Cepstral GLCM Features for Texture Analysis

• Cepstral GLCM features are defined by computing a 2D cepstral representation followed by GLCM extraction, capturing periodic and anisotropic textures.
• They integrate frequency-domain analysis with spatial statistics, significantly improving discriminative performance in tasks like melanoma detection.
• Implementation involves preprocessing, independent color channel transforms, and feature fusion with handcrafted descriptors to optimize classification metrics.

Cepstral GLCM features are a class of texture descriptors that combine the frequency-domain analytical strengths of the cepstral transform with the spatial statistical power of Gray-Level Co-occurrence Matrix (GLCM) analysis. In this context, the cepstrum translates complex repetitive structures or periodicities in images into a 2D representation, onto which GLCM statistics are computed to characterize subtle anisotropic and periodic textural patterns. This methodology enables enhanced discrimination in challenging image analysis tasks such as melanoma detection and surface classification.

1. Definition and Mathematical Principles

Cepstral GLCM features are defined by applying the Gray-Level Co-occurrence Matrix to a two-dimensional cepstral representation of an image or signal. The two-step process involves:

1. Cepstral Transformation: For a two-dimensional image $I(x, y)$, the real cepstrum $C(u, v)$ is computed as:

$$C(u, v) = \mathrm{Re} \left\{ \mathcal{F}^{-1} \left( \log | \mathcal{F}\{I(x, y)\}| \right) \right\}$$

where $\mathcal{F}$ and $\mathcal{F}^{-1}$ denote the 2D Fourier and inverse Fourier transforms, respectively.

1. GLCM Computation: The GLCM is constructed on this 2D cepstral image by tabulating the normalized co-occurrence probability $P(i, j)$ of gray-level pairs:

$P(i, j) = \frac{N(i, j)}{\sum_{i,j} N(i, j)}$

where $N(i, j)$ counts the occurrences of the value pair $(i, j)$ at a given spatial displacement and orientation in $C(u, v)$.

From the resulting GLCM, various Haralick texture features—including contrast, correlation, energy, entropy, homogeneity, and additional directionality metrics—are extracted. For example, contrast is defined as:

$\mathrm{Contrast} = \sum_{i,j} (i - j)^2 P(i, j)$

2. Cepstral Representation for Texture Analysis

The cepstral representation functions as a nonlinear frequency-domain descriptor that accentuates periodic structures, ring patterns, or regular anisotropic textures in images. For each region or color channel of an image, the 2D cepstrum reveals peaks corresponding to dominant frequencies or periodic arrangements that may be subtle or aliased in the spatial domain.

In image processing pipelines, pre-segmentation (e.g., masking lesions in dermoscopic images) is often applied to eliminate background effects. Each color channel (such as RGB, Lab, HSV, YCrCb) can be transformed into its 2D cepstral domain independently, facilitating nuanced examination of luminance and chromaticity-driven patterns.

This process is essential because many clinically or industrially relevant textures exhibit frequency-domain regularities not evident via purely spatial analysis. The cepstral transform amplifies these discriminative features, which are then quantifiable by GLCM statistics.

3. GLCM Feature Extraction from 2D Cepstral Images

Application of the GLCM to the cepstral images involves calculating gray-level dependency histograms for distinct pixel pair orientations (commonly 0°, 45°, 90°, 135°) and displacements. Thirteen Haralick features are typically extracted per orientation, encompassing:

• Contrast
• Correlation
• Energy (angular second moment)
• Homogeneity
• Entropy
• Trace
• Directionality (e.g., quotient of max/mean over directions)

For a given orientation and displacement, pixel intensity pairs $(I(u,v), I(u+\Delta u, v+\Delta v))$ in the cepstral image are binned into the GLCM, then normalized to probabilities. Calculation for multiple orientations and color channels results in a high-dimensional but informative set of features.

This approach distinguishes itself from conventional GLCM extraction on spatial images by capturing complex, periodic, and anisotropic texture signals, as demonstrated in the context of melanoma detection and validated on the ISIC 2019 dermoscopic dataset (Miller et al., 31 Aug 2025).

4. Integration with Handcrafted Feature Frameworks

Cepstral GLCM features are often integrated alongside established handcrafted descriptors including:

• Median-split color metrics (color asymmetry)
• Atypical Pigment Network (APN)
• Saliency features from Laplacian-of-Gaussian maps
• Pink region and telangiectasia metrics
• Semitranslucent area descriptors

A greedy forward feature selection algorithm can be used to fuse cepstral and non-cepstral features, iteratively retaining those that improve classification performance metrics—such as area under the ROC curve (AUC)—in XGBoost models. This systematic fusion ensures that cepstral GLCM features augment and do not redundantly replicate information contained in the original handcrafted set.

5. Performance Evaluation and Metrics

The discriminative power of cepstral GLCM features for binary classification tasks is evaluated using:

Metric	Description	Key Findings
ROC AUC	Discrimination between melanoma and nevus across thresholds	Inclusion improves AUC, reaching up to 0.9697 in feature-fused XGBoost models
Accuracy	Proportion of correctly classified cases	Cepstral features alone: ≈0.9103; further improvement when fused
F1 Score	Harmonic mean of precision and recall; reflects false negative reduction	Cepstral features enhance F1, especially in sensitive clinical contexts

Empirical results indicate that cepstral GLCM features alone provide strong classification accuracy and AUC, and their inclusion with established descriptors consistently yields improved performance metrics, most noticeably in feature sets otherwise limited in discriminative power.

6. Technical Considerations and Implementation

Key steps in implementing cepstral GLCM feature extraction include:

1. Preprocessing: Segment the region-of-interest (e.g., lesion) and process each color channel independently.
2. Cepstral Transformation: Compute the 2D cepstrum for each channel.
3. Normalization: Quantize cepstral values for suitable gray-level binning.
4. GLCM Calculation: Generate GLCMs for specified orientations and displacements.
5. Feature Extraction: Derive multiple Haralick and directional features from each GLCM.
6. Feature Selection and Fusion: Employ selection algorithms to integrate with other handcrafted features before classification.

This methodology is not restricted to dermatological tasks; it plausibly extends to applications requiring characterization of periodic or anisotropic textures that are not fully described in the spatial domain.

7. Significance and Research Implications

Cepstral GLCM features capture information complementary to that of spatial-domain GLCM or first-order statistical features. While spatial-domain Haralick statistics reflect local intensity dependencies, their cepstral-domain analogs are sensitive to frequency and periodic phenomena that typify certain natural or pathological structures (e.g., malignant lesion regularities). The observed improvement in performance metrics supports the conclusion that cepstral GLCM features introduce non-redundant discriminative value (Miller et al., 31 Aug 2025).

A plausible implication is that similar combinations of frequency-domain and co-occurrence-based approaches may benefit general texture analysis problems beyond melanoma detection. Also, the use of multichannel/multispectral data and the decoupling of luminance and chromaticity (as in Lab or YCrCb color spaces) further maximizes the capture of relevant, high-order informational structure for discriminative learning.