Abstract

This paper shows the use of a specific type of time series analyses, the so named recurrence plot (RP), for investigations of the outer hull of an imaged and pre-segmented object to derive image features suitable for usage in classificators. Additionally to the features derived by the well documented recurrence quantification analysis (RQA) a new set of features was developed based on closed structures (“eyes”) in a RP. The new features were named eye structure quantification (ESQ). Two sets of images are analysed: a) 1023 in-situ plankton images comprising nine different organism classes, and b) each 50 algorithmically created geometric shapes of five different classes. These images were characterised by standard image features, RQA quantification and the newly proposed features. A Linear Discriminant Analysis (LDA) was used to determine discriminative success between the classes of plankton organisms or geometric shapes respectively. The discriminative success was compared between a model using standard features and additional RQA and ESQ. For the high intra- and low interclass variance of the plankton contour line data set the included features enhanced discriminative success by 3 % to a maximum of 65.8 %. For the data set of geometric shapes an increase of 6.8 % to 95.2 % was observed. Although the overall increase of discriminative success was not extraordinary high by using a linear model, it can be seen that both RQA and ESQ are valuable auxiliary features to split specific classes from the entire population. Thus, they may also be valuable for methods mapping the finite dimensional feature space into higher dimensional spaces (e.g. Kernel trick, Support Vector Machines).

Highlights

  • Time series are sequences of metered values

  • The advantage of a LDA is the simple access and interpretation of the feature loadings and an initial assessment of the importance of the different variables. It could be shown, that the principle of recurrence plots and subsequent analyses can be applied to contour line data of imaged and pre-segmented objects

  • A new set of features was derived by measurement of contiguous elements of given phase space dissimilarity

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Summary

Introduction

Time series are sequences of metered values. Such readings generally have a natural chronology, are non-circular and exhibit a defined start and end for the recorded time interval. Tools for the investigation of time series include a large portfolio of forecasting, estimating or classifying methods and the identification of dependencies, harmonic anomalies or recurrences. The identification of recurrences allows identifying whether the current state of a dynamic system retraces prior observed states. Eckmann et al [1] introduced a visual method to investigate such recurrences. The respective tool is the recurrence plot (RP). It uses the time delay embedding theorem (DET, [2]) to display previously encountered states in a phase space.

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