Deriving image features for autonomous classification from timeseries recurrence plots
 Jan Schulz^{1}Email author,
 Andrea Mentges^{1} and
 Oliver Zielinski^{1}
https://doi.org/10.1186/s414760160003y
© The Author(s) 2016
Received: 30 September 2015
Accepted: 30 March 2016
Published: 23 June 2016
Summary
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 presegmented 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 insitu 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).
Keywords
Background
Time series are sequences of metered values. Such readings generally have a natural chronology, are noncircular and exhibit a defined start and end for the recorded time interval. Typical examples of time series are e.g. tidal signals, meteorological observations, stock exchange quotations or cardiograms. 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.
Especially 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. Advantageously RPs using DET not only identify parity situations but also approximations to the compared template structure with given precision. Thus, a RP identifies sections of phase space trajectories that converge. The recurrence quantification analysis (RQA) comprises a set of heuristically developed methods to derive numerical characterisations of the complexity of a RP and its smallscale features (e.g. [3–5]). Here we first investigate the use of RP and RQA for automated image discrimination and apply it to the very different field of marine plankton data.
For a wide range of marine investigations it is important to chart distribution, abundance and diversity of major plankton groups and suspended material. Traditional methods include sampling the water column by nets of fine gauze and defined mouth opening. Skilled taxonomists determine and enumerate biota from aliquots under stereomicroscopes. The human eye easily gives a first taxonomic impression based on shape and habitus of an organism. Manual arrangement to best see specific morphological characteristics (e.g. bristles, setae or body appendages) further allows a more precise taxonomic identification. Even if an object cannot be determined to species level a superordinate taxonomic group membership can be assigned; often sufficient for the scientific question at hand.
During the last decades various insitu plankton imaging systems were developed. Today most of these devices are capable to sufficiently image tiny organisms or particles for detailed analyses (e.g. [6]). Although accurate species identification often fails, the major taxonomic group membership can generally be determined. Thus, these approaches add new opportunities to net samplings and have proven to be valuable tools (e.g. [7]). By this, they can partially substitute labour and costintensive net analyses and continuously map finescale distributions of dispersed objects in the water column.
However, the sheer amount of images and data face researchers with new challenges. In contrast to net samplings in situ systems deliver two dimensional still images which represent information of incident light scattered from imaged objects at arbitrary angles and spatial alignment. Although alignment can be partially controlled by fluidic design of the sampling chambers object appearances are still highly variable (e.g. clinging or abducted antenna and body appendages). To fully utilise the advantages of insitu plankton imaging systems requires sophisticated machine vision approaches aiding researchers to handle the flood of information. For this, automatic image feature extraction and classification are required that are capable to assign major group memberships in a comparable way as a human taxonomist would.
A variety of algorithms are available to extract numerical features from 2D images and their silhouettes. Standard methods are moments derived from pattern intensity variations, colour information and geometric parameters, like roundness, compactness or elliptical shape equivalents. More sophisticated methods investigate contour lines by Fourier descriptors (e.g. [8]), characteristic inflexions (e.g. [9]) or identification of points of interest in scale space (e.g. [10, 11]).
Although, such features are generally invariant to scale, rotation and translation downstream classification systems often lack high discriminatory power for plankton specimens (e.g. [12]). An important factor is the multivariate high intraclass heteroscedasticity. This high variability is a general challenge when compiling feature sets considering contour lines of plankton species. Depending on illumination, resolution, contrast and orientation the outer contour and tissues appear highly variable. This arises from onsite illumination variations and flexibility and agility of body parts and appendages. Thus, predictability of the contour line’s curve progression is comparable with dynamic systems.
Here we present an approach to apply the recurrence plot method on circular contour line data by using a modified embedding, where the contour line data are augmented by recycled elements. The resulting RP is the basis to get a first glimpse about usefulness of RQA scalars as features for automated classification systems. For comparison we used two different image sets. The first set is composed of geometric forms, while the second is compiled from images of plankton specimens and marine snow taken under arbitrary angles and showing high morphological variability.
Methods
Images
Geometric shapes
Two sets of images were used. The first is a generic set of algorithmically created geometric shapes. This data set includes 50 shapes each out of five classes: circles, ellipses, squares, rectangles and triangles (Appendix A: Fig. 4). To minimise the impact of the contour line length the shapes where chosen to have a comparable intragroup perimeter (mean 140.57, SD 1.13).
Plankton images
Taxonomic class sizes used in the analyses
Taxon/Class  #  Total # 

Annelida  50  
 Polychaeta  50  
Appendicularia  50  
 Oikopleura  50  
Bacillariophyceae  100  
 Coscinodiscales  50  
 Rhizosoleniales  50  
Cnidaria  60  
 Medusae  30  
 Siphonophora  30  
Crustacea  515  
 Amphipoda  50  50 
 Copepoda  
○ Calanidae  125  
▪ Acartia  50  
▪ Calanus  50  
▪ Calocalanus  25  
○ Cyclopoidae  50  
▪ Oithona  50  
○ Poecilostomatoida  140  
▪ Corycaeus  50  
▪ Oncaea  50  
▪ Sapphyrina  40  
 Euphausiacea  50  
○ Genera not further separated  50  
 Ostracoda  50  
○ Genera not further separated  50  
 Nauplii  50  
○ Various genera and species  50  
Dinoflagellata  45  
 Noctiluca  45  
Marine snow  150  
 Heterogeneous marine snow particles  150  
Mollusca  28  
 Gastropoda  28  
Vertebrata  25  
 Fish larvae  25  
Total  1023 
Images were sampled with the Lightframe Onsight Keyspecies Investigation (LOKI) system [6]. The advantage of the LOKI sampling design is the high contrast imaging of minute objects at high magnifications (here ~15 μm per pixel) at very short shutter times (<30 μs) in a physically constrained volume, being transparent before and behind the depth of field. Thus, the system delivers bright and detailed images of taxons that are often destroyed during traditional net samplings. Images were manually classified by declared experts of the respective plankton taxon. The images were taken from a larger subset sampled during an earlier expedition off the coast of Peru (rf. [14]) and represent major plankton classes of the onsite community.
Standard image features
Categories of numerical features extracted for each image
STANDARD  RECURRENCE QUANTIFICATION ANALYSIS (RQA)  EYE STRUCTURE QUANTIFICATION (ESQ) 

