Segmentation of Soil Surface Roughness Features in High-Resolution DEMS

Abstract

Soil surface roughness (SSR), referring to surface irregularities, is a key parameter for assessing soil condition and tillage outcomes. Characterizing roughness at fine scales—including clods and depressions—remains challenging for 2.5D digital elevation models (DEMs) collected at the meter scale in the field. This study presents two segmentation methods for high-resolution DEMs from an agricultural site. For clod segmentation, a wavelet-based approach from the literature was used, while a novel histogram-based method was introduced for depressions. Both methods were evaluated on natural soil surfaces with varying roughness levels and a simulated surface, with and without noise, using standard metrics (recall, precision, F1-score, IoU). The best clod segmentation results were achieved on fine seedbeds (95.2% recall, 97.3% precision, 96.2% F1-score), with slightly lower but strong performance on plowed surfaces (84.2% recall, 96.9% precision, 90.1% F1-score). Due to their lower frequency, depressions were primarily assessed visually under field conditions. For the simulated surface (with ground truth), IoU values ranged from 84.2% to 87.9% for clods and around 92% for depressions, demonstrating competitive performance. Additionally, the volume of roughness features was computed and visualized using cumulative distribution functions. These segmentation methods enable monitoring of soil surface conditions, with applications in precision agriculture, surface-water interactions, and meter-scale microwave remote sensing.

1. Introduction

An interdisciplinary approach is necessary to inform choices for agricultural practice from a sustainable perspective [1]. Tillage operations aim to achieve the soil’s needed characteristics, in terms of friability, compaction, fragmentation, water content, and carbon capture, for optimal crop emergence and growth [2,3,4,5]. Soil surface roughness (SSR) contains significant information to qualify soil condition and tillage outcome [6,7,8,9]. It also influences water infiltration or runoff and soil erosion [10,11] at a small scale. Numerous studies have therefore focused on surface roughness parameterization, soil height changes, and soil cloddiness characterization, at the meter scale, for example, in recent research [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. Delineating the clods and holes or small depressions is thus a means to characterize the irregularities of the soil surface at this scale. It has long been recognized that micro-topography must be considered when mapping within-field variability [27].

Segmenting soil clods is a complex task because they can be dimly demarcated, embedded with another piece of relief or with each other. This is especially true long after tillage and among rough surfaces such as ploughings [18,28]. Several approaches were attempted, including on soil profiles [29], on 2D images [21,30,31,32,33,34,35], and on 2.5D Digital Elevation Models (DEMs) [18,28,36,37] or depth images [24]. Pre-sieved clods were used in some studies due to the complexity of the clod segmentation problem. According to ref. [24], depth images are more pertinent than RGB images for clod segmentation. For that purpose, several approaches have been proposed: contour-based methods [24,36], adapted watershed [37], dynamic contours [37], and wavelet-based methods [18,28].

Segmenting soil depressions has also been addressed in the literature at different scales [38,39,40,41,42,43,44]. At the interrill scale, micro-topography determines overland flow initiation. According to ref. [45], several configurations of extreme micro-topography type can be envisaged. These are: river-type (with connected pattern of depressions), random-type or crater-type (with connected crests that isolate the depressions). In reality, micro-topographies are often combinations of these intermediate forms. Depressions are mainly isolated from each other just after tillage and form crater-type topographies. In ref. [46], depression geometry was approximated by spherical cups, and plasticine cup-made surfaces were created for hydrological modeling. Depression storage or dead storage may be estimated by segmenting a surface DEM. Indeed, 2.5D DEMs are particularly well adapted to estimate small closed depressions, because it can be done by thresholding the elevations. For that purpose, RGB images, where color represents elevations, are appropriate to use. Histogram-based methods are quick and simple, often efficient, segmentation methods. They are particularly apt in the case of small datasets without ground truth if the regions of interest can be isolated by thresholding. Histogram thresholding methods are often based on grayscale images or on images transformed into the HSV or Lab color space when lighting and saturation are important. If the colors represent heights, there is no need to switch to the HSV or Lab color space. Thresholding the RGB channels independently is the simplest method for selecting colors related to depressions. It is a way to perform adaptive thresholding for heights. This approach is well adapted to the segmentation of depressions but not suitable for the segmentation of soil clods that may have a tilted base, different sizes, and lay at different heights. For that purpose, the boundary-based geometrical approach used in ref. [18] is more suited.

