Table 2 Symbols used and their description

\(C_u\)

Entity representing different criminals.

Set/list of all criminals in a given area.

\(c_1, c_2, ..., c_n\)

Individual criminal instances within \(C_u\).

Represents each identified criminal.

\(C_r\)

Set of criminal activities.

Different types of crime activities under detection.

\(D_E\)

Dataset used in CSV format for both crime and emotion detection.

Complete dataset, including image URLs, emotion labels, and descriptions.

F

Function that maps an input image to classified emotions.

The criminal emotion detection function.

I

Input image to the emotion detection system.

Criminal or suspect image fed into the CNN model.

\(I_{img}\)

Processed input image.

Actual image data passed into the CNN.

\(K_1\)

Kernel size of the convolution layer.

The size of the filter used for feature extraction in convolution operations.

\(U_{i0}\)

Initial weight matrix or feature input.

The starting state of feature input or weight initialization in the network.

E

Set of classified emotions \((e_1, e_2, ..., e_m)\).

Emotions detected from the criminal’s face.

M

AI model used for detection.

The CNN or other neural network model.

\(\mathcal {O}\)

Objective function to maximize detection accuracy.

Sum of accuracies over all crime and emotion classes.

\(\alpha\)

Crime classification result.

Output shows if the image is classified as a crime or non-crime.

NP

Non-criminal class image set.

Images labeled as non-crime (safe scenes).

AP

Criminal class image set.

Images labeled as crime activity.

\(\Omega\)

Set of file paths combining directory and filename.

Directory structures and filenames for all training/test images.

\(X_{train}, X_{test}\)

Training and testing image data.

Datasets are divided into training and testing for model evaluation.

\(X_{train\,rescaled}, X_{test\,rescaled}\)

Rescaled datasets (divided by 255).

Normalized training and test images for input into CNN.

\(X_{train\,sheared}, X_{test\,sheared}\)

Random shearing transformations applied to training and test images.

Augmented training and testing data with geometric distortion to improve model robustness.

\(X_{train\,zoomed}, X_{test\,zoomed}\)

Random zooming transformations applied to training and testing data.

Augmented training and testing data with different scales for learning multi-scale features.

\(X_{train\,flipped},X_{test\,flipped}\)

Random horizontal flips applied to training and testing data.

Augmented training and testing data with mirrored images for more variety.

\(shear(\cdot ), zoom(\cdot ), flip(\cdot )\)

Data augmentation functions applied.

Techniques used to diversify and enhance the dataset during preprocessing.

\(Conv2D(\cdot )\)

Convolution operation used in CNN layers.

Filters applied to input images to extract feature maps.

\(B_1, B_2\)

Bias terms added in CNN convolutions.

Model learnable parameters aiding filter responses.

\(U_l, Eml, d\)

URL, emotion label, and description in the emotion dataset.

Each row element in the emotion dataset CSV contains a link, label, and explanation.

\(U_{ret}\)

Image retrieval operation.

Downloading and loading an image from a provided URL.

\(P_d\)

Preprocessing function for resizing and normalization.

Function to standardize image size and scale values.

\(label \rightarrow int, int \rightarrow label\)

Mappings between categorical labels and integer indices.

Used to convert emotion names into numerical classes and vice versa.

\(C_1, C_2\)

Feature maps from the first and second convolution layers.

Output intermediate layers after convolutions.

P

MaxPooling output.

Reduced feature map dimension after pooling.

\(D_1, D_3\)

Dropout layers output.

Regularization technique outputs to reduce overfitting.

F (Flattened)

Flattened vector before dense layers.

Linear array from multidimensional feature maps.

\(D_2\)

Dense layer output before the second dropout.

Fully connected layer output with ReLU activation.

\(N_1, N_2\)

Number of neurons in Dense layers 1 and 2.

Defines layer sizes in the fully connected parts of the CNN.

O

Final output prediction after softmax.

Probability distribution over emotion classes.

B

Batch size.

Number of images processed per training batch.

E (epochs)

Number of complete training cycles over the dataset.

Number of complete training cycles over the dataset.