Topological analysis of the three-dimensional radiodensity distribution of fish otoliths: Point sampling effects on dimensionality reduction

Otoliths are calcified structures found in the inner ears of teleost fish, pivotal in marine biology for studies on metabolism, age, growth, and the identification of fish stocks, potentially leading to sustainable management practices. An important feature of this structure is its density, as it corresponds to modifications in the crystalline form of calcium carbonate during the fish's lifetime, resulting in variations in its final shape. The internal and external 3D radiodensity of otoliths from different species was obtained utilizing micro-computed tomography, however, an appropriate methodology for describing and conducting comparative studies on these data appears to be absent in the current body of literature. Therefore, we study otolith density variations from 3D computed tomography images, employing the Ball Mapper technique of Topological Data Analysis. We focus on reducing the computational cost of this analysis by applying probabilistic sampling and assessing its effects on the density variations provided by the Ball Mapper graph. To determine the sample size, we used the topology to establish what we term "Topological Sample Validation", which provided the minimum resolution with the same density information as raw data. Sample representativeness was validated through non-parametric statistical tests on the density variable. Based on the network's structural characteristics, network properties allowed for evaluating similarity between graphs. Besides the small sample size, remarkable correlations were obtained between age and network variables. Additionally, the Ball Mapper technique proved effective as a preprocessing algorithm for tomographic images, enabling the segmentation of undesired features in the object of interest.