In ref. [47], it has been noted that the use of photogrammetry to assess post-tillage soil quality in agricultural fields has received limited attention. In particular, automatic delineation of soil clods and depressions remains largely unexplored in 2.5D DEMs of diverse surfaces recorded in the field at the meter scale. This study addresses this gap and presents computational techniques for interpreting measurement and quantifying roughness features at the within-field scale in order to assess soil surface spatial variability. First, a wavelet-based segmentation algorithm [18], originally developed in controlled experiments, is adapted to identify soil clods under field conditions. Second, a novel algorithm, specifically designed to segment two levels of soil depressions, is proposed. Both methods are applied here for the first time to field-acquired 2.5D DEMs, enabling the derivation of roughness feature volumes. These methods will be useful for assessing surface condition in soil monitoring.

2. Materials and Methods

2.1. Digital Elevation Models of Soil Surfaces

2.1.1. Measures in the Field

Three plots were chosen for DEM recording: one prepared for rapeseed, one for maize, and one for pea, in Beauce, at an agricultural site around Illiers-Combray, France (DMS coordinates: X = 48°18′04″; Y = 1°14′54″) (see Figure 1, plots 4, 6 and 12). Two replications of ploughing, rough seedbed and fine seedbed, were thus retained for the present study, resulting in 6 DEMs of 450 by 450 mm² at a 0.5 mm resolution. The measurements were taken using a laser scanner, in April 2012, 5 to 6 months after tillage operations. One plot is shown in Figure 2.

The laser scanner was composed of a rail equipped with a laser, a motor, and a charge-coupled device (CCD) camera [48] (Figure 3). Profiles of the soil surface were measured in the x–z plane. The laser was moved along the y-axis, back and forth, to get the whole geometry and tackle the shadows created by the surface roughness, which induce around 20% of missing data. Repositioning was done by searching the best translation and rotation matching the highest clods on the two measures. This step was important for the quality of the DEMs. Indeed, when measuring elevations in the fields, slight shifts were common. Combining the two measurements allowed for reducing the missing data to around 7%, which were estimated by spline interpolation. Note that 7% is very low. Possible interpolation errors might change the boundaries of clods or depressions by a pixel. The vertical precision of the laser scanner is 0.5 mm. As there may be a bias between elevations in the two measurements, this can induce additional measurement noise consisting of peaks or blurred areas. Moreover, this study focused on the random roughness component of the surfaces. So, the DEMs were filtered and denoised using Random Forest and Singular Value Decomposition (SVD). The Random Forest algorithm allows for predicting values after learning from reliable areas [49]. It allowed for removing almost all the additional noise and strengthened the interpolation. The SVD was used for removing the deterministic component, corresponding to the first singular value, and the ground noise associated with the 5% lowest singular values (Equation (1)). Recall that singular value decomposition is a linear algebra method that expresses a matrix M as the product of three components:

$$M=U\Sigma V^{*}$$

(1)

where U is an orthogonal matrix representing the Eigen vectors in the lines space, Σ is a diagonal matrix of ordered singular values, and V* is the adjoint matrix representing the Eigen vectors in the column space [50]. The greater singular values represent the main information and the smallest represent the residual noise. The first singular value is the largest and represents the deterministic part of the surfaces well. From the second singular value onward, some aspects of the clod structure were captured. Typical thresholds for the smallest singular values, which represent noise, are 1% or 5%. There was almost no difference between these thresholds, since the corresponding singular values were very small. Finally, some residual peaks (outliers with a high elevation value) were corrected with nearest-neighbor values.

Since the deterministic part of the surfaces has been removed, they have zero mean. The other basic statistics are gathered in

Table 1. Statistics of the surface elevations.

DEM	Mean	Standard Deviation (mm)	Skewness	Kurtosis
Fine seedbed 1	0	4.72	0.71	4.24
Fine seedbed 2	0	4.50	0.64	4.22
Rough seedbed 1	0	7.69	0.87	5.15
Rough seedbed 2	0	7.40	0.55	4.41
Ploughing 1	0	18.5	0.63	3.49
Ploughing 2	0	16.6	0.48	2.85

.

2.1.2. Simulated Surface

To complete the evaluation of segmentation methods, a simulated surface was generated numerically by setting half ellipsoids corresponding to clods and depressions on a horizontal plane. This model was already used for clods in refs. [12,26]. In ref. [46], depressions were approximated using spherical cups. Half ellipsoids were preferred here, as with clods. The distribution of parameters was set from seedbeds and laboratory surface properties (Equations (2)–(5)). For the clods, semi-major axis length $a$ was drawn from a Weibull probability density function of shape parameter k = 9.4794 and scale parameter $\lambda$ = 1.3957:

$$f\left(x;k,\lambda \right)={\displaystyle \frac{k}{\lambda }}{\left({\displaystyle \frac{x}{\lambda }}\right)}^{k-1}{e}^{-{\left({\displaystyle \raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}\right)}^k}$$

(2)

and added with a minimum value of 5. Then, semi-minor axis length b and semi-height c were computed by linear regression according to the following equations:

$$b=0.74a+0.22+r_b$$

(3a)

$$c=1.63a-4.34+r_c$$

(3b)

where $r_b$ and $r_c$ are uniform random noises of standard deviation 3 and 7, respectively.

