import gradio as gr

def render_metrics():
    text = r"""
    We use **Equal Error Rate (EER %)**  a standard method used in bimoretric and anti-spoofing systems.

    ### **What is EER?**  
    Equal Error Rate (EER) is a performance metric used to evaluate biometric systems. It represents the point at which the **False Acceptance Rate (FAR)** and **False Rejection Rate (FRR)** are equal. A lower EER indicates a more accurate system.

    #### **False Acceptance Rate (FAR)**  
    FAR is the proportion of **unauthorized** users incorrectly accepted by the system.  

    $FAR = \frac{\text{False Acceptances}}{\text{Total Imposter Attempts}}$

    A high FAR means the system is too lenient, allowing unauthorized access.

    #### **False Rejection Rate (FRR)**  
    FRR is the proportion of **genuine** users incorrectly rejected by the system.  

    $FRR = \frac{\text{False Rejections}}{\text{Total Genuine Attempts}}$

    A high FRR means the system is too strict, denying access to legitimate users.

    ### EER is the point at which FAR and FRR are equal.
    """

    return gr.Markdown(text, latex_delimiters=[ {"left": "$", "right": "$", "display": False }])