Multi-directional change detection between point clouds

Highlights

• 3D change between point clouds is commonly measured normal to the local surface.

• Our approach finds a dominant movement direction (DMD) occurring at each point.

• It does this by considering local changes in multiple directions (n = 60).

• We show that the DMD can differ considerably from the surface normal.

• This can provide an important alternative view of movement:

• where overall displacement of a surface or feature is needed,

• where movement processes operate in a direction that is not surface-normal,

• where the underlying process(es) may not be known,

• where movement(s) across the point cloud scene is not oriented along a single axis.

Abstract

Point clouds continue to be acquired with greater accuracy and less occlusion over complex scenes, characterised by high roughness and topographic variation in all three dimensions. The most widely adopted approach to change detection, M3C2, measures change along the local surface normal, which varies between points and bypasses the uncertainties involved in mesh or DEM generation. While adaptive, this direction of comparison is nevertheless user-defined and becomes less relevant where the movement direction deviates from the surface normal. Measured change therefore also becomes less meaningful, as it is a projection onto this direction. Sliding of a failing slope, for example, is predominantly surface parallel rather than along the surface normal. We present an approach that derives a dominant movement direction (DMD) at each point based on multi-scale, multi-directional change quantifications. The DMDs differ from the surface normals in three LiDAR-derived test cases; a rockfall, an avalanche, and rock glacier movement, providing more accurate measures of rockfall depth and boulder movement across the rock glacier. When the direction of change detection is orthogonal to local relief (i.e. across the surface), a variable length search cylinder that intersects only a single (corresponding) surface is necessary during change detection. Where movement results in new regions of occlusion in the second point cloud, we show that the proportion of points for which no valid change could be recorded decreases by up to 15% using the DMD rather than the surface normal. We emphasise the importance of examining the direction over which change is measured, and highlight that a comparison direction that adapts to movement rather than to the local surface can provide more relevant and accurate measures of change where the movement is not orthogonal to the surface. Our approach represents a supplementary tool for cloud-to-cloud comparison, where a choice of tool should be made based on the expected DMD deviation from the surface normal.

Introduction

Point clouds are an established component of topographic mapping that have seen an increasing uptake within the geosciences (~2% of publications during 2014; Abellán et al., 2016). The introduction of terrestrial laser scanning (TLS) during the early 2000s enhanced point cloud collection from airborne laser scanning by allowing shorter survey ranges and greater variation in viewing angles. UAV-borne image acquisition and laser scanning are furthering these capabilities with their potential for increased resolution and coverage. Such platforms generally allow for a large number of imaging angles, thereby improving the performance of Structure-from-Motion for point cloud creation (Westoby et al., 2012, Carrivick et al., 2015, Carbonneau and Dietrich, 2017). While most point cloud scenes tend to exhibit a broadly planar geometry, with low relief orthogonal to the scene, almost all surfaces exhibit a degree of complexity at some scale, defined by high relief or abrupt changes in slope, aspect, or local surface roughness. Owing to the versatility in the acquisition process, surfaces that are complex and highly three-dimensional (topographic variation along all three dimensions; Brodu and Lague, 2012) can now be recorded in point cloud form with greater accuracy, coverage, and resolution (e.g. Slob et al., 2002, Riquelme et al., 2014).

Hardware and software developments, including lowering costs, have enabled a widening of the use of point clouds beyond topographic map generation (Eitel et al., 2016). Comparisons of surface topography have become a primary objective of many acquisition campaigns due to the general availability of instruments, continued growth of existing datasets, and the proven ability for improving our understanding of earth surface process dynamics (Kromer et al., 2015, Anders et al., 2019, Comber and Wulder, 2019, Williams et al., 2019). Higher accuracies and reduced ground-sampling distances have also brought point distributions more closely in line with the scale of small movements, in turn allowing for more sophisticated change detection techniques. Procedures that quantify and lower uncertainties are particularly effective for change detection of complex landforms; these include filtering of unreliable points (Williams et al., 2018), spatial and temporal averaging of point clouds (Abellán et al., 2009), and temporal averaging of differences between sequential datasets (Wheaton et al., 2010, Kromer et al., 2015). Our focus is change detection and quantification, and we present an approach that is tailored to point clouds characterised by complex topographies. The approach is advantageous where both the scene itself and the movement being measured is complex. We define this complexity as movement in a direction that differs from the surface normal, may vary between successive scan pairs, and may result from multiple superimposed processes (i.e., overlapping in space and/or time).

DEM differencing is a commonly-used method that involves the subtraction of gridded representations of successive point clouds in order to calculate elevation change on a cell-by-cell basis (e.g. Rosser et al., 2007, Rosser et al., 2013, Abellán et al., 2009). This is particularly effective when comparing near-planar surfaces; however, a critical drawback is that change is measured exclusively along a single, user-defined direction (typically the z-axis). The extent to which measured change reflects reality therefore relies on the direction of change aligning with the up-axis of the DEM (Rosser et al., 2008, Benjamin et al., 2016). This is most problematic for near-vertical surfaces, such as rock faces, where the point cloud needs to be rotated prior to gridding so that the up-axis (representing distance to the rock face) is aligned with the dominant strike.

