Information-Weighted Boundary Normalization

• The paper introduces IWBN to convert segmented tumor contours into 1D weighted signals, emphasizing locally complex regions for diagnostic clarity.
• IWBN computes local entropy and applies information-based weighting to preserve scale while amplifying diagnostically significant irregularities.
• It integrates into the XMorph pipeline, enhancing handcrafted morphological features that fuse with deep embeddings to improve tumor classification.

Searching arXiv for the cited papers to ground the article and confirm bibliographic details. Information-Weighted Boundary Normalization (IWBN) denotes a boundary-centric normalization scheme introduced within XMorph for explainable brain tumor analysis, where a segmented tumor contour is converted into a 1D radial signal and then reweighted so that boundary locations with greater local morphological complexity contribute more strongly to the representation. In XMorph, IWBN is designed to preserve scale normalization while selectively amplifying locally irregular contour segments, particularly jagged, infiltrative, or lobulated regions that are argued to be diagnostically meaningful in differentiating glioma, meningioma, and pituitary tumors (Ghahfarokhi et al., 24 Feb 2026). In a distinct line of work on imbalanced classification, a conceptually related but differently named modification to batch normalization reweights normalization statistics to match the effective sample size induced by a weighted loss; that method is termed proposed BN, or pBN, rather than IWBN (Yasuda et al., 2019). The two uses share an importance-weighted normalization logic but operate on different objects: tumor boundaries in XMorph and mini-batch activation statistics in weighted-loss neural training.

1. Definition and scope

Within XMorph, IWBN is the paper’s key novelty for turning a segmented tumor contour into a more diagnostically useful 1D signal. The method is introduced because a plain, globally normalized boundary representation can miss local irregularities that matter in brain tumor morphology, especially when malignancy is associated with infiltrative or uneven margins (Ghahfarokhi et al., 24 Feb 2026). The underlying premise is that a single global descriptor, such as fractal dimension or a single irregularity statistic, may obscure heterogeneous boundary behavior distributed unevenly along the contour.

The method is situated in a clinically motivated morphology pipeline. Pituitary tumors are described as tending to be smooth and well circumscribed; meningiomas as possibly mostly smooth but containing localized lobulations; and gliomas as often infiltrative with diffuse, uneven, chaotic margins (Ghahfarokhi et al., 24 Feb 2026). IWBN is therefore not a generic contour normalization procedure, but a mechanism intended to preserve the scale-invariant contour while reweighting it so that irregular segments contribute more strongly than regular ones.

A potential source of terminological confusion arises from the 2019 paper on imbalanced learning, which does not use the term “Information-Weighted Boundary Normalization.” Instead, it proposes a weighted version of batch normalization for use with weighted loss and refers to it as pBN (Yasuda et al., 2019). That work concerns normalization of mini-batch statistics under class-imbalance weighting rather than boundary-shape modeling. A plausible implication is that “IWBN” should be treated as XMorph-specific terminology unless explicitly broadened to cover any normalization procedure that incorporates information weights.

2. Mathematical construction in XMorph

In XMorph, IWBN is defined in three stages: boundary-to-signal conversion, local entropy estimation, and entropy-based weighting with renormalization (Ghahfarokhi et al., 24 Feb 2026).

For each predicted tumor mask, the contour is resampled to a fixed length of $N=256$ points. If $(x_i,y_i)$ is the $i$-th boundary point and $(c_x,c_y)$ is the centroid, the radial distance is

$$r_i = \sqrt{(x_i - c_x)^2 + (y_i - c_y)^2}, \quad i = 1,\dots,N.$$

The mean radius is

$\bar{r} = \frac{1}{N}\sum_{i=1}^N r_i.$

The standard scale-invariant boundary signal is then

$S_{\text{std},i} = \frac{r_i}{\bar{r}},$

where values above 1 indicate protrusions and values below 1 indicate indentations (Ghahfarokhi et al., 24 Feb 2026).

IWBN next computes a local entropy $E_i$ at each boundary point. The paper states that this local entropy is intended to quantify variability or structural complexity in the point’s neighborhood and may be based on neighborhood curvature or radial-distance variance, but it does not provide a more detailed neighborhood formula (Ghahfarokhi et al., 24 Feb 2026). These values are normalized as

$$\hat{E}_i = \frac{E_i - E_{\min}}{E_{\max} - E_{\min}},$$

which rescales entropy to $[0,1]$.

The normalized entropy is mapped to an information weight

$(x_i,y_i)$0

The constant $(x_i,y_i)$1 acts as a floor so that low-entropy regions are not assigned zero influence, and the denominator normalizes the weights to have average value 1 across the boundary (Ghahfarokhi et al., 24 Feb 2026).

