Class-Center Angular Separation in Face Recognizability

• CCAS is a recognizability score defined as the difference between CCS and NNCCS, quantifying the angular margin in embedding space.
• It distinguishes core facial features by aligning with the decision boundary, thereby enabling precise filtering of ambiguous samples.
• Integrated in TransFIRA, CCAS facilitates template aggregation by predicting frame recognizability and improving verification performance.

Searching arXiv for the primary paper and closely related FIQA work to ground the article. Class-Center Angular Separation (CCAS) is a margin-based recognizability score defined in the TransFIRA framework for face image recognizability assessment. It measures the difference between an embedding’s cosine similarity to its own class center and its maximum cosine similarity to any non-matching class center, thereby expressing recognizability as a property of the deployed encoder’s embedding geometry rather than of generic visual quality cues (Tu et al., 7 Oct 2025). In TransFIRA, CCAS functions as a decision-boundary-aligned criterion for filtering, as a target for recognizability prediction, and as a component of recognizability-informed template aggregation; it is paired with Class-Center Similarity (CCS), which captures alignment to the true class center and is used primarily for weighting (Tu et al., 7 Oct 2025).

1. Formal definition

For an image $x_i$ with embedding

$z_i = \phi(x_i),$

and identity label $y_i$, TransFIRA computes class centers $\mu_j$ and defines three related quantities (Tu et al., 7 Oct 2025).

The first is Class-Center Similarity: $$CCS_{x_i} = \frac{z_i^\top \mu_{y_i}}{\|z_i\|_2 \, \|\mu_{y_i}\|_2}.$$ This is the cosine similarity between the sample embedding and its true class center.

The second is Nearest Nonmatch Class Center Angular Similarity: $$NNCCS_{x_i} = \max_{j \neq y_i} \frac{z_i^\top \mu_j}{\|z_i\|_2 \, \|\mu_j\|_2}.$$ This is the maximum cosine similarity to any wrong-class center, corresponding to the strongest impostor class.

CCAS is then defined as

$CCAS_{x_i} = CCS_{x_i} - NNCCS_{x_i}.$

Accordingly, CCAS is the angular margin between affinity to the correct class prototype and affinity to the nearest competing prototype (Tu et al., 7 Oct 2025).

The computation of the class centers depends on the evaluation setting. If a gallery/probe split exists, class centers are computed from gallery embeddings only: $$\mu_j = \frac{1}{n_j^{\mathcal{G}}} \sum_{\substack{i \in \mathcal{G} \ y_i = j}} z_i.$$ Otherwise, the center is formed from all embeddings of class $j$: $\mu_j = \frac{1}{n_j} \sum_{i:\, y_i = j} z_i.$ Because all terms use cosine normalization, CCAS is explicitly angular and directional in embedding space rather than magnitude-driven (Tu et al., 7 Oct 2025).

2. Geometric meaning and decision-boundary alignment

The geometric interpretation of CCAS follows directly from its decomposition into CCS and NNCCS. CCS measures alignment with the true class center: high CCS indicates that the sample lies compactly within its identity cluster. NNCCS measures similarity to the most confusable impostor class. Their difference therefore quantifies relative separability with respect to the encoder’s existing class structure (Tu et al., 7 Oct 2025).

Large positive CCAS means that the sample is substantially closer to the correct center than to any competing center. CCAS near zero indicates ambiguity. Negative CCAS means that the sample is closer to some nonmatching center than to its own. In this sense, CCAS behaves as a decision-margin-like quantity in the encoder’s embedding geometry (Tu et al., 7 Oct 2025).

A central operational consequence is the natural filtering rule

$z_i = \phi(x_i),$0

which is equivalent to

$z_i = \phi(x_i),$1

This criterion is described as parameter-free, intrinsic to the encoder, and aligned with the decision boundary of the embedding space (Tu et al., 7 Oct 2025). The significance of this formulation is that recognizability is not inferred from blur, illumination, or pose in isolation; instead, it is inferred from whether the embedding occupies the correct side of the class-separation structure induced by the recognition model.

This geometric grounding distinguishes CCAS from FIQA schemes based on visual heuristics, curated annotations, or generative surrogates. A plausible implication is that CCAS can remain meaningful even when visual degradations have nonuniform effects across identities or encoders, because the score is defined relative to the operational representation itself rather than to a universal image-quality prior.

