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Research on Complexity Quantification Method for Multibeam Point Clouds Based on Feature Joint Entropy
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DOI：10.3390/jmse14090824.png)
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Abstract
En 中文
This study addresses the challenge of simplifying massive multibeam seafloor topographic point cloud datasets featuring significant spatial heterogeneity. We propose a feature joint entropy-based quantification method for seafloor terrain complexity, which provides a foundation for the adaptive and differentiated simplification of point clouds. In this method, the elevation and slope features of point clouds are treated as two-dimensional random variables that describe terrain morphology; we estimate the Shannon entropy of their joint distribution by constructing a two-dimensional adaptive histogram and use the entropy value to quantify the topographic information content and complexity of local regions. To overcome the parameter sensitivity and subjective dependence inherent in traditional fixed-bin methods, we incorporate the Minimum Description Length (MDL) principle to guide binning optimization, taking the sum of stochastic complexity and model coding length as the evaluation criterion. A dimension-alternating optimization strategy combining dynamic programming and an iterative greedy algorithm is adopted to solve for the optimal binning structure, thus achieving data-driven adaptive binning. To ensure the fairness and reliability of quantification, we adopt a fixed-point number partitioning strategy to decompose the point cloud into several independent analysis nodes and determine the minimum sample size supporting the stable estimation of entropy values through convergence analysis. Experimental results demonstrate that the proposed method, as a consistent and data-driven complexity metric, can reliably reflect the relative complexity of different seafloor terrain regions, thereby providing an objective quantitative basis for subsequent differentiated point cloud simplification.
Keywords:
multibeam bathymetry
complexity
joint entropy
Minimum Description Length (MDL)
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