Area  Clustering coefficient  Mean eye size 
Compactness  Determinism  Median pixels of eye 
Contrast  Entropy diagonal length  Number of eyes 
Eccentricity  Laminarity  Summed pixel in eyes 
Hu1Moment  Longest diagonal length  
Homogeneity  Longest vertical length  
LengthBoundary  Mean diagonal length  
Solidity  Recurrence period density  
Recurrence rate  
Recurrence time1  
Recurrence time 2  
Transitvity  
Trapping time 
Contour line extraction and measurement
The basis for the recurrence quantification analyses thus is a list of distances u, from each contour line point to the centroid. The list is shifted in a way that the first index u (1) represents the maximum distance found; increasing indices clockwise enumerate the subsequent distances (Fig. 1b).
Embedding
Dimension m and time delay t have to be chosen properly prior to analysis. To investigate their impact several tests were performed beforehand for 1 < m ≤ 10 and 1 ≤ t ≤ 10. For the examples given in this paper m = 6; t = 6; ε = 3.0 was used. Sample plots for various parameter combinations are given in Appendix B: Figs. 5, 6 and 7.
RP  Recurrence plot
Consequently, the main diagonal of such a recurrence plot represents the distance of a point to itself and is therefore 0. Once the Heaviside step function was applied all offdiagonal nonzero entries of R indicate phase space approximations smaller than ε having a distance on the contour line of ǁijǁ.
Side diagonals parallel to the main diagonal indicate that structures of the contour line are similar in phase space. The length of the similarity structure is equivalent to the length along the axis, with the latter given distance on the contour line. Among diagonal structures coherent areas exceeding ε (name “eyes”) can be found (Fig. 1ef). These patterns within a RP represent major characteristics and are investigated in detail numerically.
RQA  Recurrence quantification analysis
Parameters of the Recurrence Quantification Analysis (RQA, Table 2) were obtained using the Cross Recurrence Plot Toolbox [5, 18]. Values transferred in the function call are the embedding vectors v (i), dimension m, time delay t, size of neighbourhood ε and norm to be used (Euclidean). A total of 13 features were extracted from each RP (Table 2). Details are given in [3–5, 19] or [20]: Clustering coefficient gives the degree to which points of the phase space trajectory tend to cluster. Determinism gives the proportion of recurrent points forming diagonals. Entropy diagonal length gives the Shannon entropy of the probability distribution of the lengths of the diagonals. Laminarity gives the amount of recurrence points forming vertical structures. Longest diagonal length gives the counted length of the longest diagonal. Longest vertical length gives the counted length of the longest vertical. Mean diagonal length gives the average length of the diagonal structures. Recurrence period density gives the periodicity of the signal in the RP. Recurrence rate gives the density of observed recurrence points in the RP. Recurrence times give an estimation of the periodicity in the RP signal. Transitivity gives the probability that two points of the phase space trajectory neighbouring a third are also directly connected. Trapping time gives the average length of the vertical structures.
ESQ  Eye structure quantification
From the recurrence plot matrix R additional features were derived. In the Eye Structure Quantification (ESQ) distribution and size of enclosed structures, the socalled ‘eyes’, were measured. Due to the circular structure of an organism’s contour line opposite sides of the RP need to be interpreted as connected structures. Thus, eyes truncated at the borders of R have to be associated with their counterpart on the opposite side prior to evaluation (Fig. 1g). After identification of associated eyes, the total number of eyes, mean number of pixels per eye (e.g. mean eye size), the median of the numbers of pixels per eye, and total number of pixels in all eyes were determined. Increasing eye numbers generally indicate, that a high number of independent features recurrences in phase space are found. These are often associated with repetitive morphological structures of the object, like polychaete parapodia, silica spicules or regular diatom frustule indentations.
LDA  Linear discriminant analysis
Feature combinations used for the different LDA models
LDA setup  Included features 

1  STANDARD 
2  RQA 
3  STANDARD & RQA 
4  STANDARD & RQA & ESQ 

Coefficients of linear discriminant roots. These values represent the loadings and thus, importance of the individual features during discrimination.

Proportions of trace. These values give the variance explained by the respective root. As explained variance decreases with each successive root we give just the first roots in this paper; although for some LDA’s more roots could be given (number of roots equals number of objects or number of included features minus one; whatever is lower).

Confusion matrices. They show the rate of true positive and false positive classifications.

From the coefficients of linear discriminants, the most important features were identified that best separate objects by the respective root. A feature was considered to be important when it’s loading reached at least 10 % of the maximum feature loading on either side of a root’s spanned hyperplane.