For the depressions, semi-major axis length $a$ was taken between 10 and 50 according to the following equation:

$$a={\displaystyle \frac{\alpha }{x+\delta }}$$

(4)

with $\alpha$ = 1437.9 and $\delta$ = 1.887. Semi-minor axis length b was proportional to $a$ with a random factor between 0.6 and 0.9, and semi-height c was drawn from an exponential law of probability density of parameter µ = 3.1607:

$$f\left(x;\mu \right)=\mu e^{-\mu x}$$

(5)

and added with a minimum value of 20.

Both clods and depressions had random orientation values between $-{\displaystyle \frac{\pi }{2}}$ and ${\displaystyle \frac{\pi }{2}}$. A total of 200 clods and 100 depressions were ordered by size and set randomly on a horizontal plane without overlap.

2.2. Segmentation of the DEMs

2.2.1. Segmentation of Soil Clods

A clod is a cohesive soil aggregate, formed by desiccation, compaction or mechanical action, and larger than fine natural aggregates. From the micro-topography, we could characterize the size and shape through DEM segmentation. The principle of clod segmentation was based on initial multiresolution analysis of the surfaces to be segmented [18,28,51]. Let z = S(x, y) denote the DEM of a soil surface. The surface can be decomposed for different levels n into one approximation A_n(x, y) and the sum of n details D₁(x, y), …, D_n(x, y) (Equations (6)–(8)):

$$S\left(x,y\right)=A_n\left(x,y\right)+\sum _{k=1}^n{D}_k\left(x,y\right)$$

(6)

For n = 0, the approximation is the DEM itself and no detail is introduced:

$$S\left(x,y\right)=A_0\left(x,y\right)$$

(7)

At each level n, approximation and detail were calculated according to the following recursion:

$$A_{n-1}\left(x,y\right)=A_n\left(x,y\right)+D_n\left(x,y\right)$$

(8)

Here, the detail D_n(x, y) was the total contribution of vertical, horizontal, and diagonal details. Thus, the approximation was the low-frequency part and the detail represented the high-frequency part. It was found that most energy in a soil surface was contained in the low-frequency band. Therefore, considering the approximations of a surface allowed for extracting the clods from the smallest to the largest.

The algorithm for clod segmentation is presented in Algorithm 1.

Algorithm 1: Clod segmentation

1:   1st step: Detect the clods 2:   Comput the approximations An of the surface. 3:   For each surface approximation An, do 4:       Detect the local maxima of the surface with a moving window. 5:       For each maximum, do 6:            Estimate the clod boundary box by testing the slope. 7:            Check the difference in height to discard flat bumps and sharp peaks. 8:       End for. 9:   End for. 10: Merge the detections at the different levels n from coarse to fine by looking roughly for clod inclusion in each other. 11: 2nd step: Delineate the clods 12: For each detected clod, do 13:     Extract the local surface around the clod from the DEM. 14:     Get the centered local surface by removing the mean plane. 15:     Get clod mask by keeping the elevations above the mean plane. 16:     Extract the clod contour on the clod mask. 17:     Check the goodness of the intersection with the mean plane and refine the inclination and the height of the mean plane when needed. 18:     Check if the local surface needs to be extended. 19:     Check for the segmentation of a block of clods. 20:     Regularize the clod contour by morphological opening (or closing for too small clods). 21:     Rule out the too flat clods. 22:     Correct or rule out squared contours. 23: End for. 24: Sort the validated clod contours by decreasing size. 25: 3rd step: Overall handle of clods 26: For each validated clod contour, do 27:     Check for inclusion or partial overlapping with the other clod contours. 28:     Remove the included clods and refine the delineation of the overlapping contours. 29: End for.

It involves three main steps:

• Extraction of the local maxima and boundary boxes for each level of surface approximation retained A_n, followed by validation and rough merging of the detected clods.
• Accurate delineation of each clod contour by controlled intersection of the local soil surface and the clod base plane.
• Handling of inclusions or overlaps of the validated contours.

Thus, the main parameters that may depend on the DEM resolution and surface roughness were: the list of approximation levels of the surface, the size of moving window, the distance between maxima for rough merging, the minimum size, and the minimum height difference (estimated with deciles 0.1 and 0.9) for clod validation. In this study, the last parameters were set to constant values of 10, 14, 32, and 3% of contour length, respectively. The mother wavelet used for wavelet transform was Daubechies 9. The algorithm’s parameters and rules were designed in refs. [18,28] to maximize recall and precision, and they have a physical meaning. Here, the segmentation method is evaluated on a new dataset to demonstrate its scalability. Steps 1 and 2 account for most of the running time. In Step 1, the pairwise comparison of clods was not optimized. Step 2 becomes longer as the number of clods increases. For DEMs of 900 × 900 pixels and around 500 clods, the algorithm takes 45 min on a laptop with a 2.6 GHz Intel Core i7 processor, and MATLAB (v2022b). This time would be reduced with smaller DEMs or fewer clods.