3. Relationship to CCS and to ratio-based confidence

CCAS and CCS are complementary rather than interchangeable. CCS captures how strongly a sample matches its own class center, whereas CCAS captures how much better that match is than the best competing class match (Tu et al., 7 Oct 2025). In TransFIRA, this distinction is functional: CCS is used for weighting template contributions, while CCAS is used for filtering samples (Tu et al., 7 Oct 2025).

This division reflects two different notions of utility. CCS acts as a compactness or reliability score within the correct class manifold. CCAS acts as a discriminative separability or recognizability score, since it encodes the sample’s margin against impostor identities. The paper emphasizes that this difference matters when constructing templates from multiple frames, because a frame can be well aligned with its class center yet still be insufficiently separated from an impostor center, or vice versa (Tu et al., 7 Oct 2025).

TransFIRA explicitly contrasts CCAS with the Certainty Ratio (CR) used in CR-FIQA: $z_i = \phi(x_i),$2 with $z_i = \phi(x_i),$3 (Tu et al., 7 Oct 2025). The critique is geometric: the added constant $z_i = \phi(x_i),$4 shifts the scale arbitrarily, equal angular separations can yield very different CR values, and the resulting ratio distorts the underlying margin (Tu et al., 7 Oct 2025). The example provided compares sample A with $z_i = \phi(x_i),$5 and sample B with $z_i = \phi(x_i),$6. Both have

$z_i = \phi(x_i),$7

but their CR values differ substantially (Tu et al., 7 Oct 2025). On that basis, CCAS is presented as the more geometrically faithful quantity because it directly preserves the difference in angular similarity.

A common misconception is to treat all confidence scores derived from similarity statistics as equivalent. The TransFIRA formulation rejects that equivalence: a difference-based angular margin and a ratio with an additive offset do not encode the same boundary structure, even when both are monotone in some limited region (Tu et al., 7 Oct 2025).

4. Role in TransFIRA recognizability assessment

TransFIRA defines recognizability in embedding space and trains a recognizability prediction network to estimate both CCS and CCAS from encoder features (Tu et al., 7 Oct 2025). The predictor outputs

$z_i = \phi(x_i),$8

Training uses mean squared error against targets derived automatically from the encoder’s own embeddings: $z_i = \phi(x_i),$9 This makes CCAS a supervised target without requiring external recognizability labels, manual annotations, or backbone-specific retraining (Tu et al., 7 Oct 2025).

Evaluation in the paper includes Spearman correlation with ground-truth recognizability and FNMR–ERC AUC at various FMR levels (Tu et al., 7 Oct 2025). The reported findings state that CCAS strongly correlates with recognizability and tracks encoder reliability well. On BRIAR, CCAS and CCS achieve very high Spearman correlation with ground-truth recognizability, and TransFIRA substantially outperforms prior methods including FaceQNet, MagFace, SDD-FIQA, CR-FIQA, DifFIQA, eDifFIQA, GraFIQs, and CLIB-FIQA in recognizability alignment (Tu et al., 7 Oct 2025).

The paper further reports that CCAS predictions are strongly aligned with true recognizability and that CCAS is especially effective as a direct recognizability signal (Tu et al., 7 Oct 2025). Because the targets are constructed from encoder geometry, the resulting predictor is encoder-specific by design. This suggests that CCAS should not be interpreted as a universal aesthetic or forensic quality measure; it is a model-relative estimate of whether an input is likely to be recognized reliably by a particular encoder.

5. Filtering, weighting, and template aggregation

The principal deployment use of CCAS in TransFIRA is filtering template frames before aggregation (Tu et al., 7 Oct 2025). The filtering rule is

$y_i$0

This retains only frames predicted to be on the correct side of the encoder’s decision boundary (Tu et al., 7 Oct 2025). The retained embeddings are then aggregated with predicted CCS as weights: $y_i$1 In this strategy, CCAS removes harmful or ambiguous samples, while CCS upweights strong and compact samples (Tu et al., 7 Oct 2025).

This recognizability-informed aggregation is one of the paper’s central system-level contributions. On BRIAR Protocol 3.1, CCAS filtering alone strongly improves TAR, and the combination of Filter + Weight gives the best overall performance; the paper highlights a large gain at very low FMR, indicating particular utility in difficult surveillance settings (Tu et al., 7 Oct 2025). On IJB-C, CCAS filtering is again among the best methods, and the combined CCAS filtering and CCS weighting variant is described as best or near-best (Tu et al., 7 Oct 2025).

