3.2.1. PC Segmentation
The PC segmentation process was implemented following the methodology described above to fit planes to the PC data (
Figure 5). While applying the RANSAC algorithm, the largest planes in the original PC (
Figure 5a), corresponding to the top concrete platform of the RMB, were also detected, as illustrated by the pink, orange, and green patches in
Figure 5b. These planes were subsequently removed from the classified data, retaining only the planes representing the CAUs.
Additional challenges associated with the use of RANSAC are depicted in
Figure 5c,d. In some instances, planes were fitted across the surfaces of multiple cuboids due to their proximity or similar elevations. This phenomenon is predominantly observed in the upper zone of the RMB, where the CAUs were initially placed level, and due to the stability of these areas, they remain mostly level. Moreover, the narrow gaps between neighboring armor units often go unsampled, consolidating several wave-dissipating block poses into a singular representation, as highlighted by previous studies utilizing alternative methodologies [
57,
58]. Conversely, there are cases wherein finding a suitable plane representing specific cuboids proves challenging. This occurs predominantly at the lower levels of the RMB, where the PC exhibits lower quality and increased noise due to degraded texture of the cuboids in these areas and the presence of water, algae, etc.
The process of determining appropriate fitting parameters has been carried out iteratively, involving trials with gradual refinement until reasonably satisfactory results were achieved in terms of meaningful interpretation and comprehensiveness. The best outcomes, based on these criteria, were obtained with a minimum support points per plane of 200 and a maximum distance to the fitting plane of 0.005 m. The maximum allowable deviation in the normal direction of the plane from the estimated normal was set to 5°. The overlooking probability value was set to 0.0001, aiming to work with a low probability of missing outliers during the RANSAC plane fitting process.
To evaluate the accuracy of the RANSAC results, we chose a representative sampling area in the southeast quadrant of the RMB, encompassing approximately 1037 CAUs, which accounts for roughly a quarter of the total number of armor units. To prevent the inclusion of flooded areas, cuboids situated at elevations lower than 0 m AMSL were excluded from the sampling. As illustrated in
Figure 6, a manual sampling of this zone was performed to verify the correct classification of planes in both time periods.
Items classified as True Positives (TP) correspond to actual cuboids correctly modeled by a plane. False Positives (FP) refer to detected planes that do not precisely correspond to the top face of an individual wave-dissipating block. A significant portion of items falling into this category consists of planes fitted to the lateral faces of some cuboids. False Negatives represent actual CAUs that were not detected as planes by the RANSAC fitting, so they were manually added to account for their number. A single plane fitting two (or more) cuboids has been considered in terms of counting as two (or more) FNs. Lastly, the concept of True Negative (TN) is somewhat more abstract and includes non-cuboids correctly classified as such. As shown in
Figure 6, this class includes manually added elements like large rocks within inter-block spaces, which the algorithm correctly identified as non-cuboids.
Table 5 shows the confusion matrix containing TP, TN, FP, and FN values. These values are components of the confusion matrix which defines actual and predicted classes.
Sensitivity, specificity, precision, negative predictive value, and accuracy can be easily derived from the confusion matrix values, with the formulas mentioned in
Table 6:
Sensitivity, representing the percentage of positive cases, is 94%, while specificity, the percentage of negative cases, is 22% in our experiment. Precision achieved 94%, and accuracy, indicating the percentage of correctly identified cases, is 89%.
While these results are promising, there is potential for improvement in the method, especially in reducing FPs associated with detecting lateral faces on the CAUs. Moreover, the count of FNs is relatively high, mainly due to planes fitted to multiple Antifer blocks simultaneously. Conducting lower altitude flights with higher PC resolution could potentially enhance the detection of discontinuities between cuboids and improve sensitivity to detect outliers based on the distance to the planes.
3.2.2. RMB Stability Assessment
The maximum consensus planes obtained by applying the RANSAC algorithm to each of the dense PCs were cross-referenced through a proximity-based criterion. Through this spatial join or alignment process, a total of 3697 pairs of corresponding planes were identified across the entire surface of the breakwater.