Canonical scores. The scores of the individual objects were plotted to visualise the discriminative success among object classes for the respective roots.
Computational work
Image processing and feature extraction (RQA, ESQ) were performed in Matlab (MathWorks, 2013, v8.1.0.604). The LDA models were implemented in R (www.rproject.org), using the additional package MASS.
Results
LDA  Linear Discriminant Analysis
Geometric shapes
Standard
LDA Geometric shapes
STANDARD  LD1  LD2  LD3  LD4 

Area  −6.9626 e05  2.3917 e05  1.9991e04  3.4263e04 
Compact  −1.1407 e + 01  2.8052 e + 01  −1.0988 e + 01  −1.2826 e + 01 
Contrast  −1.4711 e06  −4.2640 e07  8.6186 e06  −3.2337 e05 
Eccentricity  −9.6114 e + 00  2.4681 e + 00  5.3053 e01  −1.1433 e + 00 
HU1  6.7315 e + 00  −1.1663 e + 01  −6.4077 e + 01  1.4417 e + 01 
Homogeneity  3.4927 e + 00  2.7952 e + 01  −7.0628 e + 01  1.7027 e + 00 
LengthBoundary  4.2602 e03  2.8937 e04  −2.5557 e02  −1.6500 e02 
Solidity  9.4545 e + 00  −3.9641 e + 01  1.4252 e + 01  3.5592 e + 01 
Proportion of Trace  0.7258  0.2602  0.0105  0.0035 
LDA Geometric shapes
STANDARD  Circle  Ellipse  Rectangle  Square  Triangle  Prediction success 

Circle  50  0  0  0  0  1.00 
Ellipse  0  45  0  5  0  0.90 
Rectangle  0  0  50  0  0  1.00 
Square  1  6  1  37  5  0.74 
Triangle  0  0  7  4  39  0.78 
Model  0.884  
RQA  
Circle  47  0  3  0  0  0.94 
Ellipse  0  41  0  6  3  0.82 
Rectangle  1  0  48  1  0  0.96 
Square  1  10  6  31  2  0.62 
Triangle  1  5  0  2  42  0.84 
Model  0.836  
STANDARD & RQA  
Circle  50  0  0  0  0  1.00 
Ellipse  0  46  0  4  0  0.94 
Rectangle  0  0  50  0  0  1.00 
Square  1  1  2  43  3  0.88 
Triangle  0  0  0  0  50  1.00 
Model  0.956  
STANDARD & RQA & ESQ  
Circle  50  0  0  0  0  1.00 
Ellipse  0  46  0  4  0  0.92 
Rectangle  0  4  49  1  0  0.90 
Square  1  3  1  43  2  0.86 
Triangle  0  0  0  0  50  1.00 
Model  0.952 
RQA
LDA Geometric shapes
RQA  LD1  LD2  LD3  LD4 

Clustering coefficient  −3.3203 e02  −7.3117 e + 01  −2.8931 e + 01  −6.0119 e + 01 
Determinism  1.4724 e + 02  −4.3258 e + 01  2.0517 e + 01  6.1069 e + 01 
Entropy Diagonal Length  1.5459 e + 00  7.7545 e01  9.2093 e01  −1.4666 e + 00 
Laminarity  −2.8086 e + 02  1.0565 e + 01  1.1170 e + 00  −2.3284 e + 02 
Longest Diagonal Length  −2.2921 e02  1.2801 e02  −1.7178 e02  −5.2463 e03 
Longest Vertical Length  −9.7082 e03  −1.7140 e03  5.9098 e03  2.1794 e03 
Mean Diagonal Length  −2.2354 e01  2.4054 e02  −2.8575 e02  −3.5738 e01 
Recurrence Period Density  −1.6803 e + 00  5.0734 e + 00  4.5539 e + 00  7.5552 e + 00 
Recurrence Rate  1.2637 e + 01  −6.0927 e + 00  1.3810 e + 01  −6.1760 e + 01 
Recurrence Time1  −1.8844 e + 01  6.3186 e + 01  3.1819 e + 01  −1.8392 e + 01 
Recurrence Time2  6.3736 e02  −1.7368 e01  5.0725 e02  −1.7492 e01 
Transitivity  −3.3545 e + 01  1.0021 e + 02  7.0535 e + 01  5.9794 e + 01 
Trapping Time  2.6801 e01  1.3032 e01  −7.1610 e03  6.1896 e01 
Proportion of Trace  0.7342  0.1413  0.0918  0.0327 
Standard & RQA
LDA Geometric shapes
STANDARD & RQA  LD1  LD2  LD3  LD4 

Area  −5,9401E05  −1,9400E04  −6,2879E05  1,0076E04 
Compact  3,5423E + 00  −2,5172E + 01  1,1080E + 01  9,1550E01 
Contrast  2,9356E06  −4,7963E06  −2,9805E06  −6,5782E06 
Eccentricity  7,2951E + 00  −6,3447E + 00  −2,1702E + 00  −9,3084E01 
HU1  1,5031E + 01  5,4044E + 01  1,4604E + 01  −1,5518E + 01 
Homogeneity  −1,4477E + 01  −2,6754E + 01  1,4672E01  −3,4403E + 00 
LengthBoundary  −2,5076E03  1,1792E02  −1,6241E03  −2,6010E03 
Solidity  1,4425E + 00  3,5392E + 01  −1,7666E + 01  3,9915E + 00 
Clustering coefficient  −2,6156E + 01  −2,8633E + 01  −3,7726E + 01  −7,8372E + 00 
Determinism  1,5009E + 01  −7,2239E + 01  8,2244E + 01  5,3571E + 01 
Entropy diagonal length  1,1423E + 00  2,3649E + 00  1,8728E + 00  −1,3749E + 00 
Laminarity  −5,2600E + 01  7,8644E + 01  −1,4305E + 02  −2,0549E + 02 
Longest diagonal length  −2,5076E03  1,1792E02  −1,6241E03  −2,6010E03 
Longest vertical length  −5,8332E03  −6,5336E03  −4,0279E03  −4,7670E03 
Mean diagonal length  −2,0581E01  −9,1709E02  −1,3184E01  −1,6458E01 
Period density  5,9440E01  −4,4322E + 00  3,2363E + 00  2,4944E + 00 
Recurrence rate  3,3347E + 01  1,4299E + 01  −1,5627E + 01  −4,9725E + 01 
RecurrenceTime1  4,3389E + 00  2,6093E + 00  −1,1137E + 00  −4,4655E + 01 
RecurrenceTime2  1,2758E02  −1,2454E01  −7,1585E02  −1,0382E01 
Transitivity  1,9919E + 01  4,1271E + 01  5,6892E + 01  −3,2801E + 01 
TrappingTime  2,4661E01  2,3180E01  2,6364E01  3,2499E01 
Proportion of Trace  0.5982  0.3163  0.0532  0.0323 
Standard, RQA & ESQ
LDA Geometric shapes
STANDARD, RQA & ESQ  LD1  LD2  LD3  LD4 