The comparison with CR-FIQA filtering is explicit. The paper contrasts $y_i$2 with $y_i$3 and concludes that $y_i$4 is much weaker and less principled, while $y_i$5 yields much better verification performance (Tu et al., 7 Oct 2025). In the TransFIRA account, this performance difference supports the claim that CCAS provides the correct geometry-based filtering rule.

A plausible implication is that the separation between filtering and weighting objectives avoids a frequent failure mode in template construction: ambiguous frames are not merely downweighted but removed, while highly characteristic frames still contribute proportionally through CCS. That decomposition is central to the TransFIRA notion of recognizability-informed aggregation.

6. Generalization, explainability, and body recognition

The paper reports that CCAS-based recognizability generalizes well across datasets and remains robust under domain shifts because it depends on relative separation rather than absolute similarity (Tu et al., 7 Oct 2025). This claim places emphasis on the margin structure of the representation: relative separability may remain stable even when the global calibration of cosine scores changes between datasets.

CCAS also appears in the paper’s explainability analyses. Under blur, moderate or heavy blur reduces CCAS, mild blur can sometimes improve it, and CCAS remains strongly correlated with ground-truth recognizability (Tu et al., 7 Oct 2025). The interpretive significance is that CCAS does not merely produce a scalar quality estimate; it exposes how specific degradations perturb the embedding’s margin against competing classes. The paper therefore uses CCAS as part of an encoder-grounded explainability framework (Tu et al., 7 Oct 2025).

A major extension is to body recognition on BRIAR using the SemReID encoder. In this setting, raw body similarity scores saturate near 1, making CCS and NNCCS poorly discriminative (Tu et al., 7 Oct 2025). To address this, the paper applies sigmoid calibration to the similarity scores, restoring useful spread over $y_i$6, while preserving the same core definition

$y_i$7

The reported findings are that, for bodies, CCAS becomes the more reliable signal than CCS and that calibrated CCAS weighting performs best (Tu et al., 7 Oct 2025). This is presented as the first recognizability-aware body recognition assessment.

The extension to body recognition shows that CCAS is not intrinsically tied to face imagery. Rather, it is tied to any embedding regime in which own-class center proximity and nearest-impostor center proximity remain meaningful after suitable calibration. That portability supports the broader view of CCAS as an encoder-grounded separability criterion rather than as a modality-specific heuristic.

7. Related center-based formulations and conceptual scope

Although the literal term “Class-Center Angular Separation” is introduced in TransFIRA, related center-based geometry appears in other domains. In semantic segmentation, “Semantic Segmentation via Pixel-to-Center Similarity Calculation” reformulates prediction as similarity between pixel features and class centers, using adaptive class centers conditioned on different scenes and explicit center-to-center separation objectives (Wu et al., 2023). The segmentation head computes

$y_i$8

and the paper reinterprets the class weight vectors as class-center embeddings (Wu et al., 2023).

Its CCS layer combines an Adaptive Class Center Module (ACCM), a Similarity Calculation Module (SCM), and a Class Distance (CD) Loss (Wu et al., 2023). For center-to-center similarity it explicitly uses a cosine formulation,

$y_i$9

and defines inter-class and intra-class objectives that push centers apart and pull pixels toward their assigned center (Wu et al., 2023). The overall loss is

$\mu_j$0

The paper does not formulate an explicit samplewise angular margin analogous to CCAS, but it implements a close equivalent at the level of class-center geometry by regulating normalized center-to-center separation and pixel-to-center compactness (Wu et al., 2023).

This comparison is useful for delimiting the scope of CCAS. In TransFIRA, CCAS is a per-sample margin against the nearest competing class center and is directly used as a recognizability score (Tu et al., 7 Oct 2025). In the segmentation work, center-based angular separation is part of the training objective for improving representation structure, not a recognizability criterion (Wu et al., 2023). The overlap is therefore conceptual rather than terminological: both approaches treat class centers as the relevant geometric primitives, but only TransFIRA defines recognizability operationally through the signed margin between own-class and nearest-impostor similarity.

Taken together, these works situate CCAS within a broader family of center-based similarity methods while preserving its specific identity: an encoder-specific, angular, decision-boundary-aligned margin used to determine whether an input is recognizable to the model that will actually perform recognition (Tu et al., 7 Oct 2025).