An Approximation of Fish School Form by an Ellipse

Abstract

Time variation of fish school form is investigated for constructing a mathematical model of schooling behavior of fish. In our earlier papers, the form of fish school was approximated by an axis, and an autoregressive model was proposed to estimate the time variation of the axis length. However, the model of school axis was not sufficient for representing school form. In this paper, the form of fish scool is expressed by an ellipse. The time series data of the position of each individual swimming in a water tank is obtained from the video data by means of image processing. As an example, we observe a fish school consisting of ten individuals. Three approximation methods, i. e. probability ellipse method, four individual method and equivalent periphery ellipse method, are proposed for determining the parameters of the ellipse. Of these methods the validity of probability ellipse method is shown from the viewpoint of accuracy.