Area  −1.1784 e04  −1.9232 e04  −1.1059 e04  1.9359 e04 
Compact  3.4301 e + 00  −2.5118 e + 01  1.1435 e + 01  2.4919 e + 00 
Contrast  1.5530 e06  −3.7785 e06  −5.2896 e06  −3.2900 e06 
Eccentricity  7.7392 e + 00  −6.2394 e + 00  −2.3488 e + 00  −5.5377 e01 
HU1  −1.1736 e + 01  5.6397 e + 01  1.5916 e + 01  1.0685 e + 01 
Homogeneity  −1.7666 e + 01  −2.6344 e + 01  1.4941 e + 00  −2.1289 e + 00 
Length Boundary  −1.7489 e02  1.2571 e02  −5.3791 e03  1.4207 e02 
Solidity  −1.4304 e + 00  3.5787 e + 01  −1.9367 e + 01  4.7933 e + 00 
Clustering Coefficient  −3.6658 e + 01  −2.5735 e + 01  −3.8500 e + 01  −7.0815 e + 00 
Determinism  2.5800 e + 01  −8.5462 e + 01  9.3743 e + 01  5.6418 e + 01 
Entropy diagonal Length  1.2321 e + 00  2.4068 e + 00  2.1062 e + 00  −1.3100 e + 00 
Laminarity  −3.7915 e + 01  1.0449 e + 02  −1.6604 e + 02  −2.3688 e + 02 
Longest diagonal Length  −1.7489 e02  1.2571 e02  −5.3791 e03  1.4207 e02 
Longest vertical Length  −6.1717 e03  −7.0950 e03  −4.9047 e03  −3.3528 e03 
Mean diagonal Length  −2.0822 e01  −7.9261 e02  −9.9609 e02  −2.1448 e01 
Recurrence period density  7.2700 e01  −5.8102 e + 00  3.4804 e + 00  4.6755 e + 00 
Recurrence rate  4.2988 e + 01  1.4841 e + 01  −1.8897 e + 01  −4.9004 e + 01 
Recurrence time1  7.8288 e + 00  3.4506 e + 00  2.8467 e + 00  −4.5792 e + 01 
Recurrence time2  1.3043 e02  −1.1242 e01  −4.3600 e02  −1.3724 e01 
Transitivity  3.0299 e + 01  4.0309 e + 01  6.5165 e + 01  −3.5768 e + 01 
Trapping time  2.7737 e01  2.1055 e01  2.2561 e01  3.5996 e01 
Mean size eyes  −5.0701 e04  −5.3573 e05  −1.5723 e04  3.5322 e04 
Median pixels in eyes  3.2251 e04  −4.0013 e05  −4.4404 e05  1.2952 e04 
Num eyes  2.0862 e03  −3.9122 e03  8.4803 e03  −1.8939 e03 
Sum pixels in eyes  1.3377 e04  −1.0762 e06  4.1416 e05  −1.6796 e04 
Proportion of Trace  0.6232  0.2984  0.0490  0.0294 
Plankton images
Standard
LDA Plankton images
STANDARD  LD1  LD2  LD3  LD4 

Area  9,5536E06  1,2253E05  −2,0796E05  2,2256E05 
Compact  3,5030E + 00  −1,7440E + 00  7,3339E + 00  8,8077E + 00 
Contrast  −6,3512E06  −2,5975E06  1,8473E05  −1,3421E05 
Eccentricity  −4,2015E + 00  1,7316E + 00  1,6618E + 00  −1,1651E + 00 
HU1  8,9741E + 02  2,9666E + 02  4,1634E + 01  −2,2460E + 02 
Homogeneity  −9,5771E + 00  −2,1946E + 01  −6,0204E + 00  −1,8834E + 01 
Length boundary  −5,3401E04  −5,7619E04  −8,0676E04  7,3831E04 
Solidity  1,6513E + 00  −8,8657E01  −8,2544E + 00  −8,1160E + 00 
Proportion of Trace  0.5193  0.2897  0.1026  0.0534 
LDA Plankton images
STANDARD  Annelida  Appendicularia  Bacillariophyceae  Cnidaria  Crustacea  Dinoflagellata  Marine snow  Mollusca  Vertebrata  Prediction success 

