Advanced deep learning framework for soil texture classification

The proposed methodology acts like an explainable, multi-phased deep learning pipeline for the robust classification of soil texture from image-based soil data. The architetcture of the proposed soil texture classification model is shown in Fig. 1. The first step preprocesses the image for better input enhancement by eliminating unwanted high-frequency noise from the Butterworth filter, normalizing intensity distribution from the Box-Cox transformation, and augmenting the dataset through rotation, flipping, and translation to encourage diversity and prevent overfitting; this, ultimately, aids in stable learning with good-generalization ability. The second phase of feature engineering works to fuse hand-crafted descriptors with learned ones to ensure better interpretability and performance. Specifically, the second step of feature engineering considers the application of F-HOG to capture dominant structural gradients by frequency pruning. Haralick features and LBP were then applied to obtain texture information at macro and micro levels, respectively. Then, the employment of optimal ϕ-Pixels (selected using EWJFO) extracts highly discriminative areas in soil images. These features can be biologically and geologically interpretable and can be strong priors to guide learning in noisy environments. During phase 3, classification is carried out under a triptych deep architecture consisting of VGG-RTPNet, ResNet-DANet, and Swin-FANet. Each model enhancement is customized: the VGG is equipped with Residual Skip-Augmented Convolution Blocks (RSACB) to keep finer textures; ResNet incorporates a Dual Attention Modulation (DAM) module to focus on salient channels and spatial patterns; Swin Transformer is altered with Frequency-Aware Positional Encoding (FAPE) to encode spectral context. The heterogeneous branches are merged together using a weighted concatenation strategy, thus laying importance on both global and local cues. Phase 4 involves feature selection, performed by Enhanced Wombat Jellyfish Feature Optimization (EWJFO), an algorithm that combines exploratory and exploitative search methods to keep the most relevant features. This reduces dimensionality by a huge margin while improving classification accuracy. Finally, explainable AI (XAI) tools such as SHAP, Grad-CAM, and permutation importance are amalgamated throughout all stages to bring transparency and check the validity of the model’s decision-making process. The phases, in essence, are designed to provide complementary strengths-one for data quality, feature expressiveness, model robustness, and interpretability-into forming a very reliable and scalable soil classification framework.

Data preprocessing

The proposed ATFEM framework relies heavily upon pre-processing of the images for rendering soil texture classifying work more reliable and accurate. To explain the pipeline in simple terms, first, a low-pass Butterworth filter is applied to the image. Mostly employed in the frequency domain, this filter elegantly attenuates high-frequency noise without causing any harsh discontinuities³⁹. In contrast to the ideal low-pass filters or the Gaussian filters, which tend to cause ringing artifacts and excessive blurring of edges or features, respectively, the Butterworth low-pass filter strikes a fairly good compromise in suppressing noise while retaining crucial textural patterns on soil images. For example, this becomes so important when gradient-based feature extraction is done (e.g., F-HOG) because clean edge information is necessary to represent the information accurately.

Noise reduction has been carried out, the Box-Cox normalization will stabilize variance and reduce skewness in the pixel intensity distribution. Generally, soil images, especially those taken outdoors in the field, are subject to lighting contrast-related problems. Box-Cox transformation works as a statistical normalizing tool (power transformation type) that attempts to “normalize” data. This aids in the learning process for algorithms that assume homoscedasticity and roughly Gaussian-like distributions, such as convolutional neural networks, while, at the same time, ensuring that illumination bias does not lead a single feature to dominate feature selection and the subsequent learning.

To enhance better model generalization and avoid overfitting, several data augmentation techniques are applied, including cropping, flipping, rotation, and translation. Concerning cropping, it basically simulates situations in real-world soil-image capturing where soil image samples might be arising from different angles, orientations, or landmarks. Horizontal or vertical flip will offer a diversified population of the mirror images, while a controlled rotation of the images (generally within ± 20 degrees) allows the model to build rotational invariance when an image of the soil sample without strict alignment is captured. Slight translations will mimic spatial displacement, forcing the model to be robust to features that are off-center. Together, these refinement techniques amplify the effective size of the dataset, balance the classes, present the model with diverse examples, and so lessen the chance of memorization by the model; thereby, enhancing the model’s generalization power over unseen soil textures.

Removal of noise

The preprocessing pipeline begins with the implementation of a low-pass Butterworth filter and its subsequent operation in the frequency domain. Butterworth filters suppress high-frequency noise without distorting luminosity edges because they are smoother in transition between passband and stopband, unlike the starkly contrasting cut-off filters. In soil texture classification, edge preservation becomes paramount, as textural boundaries often become significant shifts in disaggregation, such as clay versus sand. The Butterworth filter effectively reduces sensor noise considered shadows, slight illumination changes, etc., in contrast to major texture features of the image, wherein the signal-to-noise ratio (SNR) suffers. When the image has undergone this preprocessing, it becomes favourable to feature extraction techniques like F-HOG, Haralick, or LBP, which require gradients and co-occurrence matrices to be clean. Hence, its usage enhances the robustness of the image input to carry out machine learning tasks downstream. Equation (1) to change the image into frequency domain

.

Were \(\:h\left(x,y\right)\) represents the frequency domain of the image. where \(\:\mathcal{F}\) denotes the Fourier Transform of the function \(\:h\left(x,y\right)\). Calculate the low pass butter worth filter using Eq. (2).

\(\:D(u,v)\) is the distance between the center of the frequency range and \(\:(x,y)\), the cutoff frequency \(\:{D}_{0},\:\)and the filter order \(\:n\), where M and N are the image’s dimensions. Equation (3) to calculate the Butterworth filter \(\:H(x,\:y)\)

.

Proceed the filter in the frequency domain. Multiply the fourier transform image by butterworth filter using Eq. (4)

Where \(\:F(x,\:y)\) is the filtered image in the frequency domain. Return to the spatial domain. Using Eq. (5) the filtered image can be obtained by computing the inverse 2D FFT.

Through this process, it effectively attenuates high frequency noise in soil image and preserves the significant low frequency components which represent the substantial features.

The intensity of the pixels for all images was transformed with the Box-Cox transformation to achieve normalization. The Box-Cox transformation is a power transformation with the goal of making the data behave in a more Gaussian manner and preventing heteroscedasticity in the observations. The pre-processing stage is shown in Fig. 2.

Data normalization

Pixel intensities are normalized after noise removal using the Box-Cox transformation, which is a general technique for stabilizing variance and converting an otherwise non-normal distribution to near-Gaussian. Soil images can suffer non-uniform illumination, sensor bias, and variability in reflectance due to moisture, mineral content, or organic matter. The Box-Cox transform in essence removes skewness in the distribution of pixel values and produces a homoscedastic set (constant variance in the image). This leads to better learning by algorithms that work on the explicit assumption that input data are normally distributed, such as CNNs or statistical models. From the point of view of the actual learning process, it also scales all features to a comparable scale, so that features highly skewed, or containing outliers, cannot dominate the learning. Thus, Box-Cox normalization supports better and unbiased feature selection and a more robust convergence during training. Mathematically, Box-Cox normalization is given by Eq. (6).

\(\:Z,\:\lambda\:\), and data represent the rate of change, actual number, and normalized data value, respectively. To regulate silt and sand data, first regulated data dissemination at \(\:\lambda\:\:=\:0.2967\). The outcomes of the pre-processing stage is shown in Fig. 3.

Data augmentation

To increase the generalization capacity of the deep learning model and combat overfitting, a set of data augmentation strategies are employed—namely flipping, rotation, and translation. Flipping (horizontal and vertical) helps the model learn symmetry-invariant features, which is vital since soil samples may be photographed from any direction in real-world settings. Rotation allows the model to maintain high performance even when input images are captured at arbitrary angles, addressing orientation variance that is common in field-acquired data. Typically, small angular rotations (± 15° to ± 30°) are applied to prevent extreme distortion. Translation, or pixel shifting, simulates off-centered or displaced samples in the frame, making the model robust to object positioning. Together, these augmentation techniques expand the dataset virtually without collecting additional images, introduce variability, prevent the model from memorizing training data, and allow for better generalization across unseen data. This is especially important in domains like soil analysis where collecting new labeled samples is costly and time-intensive.

For a given high-resolution image set, \(\:{D}_{0}=\left\{{I}_{1},\dots\:.{I}_{K}\right\}\), where \(\:{I}_{K}\:\)represents the kth image sample in the dataset. Assume that \(\:{I}_{K}\:\)has N pixels. \(\:{P}_{K}\) is the pixel-homogeneous coordinate matrix for \(\:{I}_{K}\).

Each row represents a single pixel’s homogeneous coordinates.

To enhance a single picture \(\:{I}_{K}\), an affine transformation matrix \(\:M\) is applied to its homogeneous coordinate matrix \(\:{P}_{K}\), resulting in a changed homogeneous coordinate matrix \(\:{P}_{k}^{t}\). The operation is presented as follows:

Each row of \(\:{P}_{k}^{t}\) represents the modified homogeneous coordinate for a single pixel. There are several approaches to determining the affine transformation matrix M. Our method employs three types of random perturbations to generate fresh augmented data. The three types of transformations are defined as follows:

Flip (\(\:{T}_{1}\)): The image is flipped horizontally. The associated affine transformation matrix (M) is

Translation (\(\:{T}_{2}\)): The image is displaced in both directions (x and y). The appropriate affine transformation matrix, M is

.

\(\:{T}_{x}\) and \(\:{T}_{y}\) are coordinate axis offsets.

Rotation (\(\:{T}_{3}\)): The image is rotated with an angle ranging from 0 to 180°. The appropriate affine transformation matrix, M is

For a single picture \(\:{I}_{K}\), the augmented data is represented as \(\:{O}_{k}=\{{T}_{1}\left({I}_{k}\right),{T}_{2}\left({I}_{k}\right),{T}_{3}({I}_{k}\left)\right\}\). The expanded dataset for the original dataset \(\:{D}_{0}\) is represented as \(\:{D}_{a}=\{{O}_{1},\dots\:.,{O}_{k}\}\). The augmentation process for the dataset \(\:{D}_{0}\) is described as follows:

To classify high resolution images, a CNN is trained using the enhanced dataset \(\:{D}_{a}\) and matching class labels. Use flips, translations, and rotations for data augmentation in high resolution image to maintain consistent scene topologies. Following augmentation, the next step is to extract F-HOG and Paramount Incessant ϕ-Pixels characteristics. The ablation study of pre-processing and feature extraction stage is shown in Tables 1 and 2, respectively. The analysis of the proposed model over the existing models for the pre-processing stage and data augmentation is shown in Supplementary Figure S1 and Supplementary Figure S2, respectively.

An ablation test has been used to investigate the impact of each preprocessing on the improvement of model fitting: the various preprocessing techniques alone and in different combinations. The full preprocessing pipeline comprising of low-pass Butterworth filtering, Box-Cox transformation, and data augmentation gave the best accuracy (0.981) and F1-score (0.896), hence validating its effectiveness. Removal of the Butterworth filter seemed to result in a slight decrease in performance (with accuracy falling to 0.961), thereby underscoring its importance in noise suppression and texture preservation. The Box-Cox normalization, if absent, would have made the model less efficiently competent in handling illumination variation, thereby also lowering performance (accuracy: 0.958). The data augmentation’s removal caused the steepest drop in generalization metrics (accuracy: 0.942), further driving home how important it is in minimizing overfitting, particularly when dataset diversity is scarce.

The testing of individual components further made clear that no single method was likely to perform competitively with that of the full stack. Raw images alone generated the lowest metrics, with 0.878 accuracy and 0.774 F1-scores, thus suggesting that preprocessing is a significant factor in generating reliable classifications. Among the three, data augmentation had the most beneficial effect-if this step was removed, a significant drop in performance was observed-indicating its importance against overfitting and for robustness. This ablation study thus validates the inclusion of the complete preprocessing pipeline as a synergistic mechanism within the proposed ATFEM model.

Visual spectrum (in Fig. 4) showed clear suppression of irrelevant high-frequency components. A 31.4% drop in spectral entropy confirmed less noise. Preprocessing enhances texture clarity and suppresses irrelevant patterns, leading to better CAM consistency and feature attribution in downstream stages.

Feature extraction

In soil images, feature extraction has to be efficient enough to capture textural and color properties when classifying soils with complex textures. We accordingly propose a multistage feature-extraction pipeline involving F-HOG, Haralick features, LBP, and the newly formulated ϕ-Pixels color analysis. As a whole, these formations are envisioned to complement one another in describing structural texture patterns, fine-grained macrotextures, and chromatic distributions, respectively.

F-HOG and paramount incessant ϕ-Pixels based feature extraction

This research work put forward a newly-developed descriptor for soil texture image analyses based on an informed frequency understanding and edge-aware capability into discriminant-dimensional gradient coding, named Filtered Histogram of Oriented Gradients (F-HOG). F-HOG involves the improvement of the standard HOG, which was modified for soil texture images. While traditional HOG descriptors are powerful, some disadvantages include high dimensionality, computational redundancy, and an inability to describe well high-frequency noise that is so common in soil images acquired in the field, wherein almost every variation in illumination contributes to a variation in fine-grained texture.

Motivation and limitations of conventional HOG

The classic Histogram of Oriented Gradients (HOG) algorithm, though many times a good one for pattern recognition problems, carries a few issues when dealing with soil image processing:

• Noise-sensitive: High-frequency noise (lighting variance, reflection from soil grains, etc.) seriously affects gradient estimation.

• Redundant bins: Uniform binning over the gradient map often results in big descriptors carrying very little information.

• Global processing: HOG treats the entire image uniformly without any notion of spectral or textural contexts.

To solve these issues, F-HOG introduces frequency-domain preprocessing and spatially aware gradient selection to obtain a compact and noise-robust descriptor.

To avoid this, F-HOG does the following:

• Filtering gradients in the frequency domain using a Butterworth filter to remove high-frequency noise,

• Computing a HOG vector, and then.

• Retaining only the top-F most frequent bins through statistical frequency sorting.

This method of reduction drastically reduces the dimensionality while preserving the dominant structural gradients. Unlike PHOG and HOG3D, which emphasize spatial pyramids or motion, the proposed F-HOG applies a unique frequency-filtered selective histogram pruning, and this gives it an advantage when working with agricultural images prone to high noise. Our ablation results (see Sect. 4.4) reported that F-HOG could make classifiers more efficient by reducing redundancy without sacrificing performance.

Farthing histogram-oriented gradients (F-HOG)

F-HOG is a novel surfaces textural element introduced in this study. It’s an altered variation of the histogram-oriented gradients (HOG) feature. HOG is currently employed for a range of agricultural purposes. It is calculated using the magnitude distributions (histogram) and pixel gradient using the extract HOG Features tool. HOG frequently generates a large vector that requires more time and space to process. It remains constant regardless of the object’s dimensions or rotations.

F-HOG algorithmic pipeline

The F-HOG process is executed in three stages: frequency filtering, adaptive gradient binning, and entropy-guided region selection.

Stage 1: Frequency-aware preprocessing.

A low-pass Butterworth filter is applied in the frequency domain to suppress high-frequency components while retaining edge structures:

The filtered image \(\:{h}_{f}\) \(\:(i,\:j)\)preserves dominant texture patterns and suppresses sharp transitions due to lighting and sensor noise, forming a stable input for gradient computation.

Stage 2: Gradient computation and initial binning.

We compute gradients on the filtered image using standard derivative masks:

The orientation histogram is constructed per cell (e.g., 8 × 8 pixels), and magnitude-weighted voting is applied to form the raw feature descriptor.

Stage 3: Farthing Selection of Dominant Bins.

Rather than using all gradient bins, we employ a frequency-aware bin ranking mechanism. Specifically:

• Compute bin frequencies across all image patches.

• Rank bins by magnitude of appearance.

• Retain only the top-k bins (termed Farthing bins) based on a statistical cutoff (e.g., top 15% percentile or using mutual information with class labels).

This eliminates redundant or noisy bins and emphasizes the most discriminative orientations.

Stage 4: Entropy-guided spatial masking.

To further reduce descriptor redundancy, we calculate the Shannon entropy \(\:H\left(p\right)\) of gradient magnitudes in each block:

Second, sort the histogram’s graph bins in descending order according to the frequency of bin values. \(\:H\left(p\right)HoG\) size is L dimension, with L ranging from 1 to S. Vector \(\:H\:{HoG}_{Sort}\) in Eq. (14)

Third, select the first Farthing (F) pixels with the highest frequency. \(\:H\:{HoG}_{Sort}\) sort size is same to the size of \(\:H\left(p\right)\) HoG vector. Choose F pixel from \(\:H\:{HoG}_{Sort}\)by select the initial farthing. Finally, use F pixels in feature selection algorithms. As an outcome, F-HOG surpasses the original HOG in term of computing velocity and storage capacity, so the machine learning algorithm only receives a portion of its capabilities. Based on previous research, suggested using F-HOG is novel in the field of soil classified and type identified. Based on previous research, we believe our proposed work using F-HOG is novel in the field of soil classified and type determined.

Only blocks with entropy above a defined threshold are retained for final descriptor formation. This stage filters out homogeneous or overly noisy regions, ensuring that only structurally informative regions contribute to the feature vector.

The application of classical Histogram of Oriented Gradients for image processing has proven to be successful; it tends to give relatively high dimensional vectors and lets all gradient bins classify the classes regardless of whether it is useful or not. The F-HOG aims to overcome this drawback by two processes, namely: \(\:\left(i\right)\) the filtering of the input image in the frequency domain prior to the calculation of gradients to reduce noise and enhance texture clarity; and \(\:\left(ii\right)\) selection of only the top-F most common gradient orientation bins for further process after HOG histogram has been computed, which substantially reduces feature redundancy.

F-HOG presents an entirely different classical approach; hence it works in the frequency regime and based on dominant bin selection for better efficiency in highly textured, noisy scenarios such as soil image classification, while both standard HOG and its extension, namely PHOG (Pyramid HOG) targeting the capturing of spatial hierarchies, and HOG3D working with spatiotemporal volumes, do not accomplish this kind of pruning on their original descriptor set. Explicit pruning reduces complexity but can also improve performance; in this case, the final experimental results support that statement. We believe that this is the first attempt of its kind in soil texture classification.

In an effort to prove the novelty and efficacy of Filtered Histogram of Oriented Gradients (F-HOG) as an image texture descriptor, an ablation study was performed. This study could compare HOG, PHOG, and HOG3D with F-HOG on our soil images dataset. The goal was to evaluate the suitability of each variation in relation to soil texture classification, with evaluation parameters being accuracy, feature vector length (dimensionality), training time, and model interpretability.

The data given above, F-HOG outshines newer HOG-based descriptions on several levels. Classification Accuracy: F-HOG enjoys the maximum classification accuracy of 92.84%, exceeding that of HOG (89.12%), PHOG (90.25%), and HOG3D (86.40%). Dimensionality: It shrinks the dimensionality from roughly 3780 in the case of HOG to 960 in F-HOG implying lesser storage and quicker computations. Training Time: It takes about 35–60% less time to train the CNN classifier using F-HOG features compared to others. Interpretability: By selecting only the most dominant bins, F-HOG retains the most informative gradients, consequently improving interpretability and relevance in soil texture analysis. This means that F-HOG is novel in implementing both filter-domain filtering and frequency-based feature pruning and has better efficiency and accuracy than the conventional HOG and its extensions for the soil classification context. In our knowledge, there has never been a prior effort to unify these two strategies (filtering + frequency-based bin selection) explicitly for textural soil image classification, underpinning the novelty of this approach. The analysis of the feature extraction stage (without/without) is evaluated, and the outcomes acquired are shown in Supplementary Figure S3.

Haralick and LBP

To enrich the texture representation of soil images beyond directional gradients (as captured by F-HOG), this study integrates both Haralick features and Local Binary Patterns (LBP)—each offering unique insights into texture at different spatial scales. Haralick features, derived from the Gray Level Co-occurrence Matrix (GLCM), encode statistical measures of spatial relationships between pixel intensities. These features were computed over four standard directions (0°, 45°, 90°, 135°) and averaged to ensure rotational invariance. The resulting 14 Haralick descriptors, including contrast, correlation, energy, homogeneity, and entropy, capture the coarse or macrotexture patterns such as soil roughness, structural orientation, and granularity. These descriptors are particularly useful in distinguishing between compact (e.g., clayey) and granular (e.g., sandy) soils based on surface texture uniformity and intensity transitions. In parallel, Local Binary Patterns (LBP) were used to extract microtexture features, operating at the pixel level. The method involves comparing each central pixel’s intensity to its eight immediate neighbors in a 3 × 3 window. If a neighbor’s intensity is greater than or equal to the center pixel, it is assigned a value of 1; otherwise, 0. The result is an 8-bit binary number (ranging from 0 to 255) that encodes the local structure. To reduce redundancy and achieve rotation invariance, the LBP histogram was computed using the uniform pattern model, which results in a 59-dimensional feature vector. This compact and discriminative representation excels at detecting fine-grained differences between similar soil types (e.g., silt loam vs. sandy loam) and is particularly robust under varying illumination conditions. The combination of Haralick and LBP features ensures a comprehensive multiscale texture representation—where Haralick captures global spatial dependencies and LBP emphasizes localized micro-patterns. Together, they significantly improve the discriminative capability of the feature extraction pipeline, particularly when fused with F-HOG descriptors in the proposed ATFEM model.

Most frequent ϕ-pixels

While texture is critical, color distributions offer another axis of separation, particularly for soils with subtle hue differences due to mineral content or moisture. To overcome the limitations of fixed-threshold pixel selection methods in texture classification, we propose an optimization-driven ϕ-Pixel selection strategy.

Using histogram analysis, a frequency vector \(\:{C}_{hist}\) was created from the image channel, and pixels \(\:{m}_{i}\) meeting the ≥ 1/25 mean frequency condition were retained. These ϕ-Pixels are highly robust against environmental variability and form a lightweight yet informative color signature vector. They enable our classifier to associate certain tones (e.g., reddish hues for iron-rich soils) with specific texture categories.

\(\:\varphi\:-\)Pixels refer to pixel intensities most frequently found in an image channel (R, G, B), filtered through an adopted frequency threshold. These pixels encapsulate dominant color information and are thus statistically relevant when describing the texture and color distribution of the entire image. Considered in this study, a pixel value is a \(\:\varphi\:-\)Pixel if it occurs more than 4% of the total pixels in that image channel. This approach aims to reduce the noise and dimensionality but still keeps the most valuable color attributes contributing to soil type discrimination. Theoretically, one may attempt to use the top % most frequent pixel values across RGB channels (called the ϕ-Pixels) to filter out noise and concentrate on texturally important regions. But this number chosen as a fixed percentile sample lacks generalizability among datasets and soil types. It does not capitalize on unique characteristics in feature statistics or spectral dimension to ensure semantically or structurally important pixels are indeed being selected. Therefore, to mitigate both the robustness and meaningfulness of pixel-level feature selection, an optimization-based mechanism is introduced. Specifically, it aims at selecting a very compact subset of pixel intensity values while being informative enough:

• Inter-class margin maximization: different soil classes become further distinguishable.

• Intra-class variance minimizing: samples of the same class appear more uniform.

• Reduces redundancy and dimensional burden on downstream models.

• Gets a better generalization across varied soil texture, illumination, and camera conditions.

To identify the most frequent ϕ pixels in a channel. Here the channel image is represented as \(\:{C}_{img}\), The Vector \(\:{C}_{hist}\:\)is in Eq. (18).

The size of \(\:{C}_{hist}\) is \(\:S\) dimensional, with a range of 1–255. To construct a set of pixels \(\:\left(\varphi\:\right),\) select the most frequent pixels \(\:{m}_{i}\:\)from \(\:{\:C}_{hist}\). The \(\:{m}_{i}\:\)is illustrated in Eq. (19)

The ϕ-Pixel set is generated by obtaining the histogram of an image channel using one of the methods presented earlier in Sect. 3, and then selecting the intensity bins with frequencies greater than or equal to 1/25 of the total number of pixels, as given in Eq. (16). where \(\:{m}_{i}\) is the number of instances of the \(\:i\)th pixel, and \(\:k\:\)is the number of bins in the histogram\(\:{\:C}_{hist}\). The return \(\:\varphi\:\) is a set of the most common pixels.

Pixel values of intensity at the RGB soil images are frequently highly variable due to environmental noise, illuminance variations, or surface reflectance irregularities. Handcrafted texture descriptors like HOG and statistical co-occurrence matrices profit from sharp edges and good intensity distribution, for not all pixel values are useful for texture discrimination.

Earlier, a fixed fraction of the most frequently appearing pixel intensities-the ϕ-pixels-had been selected for analysis. Such a static approach is suboptimal, dataset-dependent, and theoretically inflexible. To overcome this drawback, we propose a lot of pixel-selection methods based on metaheuristic optimization, using the Enhanced Wombat Jellyfish Feature Optimization (EWJFO) algorithm.

The EWJFO algorithm combines the Wombat Optimization Algorithm’s adaptive tunneling and spiraling search techniques with the Jellyfish Search Optimizer’s global foraging and time-controlled exploration.

The hybrid mechanism guarantees:

• • The Wombat Phase: A fast local and spiral search for the most promising pixel subsets, with the wombat berm process modeled in a multi-dimensional feature space.

• • The Jellyfish Phase: These are enhanced global diversities; drifting along with ocean currents and vertical movements across the population prevents early convergence.

• • Adaptive Switching: The control mechanism dynamically shifts between the two phases, depending on the population fitness convergence and the temporal state in the optimization process.

They all collaborate in order to find an optimum set of pixel features that are statistically robust and class-discriminative, even across different datasets.

Problem formulation

Let the soil image dataset be represented as: \(\:\mathcal{I}=\{{I}_{1},{I}_{2},…..{I}_{n}\},\:{I}_{i}\in\:{\mathbb{R}}^{HxWx3}\)

Let \(\:{\mathcal{H}}_{c}\) denote the histogram of intensity values for channel c∈{R, G,B}. Each histogram consists of 256 bins representing intensity levels \(\:\mathcal{v}\)∈[0,255]. Our objective is to select a subset \(\:\phi\:\subset\:\{\text{0,1},….,255\}\:\)of intensity bins across the three channels that maximizes classification utility while minimizing redundancy.

Objective function

The selection problem is cast as a multi-objective optimization problem balancing:

Let ϕ= \(\:\{{\mathcal{v}}_{1},\:{\mathcal{v}}_{2},,,,,,.{\mathcal{v}}_{k}\}\) ​ represent a candidate set of selected pixel intensities. We define the fitness function:

Where,

\(\:{Acc}_{val}\left(\phi\:\right)\)

Validation accuracy using features extracted from \(\:\phi\:\) -pixels.

\(\:\left|\phi\:\right|\)

Number of selected bins (smaller preferred).

\(\:\alpha\:,\beta\:\) ∈[0,1]: Trade-off weights (α = 0.8,β = 0.2).

This function rewards high-accuracy, low-dimensional solutions.

EWJFO optimization framework

To optimize Eq. (6), we utilize EWJFO, a hybrid metaheuristic that combines:

• Wombat Optimization Algorithm (WOA): Excels at adaptive local search using tunneling and spiral updates.

• Jellyfish Search Optimizer (JSO): Incorporates global drift-based exploration and time-controlled behavioral phases.

A. Wombat Phase (Local Exploitation).

Each candidate solution (agent) is represented as a binary vector \(\:{X}_{i}\)∈{0,1}²⁵⁶, where \(\:i\) indicates inclusion of the pixel bin.

Wombat movement (spiral-tunneling) is expressed as:

Where,

\(\:{\mathcal{X}}_{i}^{best}:\) Current best agent.

\(\:{r}_{1}\:and\:{r}_{2}\) : Random values in [0, 1].

B. Jellyfish Phase (Global Exploration):

JSO updates agent \(\:{\mathcal{X}}_{i}^{\:}\) based on:

Ocean current drifting

Time control mechanism

Where,

\(\:{\mathcal{X}}_{i}^{mean}:\:\) Mean position of all agents.

\(\:\tau\:\in\:\left[\text{0,1}\right]\)

step-size coefficient.

\(\:T:\:\) Total number of iterations.

C. Adaptive Switching Strategy: The switching function σ
(25)