2.2.2. Segmentation of Holes and Depressions

A depression is a low point of relief. It designates a hollow of the agricultural land where water concentrates more easily. Again, its size is important, and, here, an estimation of the volume has been done without any hypothesis of shape. When representing elevations in the MATLAB Parula color map (i.e., blue, green, yellow), the deep blue part corresponded very well to the depressions. This was the case because the surfaces had zero mean and were positively skewed. The purpose of transforming the DEMs into RGB space was therefore to work with the histograms of the color channels, scaled to the full range, in order to enable adaptive thresholding. This is an original approach. The proposed method therefore consists of two steps:

• Scale images to the (1–256) range and register elevation images in RGB color space,
• Threshold the blue and green channels.

For this second step, the envelope of the channel histogram was first estimated with wavelet approximation of level 3 and mother wavelet Daubechies 15. The combination of the blue and green channels allows for the selection of colors corresponding to depressions and their deepest parts. The threshold T on the blue channel was set at the 80% percentile, and higher values were kept. This threshold allows for the selection of the blue region with some margin. Below this value, the retained regions are two large, non-meaningful areas. It would be possible to set this threshold at 90%, as it made no difference. However, a value of 95% would be too high and would lead to no more concave depressions. Two thresholds, T₁ and T₂, were used for the green channel, the median for deepest holes, the 70% percentile for the depressions, and lower values were retained. In that case, the envelope of the histogram was forced to zero near the origin. These thresholds were set to obtain closed contours that can be modeled by a simple geometric shape in the case of holes, and that reach the clod bases near null elevations in the case of depressions. This ensures the physical significance of the regions segmented as lower parts of the relief with negative elevations. An example is illustrated in Figure 4. A sensitivity analysis of depression segmentation was conducted for the threshold T₂ (

Table 2. Sensitivity of segmented depressions to T₂ threshold. Nb is the number of depressions, Pmax is the maximum value of perimeter, Hmax is the maximum mean height of depression contours, and Vtot is the total volume occupied by depressions. FS denotes fine seedbed, RS denotes rough seedbed, and PL denotes ploughing.

Surface	T2	Nb	Pmax (mm)	Hmax (mm)	Vtot (mm3)	Concave
FS 2	30%	0
	40%	4	58.5	−8.83 × 10−5	2.93 × 103	yes
	50%	34	156	−9.58 × 10−5	1.26 × 104	yes
	60%	61	298	−5.71 × 10−5	3.60 × 104	yes
	70%	174	607	−3.78 × 10−5	9.52 × 104	yes
	75%	208	743	−5.21 × 10−6	1.68 × 105	yes
	80%	219	1.22 × 103	2.55 × 10−4	2.38 × 105	no
	90%	231	6.90 × 103	1.65 × 10−4	3.20 × 105	no
RS 1	30%	0
	40%	26	108	−1.50 × 10−4	1.66 × 104	yes
	50%	54	454	−9.99 × 10−5	1.11 × 105	yes
	60%	118	754	−5.10 × 10−5	2.94 × 105	yes
	70%	131	1.85 × 103	1.78 × 10−4	4.64 × 105	yes
	75%	123	2.07 × 103	1.78 × 10−4	4.85 × 105	no
	80%	122	2.10 × 103	2.18 × 10−4	5.33 × 105	no
	90%	98	5.18 × 103	1.78 × 10−4	5.37 × 105	no
PL 2	30%	3	55.4	−1.79 × 10−3	5.93 × 103	yes
	40%	14	103	−3.10 × 10−4	3.67 × 104	yes
	50%	34	129	−2.49 × 10−4	1.13 × 105	yes
	60%	32	422	−2.22 × 10−4	3.98 × 105	yes
	70%	47	1.06 × 103	−1.56 × 10−4	7.35 × 105	yes
	75%	44	1.00 × 103	−1.03 × 10−4	9.53 × 105	yes
	80%	44	2.18 × 103	−1.54 × 10−5	1.17 × 106	yes
	90%	15	3.32 × 103	9.90 × 10−5	1.24 × 106	no

). Indeed, the threshold on the green channel is the most important for delineating depressions and could be used alone. Table 2 shows only one example per tillage practice but the analysis was done on all the surfaces. Some depressions can be segmented from thresholds as low as 30% or 40%. Increasing the threshold then results in larger and more numerous depressions. However, for some surfaces, increasing the threshold can also cause depressions to merge, thereby reducing their number. The mean height of the depression contours tends to increase, reaching or slightly exceeding zero. The total volume occupied by the depressions also increases. From 75% to 90%, depending on the surface, some depressions become too large to be meaningful and may not be concave. Therefore, a value of 70% was retained.