Annelida  15  1  0  2  30  0  0  0  2  0.30 
Appendicularia  0  37  0  0  8  1  0  0  4  0.74 
Bacillariophyceae  0  0  34  0  8  16  37  5  0  0.34 
Cnidaria  8  9  0  29  8  2  3  1  0  0.48 
Crustacea  21  2  6  4  455  0  15  4  3  0.89 
Dinoflagellata  0  1  3  0  0  38  0  3  0  0.84 
Marine snow  4  2  23  0  103  0  18  0  0  0.12 
Mollusca  0  0  8  0  6  3  2  9  0  0.32 
Vertebrata  3  10  0  0  8  0  0  0  4  0.16 
Model  0.628  
RQA  
Annelida  5  1  0  15  29  0  0  0  0  0.10 
Appendicularia  0  24  0  0  23  0  0  0  3  0.48 
Bacillariophyceae  0  0  35  0  22  26  12  5  0  0.35 
Cnidaria  6  2  0  13  33  0  0  0  6  0.22 
Crustacea  7  6  10  16  432  0  28  0  11  0.85 
Dinoflagellata  0  0  12  0  6  22  4  1  0  0.49 
Marine snow  0  0  14  3  107  8  17  1  0  0.11 
Mollusca  0  0  4  0  19  2  3  0  0  0.00 
Vertebrata  0  8  0  1  4  0  0  0  12  0.48 
Model  0.550  
STANDARD & RQA  
Annelida  22  1  0  3  24  0  0  0  0  0.44 
Appendicularia  0  39  0  0  6  0  0  0  5  0.78 
Bacillariophyceae  1  0  48  0  3  20  20  8  0  0.48 
Cnidaria  10  1  1  39  5  0  1  2  1  0.65 
Crustacea  18  3  6  2  437  0  33  7  4  0.86 
Dinoflagellata  0  1  3  0  0  34  0  7  0  0.76 
Marine snow  2  2  20  1  86  1  33  5  0  0.22 
Mollusca  0  0  5  0  6  2  4  11  0  0.39 
Vertebrata  1  7  0  0  7  0  0  0  10  0.40 
Model  0.661  
STANDARD & RQA & ESQ  
Annelida  24  1  0  3  22  0  0  0  0  0.48 
Appendicularia  0  40  0  0  5  0  0  0  5  0.80 
Bacillariophyceae  1  0  47  0  2  21  22  7  0  0.47 
Cnidaria  6  1  0  36  6  0  4  4  3  0.60 
Crustacea  19  4  5  2  436  0  30  7  7  0.85 
Dinoflagellata  0  1  3  0  0  33  0  8  0  0.73 
Marine snow  2  2  19  1  89  1  31  5  0  0.20 
Mollusca  0  0  4  0  5  2  5  12  0  0.43 
Vertebrata  1  7  0  0  6  0  0  0  11  0.44 
Model  0.658 
RQA
LDA Plankton images
RQA  LD1  LD2  LD3  LD4 

Clustering coefficient  9,1646E + 00  1,9776E + 01  −3,6456E + 01  −1,1311E + 01 
Determinism  1,2212E + 02  1,3704E + 01  9,8008E + 01  8,7217E + 01 
Entropy diagonal length  4,7223E01  −2,2824E + 00  3,7802E02  1,0338E + 00 
Laminarity  −1,6675E + 02  3,8020E + 01  −1,5864E + 02  −2,2712E + 02 
Longest diagonal length  −2,2621E04  −5,7530E04  −8,2800E04  3,0824E04 
Longest vertical length  −4,4431E04  2,7945E03  4,2438E03  −3,9008E03 
Mean diagonal length  1,2616E02  1,0422E01  −1,3931E02  5,9189E02 
Recurrence period density  4,0592E + 00  5,9616E + 00  1,3806E + 00  −4,4946E + 00 
Recurrence rate  6,6090E + 00  1,0217E + 01  −6,5513E + 00  8,8718E + 00 
Recurrence time1  −1,5261E + 00  1,6415E + 00  −5,5278E + 00  9,3753E01 
Recurrence time2  −5,3167E03  −4,8862E03  2,3380E02  5,0237E02 
Transitivity  −1,7820E + 01  −1,1284E + 01  1,6588E + 01  2,1919E + 00 
Trapping time  2,4517E03  −8,2911E02  −4,2520E02  −1,3478E01 
Proportion of Trace  0.6066  0.1977  0.1317  0.0281 
Standard, RQA
LDA Plankton images
STANDARD & RQA  LD1  LD2  LD3  LD4 

Area  8,3468E06  −8,5546E06  2,3240E05  1,2083E05 
Compact  2,8489E + 00  −1,1584E + 00  −6,0993E01  1,1657E + 01 
Contrast  −4,3517E06  4,8338E07  −1,6700E05  −4,2536E06 
Eccentricity  −3,3070E + 00  −5,1458E01  −2,8622E01  −1,9799E + 00 
HU1  8,1832E + 02  −3,9860E + 02  1,5677E + 02  −7,3236E + 00 
Homogeneity  −1,0228E + 01  1,1102E + 01  6,8220E + 00  −7,5339E01 
Length boundary  −2,0340E04  2,1637E04  6,8411E04  2,4935E04 
Solidity  1,7137E + 00  1,7562E + 00  4,4218E + 00  −7,7258E + 00 
Clustering coefficient  6,8073E + 00  −1,8136E + 01  −4,4149E01  −1,8076E + 01 
Determinism  −6,0420E + 01  −6,0060E + 01  8,9124E + 00  7,5204E + 01 
Entropy Diagonal length  −1,2037E01  6,6271E01  2,2168E + 00  8,3095E01 
Laminarity  8,1272E + 01  6,4581E + 01  −5,1721E + 01  −1,3652E + 02 
Longest diagonal length  −2,0340E04  2,1637E04  6,8411E04  2,4935E04 
Longest vertical length  4,4576E04  −5,3818E04  −5,0247E03  4,8416E04 
Mean diagonal length  −7,4275E04  −3,6588E02  −6,5053E02  −2,0883E02 
Recurrence period density  −6,5591E01  −4,1900E + 00  −3,3693E + 00  3,1853E + 00 
Recurrence rate  −3,1627E + 00  −9,4214E + 00  1,2058E + 00  3,9744E + 00 
Recurrence time1  1,7024E + 00  −4,0523E01  8,3799E01  −1,7335E + 00 
Recurrence time2  −1,2678E02  1,3795E02  −1,1402E02  −2,7078E04 
Transitivity  3,2961E + 00  1,7547E + 01  −6,0033E + 00  6,6110E + 00 
Trapping time  1,9478E02  8,2368E03  8,0562E02  1,2844E02 
Proportion of Trace  0.4158  0.3135  0.1500  0.0578 
Standard, RQA, ESQ
LDA Plankton images
STANDARD, RQA & ESQ  LD1  LD2  LD3  LD4 