The information-weighted signal is then

$(x_i,y_i)$2

This final renormalization preserves comparability across cases after the pointwise modulation by local information weights. In effect, the original scale-normalized contour is multiplied by a local information weight and then renormalized.

The paper also defines three summary measures derived from this construction:

$(x_i,y_i)$3

for Mean Local Entropy,

$(x_i,y_i)$4

for Weight Range, and

$(x_i,y_i)$5

for Enhancement Factor (Ghahfarokhi et al., 24 Feb 2026). EF is presented as the most direct indicator of how much IWBN amplifies boundary variability; values greater than 1 are interpreted as stronger emphasis of diagnostically relevant irregularity.

3. Position within the XMorph architecture

IWBN is located in Stage 2, Tumor Specific Feature Extraction, after segmentation and before fusion and classification in XMorph (Ghahfarokhi et al., 24 Feb 2026). The workflow begins with DeepLabV3 segmentation to extract the tumor mask, followed by boundary sampling into a 1D radial contour signal. IWBN is then applied to emphasize informative boundary segments.

The resulting boundary representation contributes to a broader handcrafted feature vector that includes geometric features such as irregularity and roughness, nonlinear chaotic descriptors such as fractal dimension, entropy measures, and Lyapunov exponent, and clinical biomarkers such as REI, skull-to-tumor distance, and midline shift (Ghahfarokhi et al., 24 Feb 2026). In parallel, a ResNet-50 extracts deep features from the full MRI slice. These handcrafted and deep features are fused and classified by XGBoost.

IWBN does not directly modify the ResNet-50 branch. Its function is instead to strengthen the Tumor Specific Features branch prior to multimodal fusion. This suggests that IWBN’s principal role is representational rather than end-to-end architectural: it improves the discriminability of a handcrafted morphological descriptor that is later combined with deep embeddings (Ghahfarokhi et al., 24 Feb 2026).

XMorph also integrates an explainability stack composed of GradCAM++ and an LLM-based textual rationale generator. IWBN is particularly relevant here because its derived features are among those passed into SHAP and then into the GPT-5 prompt (Ghahfarokhi et al., 24 Feb 2026). The paper emphasizes a division of explanatory labor: GradCAM++ indicates where the model focused, whereas IWBN-derived features help express what boundary property was diagnostically important, such as high boundary entropy, localized lobulation, or infiltrative irregularity.

4. Implementation details and training configuration

The explicit implementation details tied to IWBN in XMorph are limited but concrete. Boundary resampling length is fixed at $(x_i,y_i)$6 points (Ghahfarokhi et al., 24 Feb 2026). The hyperparameter table lists the IWBN weighting parameter as $(x_i,y_i)$7, while the text uses $(x_i,y_i)$8 for weighting strength; the paper presents $(x_i,y_i)$9 as the implemented choice for that role.

The feature pipeline is computed after segmentation with DeepLabV3. Features are z-score normalized within each training fold before classification, and the full classification evaluation uses five-fold stratified cross-validation (Ghahfarokhi et al., 24 Feb 2026). The downstream classifier is XGBoost with 300 estimators, max depth 8, and learning rate 0.05. For entropy features, the hyperparameter table lists $i$0 and $i$1, described as standard parameters commonly used for entropy computation in nonlinear signal analysis (Ghahfarokhi et al., 24 Feb 2026).

Segmentation uses input size $i$2, the Adam optimizer with learning rate $i$3, and a combined CrossEntropy + Dice loss (Ghahfarokhi et al., 24 Feb 2026). The paper does not provide a separate training loop or pseudocode exclusively for IWBN; instead, the method is embedded in the boundary-feature extraction stage.

In the imbalanced-learning paper, the analogous normalization idea is implemented as weighted batch normalization under weighted loss. There, the relevant statistics are computed from weighted affine activations using

$i$4

and

$i$5

(Yasuda et al., 2019). That paper emphasizes that the modification introduces no new hyperparameters. Although this is not XMorph’s IWBN, it provides an example of importance-weighted normalization in a different technical setting.

5. Empirical evidence and discriminative behavior

XMorph does not provide an isolated ablation that removes IWBN alone and reports classification performance without it (Ghahfarokhi et al., 24 Feb 2026). Accordingly, the evidence for IWBN is indirect but still quantitative and qualitative.

