 0.980±0.011 | 0.600±0.186 | 0.634±0.143 | 0.612±0.166 |
\(\frac {5}{6}\)
| 0.981±0.012 | 0.665±0.183 | 0.671±0.140 | 0.663±0.161 |
1 | 0.981±0.012 | 0.645±0.187 | 0.590±0.157 | 0.611±0.166 |
Accuracy | Precision | Recall | Dice | |
---|---|---|---|---|
(a) Threshold t is selected to maximize the Dice coefficients against the ground truth | ||||
Stamatakis et al., 2005 | 0.954±0.016 | 0.498±0.179 | 0.511±0.174 | 0.504±0.152 |
Seghier et al., 2008 | 0.969±0.012 | 0.568±0.169 | 0.539±0.153 | 0.546±0.151 |
Sanjuan et al. 2013 | 0.971±0.011 | 0.616±0.148 | 0.599±0.133 | 0.607±0.122 |
Proposed Method | 0.985±0.011 | 0.783±0.143 | 0.685±0.131 | 0.731±0.106 |
(b) Threshold t is selected by following Eq. (8) without using the ground truth for the proposed method, | ||||
while the thresholds for the comparison methods are the ones suggested in their respective papers | ||||
Stamatakis et al., 2005 | 0.954±0.016 | 0.478±0.182 | 0.513±0.177 | 0.489±0.154 |
Seghier et al., 2008 | 0.969±0.012 | 0.471±0.179 | 0.542±0.157 | 0.506±0.153 |
Sanjuan et al. 2013 | 0.971±0.011 | 0.526±0.163 | 0.604±0.134 | 0.557±0.131 |
Proposed Method | 0.981±0.011 | 0.717±0.151 | 0.707±0.134 | 0.698±0.118 |
Experiment results on MICCAI BRATS 2012 dataset
Accuracy | Precision | Recall | Dice | |
---|---|---|---|---|
(a) Threshold t is selected to maximize the Dice coefficients against the ground truth | ||||
Stamatakis et al., 2005 | 0.987±0.012 | 0.401±0.217 | 0.532±0.168 | 0.457±0.221 |
Seghier et al., 2008 | 0.987±0.011 | 0.623±0.179 | 0.484±0.151 | 0.545±0.157 |
Sanjuan et al. 2013 | 0.990±0.011 | 0.696±0.157 | 0.523±0.130 | 0.597±0.119 |
Proposed Method | 0.992±0.011 | 0.830±0.086 | 0.555±0.131 | 0.665±0.120 |
(b) Threshold t is selected by following Eq. (8) without using the ground truth for the proposed method, | ||||
while the thresholds for the comparison methods are the ones suggested in their respective papers | ||||
Stamatakis et al., 2005 | 0.987±0.012 | 0.395±0.224 | 0.530±0.174 | 0.453±0.233 |
Seghier et al., 2008 | 0.987±0.011 | 0.601±0.184 | 0.485±0.149 | 0.537±0.163 |
Sanjuan et al. 2013 | 0.990±0.011 | 0.686±0.161 | 0.524±0.129 | 0.594±0.124 |
Proposed Method | 0.991±0.011 | 0.792±0.104 | 0.559±0.127 | 0.654±0.123 |
Discussion
Accuracy | Precision | Recall | Dice | |
---|---|---|---|---|
Using the proposed enantiomorphic normalization | ||||
Initial LPM | 0.964±0.012 | 0.555±0.196 | 0.589±0.151 | 0.548±0.168 |
Unsupervised classification | 0.981±0.012 | 0.665±0.183 | 0.671±0.140 | 0.663±0.161 |
Combined classification | 0.983±0.011 | 0.780±0.144 | 0.684±0.136 | 0.731±0.106 |
Using the ground-truth lesion mask for USN | ||||
Initial LPM | 0.971±0.012 | 0.608±0.193 | 0.587±0.147 | 0.595±0.163 |
Unsupervised classification | 0.981±0.012 | 0.691±0.174 | 0.678±0.138 | 0.677±0.164 |
Combined classification | 0.985±0.010 | 0.794±0.141 | 0.701±0.127 | 0.743±0.101 |
Block size | Accuracy | Precision | Recall | Dice |
---|---|---|---|---|
3 × 3 ×3 | 0.983±0.011 | 0.722±0.153 | 0.683±0.133 | 0.701±0.112 |
5 ×5×5 | 0.983±0.011 | 0.783±0.143 | 0.684±0.131 | 0.731±0.106 |
7 ×7×7 | 0.984±0.011 | 0.785±0.142 | 0.691±0.127 | 0.733±0.106 |