Area  7,9128E06  −7,4814E06  −2,0536E05  −1,9393E05 
Compact  3,5193E + 00  −1,9512E + 00  5,9329E01  −1,1089E + 01 
Contrast  −4,0052E06  −2,7805E06  1,3528E05  7,4554E06 
Eccentricity  −3,0145E + 00  −1,2020E + 00  1,3014E01  1,6067E + 00 
HU1  8,3916E + 02  −3,0765E + 02  −8,7893E + 01  −7,9133E + 01 
Homogeneity  −1,0727E + 01  7,8797E + 00  −8,9586E + 00  7,7979E01 
Length boundary  −4,6620E04  −6,1266E04  −1,4366E03  1,3844E04 
Solidity  1,1912E + 00  2,3733E + 00  −4,3375E + 00  6,8645E + 00 
Clustering coefficient  7,3574E + 00  −1,4573E + 01  3,1754E + 00  1,7005E + 01 
Determinism  −6,7257E + 01  −5,9122E + 01  −6,8447E + 00  −6,9468E + 01 
Entropy diagonal length  −1,0037E01  9,8246E01  −1,8145E + 00  −1,1907E + 00 
Laminarity  9,4881E + 01  5,1073E + 01  4,1259E + 01  1,2378E + 02 
Longest diagonal length  −4,6620E04  −6,1266E04  −1,4366E03  1,3844E04 
Longest vertical length  6,7974E04  −4,3464E04  5,0085E03  −1,0819E04 
Mean diagonal length  4,3436E03  −4,0438E02  6,0747E02  3,6780E02 
Recurrence period density  −1,3176E01  −4,2263E + 00  3,7156E + 00  −3,2918E + 00 
Recurrence rate  −3,2024E + 00  −5,5922E + 00  2,4596E + 00  −7,2368E + 00 
Recurrence time1  1,6874E + 00  7,3116E01  2,1852E02  8,4096E01 
Recurrence time2  −1,1802E02  1,0745E02  7,7042E03  9,9184E03 
Transitivity  2,8574E + 00  1,4969E + 01  2,9577E + 00  −5,0812E + 00 
Trapping time  1,6490E02  1,3611E02  −7,2016E02  −3,7084E02 
Mean size eyes  −5,7648E06  1,3136E05  8,6921E06  −2,4460E05 
Median pixels in eyes  5,2174E06  −9,6114E06  −3,9947E06  1,2096E05 
Num eyes  5,3709E03  −2,6717E03  2,0588E03  −5,2218E03 
Sum pixels in eyes  1,4634E07  6,8848E07  6,0735E07  −1,2721E07 
Proportion of Trace  0.4015  0.3218  0.1488  0.0600 
Importance of the image features
Geometric shapes
LDA Geometric shapes
Analyses  Hyperplane side  LD1  LD2  LD3  LD4 

STANDARD     Compact   HU1   Compact   Compact 
 Eccentricity   Solidity   HU1   HU1  
+   HU1   Compact   Solidity   Solidity  
 Homogeneity   Homogeneity  
RQA     Laminarity   Clustering coefficient   Clustering coefficient   Clustering coefficient 
 Transitivity   Determinism   Laminarity  
 Recurrence rate  
+   Determinism   Laminarity   Recurrence time 1   Determinism  
 Transitivity   Determinism   Recurrence period density  
 Recurrence Rate   Transitivity  
 Transitivity  
STANDARD & RQA     Homogeneity   Determinism   Solidity   Recurrence rate 
 Clustering coefficient   Compact   Recurrence rate   Transitivity  
 Laminarity   Homogeneity   Clustering coefficient   Laminarity  
 Clustering coefficient   Laminarity   Recurrence time 1  
+   Eccentricity   HU1   Determinism   Determinism  
 Determinism   Solidity   Compact  
 Compact   Recurrence rate   HU1  
 HU1   Transitivity   Transitivity  
 Recurrence rate   Laminarity  
 Transitivity  
 Recurrence Time 1  
STANDARD & RQA & ESQ     HU1   Determinism   Solidity   Recurrence rate 
 Homogeneity   Compact   Recurrence rate   Transitivity  
 Clustering coefficient   Homogeneity   Clustering coefficient   Laminarity  
 Laminarity   Clustering coefficient   Laminarity   Recurrence Time 1  
+   Eccentricity   HU1   Determinism   Determinism  
 Determinism   Solidity   Compact   HU1  
 Recurrence rate   Recurrence rate   HU1  
 Transitivity   Transitivity   Transitivity  
 Recurrence time 1   Laminarity 
Plankton Images
LDA Plankton images
Analyses  Hyperplane side  LD1  LD2  LD3  LD4 