A table of morphological and information-weighted features reports class-dependent IWBN statistics across tumor types (Ghahfarokhi et al., 24 Feb 2026):

Tumor class	Mean Local Entropy	Weight Range / Enhancement Factor
Glioma	$i$6	$i$7 / $i$8
Meningioma	$i$9	$(c_x,c_y)$0 / $(c_x,c_y)$1
Pituitary	$(c_x,c_y)$2	$(c_x,c_y)$3 / $(c_x,c_y)$4

These values indicate that IWBN-derived metrics are not trivial duplicates of the standard boundary signal. They vary across classes and appear to capture different morphological regimes (Ghahfarokhi et al., 24 Feb 2026). The higher Mean Local Entropy reported for glioma is consistent with the paper’s description of gliomas as infiltrative and diffusely irregular, whereas lower values for pituitary tumors align with smoother morphology.

The figure-based qualitative validation follows the same pattern. Pituitary tumors are described as showing low entropy and evenly distributed low weights; meningiomas as showing localized high-entropy lobulated regions with correspondingly high weights; and gliomas as showing widespread high entropy and multiple high-weight hot spots (Ghahfarokhi et al., 24 Feb 2026). This suggests that IWBN functions as a local emphasis mechanism rather than a mere global perturbation of the contour signal.

At the system level, the full hybrid framework reaches 96.0% accuracy, while the tumor-specific feature branch alone reaches 90.0% accuracy (Ghahfarokhi et al., 24 Feb 2026). The paper attributes the strength of the tumor-specific feature set partly to the inclusion of IWBN alongside chaos-based and clinical descriptors, but does not isolate its contribution numerically.

The 2019 batch-normalization paper, by contrast, does provide direct comparative evidence for its weighted normalization variant. On highly imbalanced MNIST binary tasks, WLF+pBN outperforms both LF+sBN and WLF+sBN in all experiments (Yasuda et al., 2019). For example, in the 0 vs 1 task, WLF+pBN yields 99.8% accuracy for class 0, 87.5% for class 1, and 93.2% overall, compared with 100%, 63.3%, and 80.28% for WLF+sBN. These results demonstrate the general utility of aligning normalization statistics with an imposed weighting scheme, though they do not constitute evidence about XMorph’s contour-based IWBN specifically.

6. Clinical interpretation, related methods, and limitations

The clinical rationale for IWBN in XMorph is that tumor boundary morphology matters because malignancy is often reflected not only in size but also in how the tumor grows into surrounding tissue (Ghahfarokhi et al., 24 Feb 2026). Smooth, well-circumscribed boundaries are described as more typical of benign or less aggressive lesions; localized lobulations and protrusions may indicate heterogeneity in growth behavior; and diffuse irregularity and boundary chaos are characterized as features of infiltrative malignancy, especially glioma.

IWBN operationalizes this reasoning by assigning higher importance to boundary points with high local entropy. In computational terms, it makes the classifier more sensitive to small but meaningful shape anomalies that may be diluted by global metrics (Ghahfarokhi et al., 24 Feb 2026). This is particularly relevant when tumors have similar overall size or approximate shape but differ in subtle boundary details.

The method should nevertheless be distinguished from both conventional global descriptors and from weighted normalization in network training. Conventional global descriptors such as fractal dimension or a single irregularity statistic summarize morphology at the object level, whereas IWBN redistributes importance along the contour before feature summarization (Ghahfarokhi et al., 24 Feb 2026). Conversely, the weighted BN method of the imbalanced-learning paper redefines normalization statistics over mini-batch activations so that the effective batch size becomes

$(c_x,c_y)$5

instead of the literal mini-batch cardinality $(c_x,c_y)$6 (Yasuda et al., 2019). The shared theme is consistency between an information measure and a normalization rule, but the underlying domains and objectives differ substantially.

Several limitations are explicit in the available evidence. XMorph does not present a clean with-IWBN versus without-IWBN classification comparison, so the isolated effect of the method remains unquantified (Ghahfarokhi et al., 24 Feb 2026). The paper also does not provide a detailed neighborhood formula for the local entropy beyond stating that it can be based on neighborhood curvature or radial-distance variance. A plausible implication is that implementation details of entropy estimation may materially affect reproducibility and sensitivity. Even so, the reported class-separated statistics and qualitative visualizations support the interpretation that IWBN captures localized boundary complexity rather than merely rescaling the contour.

Taken together, IWBN is best understood as a contour-level, entropy-weighted normalization mechanism that augments a scale-invariant radial tumor boundary signal by emphasizing locally complex segments (Ghahfarokhi et al., 24 Feb 2026). In XMorph it functions as a morphology-sensitive component of a handcrafted feature branch that is subsequently fused with deep visual features and explainability modules. In broader methodological context, it belongs to a family of weighting-aware normalization ideas that seek to align representation with the distribution of diagnostically or statistically important information, though only XMorph applies that principle directly to tumor boundary morphology.