Defining thresholds as percentiles rather than fixed values makes the algorithm adaptive and applicable to different soil surfaces, regardless of the elevation range. In this study, the standard deviation varies by a factor up to three. At the selected percentiles, the variability in the actual threshold values for the blue and green channels is of around 8%, whereas at other percentiles, it can reach 20%. Histogram thresholding is also a simple and quick method. The running time for segmentation of depressions was of less than 5 s.

2.3. Performance Assessment

The goodness of segmentation could be appreciated qualitatively, visually, and quantified by indices. For the evaluation of detection results, recall, reflecting the percentage of clods well detected, precision, representing the percentage of correct predictions as clods, and the F1-score, a balance between the two, are reference metrics. For contour evaluation, the IoU (Intersection over Union) is a reference metric. It represents the proportion of the common region area between a segmented region and its ground truth.

Due to visual bias and the inherent limitations of representation of 2.5D DEMs measured in the field, obtaining a ground truth for contour delineation was not feasible. Consequently, IoU metrics could not be computed in this context. To evaluate object detection, it was necessary to zoom in on smaller areas to perform an object-by-object evaluation. The segmentation was first applied to the entire DEMs and visually assessed. Then, smaller samples of 400 × 400 pixels were extracted to estimate recall, precision, and F1-score for the clods, which were sufficiently numerous for these metrics to be meaningful. Depressions were not numerous enough to allow for a quantitative evaluation of their detection. Nevertheless, the quality of the boundary delineation of clods and depressions was assessed using the IoU metric on simulated surfaces, for which the ground truth is known.

3. Results

3.1. Segmentation of the Real Surfaces

The first results presented are those with DEMs recorded in the field. Figure 5a shows a 3D view and Figure 5b a top view of a fine seedbed. Units are 0.5 mm, which means that there is 0.5 mm between two points. For this surface, 581 clods, 203 depressions and 56 deep holes were segmented. One can see that the micro-topography has been well captured. For fine seedbeds, levels A2–A5 of surface approximation were retained. Quantitative indices were estimated on two smaller samples located in the upper left and right corners. Figure 6 displays one of them. Out of 130 clods, 123 were correctly segmented (true positives), 7 were missed (false negatives) and 3 contours were not really clods (false positives). Thus, recall was 94.6%, precision 97.6% and the F1-score 96.1%. In some cases, the delineation included two clods that form a block. This occurred because the surface had weathered over a few months after tillage. On Figure 6b, one can see small holes or depressions just at formation, and larger ones. The delineation of holes or depressions matched well with some clod bases. A few clods were located in depth and were contained within depressions or the deepest holes. In the second sample, there were 122 clods: 115 true positives, 7 false negatives, and 2 false positives, resulting in a recall of 94.3%, a precision of 98.3%, and an F1-score of 96.3%.

Table 3. Indices of clod detection for fine seedbed DEMs.

Sample	Nb Clods	Recall	Precision	F1-Score
S1	130	94.6%	97.6%	96.1%
S2	122	94.3%	98.3%	96.3%
S3	133	96.2%	96.2%	96.2%
S4	138	95.7%	97.1%	96.4%
Overall	523	95.2%	97.3%	96.2%

summarizes the evaluation of clod segmentation for both fine seedbed DEMs and two samples per DEM. The results were relatively stable. Some samples of fine seedbed surfaces had slightly more or slightly fewer clods. There was sometimes uncertainty as to whether a bump was a clod or part of the support. Overall, the results were very good, with indices above 95%.

An example of rough seedbed surface is shown in Figure 7. For this surface, 528 clods, 131 depressions and 54 deeper holes were segmented. These were fewer than for the fine seedbeds. Some clods appeared larger. The surface exhibited both fine seedbed-like areas and coarser regions, resulting in fewer clods and more complex relief features. Additionally, the elevation range was −40 to 60 height samples (i.e., 100 × 0.5 = 50 mm) compared to −20 to 40 height samples (30 mm) for the fine seedbeds. For these rough seedbed surfaces, the retained segmentation levels were A2–A6 for surface approximations—one more level than for the fine seedbeds. As before, it was occasionally difficult to determine whether certain bumps should be classified as clods or as part of the support.

Table 4. Indices of clod detection for rough seedbed DEMs.