STANDARD     Eccentricity   Homogeneity   Homogeneity   HU1 
 Homogeneity  
+   HU1   HU1   Compact   Compact  
 HU1  
RQA     Laminarity   Entropy Diagonal length   Clustering coefficient   Laminarity 
 Transitivity   Transitivity   Laminarity  
+   Determinism   Clustering coefficient   Determinism   Determinism  
 Laminarity   Transitivity   Recurrence rate  
 Recurrence period density  
 Determinism  
 Recurrence rate  
STANDARD & RQA     Determinism   Determinism   Transitivity   Clustering coefficient 
 Homogeneity   HU1   Laminarity   Laminarity  
+   HU1   Homogeneity   HU1   Determinism  
 Transitivity   Compact  
 Laminarity  
STANDARD & RQA & ESQ     Determinism   Determinism    HU1   Determinism 
 Homogeneity   HU1   Homogeneity   HU1  
 Compact  
+   HU1   Transitivity   Laminarity   Clustering coefficient  
 Laminarity   Laminarity   Laminarity  
 Homogeneity 
Discussion
Method
The first principle task of this study was to apply the wellestablished methods of Recurrence Plots (RP) and Recurrence Quantification Analysis (RQA) in the new context of circular contour line data of an imaged object’s outer hull. To set up the circular contour line data for the proposed methods, each point of the contour line was enumerated and its distance to an arbitrary point was calculated. This arbitrary reference point was static. In contrast to traditional RP and RQA investigations, we augmented the contour line distance data during the embedding process. Thus, the distance data are recycled to allow creating a number of embedding vectors equal to the number of contour lines points. By this, opposite sides of the RP wrap up. This allowed the introduction of the eye structure quantification (ESQ).
Image discrimination
The second principle task was to perform an initial test of these methods on both real life plankton data of high contour line variability and a synthetic sample data with similar intraclass structure and symmetry.
The multivariate analyses revealed that neither RQA nor RQA & ESQ are well suited as exclusive features for the classification task at hand. Nevertheless, used in combination with the STANDARD features, they increased discrimination success.
An important feature of the STANDARD feature class was the HU1moment, which is scale and transformation invariant. Therefore it is able to describe the characteristic shape of an organism irrespective to camera rotation in plane view or magnification. One of the key features of the RQA was the Recurrence rate, which simply gives the density of observed recurrences indicating the degree to which the organism’s contour line exhibits repetitions of similar structures (e.g. polychaete parapodia). It is thus a measure of the structural regularity of the organism. The key RQA features Laminarity and Determinism focus on the vertical and diagonal structures. These two features have been shown before to be some of the most characteristic properties of an RP (details on RQA and how to read an RP can be found in [20]). They characterise diagonals and vertical lines and thus, length and type of contour line segment similarity. The key feature Transitivity further gives a probability on the phase space neighbourhood situation.
As successive roots explain less of the observed variance, the general discrimination success is often identified by plotting the scores of the first roots (Figs. 2 and 3). Within the plots better clustering of objects of the same class and better separation among classes mean a higher discrimination success. The ability to discriminate between classes of similar shape structure can be improved by using RQA parameters. There is also an indication, that the use of ESQ can further improve discrimination between objects of different size classes and regularity (e.g. Appendicularians and Vertebrata vs. Crustaceans), but does not improve general classification. However, these improvements can be used to separate at least 1–2 classes from the entire population. After excluding identified classes a downstream model with less classes allows improving discrimination during the next iterations.
Study design
This study is a first conceptual approach to introduce and test the general usability of RQA and ESQ feature sets for image classification. In the overview presented here, some pretests and verifications (e.g. [24]) have been intentionally neglected and the approach was directly applied to a highly diverse plankton set. Criticisms may include, that objects were analysed by using a ‘onefitsall’ embedding approach and analysed diagonal/vertical line length histograms for several features included lengths as low as 2 recurrence points. Nevertheless, it was found that classificatory systems can benefit from the use of RQA features. Thus, this paper primarily sketches out the method and gives first examples how to use it. We assume that the ESQ features gain higher importance with decreasing neighbourhood threshold ε. Thus, future work needs to focus on avoidance of potential problems and consideration of specific adaptations. In detail it seems appropriate to use recurrence analyses with RQA and ESQ specifically in tailored models, to first split distinct classes from the image population. In succeeding steps then better customised RQA and ESQ with adjusted values for m, t and e can be used.
It is also obvious that some of the included features, especially those that characterise textural properties, are barely sufficient for proper discrimination of the geometrical line art shapes. Respectively the parameter Contrast showed negligible loadings (Table 4, Tables 6 and 7). However, to date these features are important in automated plankton discrimination and often appear to be among the most important ones in plankton discrimination [12].
It is also clear that Linear Discriminant Analysis is not the most powerful classificatory system available for such multivariate data. As an LDA tries to insert separating hyperplanes in a dimensional space that is defined by the number of given variables, linear classifications often fail. Especially for low inter and high intraclass variances, as generally expected for insitu plankton images, it is recommended to apply methods for mapping input features into higher dimensional spaces, using the kernel trick (e.g. Support Vector Machines). However, the advantage of a LDA is the simple access and interpretation of the feature loadings and thus an initial assessment of the importance of the different variables.
