## 3 Proposed FP-SFOA-DQN-FL for Real-World Object Recognition in FL
### Feature Extraction  
The extraction of features is the most significant phase performed to extract the relevant features for future processing of object recognition. More appropriate features being extracted results in accurate object-recognition performance. Here, the features extracted at this step are described as follows:  
Regarding the detected result \(\mathrm{D_{a}}\) of the object-detection process, the features are extracted. 1. Shape Local Binary Texture (SLBT)  
The SLBT feature [31] is an integration of shape and texture information. SLBT is similar to that of the active appearance model (AAM), and it considers LBP texture features rather than intensity measures. In AAM, direct intensity values from shape-free patches are employed for texture modeling. However, SLBT performs LBP over a shape-free patch to obtain illumination and unchanged noise features. LBP feature extraction is fast and simple. Consider a \(3\times 3\) window with a center pixel, where its intensity measure is represented as \(l_{c}\), and its local texture is represented as  
\[Pix=pix\left(l_{J}\right) \tag{19}\]  
Here, \(l_{J}\) is associated with the grey measures of eight adjacent pixels in which (\(J=0\), \(1\), \(2\), \(3\), \(\ldots\),\(7\)). These adjacent pixels are threshold with the middle value \(l_{c}\) as \(pix(Aa(l_{0}-l_{c}),\ldots,\ Aa\ (l_{7}-l_{c}))\), and the function \(Aa(N)\) is expressed as  
\[Aa\left(N\right)= \begin{cases}1,&N>0\\ 0,&N\leq 0\end{cases}  \tag{20}\]  
\[LBP=\sum_{J=0}^{7}Aa\left(l_{J}-l_{C}\right)2^{J} \tag{21}\]  
The LBP pattern at the middle pixel \(l_{c}\) is achieved using the above equation, and the image result obtained from SLBT is denoted as \(V_{1}\). 2. Speeded-Up Robust Feature (SURF);  
SURF [32] is a local feature descriptor that is highly employed for functions like classification, object recognition, and 3D reconstruction. The identifier determines the interest points highlighted in the image, whereas the descriptor explains the features of interest points. Such features are invariable to shifting, rotation, and scaling. The SURF feature result \(V_{2}\) is defined as follows:  
\[V_{2}\left(\aleph,\,\delta\right)= \begin{cases}\mathrm{H_{uu}}\left(\aleph,\, \delta\right)&\mathrm{H_{uv}}\left(\aleph,\,\delta\right)\\ \mathrm{H_{uv}}\left(\aleph,\,\delta\right)&\mathrm{H_{vv}}\left(\aleph,\, \delta\right)\end{cases}  \tag{22}\]  
Here, \(\mathrm{H_{uu}}\left(\aleph,\,\delta\right)\), \(\mathrm{H_{uv}}\left(\aleph,\,\delta\right)\), and \(\mathrm{H_{vv}}\left(\aleph,\,\delta\right)\) represent the convolution of the Gaussian second-order derivative. 3. Scale-Invariant Feature Transform (SIFT)  
SIFT [33; 34] is a local key point descriptor, and this descriptor effectively refines the object features by considering various scales, illumination, rotation, and geometric transformations. It completely eliminates the probability of distortion caused by clutter, occlusion, or noise. It acquires the detected object image and results in a group of features as an outcome. The four phases included in SIFT are scale-space extrema identification, key point localization, orientation allotment, and key point descriptor. SIFT constructs a multi-resolution pyramid on the input image. At the initial phase, a variation of Gaussian is performed to determine the local extrema. The selected extrema are assumed as the key points. The Gaussian blurred image is represented as  
\[Ll\left(\mathrm{U}u,\,\forall v,\,\mu\right)=Gg\left(\mathrm{U}u,\,\forall v,\,\mu\right)\,*D_{a} \tag{23}\]Here, \(D_{a}\) is the detected object image. The variation of the Gaussian point is obtained by convolving the Gaussian distribution with the detected object image. \[DoG\left(Uu,\,Vv,\,\mu\right)=\left(Gg\left(Uu,\,Vv,\,K\mu\right)-Gg\left(Uu,\, Vv,\,\mu\right)\right)*D_{a} \tag{24}\]  
\[DoG\left(Uu,\,Vv,\,\mu\right)=Ll\left(Uu,\,Vv,\,K\mu\right)-Ll\left(Uu,\,Vv,\,\mu\right) \tag{25}\]  
The candidate key point is selected based on the pixel value.