Cloud-to-cloud techniques overcome uncertainties in DEM differencing by preserving the 3D geometry of point clouds throughout the change detection process, measuring change along directions unique to each point rather than along a single axis. These approaches are generally slower in terms of computation time but, critically, are better suited to complex point clouds as they remove the need to grid or mesh either surface. In its simplest form, change between two point clouds can be computed as the distance between each point and its closest neighbour in the next point cloud (Girardeau-Montaut et al., 2005). An extension of this approach is the creation of distance vector sets between corresponding point pairs or objects, which can be separated into rotational and translational components (Monserrat and Crosetto, 2008, Oppikofer et al., 2008, Oppikofer et al., 2009, Travelletti et al., 2008, Carrea et al., 2012, Ghuffar et al., 2013). These approaches build on techniques for object tracking in imagery (e.g., Dall’Asta et al., 2017) and consist of manual or semi-automated feature tracking on masses that are creeping, such as landslides, or tilting, such as rock pinnacles. Point pairs can be manually defined using topographic features distinguishable in both clouds, while automated approaches aim to isolate individual discontinuities or planar surfaces (e.g., Viero et al., 2010) by region growing. Various geometric measures can be applied as criteria for growth, and the finding of corresponding features can be automated using thresholds of geometric and positional similarity (e.g., Hosseinyalmadary et al., 2015). Building on this, supervised classification has been used to identify corresponding regions of landslides based on their morphometry within a time series of point clouds (Mayr et al., 2017). This provides geomorphologically relevant features, such as headscarps, for object tracking but requires a priori knowledge of these features in order to ensure that they are accurately delineated. While manual point picking overcomes this need, it reduces the number of features that can be tracked and is usually less accurate. This is compounded by the fact that the geometry of a given object with high positional similarity will still differ between two point clouds due to inherent variabilities in point distributions, densities, occlusions, and, where different instruments are used, accuracies. Further, point clouds captured by laser scanning and photogrammetric techniques do not have a 1:1 correspondence, such that point spacing will always be an approximation subject to ground-sampling distance. As a result, the considerable parameter testing and a priori knowledge required for point cloud-based object-tracking means that, generally, it is best applied to simple cases where movement is uniform and well-defined.

The Multiscale Model-to-Model Cloud Comparison approach (M3C2; Lague et al., 2013) has been widely adopted in point cloud-based monitoring, removing the need to grid point cloud data (Schürch et al., 2011) and measuring change over a direction that varies across the point cloud according to the local topography. Its application has been widespread within geomorphology, including for lava lakes (Smets et al., 2016), bedrock gorges (Beer et al., 2017, Cook, 2017), landslides (Stumpf et al., 2015), cliff erosion (Warrick et al., 2017), moraine complexes (Westoby et al., 2016), glacier surfaces (Midgley and Tonkin, 2017), and rock glacier surface change (Zahs et al., 2019). At each point, a vector orthogonal to the local surface (surface normal) forms the axis of a cylinder. A Centre of Gravity (CoG) is then calculated for each cloud as the mean position of points that fall within the cylinder. These CoGs are projected onto the cylinder’s axis and the distance between the two is recorded. Variations in point density between point clouds are accounted for by comparing neighbourhood means inside the cylinder, and are also used in estimating a threshold for significance of the resulting change value. As an example, a lower number of points in either point cloud results in higher uncertainty.

When using M3C2, the most suitable local surface normal is derived using the scale at which the point neighbourhood is most planar. Although this vector is generally calculated on a pointwise basis and is spatially variable as a result, it remains a single, predefined input that determines the direction of change measurement. The offset between the surface normal and the direction in which movement actually occurs is, therefore, a critical determinant of both the magnitude of recorded change and the relevance of this change from a geomorphic standpoint. This is yet to be addressed by the geomorphic community, and can be considered most simply in light of the fact that most change is driven to some extent by gravity; as a surface is inclined, the gravitational component perpendicular to the surface (akin to the surface normal) decreases while the shear stress (parallel to the surface) increases. Replacing these stresses with movement direction highlights the inherent difficulties in assuming that change operates in the direction in which a surface is oriented. This is most significant where quantifying displacement is the primary objective of an analysis; a surface may be mobile, but the magnitude and extent of movement in the normal direction may be minimal (Fig. 1a–b). Movement of a failing slope, for example, is predominantly parallel to the overall slope angle, with changes in the normal direction (i.e., out of the surface) generally lower than the true displacement. Analogous to this is attempting to quantify river flow by measuring changes to the height of the water surface (Rosser et al., 2008). While movement along a perfectly planar surface would be impossible to detect, most natural surfaces contain a degree of roughness or features that are measurable by laser scanning.

The direction of surface change may vary across a point cloud, particularly where multiple types of movement occur and where these movement types may or may not be superimposed. This adds further uncertainty to measures of change along the surface normal; although these are adaptive to the local geometry around each point, they do not account for change to the subsequent point cloud. Changes at the surface of a failing hillslope, for example rockfalls, may reflect localised surface strains as well as overall sliding of the mass defined at the shear zone. Similarly, the movement of a point on a rock glacier may reflect vertical motions that result from thawing or heaving of the ice core/permafrost, as well as downslope creep. The result is that measured changes may fail to accurately reflect the direction and magnitude of displacements, as well as their variability across a point cloud. This becomes even more relevant when dealing with very large numbers of epochs (i.e., 10²–10⁵) collected from monitoring installations, such as fixed terrestrial laser scanners or cameras for time lapse photogrammetry. In such datasets, the magnitudes and directions of change obtained are highly dependent on the selection of epochs for change quantification.

We present a data-driven approach that draws on successive 3D point clouds in order to automatically ascertain the dominant movement direction (DMD) unique to each point, and the magnitude of movement along this direction. The approach is intended to provide a deeper understanding of the direction, magnitude, and spatial distribution of surface changes across a point cloud scene. The datasets examined here were acquired using both terrestrial and UAV-borne laser scanning, although we note that our method is suitable for application to point clouds derived through other means. We use three datasets, including a rockfall (a spatially discrete event), a snow avalanche (erosion and accumulation over a non-textured surface), and a rock glacier (a textured, creeping surface). For each, our results are compared to the change measured along the surface normal in order to examine the differences in movement direction and magnitude measured using both approaches.