EMBC07 Curvature Feature Detection

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    Abstract Specific features of hemodynamic signals areinvaluable for elucidating ventricular and vascular function. Asemi-automatic algorithm is presented that enables accuratedetection of any feature in any hemodynamic signal, usingfeature extraction from local maxima and minima in signalcurvature. A particular feature is selected manually in the firstbeat and then detected automatically in subsequent beats.

    I. I NTRODUCTION NALYSIS of features within hemodynamic signals has become an increasingly important tool in cardiovascular

    research. Recent advances in time-domain analysis have

    revealed that detailed evaluation of ventricular or aortic pressure and flow signals, for example, provides a great dealof information about heart function and ventricular-vascularcoupling [1-3]. Other derived signals, such as wave intensity[2], require measurements on forward-running and reflectedwaves, with accurate detection of the start, peak and end ofthese waves.

    In general, a feature of a hemodynamic signal may referto a local maximum or minimum, or to a localized bend orcorner in the signal. Detection of such features can be

    performed manually by positioning vertical cursors in agraphical user interface (GUI). This method is time

    consuming, however, since in any given study there may bemany features of interest in several signals, and these must be detected in many beats. Another option is to design fullyautomatic algorithms to detect specific features. Thedrawback of this approach is that a given feature may appearunder certain physiological conditions but not others. In doseresponse-type studies, for example, features may graduallyappear or disappear and thus vary greatly in relative size [4].Designing unique and robust automatic algorithms for everytype of feature of interest is thus quite impractical.

    The aim of this study was to develop a versatile semi-automatic algorithm where automatic feature extraction isused in conjunction with manual detection of specific

    Manuscript accepted June 6, 2007. This work was supported in part byfunds from the Australia and New Zealand Childrens Heart ResearchCentre.

    J. P. Mynard is with the Heart Research Group, Murdoch ChildrensResearch Institute, Melbourne, Australia (phone: 61 3 9345 5922; fax: 61 39345 4220; e-mail: [email protected]).

    D. J. Penny, is with the Heart Research Group, Murdoch ChildrensResearch Institute, Melbourne, Australia (e-mail: [email protected])

    J. J. Smolich is with the Heart Research Group, Murdoch ChildrensResearch Institute, Melbourne,Australia(e-mail: [email protected]).

    features in hemodynamic signals. The benefits of thisapproach are threefold: 1) a single semi-automatic algorithmcan be applied to any feature of any signal; 2) although in

    part manually driven, this algorithm vastly reduces analysistime; 3) the precise location of features that may be difficultto identify visually can be determined objectively.

    The algorithm presented in this manuscript employedsignal curvature to extract features. Curvature is traditionallyused in image-processing to locate corners in an image. Ithas also been used for feature extraction in time signals suchas the electrocardiogram (ECG) [5], but has not previously

    been applied to hemodynamic signals.

    II. METHODS AND MATERIALS

    A. Semi-automatic AlgorithmThe components of the semi-automatic algorithm, which

    are displayed in the flow diagram of Fig. 1, are as follows.1) For the signal being analyzed, a set of features is

    automatically extracted (see section B) and the time and type(i.e. curvature maximum or minimum) of each feature isstored. The types of features extracted and the sensitivity ofthe detection can be set or adjusted by the user.

    2) Using a custom-designed GUI, the user is presented

    with a vertical cursor which can be positioned manually.Left- and right-arrow buttons are then used to snap the cursorto the nearest feature or to scroll through the features. Oncethe desired feature has been identified, the user clicks aNext button.

    3) The code then estimates the location of the definedfeature in the next beat using a two-step process. a) An initialestimate is obtained in one of two ways. If beat onsets have

    previously been detected, the time of the feature in the next beat is estimated to occur at the same isochrone (relative to beat onset) as the feature in the previous beat. Alternatively,if beat onsets are not known, the next feature is estimated to

    occur one heart period after the initial feature. Heart periodis calculated from the fundamental frequency of the signal,found by performing a Fast Fourier Transform (FFT) of thewhole channel and detecting the first significant spectral

    peak above the respiratory frequency range. However, ifseveral feature detections have already been confirmed, theheart period can also be estimated from the average period

    between previous detections. b) From this initial estimate,the nearest feature of the correct type is found. If the time

    between the nearest feature and the initial estimate is greater

    A Semi-Automatic Feature Detection Algorithm for HemodynamicSignals using Curvature-Based Feature Extraction

    Jonathan P. Mynard, Member, IEEE , Daniel J. Penny, and Joseph J. Smolich

    A

    Proceedings of t he 29th Annual InternationalConferenc e of the IEEE EMBSCit Internationale, Lyon, France

    Aug ust 23-26, 2007.

