Effects of 3D Images Resolution Aiming to Reveal Bone Density Variations in the Complete Structure of Otoliths
Computed microtomography; big data; proportional stratified sampling; Topological Data Analysis, Ball Mapper; Computational cost.
In this article, we present a comparative study of otolith density variations using Topological Data Analysis (TDA). Otoliths are calcified structures found in the inner ear of teleost fish, crucial in marine biology for studying metabolism, age, growth, and identifying fish stocks, leading to sustainable fisheries management practices. A relevant property of this structure is density, as it refers to modifications in the crystalline form of calcium carbonate during the fish lifetime. Aiming to reveal otolith density variations from 3D computed tomography images, we employed the Ball Mapper (BM) algorithm of TDA. To achieve computational gains in our analysis, we initially investigated how much resolution would provide density variations similar to raw data. We applied popular probabilistic sampling techniques to reduce data resolution and assessed their effects on density variations provided by BM graphs. To establish the minimum resolution, we utilized BM itself to perform what we call topological sample validation, which suggested a resolution starting from 5% of the images. The representativeness of the samples was verified through non-parametric statistical tests on the density variable. Based on the structural characteristics of the graph networks, topological invariants allowed us to assess the similarity between graphs. The 95% data reduction in otoliths substantially decreased computational time and suggests that this procedure could be useful when applying topology to higher-dimensional data analyses.