# Computer Vision Techniques for Growth Prediction:
## 3 Results (Extraction & Analysis)
### Rq2: Which Technologies Are Used for Growth Prediction Using Image Processing?
#### 3.4.1 Lstm (Long Short-Term Memory)  
LSTM was the most frequently selected technology, with 5, GAN and U-net with 4, and STN with 3. LSTM networks are a type of recurrent neural network called RNNs. The strength of LSTM is that it learns on time-series data and thus has a high affinity for predicting the growing data associated with time-series. The LSTM algorithm was first introduced in 1995 and had a long history as a machine learning algorithm. However, it still provides highly accurate region detection and stock price prediction results [87; 88; 89]. LSTMs [31] are trained as outputs by combining several interacting gates. The sigmoid layer \(\sigma\), called the \"input gate layer,\" determines which values to update and combines them with the current sequence. The final decision is made at the \"output gate layer\"  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Number of Studies** & **Formula** \\ \hline DC (dice coefficient, F1 score) & 12[29; 30; 32; 37; 46; 61] & \(2\times\frac{|P\cap GT|}{|P|+|GT|}\), \\  & [33; 34; 39; 73; 74; 76] & \(P\) is a set of prediction values, \\  & [33; 34; 39; 73; 74; 76] & \(G\)T is a set of ground truth. \\  & 9 & \\ RMSE (root-mean-squared error) & [29; 30; 32; 61] & \(\sqrt{\frac{1}{N}\sum_{i=1}^{N}(y^{(i)}-\widehat{y}^{(i)})^{2}}\) \\  & [37; 38; 68; 69] & \(\frac{1}{N}\sum_{i=1}^{N}(y^{(i)}-\widehat{y}^{(i)})^{2}\) \\ MSE (mean squared error) & [40; 53; 65; 66; 67; 69] & \(\frac{TP}{TP+FN}\), \\ Recall, Sensitivity & [29; 37; 61; 74; 78] & \(TP\) and \(FN\) are the number of true positives and false negatives. \\ RVD (relative volume difference) & [30; 37; 46; 61; 74] & \(\frac{||P|-|GT||}{|P|}\) \\ \(R^{2}\) (coefficient of determination) & [5] & \(1-\frac{\sum_{i=1}^{N}(y^{(i)}-\widehat{y}^{(i)})^{2}}{\sum_{i=1}^{N}(y^{(i)} -g)^{2}}\) \\ JI (Jaccard index) & [33; 37; 39; 76] & \(\frac{|P\cap GT|}{|P\cup GT|}\) \\ PSNR (peak signal-to-noise ratio) & [34; 35; 36; 59] & \(10 log(\frac{g^{2}}{MSE})\), \\  & [34; 35; 36] & \(s\) is max-pixel-value in the image \\  & & \(\frac{(2\mu_{A}\mu_{B}+\mathrm{C}_{1})(2\sigma_{AB}+\mathrm{C}_{2})}{(\mu_{A}^ {2}+\mu_{B}^{2}+\mathrm{C}_{1})(\mu_{A}^{2}+\mu_{B}^{2}+\mathrm{C}_{2})}\), \\ SSIM (structural similarity) & [34; 35; 36] & where \(\mu\) is the mean, \(\sigma\) is the \\  & & standard deviation, \\  & & \(C\) is a predefined constant \\ MAPE (mean absolute & 3 & \(\frac{1}{N}\sum_{i=1}^{N}|100\times\frac{y^{(i)}-\widehat{y}^{(i)}}{y^{(i)}}|\) \\ percentage error) & [31; 41; 68] & \(\frac{TN}{TN+FP}\), \\ Spec (Specificity) & 3 [29; 37; 78] & \(TN\) and \(FP\) are the number of \\  & & true negatives \\ MAE (mean absolute error) & 2 [34; 38] & \(\frac{1}{N}\sum_{i=1}^{N}|y^{(i)}-\widehat{y}^{(i)}|\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Metrics for evaluation of prediction.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Name** & **Number of Studies** & **Conditions Included** \\ \hline The governing equation & & \\ (partial differential & 8 & Navier-Stokes Equations (3) \\ equation, PDE) & & \\ Finite element method & 6 & High-Fidelity Model (HFM) (1) \\ (FEM) & 2 & Low-Fidelity Model (LFM) (1) \\ growth and remodeling & 2 & \\ (G \& R) model & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Distribution of non-machine learning methods.  
through the \"forget gate layer\" \(f_{t}\). This is often expressed as a combination of a sigmoid function at the input gate layer and a tan function at the forget gate layer. The following formula can calculate \(f_{t}\):  
\[f_{t}=\sigma(W_{f}x_{t}+U_{f}h_{t-1}+b_{f}), \tag{1}\]  
where \(W_{f},U_{f}\) are weighted matrices, \(h_{t}\) is the output of the last time step, and \(b_{f}\) is a bias. LSTM can efficiently learn the degree of recall/forget of long-term memories through the forget gate layer.