Conclusions
It could be shown, that the principle of recurrence plots and subsequent analyses can be applied to contour line data of imaged and presegmented objects. The tailored embedding algorithm enabled our application to derive new image features for automated classification systems of plankton organisms. Additionally, a new set of features was derived by measurement of contiguous elements of given phase space dissimilarity (eyestructures in the recurrence plots).
The discriminative success of the LDA was enhanced by using a combination of standard image features, recurrence quantification analysis features and the newly proposed eyesize features. This improvement was observed both for the synthetic data set of geometric and the realworld phytoplankton images. The characterization of images by recurrence quantification analysis and eye structure quantification offers auxiliary image features that could not be derived by applying standard image features alone. We recommend the use of the standard features in combination with the features derived from the application of recurrence analysis to discriminate between classes of phytoplankton. With further improvements the class of such methods may further improve automated plankton identification, which represents an important step forward in the effective processing of large numbers of underwater images and autonomous monitoring stations.
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 Eckmann, J.P., Kamphorst, S.O., Ruelle, D.: Recurrence Plots of Dynamical Systems. Europhys. Lett. 4, 973–977 (1987)ADSView ArticleGoogle Scholar
 F. Takens, “Detecting strange attractors in turbulence” in Lecture Notes in Mathematics, David Rand, and LaiSang Young, ed., 366–381 (Springer, Warwick, 1981). doi://101007BFb0091924.Google Scholar
 J. P. Zbilut and C. L. Webber, “Embeddings and delays as derived from quantification of recurrence plots” Physics Letters A 171, 199–203 (1992). doi://10.1016/03759601(92)90426M.
 Webber, C.L., Zbilut, J.P.: Dynamical assessment of physiological systems and states using recurrence plot strategies”. J. Appl. Physiol. 76, 965–973 (1994)Google Scholar
 N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, and J. Kurths “Recurrenceplotbased measures of complexity and their application to heartratevariability data” Physical Review E 66, 026702 (2002). doi://10.1103/PhysRevE.66.026702.
 Schulz, J., Barz, K., Ayon, P., Lüdtke, A., Zielinski, O., Mengedoht, D., Hirche, H.J.: Imaging of plankton specimens with the Lightframe Onsight Keyspecies Investigation (LOKI) system”. J. Eur. Opt. Soc. Rapid Publ 5, 10017s (2010)View ArticleGoogle Scholar
 MacLeod, N., Benfield, M.C., Culverhouse, P.F.: Time to automate identification. Nature 467, 154–155 (2010)ADSView ArticleGoogle Scholar
 Persoon, E., Fu, K.S.: Shape discrimination using Fourier descriptors. IEEE Trans. Syst. Man Cybern. 7, 170–179 (1977)MathSciNetView ArticleGoogle Scholar
 Mokhtarian, F.: SilhouetteBased Isolated Object Recognition through Curvature Scale Space. IEEE Trans. Pattern Anal. Mach. Intell. 17, 539–544 (1995)View ArticleGoogle Scholar
 D.G. Lowe “Object recognition from local scaleinvariant features” Proceedings of the International Conference on Computer Vision 2, 1150–1157 (1999). doi://10.1109/ICCV.1999.790410.
 Bay, H., Tuytelaars, T., Van Gool, L.: SURF – Speeded Up Robust Features. In: Leonardis, A., Bischof, H., Axel, P. (eds.) Computer Vision – ECCV 2006, pp. 404–417. Springer Verlag, Berlin Heidelberg (2006)View ArticleGoogle Scholar
 Hu, Q.: “Application of statistical learning theory to plankton image analysis” PhD Thesis Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, Supervisors: Cabell S. Davis and Hanumant Singh. (2006)View ArticleGoogle Scholar
 J. Schulz, K. Barz, P. Ayon, and H.J. Hirche “A sample data set of plankton and particles for automated image classification systems sampled off the Peruvian coast” Pangaea Data Publisher System for Earth & Environmental Science, Registration in progress.Google Scholar
 H.J. Hirche, K. Barz, P. Ayón, and J. Schulz “High resolution vertical distribution of the copepod Calanus chilensis in relation to the shallow oxygen minimum zone off northern Peru using LOKI, a new plankton imaging system” Deep Sea Research Part I 88, 63–73 (2014). doi://10.1016/j.dsr.2014.03.00.
 Patton, D.R.: A Diversity Index for Quantifying Habitat Edge. Wildl. Soc. Bull. 3, 171–173 (1975)Google Scholar
 Hu, M.K.: Visual Pattern Recognition by Moment Invariants. IRE Trans. Inf. Theory IT8, 179–187 (1962)MATHGoogle Scholar
 Gonzalez, R.C., Woods, R.E., Eddins, S.L.: “Script: invmoments” Digital Image Processing Using MATLAB, Revision: 1.5, Date: 2003/11/21 14:39:19, PrenticeHall. (2004)Google Scholar
 Marwan, N. “Cross Recurrence Plot Toolbox for Matlab, Reference Manual. Version 5.17, Release 28.16” http://tocsy.pikpotsdam.de/CRPtoolbox/.
 J. Gao, and H. Cai, “On the structures and quantification of recurrence plots”. Physical. Letters, A 270, 75–87, doi://10.1016/S03759601(00)003042
 Webber, C.L., Marwan, N.: Recurrence Quantification Analysis (Springer International Publishing. (2015)Google Scholar
 Fisher, R.A.: The utilization of multiple measurements in taxonomic problems. Ann. Eugenics 7, 179–188 (1936)View ArticleGoogle Scholar
 Jennrich, R.I.: Stepwise regression. In: Enslein, K., Ralston, A., Wilf, H.S. (eds.) Statistical Methods for Digital Computers. Wiley, New York (1977)Google Scholar
 Jennrich, R.I.: Stepwise discriminant analysis”. In: Enslein, K., Ralston, A., Wilf, H.S. (eds.) Statistical Methods for Digital Computers. Wiley, New York (1977)Google Scholar
 Marwan, N.: How to avoid potential pitfalls in recurrence plot based data analysis. Int. J. Bifurcation Chaos 21, 1003–1017 (2011)ADSMathSciNetView ArticleMATHGoogle Scholar