Given two neuron trees T 1 and T 2 , in (Step 1) we first map them to their respective persistence diagrams D 1 and D 2 induced by some descriptor function(s). In (Step 2), we further vectorize these persistence diagrams into persistence feature vectors, say V 1 and V 2 respectively. It is desirable that such a feature generation and vectorization process is stable in the sense that "small perturbations" in input neuronal trees and in the induced descriptor functions should only cause small changes in the distances between them. Making such a stability statement precise is not trivial, depending also on how "perturbations" are modeled and measured. While we do not yet have a full stability statement for our persistence-based feature vectors, below we discuss some partial results. We separately consider the stability for persistence diagrams (after Step-1) and that of persistence-based feature vectors (after Step-2).

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<p><strong>Abstract.</strong> Geomorphic processes occur spatially variable and at varying magnitudes, frequencies and velocities, which poses a great challenge to current methods of topographic change analysis. For the quantification of surface change, permanent terrestrial laser scanning (TLS) can generate time series of 3D point clouds at high temporal and spatial resolution. We investigate how the temporal interval influences volume change observed on a sandy beach regarding the temporal detail of the change process and the total volume budget, on which accretion and erosion counteract. We use an hourly time series of TLS point clouds acquired over six weeks in Kijkduin, the Netherlands. A raster-based approach of elevation differencing provides the volume change over time per square meter. We compare the hourly analysis to results of a three- and six-week observation period. For the larger period, a volume increase of 0.3&amp;thinsp;m³/&amp;thinsp;m² is missed on a forming sand bar before it disappears, which corresponds to half its volume. Generally, a strong relationship is shown between observation interval and observed volume change. An increase from weekly to daily observations leads to a five times larger volume change quantified in total. Another important finding is a temporally variable measurement uncertainty in the 3D time series, which follows the daily course of air temperature. Further experiments are required to fully understand the effect of atmospheric conditions on high-frequency TLS acquisition in beach environments. Continued research of 4D geospatial analysis methods will enable automatic identification of dynamic change and improve the understanding of geomorphic processes.</p>