# Human-Touch-Inspired Material Recognition for Robotic Tactile Sensing
## 3 Methodology
### Feature Extraction Mimicing Human Tactile Perception  
The human-like slide action was carried out to perceive three time sequences, which are relevant to the compliance and texture properties of the material. However, the dimensionality of the sequences is 300, which is still large for material recognition. Inspired by dynamic tactile sensing of humans, 11 features were extracted from the three sequences based on the statistics and Wavelet transformation. Features based on the statistics characterize the consistency and complexity of the sequence, while the features based on the Wavelet transformation can be used to analyze non-stationary signals. Since the textures of the materials are irregular and non-uniform, using Wavelet instead of Fourier transform is more suitable [33]. The first three features are the means of the three sequences. As the three features are relevant to the sustained pressure and texture, they are the analogs to stimuli sensed by Ruffini Corpuscle and Merkel Cells. The next five features are the L1 norms of the cA4, cD4, cD3, cD2, and cD1 coefficients, which are generated by a level-4 discrete Wavelet transformation (DWT) of the sequence \(\mathsf{S}_{\text{s}}\), and db3 is used as the wavelet. The cD4, cD3, cD2, and cD1 coefficients provide the detail information of vibration at different frequency durations for the slide action, which is similar to the signal of the Pacinian Corpuscle and Meissner's Corpuscle. The cA4 coefficient provide the approximate information of vibration, which is relevant to the signal of Merkel Cells. The ninth feature is the absolute energy of the sequence \(\mathsf{S}_{\text{s}}\), which is the sum of the squared values:  
\[E=\sum_{i=1,\ldots,n}x_{i}^{2} \tag{1}\]  
where \(x\) is the sequence. The absolute energy is also similar to the signal of Merkel Cells. The tenth feature is the complexity-invariant distance (CID) of the sequence \(\mathsf{S}_{\text{s}}\), as CID is an estimate for a time sequence complexity [34]. If the sequence is complicated, there are more peak-valley values in the sequence. Hence, CID provides the frequency information of vibration, which is similar to the signal of the Pacinian Corpuscle. It gives the value of:  
\[\sqrt{\sum_{i=0}^{n-2 lag}\left(x_{i}-x_{i+1}\right)^{2}} \tag{2}\]  
The last feature is the standard deviation of \(\mathsf{S}_{\text{s}}\), which is relevant to the material texture that is sensed by the Merkel Cells. The 11 features constitute the feature vector of the sample, which will be used for material recognition, and the features, the meanings they represent, and the corresponding tactile stimulus are displayed in detail in Table 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Features** & **Meaning** & **Tactile Stimulus** \\ \hline Mean of \(\mathsf{S}_{\text{s}}\) & Real contact area & Sustained pressure and texture \\ Mean of \(\mathsf{S}_{\text{v}}\) & Pressure distribution & Texture \\ Mean of \(\mathsf{S}_{\text{s}}\) & Contact pressure & Sustained pressure \\ Absolute Energy of \(\mathsf{S}_{\text{s}}\) & Contact force and amplitude of vibration & Sustained pressure and low frequency \\ Standard Deviation of \(\mathsf{S}_{\text{s}}\) & Consistency of contact force & Texture \\ cA4 of \(\mathsf{S}_{\text{s}}\) & Approximate information of vibration & Sustained pressure \\ cD4 of \(\mathsf{S}_{\text{s}}\) & Detail information of vibration & Low frequency vibration \\ cD3 of \(\mathsf{S}_{\text{s}}\) & Detail information of vibration & Medium-low frequency vibration \\ cD2 of \(\mathsf{S}_{\text{s}}\) & Detail information of vibration & Medium-high frequency vibration \\ cD1 of \(\mathsf{S}_{\text{s}}\) & Detail information of vibration & High frequency vibration \\ CID of \(\mathsf{S}_{\text{s}}\) & Approximate frequency of vibration & High frequency vibration \\ \hline \hline \end{tabular}
\end{table}
Table 3: The 11 features, their meaning, and the corresponding tactile stimulus that sensed by mechanoreceptors.