# Antispoofing Performance Metrics: Types and Details

## Antispoofing Performance Metrics: Role, Types, Standards

Performance metrics play an important role in the testing of biometric systems. They help to reveal error rates, execute a full-scale security test and eradicate possible vulnerabilities. Common errors in a biometric system occur when a detection system fails to recognize biometric data. (Facial features, head volume and contours in the case of facial recognition).

The groundwork for the metrics is provided by the following standards:

In simple terms, these metrics help evaluate whether a detection system is able to effectively prevent Presentation Attacks (PAs).

To ensure that test results are accurate, two central evaluation parameters are proposed:

- Attack presentation classification error rate (APCER)
- Bona fide presentation classification error rate (BPCER)

## ISO Metrics for PAD System Evaluation

The PAD system evaluation includes various rate-based metrics. Their purpose is to assess the "readiness" of a system to identify a bona fide presentation attack, its instruments, attack frequency and error rate. The evaluation also examines and evaluates the subsystems of a PAD system as a test subject.

The metrics cover the following factors:

- Test subject number
- Presentation attack instruments and species
- Artifact and present non-conformant characteristics
- Description of output information provided by the PAD system

The end goal of the evaluation is to reveal whether a biometric system — as well as its subsystems — can *successfully* detect a presentation attack.

There are a few principal metrics types.

### Classification Metrics

This type involves APCER and BPCER evaluations.

APCER is used to calculate PAI species (PAIS) with this formula:

[math]\displaystyle{ APCER{\scriptstyle\text{PAIS}}=1-\left ( \frac{1}{N{\scriptstyle\text{PAIS}}} \right )\sum_{i=1}^{N_{PAIS}}Res_i }[/math]

Transcript:

— The attack presentation number for a specific PAIS.**N**_{pais}— If at least one presentation turns out to be an attack, it takes value 1. If not, it retains value 0.**Res**_{i}

The evaluation assesses the accuracy of the biometric system in the form of: (a) correctly classified and, (b) incorrectly classified results. Parameters evaluated on the basis of PAI series, by capture subject and species are also be specified.

Next, the PAD’s subsystem is tested. The test evaluates how well a subsystem detects PAIS in the context of a specific Attack Potential (AP). This implies reporting an accurate number of artifact presentations.

The following formula is used for this purpose:

[math]\displaystyle{ APCER_{AP}=\max_{PAIS\in{A_{AP}}}\Bigl(APCER_{PAIS}\Bigr) }[/math]

Transcript:

— A PAIS subgroup with a certain attack potential.**Α**_{AP}

The attack potential is estimated with the help of ISO/IEC 19989.

The second type of evaluation, BPCER is used for calculating and reporting bona fide presentations using the following formula:

[math]\displaystyle{ BPCER={\textstyle \sum_{i=1}^{N_{BR}}Res_i\over {N_{BF}}} }[/math]

Transcript:

— Amount of the bona fide presentations.**N**_{BF}— Again, it assumes value 1 if at least one PA attempt is registered. Otherwise, it retains value 0.**Res**_{i}

As a result, the reported bona fide presentations are classified correctly or incorrectly. (by total amount or by capture subject)

One essential clause states that APCER and BPCER test results cannot be put into an aggregate report. However, it is possible to report a PAD system’s performance as a BPCER figure accompanied by a specific APCER.

### Non-response Metrics

Non-response metrics evaluate instances when the PAD system is unable to detect a presentation attack at all.It is important to take into account the effect of non-responses during the evaluation process. Based on the manufacturer’s recommendations, it is crucial to point out conditions, under which a non-response belongs to the classification error rate.

Two chief metrics are used for this:

**Attack Presentation Non-Response Rate (APNRR)**. It is calculated for each PAIS and also includes the sample size for modeling the computed rate.**Bona Fide Presentation Non-Response Rate (BPNRR)**. It includes the sample size to provide the computed rate.

## APCER/BPCER Graphical explanation

### Generalization Metrics

Generalization metrics include the following:

**Half Total Generalization Error Rate (HTGER)**. It is defined as the Average Classification Error Rate (ACER) computed for all the protocol variants.

HTGER is calculated according to this formula:

[math]\displaystyle{ HTGER=\Bigl(\frac{1}{N_{GP_S}}\Bigr)\sum_{i=1}^{N_{GP_S}}ACER\bigl({GP}_i\bigr) }[/math]

**Worst Case Generalization Error Rate (WCGER)**. This is the "worst case" scenario, which includes the __highest__ or __maximum__ ACER value computed for all the protocol variants.

It is calculated according to this formula:

[math]\displaystyle{ WCGER=\max_{{GP}_S}\Bigl(APCER_{GP}\Bigr) }[/math]

### Demographic bias metric (statistical parity)

This metric implies "fair" and unbiased error distribution. It implies that a proportionate amount of errors occur in each demographic group (genders, ages, ethnicities, religions etc.). It is important to ensure demographic parity to provide efficacy and ethical approach to the subject.

To detect lack of demographic parity, Statistical Parity Difference can be employed:

[math]\displaystyle{ SPD = Pr (Y = 1|A = 1) - Pr (Y = 1|A = 0) }[/math]

Transcript:

**Y**denotes a binary predictor.**A**denotes protected attributes: sex, skin tone, age, etc.

For each specific demographic group the individual Demographic Bias Metric (DBM) can be calculated:

[math]\displaystyle{ DBM=\frac{1}{{\left\vert {DG}_{pairs} \right\vert}{\left\vert {\omega}_{points} \right\vert}}\cdot
\textstyle \sum_{j,k\in\{{{DG}_{pairs}}\}} \displaystyle \textstyle \sum_{i\in{\omega_{points}}} \displaystyle\left\vert {{BPCER}(i, j)-{BPCER}(i, k)} \right\vert }[/math]

Transcript:

— A number of demographic group pairs:**DG**_{pairs}*Male*—>*Female*,*Young*—>*Senior*,*Dark-skinned*—>*Light-skinned*, etc.

Note: There can be multiple pairs for a single demographic group.

### Demographic bias metric (from facial recognition)

To propose a truly bias-free solution, a challenge dubbed Looking at People Fair Face Recognition challenge ECCV2020 was proposed.

To prevent potential ethnicity bias, the following formula was suggested:

[math]\displaystyle{ {Bias}_{EER}=\sum_{e}{ERR}_e-{min}_{e'}{ERR}_{e'} }[/math]

Transcript:

— The error metrics APCER, BPCER, or ACER.**ERR**— ethnicity.**e**— Ethnicity with the lowest ERR value.**e'**— Total bias rate of the algorithm in one metric.**Bias**_{EER}

This formula helps to attest an algorithm as fair if only it generates the same ACER metric error rate for all ethnicities.

## References

- ISO/IEC 19795-1
- ISO/IEC DIS 30107-3
- ISO/IEC 30107-1:2016
- ISO/IEC 30107-3, First edition 2017-09
- An example of the Presentation Attack Species
- ISO/IEC 19989
- BPCER/APCER help to achieve a higher PAD accuracy rate
- Face presentation attack detection. A comprehensive evaluation of the generalisation problem
- Looking at People Fair Face Recognition challenge ECCV2020
- CASIA-SURF CeFA: A Benchmark for Multi-modal Cross-ethnicity Face Anti-spoofing