While the correlation method used here is advantageous due to its inherent simplicity, it is not without its drawbacks. The effectiveness of this method relies significantly on the precision of the RANSAC algorithm in detecting and segmenting planes. Any inaccuracies in the segmentation of either PC, such as FPs or FNs, directly impact the subsequent plane matching phase. Essentially, an orphan plane, which exists in one dataset without a counterpart in the other, may be matched with the nearest available plane. This could result in semantic inconsistencies and distort subsequent analyses, although it does provide the advantage of generating a comprehensive and continuous dataset. To address these issues, the spatial join tool introduces a distance field within the outcome, representing the spatial closeness of linked geometries. This enables the definition of a specific tolerance threshold to prevent these inconsistencies.
The normal vectors of the fitted planes for each corresponding pair of block faces can be acquired to estimate the tilt angle within a single block.
Figure 7 illustrates the overall inclination values obtained for each cuboid in the RMB, categorized based on their magnitudes.
In the graphics presented in
Figure 8, a more detailed breakdown of these inclinations, considering both magnitude and inclination direction, is provided. Analysis of these figures allows us to deduce that the most significant instabilities of the blocks occur in the predominant southwest (SW) direction, aligning with the most exposed flank of the breakwater. Some tilting of the cuboids is also noticeable in the northeast (NE) body of the RMB, although the movements detected here are generally much smaller. In terms of magnitude, it is observed that 61.1% of the wave-dissipating blocks undergo rotations of zero or less than 1°, and 91.7% experience movements of less than 2° based on data derived from the RANSAC method. However, it is worth noting that rotations of certain CAUs can, in specific cases, exceed 50°.
In
Figure 9, an illustrative region displaying relatively stable blocks within the southwest (SW) body is presented. Evaluating displacements or rotations solely through a visual examination of orthophotos from two different time periods poses a significant challenge. Factors like variations in imaging texture due to cuboid shading, the presence of biofilm, algae, etc., add complexity to the visual comparison of the orthophotos. Nonetheless, careful observation may suggest some rotation in the lower-right cuboid of the image.
In the case of DoD, discerning any form of displacement or rotation is challenging, especially for cuboids with significant displacements. Unlike cuboids with noticeable movements, it is difficult to infer any changes in the elevations of rotated CAUs, as these elevations may remain relatively stable despite the rotation. Some elevation fluctuations are observable within inter-block spaces, potentially attributed to the movement of small stones in the underlayer or artifacts in the DSMs caused by occluded regions. The DoD represents elevation changes on a cell-by-cell basis, typically along a predefined direction, often the Z-axis (vertical direction). While the simplicity of the DoD method is advantageous, it does have limitations in intricate contexts, such as overhangs and nearly vertical slopes, where vertical differences may not provide comprehensive insights. Similar findings have been reported in previous studies [
60]. Consequently, the precision of interpreting elevation differences along the edges of each CAU is not entirely accurate when using a traditional 2.5D method for change detection like DoD. As illustrated in
Figure 9d, the RANSAC-based plane-fitting method demonstrates increased sensitivity, showcasing its effectiveness even in more stable regions of the RMB model.
Operating at the level of individual cuboids, the proposed methodology allows for a more detailed analysis of the structure. The graphs in
Figure 10 present both a global analysis (
Figure 10a) and a zonal breakdown of cuboid counts against their detected inclinations. The zonal analysis divides the total count of CAUs into five principal zones characterizing the RMB. The crest of the detached breakwater, referred to as RMB top, spans its entire length and includes three rows of wave-dissipating blocks on each side of the central platform. Due to the substantial number of blocks within this area, it exhibits a relatively low occurrence of CAU inclinations, as illustrated in
Figure 10b. In the breakwater heads (
Figure 10c,d), a limited number of units exhibit relatively high shifts, primarily found in the northwest (NW) head. Furthermore, the southwest (SW) body zone shows significantly higher CAU inclinations than the inner breakwater region (
Figure 10e,f), which is consistent with its exposure to wave action. Beyond this simplified examination, the results underscore the potential of these methods to provide quantitative assessments of the extent of damage.