Sample	Nb Clods	Recall	Precision	F1-Score
S1	133	94.7%	95.5%	95.1%
S2	94	88.2%	96.5%	92.2%
S3	119	94.1%	96.6%	95.3%
S4	88	94.3%	94.3%	94.3%
Overall	431	93.5%	95.7%	94.6%

presents the indices for two samples per DEM of rough seedbeds. The indices were generally stable, with the exception of one recall value dropping to 88.2%. Overall, the indices exceeded 93%, demonstrating very good performance. The delineation of holes or depressions again matched well with some clod bases, and as with fine seedbeds, a few clods were located in depth and contained within depressions or the deepest holes. Therefore, the proposed segmentation method proved well-adapted to seedbeds.

The case of ploughing surfaces was more complicated due to the superposition of different roughness. The largest clods or bulges were not always segmented as a whole if they contained several bumps. Including higher levels of approximation (A7–A9) did not bring any improvement. In this case, the question arose as to whether some bulges were large clods that should be considered as single objects or whether they were part of the support containing smaller clods on top (see Figure 8). Figure 8 shows one of the two DEMs of ploughed surfaces. It can be observed that the surface had a greater range of elevations (−50 to 100 height samples, i.e., 75 mm) and that some parts were coarser than others. For this surface, 237 clods, 47 depressions, and 34 deep holes were segmented. These were fewer than for seedbeds. Again, the depressions corresponded well with the clod bases. Here, identifying clod contours was more difficult than for seedbeds, and the visual bias was higher due to the complex micro-topography.

Table 5. Indices of clod detection for ploughing DEMs.

Sample	Nb Clods	Recall	Precision	F1-Score
S1	70	80.0%	98.2%	88.2%
S2	75	85.3%	97.0%	90.8%
S3	57	86.0%	98.0%	91.6%
S4	96	85.4%	95.3%	90.1%
Overall	298	84.2%	96.9%	90.1%

shows the indices of clod detection for two samples per DEM. The number of clods varied significantly depending on the studied sample of the surface. Recall ranged between 80% and 86%, and precision ranged between 95.3% and 98.2%, indicating that some clods were not detected, but the detections were reliable. The F1-scores remained quite stable around 90%. The results were still good, but the segmentation method reached its limits, performing better on fine seedbeds that had less variability in clod size and a flatter support structure for clods.

3.2. Segmentation of the Simulated Surface

Now let us consider the simulated surface to quantify the accuracy of contour delineations for clods and depressions. For this surface, using the Daubechies 9 wavelet applied to in-field surfaces induced too many undulations; so, Daubechies 3 was used instead [51]. As the surface was already smooth, no approximation was needed. When adding some random noise, levels 1 and 2 were used for moderate and higher cases, respectively. Figure 9 shows the delineations of segmented clods and depressions (dotted lines) and the ground truth (solid line) for the simulated surface without noise.

Table 6. IoU values for simulated surface.

IoU	Mean	Standard Deviation	Minimum	Maximum
Depressions (no noise)	91.8%	4.8%	78.8%	98.4%
Depressions (SNR < 50% for ½)	91.8%	4.5%	79.5%	97.8%
Depressions (SNR < 10% for ½)	91.8%	3.9%	80.7%	97.5%
Clods (no noise)	87.9%	4.4%	78.0%	95.5%
Clods (SNR < 50% for ½)	87.6%	12.0%	0%	95.6%
Clods (SNR < 10% for ½)	84.2%	21.5%	0%	96.3%

presents the IoU values obtained in the three cases: (1) surface without noise, (2) surface with moderate noise, and (3) surface with higher noise. The variance in the noise added to the surface was computed separately for clods and depressions, as they differ significantly in size. Moreover, because the ranges of clods and depressions were large, the signal-to-noise ratio (SNR) was different for each clod and each depression. Therefore, median values were reported in the table. The depressions were segmented with very good IoU values near 92% on average, and the method was robust against noise. Note that the simulated surface had a color map slightly different from in-field surfaces due to horizontal support; so, the thresholds on histograms corresponded to slightly different elevations. Consequently, the green threshold was fixed for the simulated surface. With a median SNR of 50%, the lowest decile had a SNR under 20%, and with a median signal-to-noise ratio of 10%, the lowest decile SNR was under 4%. Hence, all depressions were well segmented even in the presence of high noise. For clods, the results were also very good but more affected by noise due to a wider range of clod sizes. Some clods were not detected in the presence of noise, while the noise induced small bumps that were segmented as clods. To quantify the quality of delineation, only detections were considered for IoU statistics. Average IoU values were close to 88% in the first two cases and around 84% in the last one. With a median SNR of 50%, the lowest decile had an SNR below 4%. When the median SNR was 10%, the lowest decile SNR dropped below 0.8%. The noise condition was thus harder for clods than for depressions.

3.3. Application to Spatial Variability Quantification

An application of the proposed segmentation methods could be the computation of the volume of the segmented features to characterize their size and within-field spatial variability. Figure 10a shows the cumulative density function (CDF) of the clod volumes for each replicate of the soil surfaces. Since the volumes were more spread out and larger for ploughings than for seedbeds, a decimal logarithm scale was used for display. The fine seedbeds showed the smallest clod volumes, while the rough seedbeds were very similar but contained some larger clods. Notably, one rough seedbed and one fine seedbed showed the same volumes for the 20% smallest clods. However, when considering larger clods, the differences become more pronounced. The two ploughings were clearly distinct, with significantly larger clods. These results are consistent. The CDF plots also reveal the range of clod volumes obtained on bare soil a few months after soil preparation:

• Fine seedbeds: ~2 × 10² to ~3 × 10⁴ mm³;
• Rough seedbeds: ~2 × 10² to ~10⁵ mm³;
• Ploughings: ~3 × 10² to >10⁵ mm³.

Likewise, the CDF of the depression volumes for each replicate of soil surface can be seen in Figure 10b. The order of magnitude of depression volume is rather close to that of the clods, but slightly more spread out. Indeed, the small depressions are smaller than the smallest clods. This can be caused by a threshold for minimum size to validate clod delineation. Under this threshold, one should obtain aggregates, which are more difficult to study one by one, and were not tackled in this study. Also, both CDFs of clod volumes for ploughings were truncated so that Figure 10a is more intelligible. The convergence towards 1 would be obtained for volumes of clods of around 5 × 10⁵ mm³. For depressions, the largest values were around 7 × 10⁵ mm³. The seedbeds were grouped, and the ploughed surfaces were again clearly distinct, with larger depressions. An interesting finding is that the effect of the soil preparation is more expected for clod distribution than for depression distribution. In particular, the difference between a fine seedbed and a rough seedbed is clearer considering the clods.

To reflect the spatial variability in roughness features, the variation coefficients were estimated for clods and depressions. The variation coefficients for clod volumes were, respectively, 1.42 and 1.13 for fine seedbeds, 2.13 and 2.68 for rough seedbeds, and 3.77 and 3.49 for ploughings, which is very discriminant of the tillage operations and the soil surface roughness. For depression volumes, in the same order of surfaces, the coefficients of variation amounted, respectively, to 4.85, 4.27, 4.96, 7.18, 3.90, and 2.68. The fine seedbeds had around 190 depressions due to small irregularities of the microrelief of the surface. It led to great variations in the size of depressions. The ploughings were coarser and smoother surfaces with only about forty depressions of larger size, which led to globally smaller coefficients of variation. The rough seedbeds were in between, with around 130 depressions and rather fine parts and coarser parts, which led to the maximum coefficients of variation.

4. Discussion

As shown in Table 1, the standard deviations of elevations are typical for the roughness of small, medium, and large soil surfaces measured in the field. Note that the DEMs were acquired a few months after tillage operations, which resulted in lower elevation standard deviations than those immediately after tillage. The probability density functions (PDFs) of elevations are positively skewed, indicating that having more clods than depressions is consistent. Finally, the kurtoses are greater than three, with one exception, indicating that the elevation PDFs are not Gaussian. In total, there are approximately 2800 clods, of which 1250 were analyzed individually to estimate quantitative indices. These indices are therefore statistically meaningful.

In the literature, the wavelet-based clod segmentation algorithm was evaluated on handmade soil surfaces of sieved clods (laboratory surfaces) in ref. [18]. It showed strong performance and robustness, with average overlap rates (IoU indices) ranging between 55.1% and 79.9%, for instance evaluation, i.e., clod by clod. This corresponded to goodness of agreement (i.e., reflecting probability of having a high IoU) between 65.1% and 86.1% when compared with other methods. The equivalent diameters derived from this method and manual segmentation yielded a very good regression equation of 0.93x + 1.9 mm, with R² = 99%. This method was also evaluated on both real and laboratory surfaces in ref. [28] for the detection task, resulting in a sensitivity or recall of 83.6% and a precision of 93.6%, yielding an F1-score of 88.3%. Note that in the cited paper, the precision was mistakenly called specificity, and only the detection of clods was performed. In the present study, for in-field DEMs, the average recall, precision and F1-score were, respectively, 92.0%, 96.7%, and 94.2%, showing the scalability of the method. For simulation, IoU ranged from 84.2% to 87.9%. These results were thus better due to the relevance of steps 2 and 3 of the segmentation algorithm, which were specifically designed for clod delineation.

In ref. [21], for 2D images segmentation using deep learning under laboratory conditions, mean IoU values ranged from 41.3% to 79.3% depending on clod size class, with an average of 55.7%. This was lower than the proposed method, highlighting the complexity of the clod segmentation problem. Note that in the present study, the simulated surface was less realistic than laboratory or field surfaces. However, the excellent visual agreement of the boundaries for seedbeds and ploughed surfaces demonstrates the robustness of the method when applied in real conditions. In ref. [34], deep learning was also used for soil block identification. Average precision, recall, and F1-score were 87.3%, 87.8% and 88%, respectively, but only for the training dataset. These results are again lower than those obtained in the present study. In ref. [35], a preliminary study on deep-learning-based clod segmentation was proposed. It resulted in the detection of 103 clods on a 2D image. While segmented clod areas were presented, only the clod fraction (i.e., the ratio of total clod area to image area) was evaluated, and no assessment of the clod boundaries was provided.

To the best of our knowledge, no segmentation of depressions has been published at the small scale addressed in the present article. Topographic depressions have instead been studied at a meter-scale resolution. In ref. [44], karst depressions were segmented on 30 m resolution DEMs using deep learning with DEMs and derived variables as inputs. The best result achieved an F1-score of 85.1% and an IoU of 74.0%. The method presented in the present paper based on millimeter-scale resolution achieved better IoU values with an average of 91.8% on simulated surfaces, and visually comparable agreement on in-filed surfaces. Quantifying the segmentation of depressions remains challenging. Using a higher threshold on the green channel would have produced more extensive depressions. However, we have chosen to keep closed contours possibly modellable. Ultimately, the surface will be considered as the sum of clods, holes and depressions, supported by a base surface, as was the case for the simulated surface.

Clod segmentation proved more challenging than depression segmentation, leading to a more complex algorithm for clod detection. Optimal results were obtained for fine seedbeds, with excellent performance (F1-score and recall of 96.2% and 95.2%). However, performance was less strong (F1-score and recall of 90.1% and 84.2%), although still robust, for coarser ploughed surfaces. In that case, distinguishing between clods and the supporting terrain remains ambiguous and warrants further investigation. Several factors may contribute to this difficulty:

(1)

The number of singular values allocated to the deterministic component may need adjustment for rougher surfaces;

(2)

The choice of mother wavelet (e.g., Daubechies 9) and its family number may not be optimal for such surfaces;

(3)

Higher family numbers introduce more oscillations, potentially complicating the delineation of large clod contours.

Clods and depressions can be characterized by their size. In this study, this was done using volumes without any assumption about shape. For the simulated surface, for which the true volumes are known, the errors in the total volume occupied by clods and depressions were estimated at 6.9% and 2.3%, respectively, with a slight underestimation in each case. CDF plots are useful for characterizing tillage and surface conditions. Moreover, the spatial variability in clod volumes, quantified by the coefficient of variation, is highly discriminative of the roughness resulting from tillage operations and weathering. Indeed, the coefficients of variation were 1.42 and 1.13 for fine seedbeds, 2.13 and 2.68 for rough seedbeds, and 3.77 and 3.49 for ploughed surfaces, showing similar values across surface replications and an increasing order of magnitude as the surface becomes coarser.

The proposed segmentation methods thus provide a powerful tool for the quantitative assessment of agricultural surfaces, enabling precise characterization of soil clods and depressions while addressing both research and practical management needs. They allow for the derivation of morphometric indicators (size, shape, spatial distribution) and support automated classification of surface conditions. This will facilitate temporal monitoring of post-tillage evolution. The added value of the 2.5D representation compared to 2D lies in the ability to compute volumes of clods and depressions. Future applications may include hydrological and erosion studies, such as estimating water retention capacity and the spatio-temporal evolution of surface roughness. The combination of millimeter-scale resolution with meter-scale coverage also makes these methods relevant for remote sensing applications. They further open the way to surface modeling and the estimation of radar signatures using electromagnetic simulations [12].

5. Conclusions

This study explored automatic DEM interpretation to assess post-tillage soil quality and presented computational methods for quantifying field-scale roughness features. Two segmentation methods for delineating clods and small depressions were evaluated, and their application for studying spatial variability was demonstrated. Field-measured DEMs confirmed the relevance of the proposed approaches, with indices outperforming those reported in the literature.

These methods enable both global statistics on clod and depression size and shape, and precise localization of these features. They not only improve the quantitative characterization of soil surface roughness, but also pave the way for operational applications, including automated classification and high-resolution temporal monitoring of surface condition. Their unique combination of field-scale coverage and millimeter-scale resolution offers strong potential for advancing hydrological modeling, erosion assessment, and remote sensing of soil surface conditions.

Future work will focus on modeling clods and depressions to complete the characterization of surface roughness and simulate realistic soil surfaces, including the support structure of these features and deterministic components of the surface.