New parameterisation method for three-dimensional otolith surface images

Abstract

The three-dimensional (3-D) otolith shapes recently included in the Anàlisi de FORmes d’Otòlits (AFORO) database are defined by means of clouds of points across their surfaces. Automatic retrieval and classification of natural objects from 3-D databases becomes a difficult and time-consuming task when the number of elements in the database becomes large. In order to simplify that task we propose a new method for compacting data from 3-D shapes. The new method has two main steps. The first is a subsampling process, the result of which can always be interpreted as a closed curve in the 3-D space by considering the retained points in an appropriate order. The subsampling preserves morphological information, but greatly reduces the number of points required to represent the shape. The second step treats the coordinates of the 3-D closed curves as periodic functions. Therefore, Fourier expansions can be applied to each coordinate, producing more information compression into a reduced set of points. The method can reach very high information compression factors. It also allows reconstruction of the 3-D points resulting from the subsampling process in the first step. This parameterisation method is able to capture 3-D information relevant to classification of fish species from their otoliths, providing a greater percentage of correctly classified specimens compared with the previous two-dimensional analysis.