Journal Title: Pattern Recognition

Title of the Manuscript: FedSegment: A Novel Federated Learning Framework for Semantic Segmentation of Secondary Screen Cabinet Terminal Block in Smart Substation

Authors: Rong Xie, Zhong Chen, Weiguo Cao, Congying Wu and Tiecheng Li

Symbols and Notations Used in the Methodology (Install MathJax Plugin for Github)

Symbol	Description
$F$	Input feature map extracted by the encoder.
$F'$	Feature map after channel attention: $ F' = M_c(F) \otimes F $.
$ F''$	Feature map after spatial attention: $ F'' = M_s(F') \otimes F' $.
$ M_c(F) $	Channel attention map generated from $ F $.
$ M_s(F) $	Spatial attention map generated from $ F $.
$ \sigma(\cdot) $	Sigmoid activation function.
$ \operatorname{MLP}(\cdot) $	Multi-Layer Perceptron in channel attention.
$ \operatorname{MaxPool}(F) $	Global max pooling applied to $ F $.
$ \operatorname{AvgPool}(F) $	Global average pooling applied to $ F $.
$ f^{7 \times 7}(\cdot) $	$ 7 \times 7 $ convolution operation in spatial attention.
$ [\cdot , ; , \cdot] $	Concatenation operator along the channel dimension.
$ \otimes $	Element-wise multiplication operator.
$ l $	Security parameter determining key sizes.
$ p $	Large prime number, $ p > 2^l $, order of the groups.
$ G_1 $	Cyclic additive group of order $ p $.
$ G_2 $	Cyclic multiplicative group of order $ p $.
$ e(\cdot, \cdot) $	Bilinear pairing function, $ e: G_1 \times G_1 \rightarrow G_2 $.
$ P $	Generator of the group $ G_1 $.
$ H_1(\cdot) $	Hash function, $ H_1: {0,1}^* \rightarrow G_1 $.
$ H_2(\cdot) $	Hash function, $ H_2: {0,1}^* \times G_1 \rightarrow \mathbb{Z}_p^* $.
$ H_3(\cdot) $	Hash function, $ H_3: {0,1}^* \rightarrow \mathbb{Z}_p^* $.
$ X_{\text{TTP}} $, $ Y_{\text{TTP}} $	Private key and public key of the TTP.
$ X_{\text{CS}}' $, $ Y_{\text{CS}}' $	Private and public key components of the Cloud Server (CS).
$ X_{\text{PS}}' $, $ Y_{\text{PS}}' $	Private and public key components of the Power Station (PS).
$ X_s' $, $ Y_s' $	Private and public key components of substation $ s $.
$ ID_{\text{CS}} $, $ ID_{\text{PS}} $, $ ID_s $	Identity strings of CS, PS, and substation $ s $.
$ s_{cp} $, $ s_{ip} $	Shared secrets for secure communication.
$ M $, $ M_1 $, $ M_2 $	Training parameters; $ M_1 $ for substations, $ M_2 $ for PS.
$ T_s $, $ T_i $	Timestamps or session identifiers.
$ r $, $ v $	Random parameters used in signature generation.
$ D_s $, $ D_i $	Hash values used for signature verification.
$ k_s $, $ k_i $	Signature components computed by participants.
$ U_s $, $ U_i $	Signature components involving private keys and hash functions.
$ \sigma_s $, $ \sigma_i $	Signatures composed of signature components.
$ Z_s $, $ Z_i $	Session parameters in signature generation.
$ Z_s' $, $ Z_i' $	Encrypted session parameters sent to PS and CS.
$ \operatorname{Enc}_s(\cdot) $, $ \operatorname{Enc}_i(\cdot) $	Encryption functions.
$ \operatorname{Dec}_s(\cdot) $, $ \operatorname{Dec}_i(\cdot) $	Decryption functions.
$ req_s $, $ req_i $	Update request messages sent by participants.
$ R $	Set of requests used in batch verification.
$ N $, $ M $	Number of substations $ N $ and power stations $ M $ involved.
$ I_0 $, $ I_0' $	Original image dataset and preprocessed image dataset.
$ I(x, y) $	Pixel value at position $ (x, y) $ in image $ I $.
$ I'(x, y) $	Pixel value after transformations.
$ R(I(x, y), \theta) $	Rotation of pixel $ I(x, y) $ by angle $ \theta $.
$ Z(I(x, y), s) $	Zoom operation on pixel $ I(x, y) $ with scale $ s $.
$ C(I(x, y), \alpha) $	Contrast adjustment of pixel $ I(x, y) $ by factor $ \alpha $.
$ D(I(x, y), \delta) $	Distortion applied to pixel $ I(x, y) $ with magnitude $ \delta $.
$ p_{\text{rot}} $, $ p_{\text{zoom}} $	Probabilities of rotation and zoom transformations.
$ p_{\text{con}} $, $ p_{\text{dist}} $	Probabilities of contrast adjustment and distortion.
$ \epsilon $	Gaussian noise sampled from $ \mathcal{N}(0, I) $.
$ \overline{a}_t $	Cumulative product of noise schedule parameters up to time $ t $.
$ I_t' $	Noisy image at timestep $ t $ in the diffusion process.
$ \epsilon_\theta(I_t', t) $	Predicted noise by the neural network at time $ t $.
$ \hat{I}_0' $	Estimated original image from noisy image $ I_t' $.
$ D_{\text{CLIP}} $	CLIP-based loss function measuring image-text discrepancy.
$ \text{CLIP}_{\text{img}}(\cdot) $	Image encoder of the CLIP model.
$ \text{CLIP}_{\text{txt}}(\cdot) $	Text encoder of the CLIP model.
$ d $	Text description or prompt for image generation.
$ m $	Mask indicating the region of interest in the image.
$ D_c $	Cosine distance function for embeddings.
$ \odot $	Element-wise multiplication (Hadamard product).
$ I_{t-1,\text{fg}}' $, $ I_{t-1,\text{bg}}' $	Denoised images of foreground and background at time $ t-1 $.
$ I_{t-1}' $	Combined denoised image at time $ t-1 $.
$ \text{fea}_0 $, $ \text{fea}_1 $	Feature maps from local (student) and global (teacher) models.
$ \text{Sim} $	Adjusted feature similarity matrix.
$ \text{FFT}(\cdot) $, $ \text{IFFT}(\cdot) $	Fourier Transform and Inverse Fourier Transform.
$ \alpha $	Coefficient adjusting frequency domain response.
$ L_{\text{pair}} $	Feature similarity loss between local and global models.
$ \text{KL}(\cdot, \cdot) $	Kullback-Leibler divergence function.
$ \text{Softmax}(\cdot) $	Softmax function for normalization.
$ S_{\text{sim}} $, $ T_{\text{sim}} $	Similarity matrices from student and teacher models.
$ T $	Temperature parameter in the softmax function.
$ B $	Batch size in training.
$ L_{\text{CE}} $	Cross-entropy loss for the segmentation task.
$ L_{\text{total}} $	Total loss including $ L_{\text{CE}} $ and $ L_{\text{pair}} $.
$ \beta $	Hyperparameter controlling the weight of $ L_{\text{pair}} $.
$ \log(\cdot) $	Natural logarithm function.
	Semantic Segmentation Model Symbols
	Anonymous Identity Authentication Protocol Symbols
	Stabilization Strategy Symbols

Ideal Model:

Federated Model:

FedSegment:

Semantic Segmentation:

Anonymous Protocol:

Data Augmentation: