Image-Based Interpolation of Soil Surface Imagery for Estimating Soil Water Content

Abstract

Soil water content (SWC) critically governs the physical and mechanical behavior of soils. However, conventional methods such as oven drying are laborious, time-consuming, and difficult to replicate in the field. To overcome these limitations, we developed an image-based interpolation framework that leverages histogram statistics from 12 soil surface photographs spanning 3.83% to 19.75% SWC under controlled lighting. For each image, pixel-level values of red, green, blue (RGB) channels and hue, saturation, value (HSV) channels were extracted to compute per-channel histograms, whose empirical means and standard deviations were used to parameterize Gaussian probability density functions. Linear interpolation of these parameters yielded synthetic histograms and corresponding images at 1% SWC increments across the 4–19% range. Validation against the original dataset, using dice score (DS), Bhattacharyya distance (BD), and Earth Mover’s Distance (EMD) metrics, demonstrated that the interpolated images closely matched observed color distributions. Average BD was below 0.014, DS above 0.885, and EMD below 0.015 for RGB channels. For HSV channels, average BD was below 0.074, DS above 0.746, and EMD below 0.022. These results indicate that the proposed method reliably generates intermediate SWC data without additional direct measurements, especially with RGB. By reducing reliance on exhaustive sampling and offering a cost-effective dataset augmentation, this approach facilitates large-scale, noninvasive soil moisture estimation and supports machine learning applications where field data are scarce.

1. Introduction

Soil is a complex medium composed of minerals, organic matter, air, and water. Among these constituents, soil moisture is one of the most critical variables in agricultural and hydrological processes because it governs the exchange of water and energy between the land surface and atmosphere. Soil water content (SWC), calculated as the volumetric proportion of water contained within soil pores, largely dictates the soil’s physical and mechanical behavior [1]. As a key nexus variable linking weather, climate, ecosystem dynamics, and surface energy balance, SWC underpins feedback mechanisms related to climate change and is indispensable for predicting landslides and soil erosion [2,3]. Recent research shows that accurate knowledge of soil moisture can enhance climate prediction modeling, drought monitoring, yield forecasting, and crop growth management [4,5,6].

Soil water data can be collected using several methods. The oven-drying method remains the canonical laboratory procedure for quantifying soil moisture, while neutron scattering, time-domain reflectometry, capacitance probes, and frequency-domain reflectometry are widely used alternatives [7,8,9,10]. However, the accuracy of these techniques is strongly soil-dependent and easily affected by texture, salinity, porosity, and organic matter, and their deployment is often limited by high cost, intricate installation, and site-specific calibration requirements [11,12,13]. Moreover, conventional measurements are typically obtained at the point or plant scale, restricting their applicability to larger areas [14].

To bridge these spatial gaps, researchers have interpolated point observations [15] and developed diverse approaches for large-area monitoring, including remote sensing. Internet-of-Things sensor networks now deliver real-time data streams linking soil moisture to yield and simultaneously record temperature, nitrogen, and other agronomic indicators [16,17]. Shallow soil moisture retrieval using ground-penetrating radar has also been explored; however, this method depends on subsurface reflectors and a stable dielectric–moisture relationship, making generalization across soil types difficult [18]. Satellite platforms have achieved regional-to-global estimates of surface soil moisture, and recent work has combined vegetation indices with thermal infrared data for efficient retrievals [19,20,21]. Moreover, open-source tools have demonstrated the potential of automated satellite imagery processing, allowing large-scale agricultural monitoring [22]. Nevertheless, scale mismatches between coarse satellite footprints and ground truth can lead to substantial errors [6].

Therefore, unmanned aerial vehicles (UAVs) with RGB cameras have gained traction for cost-effective mesoscale mapping. Many UAV studies have employed linear regression–based statistical models for moisture estimation [23,24]. Soil reflectance in the visible range (≈400–700 nm) typically decreases as soil water content rises because thin water films suppress multiple scattering and increase the effective refractive index, lengthening photon path lengths and enhancing absorption by pigments and organics. Consequently, soil generally darkens across R, G, and B channels with increasing moisture. Moreover, linear relationships with both wavelengths and reflectance were reported in a domain of 5-25% of SWC, which indicates that simple linear models could be useful in these data [25,26,27].

However, because image data are sensitive to ambient illumination, sensor quality, and environmental conditions, ensuring robust accuracy and reliability is essential. A basic attempt to achieve this goal is to use different color spaces or light ranges. While recent studies show that a variety of color spaces can be used when analyzing an image, RGB and HSV color spaces are considered highly related to SWC and are therefore widely used [28,29,30]. Camera-based SWC estimation using RGB/HSV under controlled or field illumination has been repeatedly demonstrated, and recent studies emphasize illumination or color calibration as a prerequisite for reliable color–moisture links [31,32]. Consequently, numerous studies now fuse traditional color-space statistics with machine learning algorithms to capture the nonlinear relationship between spectral signatures and SWC [32,33].

Machine learning approaches leverage large training sets to model complex, nonlinear links between moisture and remote-sensing variables. Beyond numerical simulations of infiltration and subsurface redistribution [34], recent UAV-based works have combined RGB and thermal imagery with techniques such as Least Absolute Shrinkage and Selection Operator (LASSO), support vector machines, and gradient-boosted models to predict moisture at multiple depths [35,36]. However, performance often degrades in topographically complex terrain. For example, both Soil Moisture Analytical Relationship (SMAR) and regression-based models yield accurate root-zone soil moisture at calibrated sites, but their accuracy varies significantly with terrain and season [37]. High accuracy also hinges on abundant, region-specific training data, which can be operationally burdensome [34,38]. Crucially, missing soil moisture observations cannot be resampled, and even oven drying can cause evaporative losses during sample handling, complicating the acquisition of precise target moisture levels.

To mitigate these challenges, this study proposes an alternative strategy that exploits color-space histogram analysis and interpolation. We assessed its reliability using the dice score (DS), Bhattacharyya distance (BD), and Earth Mover’s Distance (EMD) [39,40]. Compared with machine learning models, this approach requires fewer computational resources, and relative to oven drying and other methods, it saves considerable time, labor, and cost.

2. Materials and Methods

2.1. Soil Sampling

Soil samples were collected from an agricultural parcel in Bubuk-myeon, Miryang-si, Republic of Korea (Figure 1). This field, typically used for forage crops, rice, and soybeans, was fallow at the time of sampling, and the soil type is shown as silt loam according to the USDA (United States Department of Agriculture Soil Taxonomy) standards. Immediately after collection, the samples were sealed in airtight containers and transported to the laboratory. Upon arrival, coarse organic debris such as roots and leaves was removed. The soil was then oven-dried for 24 h at 105 °C to achieve constant mass. Gravel and other coarse fractions were eliminated by sieve separation, retaining material with a particle diameter of ≤2.00 mm. Finally, approximately 210 g of the processed soil was placed in a square acrylic mold (80 mm × 80 mm, 22 mm high), and its surface was leveled with a tamping rod.

For each moisture level, water mass (W_w, g) corresponding to a prescribed percentage of the dry mass (W_d, g) was added using a pipette, with the moisture content increasing in 3% increments, and the soil was thoroughly mixed. After a 5 min equilibration period to allow uniform wetting, a surface image was recorded. All data were collected on 16 December 2024.

$$Soil\; water\; content=(W_w/W_d)\times \mathrm{100\%}.$$

(1)

2.2. Image Acquisition Setup and Preprocessing

To ensure uniform imaging conditions, a dedicated studio was constructed, as shown in Figure 2. The acrylic mold was centered beneath two ceiling-mounted LED lamps positioned 30 cm above the sample to minimize shading. Images were captured from above using a remotely triggered smartphone camera (Samsung Galaxy S22 Ultra, Suwon, Republic of Korea) [41]. Key camera parameters are summarized in

Table 1. Basic specifications of the camera.

Attributes	Specification
Image Resolution	108.0 MP
Aperture	F/1.8
OIS (Optical Image Stabilization)	Yes
PDAF (Phase Detection Autofocus)	Yes
Laser AF Sensor	Yes
Digital Image Pixel Size	9000 × 12,000 pixel
Zoom	2 × (f/1.8)
Focal Length	6.4 mm
Shutter Speed	1/125 sec
ISO Sensitivity	120

. Remote operations eliminated motion blur and guaranteed consistent image quality.

The region of interest was restricted to the soil surface by cropping the acrylic frame, background, and peripheral areas. The resulting image tiles measured 4000 × 4000 pixels (Figure 3a).

While the intended SWCs were 3%, 6%, 9%, 12%, 15%, 18%, and 21% (on a dry mass basis), the actual values obtained were 3.83%, 5.33%, 6.75%, 8.41%, 10.32%, 11.91%, 13.16%, 14.83%, 15.97%, 17.26%, 19.17%, and 19.75% (12 images in total; Figure 3b). Deviations from the target levels and the unequal spacing between successive contents were attributed to evaporative loss, imperfect homogenization, and the high sensitivity of the small sample mass to incremental water additions.

2.3. Processing and Interpolation of Histograms

This study employs both the RGB and HSV color spaces. However, because the interpolation method is identical for both, we illustrate the procedure using RGB as an example. Each pixel contains red, green, and blue intensities; thus, an empirical histogram can be computed for every channel. Because soil color varies continuously with added moisture, the color statistics associated with an intermediate target content can, in principle, be inferred from neighboring images.

Nevertheless, raw histograms do not follow ideal normal shapes, and both skewness and dispersion differ across channels. Therefore, direct interpolation of these empirical distributions yields poor estimates. Accordingly, for each channel, the arithmetic mean (μ) and standard deviation (σ) were extracted, and a theoretical normal probability density function (PDF) was generated under the assumption of Gaussian behavior. The PDF was then scaled so that its peak height matched that of the observed histogram, which will be hereinafter referred to as the “tuned histogram” (Figure 4). A fine adjustment of the tail ratio ensured optimal alignment between the two curves, thereby capturing the moisture-induced color shift more faithfully. Finally, synthetic pixel values were drawn from the scaled PDF to create artificial images (Figure 5).

2.4. Generation of Target Moisture Images via Linear Interpolation

To reproduce the color statistics corresponding to an arbitrary target SWC, linear interpolation was applied channel-wise to three descriptive statistics: mean ($\mu$), standard deviation ($\sigma$), and peak height ($h_p$). Two reference images—A and C—with SWCs W_A and W_C that bracket the desired level W_B were selected, where $W_A$ < $W_{B }$ < ${ W}_C$. The distance ratio ($r$) was computed as follows:

$$r=(W_B-W_A)/(W_C-W_A).$$

(2)

The statistics for the target image were estimated as

$${\mu }_{inter}=r\times {\mu }_A+(1-r)\times {\mu }_C,$$

(3)

$${\sigma }_{inter}=r\times {\sigma }_A+(1-r)\times {\sigma }_C,$$

(4)

$$h_{p, inter}=r\times h_{p, A}+\left(1-r\right)\times h_{p, C}.$$

(5)

Assuming near-Gaussian behavior, the PDF for each channel was drawn according to ${\mu }_{inter}$ and ${\sigma }_{inter}$ and then rescaled according to $h_{p, inter}$. Random sampling produced replicable RGB and HSV images representative of the target SWC.

2.5. Similarity Assessment Between Histograms

Because all histograms share an identical domain (0–255 for R, G, B, S, V; 0–199 for H) but differ in total pixel count after probability conversion, scaling, and interpolation, their similarity was quantified using two complementary metrics: DS, which is insensitive to absolute scaling; BD, which compares the shapes of the normalized PDFs; and EMD, which could show distribution change.

2.5.1. Dice Score

DS gauges the overlap between two distributions based on the harmonic mean of their intersection and individual magnitudes as follows:

$$DS\left(X, Y\right)=\left(2\left|X\cap Y\right|\right)/(\left|X\right|+\left|Y\right|).$$

(6)

In short, DS is calculated by dividing twice the number of overlapping pixels between two histograms by the total number of pixels in both histograms. Values of DS range from 0 to 1, while those approaching 1 indicate high similarity [39].

2.5.2. Bhattacharyya Distance

Let $p_i$ and $q_i$ be the normalized probabilities in bin i for the two histograms. The Bhattacharyya coefficient (BC) is expressed as

$$BC={\sum }_{i=1}^N\sqrt{p\left(i\right)\times q\left(i\right)},$$

(7)

and the corresponding BD is

$$BD=-\mathrm{l}\mathrm{n}\left(BC\right).$$

(8)

Values of BD approaching 0 indicate high similarity, whereas values near 1 signify substantial divergence [39].

2.5.3. Earth Mover’s Distance

EMD was used to compare two normalized signatures $P={\left\{\left(x_i, w_i\right)\right\}}_{i=1}^m$ and $Q={\left\{\left(y_j, v_j\right)\right\}}_{j=1}^n$, where $x_i$, and $y_j$ are bin centroids with frequencies of $w_i$ and $v_j$. Let $d_{ij}$ be the ground distance between $x_i$ and $y_j$ and the flow that minimizes the total cost between the two be $F=[f_{ij}]$.

$$Cost\left(P,Q,F\right)={\sum }_{i=1}^m{\sum }_{j=1}^n{d}_{ij}{f}_{ij},$$

(9)

The constraints are

$$f_{ij}\ge 0 1\le i\le m, 1\le j\le n,$$

(10)

$${\sum }_{j=1}^n{f}_{ij}\le w_{p_i} 1\le i\le m,$$

(11)

$${\sum }_{i=1}^n{f}_{ij}\le w_{q_i} 1\le j\le n,$$

(12)

$${\sum }_{i=1}^m{\sum }_{j=1}^n{f}_{ij}=\mathrm{m}\mathrm{i}\mathrm{n}\left({\sum }_{i=1}^m{w}_{p_i}, {\sum }_{j=1}^n{w}_{q_i}\right),$$

(13)

The optimal flow $f_{ij}$ solves the following:

$$EMD(P, Q)={\displaystyle \frac{{\sum }_{i=1}^m{\sum }_{i=1}^n{d}_{ij}{f}_{ij}}{{\sum }_{i=1}^m{\sum }_{i=1}^n{f}_{ij}}}.$$

(14)

Values of EMD decreasing to 0 indicate high similarity, and increasing to 1 indicates the opposite [40].

2.5.4. Derivation of the Similarity Metric Threshold and Statistical Analysis

Using a new dataset of seven original soil-surface images ordered by SWC, we estimated a threshold that reflects natural variability among distinct SWC states (Figure 6). Consecutive images were treated as near neighbors, and the threshold was set to the smallest value observed among the similarity values calculated by the neighboring pairs. This choice yields a strict, utility-oriented cutoff: a generated image must be at least as close to its target as any two different originals ever are to each other. Although the SWC spacing in this new dataset is uneven and sometimes wider than in the original study, several pairs like 0% and 2.63%, 2.63% and 5.17%, and 14.67% and 18.42% remain visually close, making this cutoff conservative but informative.

In evaluation, a generated image is deemed “similar” to its target original if its R, G, and B similarity results do not exceed the threshold. For higher-is-better scores such as dice, the similarity results should exceed the threshold. The threshold is pre-specified from original–original comparisons only and is not tuned on generated images, avoiding circularity.

We evaluated similarity against pre-specified thresholds using one-sided Wilcoxon signed-rank tests (DS: DS − TDS > 0; BD/EMD: T − metric > 0; significance levels: p < 0.05 (***), p < 0.01 (**), p < 0.001 (*), ns = not significant). Channel effects within each color space (RGB; HSV) were assessed with Friedman tests followed by Wilcoxon signed-rank post hoc comparisons with Holm correction. Monotonic associations with soil water content (SWC) were analyzed using Spearman’s ρ. We contrasted an operating window (10.32–14.83% SWC) against other conditions using one-sided Mann–Whitney U tests on threshold-centered differences. For Wilcoxon tests, we report the test statistic (W), p-value, and Hodges–Lehmann median difference with 95% bootstrap confidence intervals. Statistical significance was set at α = 0.05 (two-sided unless otherwise stated). All analyses were nonparametric (n = 10 per series).

3. Results and Discussion

3.1. Determining Thresholds

3.1.1. Calculation of Thresholds for Each Color Space and Similarity Metrics

Three similarity metrics were computed for each color space using an independent dataset and are summarized in the corresponding tables (

Table 2. Bhattacharyya distance (BD) for RGB and HSV channels between images with adjacent SWCs.

SWC (%)	R	G	B	H	S	V
0.00 ↔ 2.63	0.013	0.016	0.014	0.012	0.866	0.013
2.63 ↔ 5.17	0.053	0.065	0.065	0.022	0.062	0.053
5.17 ↔ 8.09	0.360	0.355	0.207	0.290	0.113	0.360
8.09 ↔ 12.05	0.212	0.169	0.068	0.106	0.029	0.212
12.05 ↔ 14.67	0.370	0.203	0.021	0.169	0.053	0.370
14.67 ↔ 18.42	0.018	0.007	0.003	0.004	0.006	0.018

,

Table 3. Dice score (DS) for RGB and HSV channels between images with adjacent SWCs.

SWC (%)	R	G	B	H	S	V
0.00 ↔ 2.63	0.869	0.852	0.863	0.873	0.866	0.869
2.63 ↔ 5.17	0.719	0.687	0.688	0.833	0.693	0.719
5.17 ↔ 8.09	0.341	0.344	0.470	0.405	0.596	0.341
8.09 ↔ 12.05	0.462	0.509	0.676	0.657	0.797	0.462
12.05 ↔ 14.67	0.350	0.488	0.832	0.532	0.752	0.350
14.67 ↔ 18.42	0.854	0.915	0.955	0.929	0.916	0.854

and

Table 4. Earth Mover’s Distance (EMD) for RGB and HSV channels between images with adjacent SWCs.

SWC (%)	R	G	B	H	S	V
0.00 ↔ 2.63	0.019	0.020	0.017	0.001	0.022	0.019
2.63 ↔ 5.17	0.039	0.041	0.037	0.002	0.051	0.039
5.17 ↔ 8.09	0.098	0.089	0.060	0.007	0.075	0.098
8.09 ↔ 12.05	0.063	0.050	0.027	0.005	0.034	0.063
12.05 ↔ 14.67	0.076	0.047	0.014	0.006	0.034	0.076
14.67 ↔ 18.42	0.017	0.008	0.004	0.001	0.012	0.017

). Consistent with visual inspection, the images at 0.00% and 2.63% moisture, and especially those at 14.67% and 18.42%, exhibited high similarity. The results show that the similarity differs significantly between the visually similar images and the non-similar images.

3.1.2. Thresholds Determined for Each Color Space and Similarity Metrics

For threshold selection, the average of the maximum two similarity metric values observed among the adjacent image pairs in the dataset was adopted as the threshold for each metric and channel; the resulting thresholds are reported in the table below (

Table 5. BD, DS, and EMD thresholds for RGB and HSV channels.

Similarity Metrix	R	G	B	H	S	V
BD	0.015	0.011	0.008	0.008	0.018	0.015
DS	0.862	0.884	0.909	0.901	0.891	0.862
EMD	0.018	0.014	0.009	0.001	0.017	0.018

).

3.2. RGB Histogram Analysis

3.2.1. RGB Channel Mean Trends

For all 12 moisture levels (ranging from 3.83% to 19.75%), the mean RGB intensity was computed and plotted on a 0–255 scale (Figure 7). R decreases from 183.87 to 133.59, G from 147.11 to 88.30, and B from 95.80 to 50.14. The largest span is observed for G (58.81) and the smallest for B (45.66). Although the three ranges overlap by roughly ten digital numbers, the overall ranking consistently remains R > G > B.

All channels reach their maximum at 3.83% SWC. However, the minima for R and G occur at 19.17%, whereas B reaches its minimum at 14.83% and then increases slightly. The steepest declines occur between 11.91% and 13.16% for R and G and between 5.33% and 6.75% for B. Generally, the mean intensity declines with increasing moisture. Before 13.16%, the reductions in R and B are similar, whereas beyond 13.16%, R and G exhibit comparable slopes. After hitting a minimum of 13.16%, B increases modestly, and beyond 19.17%, all three means exhibit a collective upturn.

3.2.2. RGB Channel Standard Deviation (SD) Trends

The peak height, defined as the frequency of the modal bin in each histogram, does not change monotonically but oscillates, alternating between successive increases and decreases across the moisture gradient (Figure 8a). Between 3.83% and 8.41%, the R peak is significantly higher than those of G and B, but the gap narrows, and after 11.91%, the peak heights become comparable. In every channel, the maximum peaks occur at 3.83% and the minimum at 11.91%. The largest absolute peak counts are for R (425,323) and G (390,580), and the smallest for B (341,350). The greatest negative slope is observed between 3.83% and 5.33% for R and G and between 15.97% and 17.26% for B, although the magnitudes of these slopes are nearly identical. Overall, the peak heights decline with moisture up to 11.91%, after which they fluctuate. A collective upturn beyond 19.17% indicates a change—most likely surface water film formation.

Overall, SD exhibits an approximately inverted pattern relative to the peak height, although the two metrics do not align perfectly (Figure 8b). Across all three channels, there is no clear inflection in the 6.75% to 8.41% moisture content range. In contrast, the amplitude of fluctuation between 19.17% and 19.75% diverges markedly.

3.2.3. Similarity Between Tuned and Interpolated RGB Histograms: Visual Assessment

For each moisture level (3.83%, 5.33%, 6.75%, …, 19.75%), an interpolated histogram was generated from its two flanking images. Using 5.33% as an example, the histograms of 3.83% and 6.75% were interpolated and compared with the measured 5.33% histogram. The solid and dashed lines denote the tuned and interpolated data, respectively (Figure 9). Although small discrepancies appear in peak height and position, especially for B at 6.75%, the overall means are well reproduced, confirming that center-of-mass statistics are captured accurately. The pronounced B channel errors are attributed to the irregular, nonmonotonic evolution of its peaks in the raw data.

3.3. Similarity Analysis for RGB Channels

3.3.1. Statistical Summary of BD Across RGB Channels

Across all RGB channels, the overall mean BD is 0.011, with an SD of 0.025. The per-channel means are 0.009 for R, 0.009 for G, and 0.014 for B. The corresponding SD values are 0.006 for R (lowest), 0.028 for B (highest), and 0.021 for G (Figure 10 and

Table 6. BD for RGB channels.

SWC (%)	R BD *	G BD ns	B BD ns
5.33	0.001	0.000	0.018
6.75	0.003	0.002	0.036
8.41	0.005	0.004	0.009
10.32	0.002	0.002	0.003
11.91	0.011	0.010	0.008
13.16	0.011	0.012	0.012
14.83	0.010	0.009	0.007
15.97	0.016	0.015	0.014
17.26	0.015	0.017	0.017
19.17	0.019	0.021	0.018

Asterisks denote one-sided Wilcoxon tests vs. thresholds (T_BD: R 0.015, G 0.011, B 0.008): R p = 0.0137 (*), G p = 0.3577 (ns), and B p = 0.9580 (ns). Channel effect (RGB): not significant (Friedman, p ≥ 0.358); therefore, there is no letter labeling.

). For BD, the thresholds were 0.015 (R), 0.011 (G), and 0.008 (B). R passed at seven intervals and failed at 15.97% and 19.17%, G passed at six intervals and failed from 13.16% onward except for a recovery at 14.83%, and B passed at three intervals (10.32%, 11.91%, and 14.83%). Three-channel concurrence occurred at 10.32%, 11.91%, and 14.83%. These outcomes underscore BD’s sensitivity to mismatches in distributional shape (peak/tail structure): as moisture increases, shape discrepancies accumulate, leading G to drop earlier and R to fall below the criterion at the higher moisture levels.

3.3.2. DS Analysis for RGB Channels

The DS values for the RGB channels were plotted (Figure 11) and listed (

Table 7. DS for RGB channels.

SWC (%)	R DS ***	G DS **	B DS ns
5.33	0.971	0.979	0.853
6.75	0.929	0.934	0.785
8.41	0.926	0.928	0.901
10.32	0.953	0.957	0.939
11.91	0.894	0.893	0.902
13.16	0.907	0.901	0.899
14.83	0.904	0.913	0.918
15.97	0.883	0.889	0.885
17.26	0.889	0.884	0.881
19.17	0.880	0.875	0.883

One-sided Wilcoxon vs. T_DS (R 0.862, G 0.884, B 0.909): R p = 9.8 × 10⁻⁴ (***), G p = 0.0098 (**), B p = 0.9580 (ns). Higher DS indicates higher similarity. Channel effect (RGB): not significant.

). The R and G channels exhibit high similarity, whereas the B channel shows a comparatively lower similarity. All three channels yield values below their respective thresholds, indicating that the interpolated histograms closely match the original tuned histograms. The overall mean DS is 0.905, with an SD of 0.037. For DS, the thresholds were 0.862 (R), 0.884 (G), and 0.909 (B). Under these criteria, the R met the criterion across all ten intervals from 5.33 to 19.17%. G passed nine of ten intervals, failing only at 19.17%, and B passed two intervals at 10.32% and 14.83%. Notably, all three channels passed simultaneously at 10.32% and 14.83%. This pattern is consistent with DS’s emphasis on global overlap: R and G generally retain sufficient overlap, whereas B frequently falls short, likely reflecting insufficient common support or sparsity in parts of the distributions.

3.3.3. EMD Analysis for RGB Channels

The EMD values for the RGB channels were plotted (Figure 12) and listed (

Table 8. EMD for RGB channels.

SWC (%)	R EMD **	G EMD ns	B EMD ns
5.33	0.003	0.004	0.019
6.75	0.008	0.007	0.032
8.41	0.013	0.018	0.013
10.32	0.006	0.008	0.011
11.91	0.011	0.011	0.01
13.16	0.016	0.017	0.012
14.83	0.012	0.012	0.009
15.97	0.014	0.013	0.012
17.26	0.011	0.014	0.014
19.17	0.019	0.02	0.017

One-sided Wilcoxon vs. T_EMD (R 0.018, G 0.014, B 0.009): R p = 0.0020 (**), G p = 0.2541 (ns), B p = 0.9951 (ns). Lower EMD indicates higher similarity. Channel effect (RGB): not significant.

). For EMD, the thresholds were 0.018 (R), 0.014 (G), and 0.009 (B). R passed nine of ten intervals, exceeding the threshold only at 19.17%. G passed seven with exceedances at 8.41%, 13.16%, and 19.17%, and B passed only one, which is 14.83% SWC. A simultaneous three-channel pass occurred only at 14.83%. This pattern reflects EMD’s responsiveness to translational drift: G begins to exceed the criterion where distributional shifts intensify, and R does so only at the maximum SWC.

3.4. HSV Histogram Analysis

3.4.1. Channel Mean Trends

Across the full moisture spectrum (3.83% to 19.75%), the mean HSV values were computed to assess how hue (H), saturation (S), and value (V) responded to increasing SWC (Figure 13). H exhibits a gradual decline, falling from 17.62 at 3.83% to a minimum of 13.01 at 19.17%, with a slight rebound to 13.13 at 19.75%. In contrast, S begins at 122.64, rises to a maximum of 168.10 at 13.16%, and then decreases to 146.10 by 19.75%. V steadily decreases from 183.87 at 3.83% to 131.59 at 19.17% before increasing modestly to 133.96 at 19.75%. The smallest overall span is for H (≈4.61 units), intermediate for S (≈45.46 units), and largest for V (≈52.28 units), indicating that chromaticity and brightness are more sensitive to moisture changes than H.

All three channels attain their highest mean at the lowest moisture level (3.83%), whereas their minimum means appear between mid- to high SWCs; H and V both bottom out at 19.17%, while S peaks at 13.16% and then declines. The steepest drop in H occurs between 6.75% and 8.41% (from 17.94 to 16.36), S rises most sharply between 5.33% and 6.75% (from 130.58 to 153.24), and V decreases most rapidly between 8.41% and 10.32% (from 170.63 to 163.68). Beyond 13.16%, S and V continue downward with comparable slopes, whereas H maintains its slower descent. A slight uptick in H and V after 19.17% suggests a marginal reversal at the highest moisture. In summary, H declines monotonically with increasing moisture, S follows a unimodal trajectory of rising and then falling, while V decreases until the later stages of moisture increase before exhibiting a minor recovery.

3.4.2. HSV Channel Peak Height and SD Trends

The peak frequencies and SD for each HSV channel, defined as the counts of the modal histogram bin, were plotted against the moisture level (Figure 14a,b). Rather than varying monotonically, the peak heights oscillate with alternating increases and decreases as SWC rises. At 3.83% moisture, H attains its global maximum, far exceeding S and V. Between 3.83% and 5.33%, all three channels experience their steepest declines. Thereafter, H rebounds sharply at 6.75%, only to decrease again at 8.41%, illustrating its alternating pattern. In contrast, S and V continue to decline until 11.91%, when they reach their minimum. Beyond 11.91%, S partially recovers and then oscillates modestly, whereas V also rebounds at 15.97% before fluctuating at higher moisture levels. Notably, H again peaks at 19.17% and decreases by 19.75%, marking the channel’s second-largest amplitude change. Overall, H consistently exhibits the highest absolute modal counts across the moisture gradient, whereas S and V follow similar mid-range troughs (both minimal at 11.91%) before modestly recovering at elevated SWCs. These trends indicate that H distributions remain highly concentrated (large modal peaks) under varying moisture levels, whereas S and V distributions broaden (lower modal counts) until mid-moisture levels and then partially reconcentrate at higher moisture levels.

SD shows a similar pattern to the peak heights, but it does not precisely replicate the specific patterns. The peak height differs by approximately twice the value at 3.83% SWC, and the difference sharply decreases until 8.41%, where S and V reach almost the same value. Meanwhile, H does not change significantly for either its peak height or SD.

3.4.3. Similarity Between Tuned and Interpolated HSV Histograms: Visual Assessment

For each moisture level, an interpolated histogram was generated from its two flanking images. Solid lines denote interpolations, while dashed lines indicate tuned interpolations (Figure 15). While discrepancies appear in peak height and position, especially for S at 5.33% and 6.75%, the overall means are well reproduced, confirming that center-of-mass statistics are captured accurately.

3.5. Simularity Analysis for HSV Channels

3.5.1. Statistical Summary of BD Across HSV Channels

Across the three HSV channels, the BD values between interpolated and original histograms average 0.0363 (σ = 0.0494), indicating significant variation in interpolation fidelity depending on the channel (Figure 16 and

Table 9. BD for HSV channels.

SWC (%)	H BD ns c	S BD ** b	V BD * a
5.33	0.033	0.045	0.001
6.75	0.252	0.090	0.003
8.41	0.079	0.022	0.005
10.32	0.011	0.005	0.002
11.91	0.047	0.011	0.011
13.16	0.050	0.015	0.011
14.83	0.023	0.012	0.010
15.97	0.048	0.020	0.016
17.26	0.072	0.018	0.015
19.17	0.125	0.018	0.019

One-sided Wilcoxon vs. TBD (H 0.008, S 0.018, V 0.015): H p = 1.000 (ns), S p = 0.0070 (**), V p = 0.0137 (*). Different letters (a–c) within the header denote channel differences in HSV (Friedman + Wilcoxon post hoc, Holm-adjusted, α = 0.05): V^a<S^b<H^c (lower is better).

). Using BD thresholds of 0.008 (H), 0.018 (S), and 0.015 (V), H failed at all intervals (0/10); S passed at 10.32%, 11.91%, and 13.16% (4/10); and V passed from 5.33% through 14.83% (7/10) but failed thereafter at 15.97% (=0.016), 17.26% (=0.015), and 19.17% (=0.019). No image achieved a simultaneous three-channel pass. These outcomes indicate that morphological discrepancies (peak and tail structure) remain small for V up to ~15% of SWC, are moderate for S in the mid-range, and are persistent for H.

3.5.2. Statistical Summary of DS Across HSV Channels

The DS values for all HSV channels were plotted (Figure 17) and listed (

Table 10. DS for HSV channels.

SWC (%)	H DS ns c	S DS ** b	V DS * a
5.33	0.738	0.760	0.971
6.75	0.473	0.664	0.929
8.41	0.661	0.858	0.926
10.32	0.902	0.926	0.953
11.91	0.832	0.911	0.894
13.16	0.745	0.894	0.907
14.83	0.844	0.903	0.904
15.97	0.828	0.875	0.883
17.26	0.743	0.882	0.889
19.17	0.696	0.849	0.880

One-sided Wilcoxon vs. T_DS (H 0.901, S 0.891, V 0.862): H p = 0.9951 (ns), S p = 0.0039 (**), V p = 9.8 × 10⁻⁴ (*). Letters: V^a>S^b>H^c (higher is better).

). With DS thresholds of 0.901 (H), 0.891 (S), and 0.862 (V), the V channel passed across the full range (5.33–19.17%; 10/10), S passed only in the mid-range (10.32–14.83%; 4/10), and H passed at a single moisture level (10.32%; 1/10). A concurrent pass of all three HSV channels occurred only at 10.32%. This pattern reflects DS’s emphasis on global overlap: V maintains consistently high overlap, S aligns only around 10–15% moisture, and H exhibits generally poor overlap.

3.5.3. Statistical Summary of EMD Across HSV Channels

The EMD values for all HSV channels were plotted (Figure 18) and listed (

Table 11. EMD for HSV channels.

SWC (%)	H EMD ns c	S EMD * b	V EMD ** a
5.33	0.002	0.027	0.003
6.75	0.006	0.056	0.008
8.41	0.004	0.024	0.013
10.32	0.002	0.013	0.006
11.91	0.001	0.013	0.011
13.16	0.003	0.016	0.016
14.83	0.001	0.014	0.012
15.97	0.002	0.019	0.014
17.26	0.002	0.014	0.011
19.17	0.003	0.021	0.019

One-sided Wilcoxon vs. T_EMD (H 0.001, S 0.017, V 0.018): H p = 0.9951 (ns), S p = 0.0445 (*), V p = 0.0020 (**). Letters: V^a<S^b<H^c (lower is better).

). With EMD thresholds of 0.001 (H), 0.017 (S), and 0.018 (V), V passed at all intervals except 19.17% (0.019; 9/10); S passed at 10.32%, 11.91%, 13.16%, 14.83%, and 17.26% (5/10) while failing at 5.33%, 6.75%, 8.41%, 15.97%, and 19.17%; and H failed everywhere (0/10). No image produced a simultaneous three-channel pass. The results are consistent with EMD’s sensitivity to translational drift: V remains stable except at the terminal moisture level, S shows increased drift at early and late moisture contents, and H is penalized by even small hue shifts under the current, very stringent threshold.

3.6. Significance Testing of Similarity Metrics

As summarized in Table 6, Table 7, Table 8, Table 9, Table 10 and Table 11, R and V met all three pre-specified criteria (Wilcoxon one-sided against thresholds: DS p = 9.8 × 10⁻⁴; BD p = 0.0137; EMD p = 0.002), whereas G was significant for DS only (p = 0.0098). In HSV, channel effects were large across metrics (Friedman: DS χ² = 18.2, p = 1.12 × 10⁻⁴; BD χ² = 15.74, p = 3.81 × 10⁻⁴; EMD χ² = 19.54, p = 5.7 × 10⁻⁵), with post hoc tests indicating V > S ≫ H (Holm-adjusted p < 0.05); RGB showed no significant channel differences (p ≥ 0.358). With increasing SWC, similarity degraded monotonically for R(=V) and G (DS ρ = −0.915, p = 2.0 × 10⁻⁴; BD ρ ≥ 0.912, p ≤ 2.4 × 10⁻⁴; EMD ρ ≥ 0.673, p ≤ 0.033) but not for B/H/S. The operating window (10.32–14.83% SWC) improved similarity for B/H/S (e.g., DS: B U = 23, p = 0.0095; H U = 23, p = 0.0095; S U = 24, p = 0.0048), while R andV remained consistently high.

3.7. Estimation of Missing Moisture Levels

Using the interpolation scheme detailed above, we filled the measurement gap between 4% and 19% SWC at 1% increments. For each synthetic level, an RGB histogram was first estimated and then converted into a soil surface image. The generated images were arranged alongside the twelve reference photographs to facilitate visual inspection (Figure 19).

3.8. Comparison of Statistical Descriptors

The statistical continuity of the mean and SD values between the observed and interpolated data of the RGB and HSV color channels was analyzed (Figure 20 and Figure 21). The mean value declines or increases smoothly with increasing SWC depending on the channel, and the curve derived from the synthetic images merges seamlessly with that of the observations, confirming that the interpolation preserves low-order statistics. SD does not always vary linearly with moisture. Consequently, the interpolated trajectory is smoother than the measured one, which contains local extrema reflecting nonmonotonic spectral behavior.

Although minor differences in the similarity metric results exist between the channels, the interpolation has been performed smoothly. Because the procedure relies solely on previously acquired images, it offers a low-cost, data-efficient alternative for estimating soil moisture, which is potentially valuable for remote sensing, environmental monitoring, and automated decision systems. Nevertheless, the interpolation accuracy for the B channel is relatively weaker owing to its more erratic response to moisture. Future work should therefore investigate nonlinear interpolation schemes using a leave-one-out method or explore various color spaces. Furthermore, assessing how the initial data fidelity propagates to the final estimates is crucial. Integrating multiple similarity metrics to adaptively diagnose and optimize the interpolation quality also appears promising.

4. Discussion

This study demonstrates that the RGB and HSV histograms of soil surface images can be roughly modeled using channel-wise Gaussian PDFs parameterized by their empirical mean and SD. After additional scaling via SD to match the peak height of the histogram of the original image, linear interpolation of these parameters enables reliable reconstruction of missing soil water levels. Then, we evaluated a histogram-based interpolation framework that generates intermediate soil-color distributions as a function of SWC. Using RGB and HSV color spaces and three complementary similarity metrics, we found clear, channel-specific behaviors that are consistent across datasets.

First, luminance-linked channels such as R and V were the most stable. DS remained high across the SWC range, BD increased only beyond mid-SWC, and EMD exceeded its threshold chiefly at the maximum SWC, indicating strong global overlap, modest shape divergence, and limited drift until late stages. G was reliable at low–mid SWC but exhibited earlier drift: EMD crossed its threshold from the low-teens, and BD later signaled growing shape mismatch. By contrast, B and H were structurally fragile: B showed persistent drift and illumination sensitivity, and H failed almost universally under a stringent EMD threshold and is intrinsically unstable at low saturation due to circular wrap-around, which seemed to originate from the point that the histogram of H itself is highly concentrated in a narrow range.

Second, the metrics captured different but convergent signals. DS was permissive until global overlap degraded, BD flagged peak/tail mismatches earlier at higher SWC, and EMD provided the earliest warnings of distributional shift, which was notable for G. BD and EMD were strongly correlated channel-wise, indicating that shape change and position shift often co-occur. Change-point analyses identified a behavioral transition near ~10–12% SWC. EMD growth slowed after ~10%, whereas BD steepened after ~12%, suggesting early relocation of distributions followed by progressive reshaping. Accordingly, cases with EMD rising while DS remains high indicate dominant mean shift, BD rising with DS high indicates dispersion/shape change, and DS dropping signals global overlap loss, providing a diagnostic map from metric patterns to underlying distributional causes.

Third, the most consistent agreement across metrics and color spaces occurred between 10.32% and 14.83% SWC. In this window, S and V were simultaneously strong, R passed throughout, and G passed in most intervals, yielding the highest multi-metric, multi-channel consensus. Beyond ~16% SWC, both BD and EMD deteriorated (particularly V_BD, V_EMD, and G_EMD), reducing similarity confidence. High consistency across metrics and color spaces in this window indicates that both location and shape are preserved, supporting the robustness of histogram-based interpolation for SWC retrieval in this regime.

Limitations and avenues for improvement are clear. Thresholds were strictly calculated, and H is penalized by both circular geometry and low saturation; adopting a circular EMD with saturation-weighted distances would yield fairer hue judging. B’s sensitivity to illumination and white balance argues for color-constancy and brightness-standardization preprocessing before assessment. Finally, while Gaussian tuning captured central tendencies well, channels exhibiting nonmonotonic or multi-modal behavior may benefit from mixture models or nonlinear/quantile-based interpolation and even evolve into a better model that could predict inconsistent changes in color space histograms.

5. Conclusions

Histogram-based interpolation provides a low-cost, data-efficient means to synthesize intermediate soil-color distributions at target SWC levels without extensive training data. Across metrics and color spaces, luminance-linked channels such as R and V were the most robust: DS remained high, BD and EMD stayed within thresholds through mid SWC, and failures concentrated at the highest SWC only. It is not a substitute for physical measurements (e.g., oven drying) but a complementary tool that simulates unmeasured states, supports exploratory analysis of color–moisture relationships, and alleviates label scarcity for data-driven models (e.g., semi-supervised learning or domain adaptation).