    FrA07.1

    1-4244-0788-5/07/$20.00 2007 IEEE 1691

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    Fig. 1. Flow diagram of the semi-automatic algorithm for feature detection.

    than a set limit, the detection is deemed to have failed. If adetection failure occurs (e.g. due to an ectopic beat or theabsence of that feature), the user is prompted to manually

    position the cursor for this beat and the next. Otherwise, step3 is repeated automatically as long as the defined feature issuccessfully located in subsequent beats.

    4) After detection in all beats is complete, the features aredisplayed with one vertical cursor for each beat. The usercan then confirm the detections visually and makeadjustments manually if needed.

    B. Feature ExtractionA feature is defined as the time of a local maximum or

    minimum in signal curvature ( ). For a function y = f(t),curvature is defined [6] as

    ( )( )2

    2

    322

    ( )

    1

    d ydt

    dydt

    t =+

    (1)

    Implementation of this equation directly on sampled dataresults in large spurious curvature peaks associated withsmall high-frequency fluctuations in the signal (see Fig. 2b).To generate a curvature signal that is less sensitive to smallfluctuations, an axis transformation was performed from t toa variable x, where

    dy dy t

    dx dt x

    =

    and

    2 2 2

    2 2 2

    d y d y t

    dx dt x

    =

    (2)

    Here t is the sample time and x is a value that results inan x-axis that is approximately orthogonal to the y-axis, i.e.on average y x or y/ x tan(45 ), where y is thechange in the signal over one sample. x is thus calculated as

    Fig. 2. Calculation of curvature for a) left-ventricular pressure using b) x= t = 0.002, c) x from the method described and d) a x 50 timesgreater.

    the median of all ys that are greater than 0.1% of themaximum y (this avoids including data segments that areeffectively flat-line in the calculation). In the resultingcurvature signal, the peaks accurately identify the timing offeatures and the magnitudes of these peaks are greater formore significant features (see Fig. 2c). Fig. 2d shows thatlarger values of x emphasize significant features further, butresult in an unacceptable loss of accuracy.

    The derivatives were calculated using the standardSavitzky-Golay filter method [7] by using fitting coefficientsof 4 th order polynomials on 5 points, where for the i-th data

    point, the k -th time derivative is given by

    !k n mik i mk k

    m n

    d y k a y

    dt t +

    ==

    (3)

    where n = 2 and mk a refers to the m-th coefficient for the k -th

    derivative. Incorporating (3) and (2) into (1) gives the finalequation which was used to generate the curvature signals:

    22

    32 2

    1

    2

    ( )

    11

    nm

    i mm n

    i

    n mi m

    m n

    a y xt

    a y x

    +=

    +=

    =

    +

    (4)

    A final step in the feature extraction was included tofurther emphasize significant features and attenuateinsignificant features without losing accuracy. This wasachieved by adjusting the amplitudes of curvature peaks

    based on the premise that the significance of a givencurvature peak is high if the time between it and the next or

    Extract Features(store timing and types)

    Automaticdetection of nextfeature failed or

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    Fig. 6. The semi-automatic algorithm applied to changing signal morphology. In the first beat, the feature was chosen by the user via the snap-to GUI.After user confirmation in the following beat, the feature was then detected automatically in all subsequent beats.

    Fig. 7. Sequential application of the semi-automatic algorithm to four different features in the first beat, with accurate detection of the same feature insubsequent beats.

    first wave and immediately following smaller negative waveof Fig. 5) or as inflection points (e.g. on the downward limbof the aortic flow signal in Fig. 4). The use of curvature thusenables accurate detection of local maxima and minima, andalso more gentle corners that are particularly difficult todetect precisely with manual techniques. This accords withthe advantage of using a curvature approach to detect thestart and end of the Q- and T-waves respectively in the ECG[5].

    Fig. 6 shows detection of a feature with changingmorphology using the semi-automatic algorithm. In the first

    beat the user-selected feature was a small local minimum.This feature was then detected automatically in the next beat,and confirmed by the user without needing adjustment. Thefeature was then detected automatically in remaining beatswithout user input. The algorithm reliably detected thisfeature in all beats even though it started as a local minimumand changed into a localized bend in later beats.

    In Fig. 7 the semi-automatic algorithm was applied 4 timesto the same signal. The user selected a different feature eachtime in the first beat, and these were all detected successfullyand automatically in the following beats.

    It is important to stress that the method described is notintended for noisy data or signals with highly variable heart

    rates, as additional adjustments to the algorithm would berequired for such signals. While we have demonstrated thatthe algorithm is robust and useful for a wide range ofapplications, further research would be required to compareit with other algorithms and to investigate specific clinicalapplications.

    IV. CONCLUSION A versatile, semi-automatic algorithm enabling extraction

    of features in hemodynamic signals via local maxima and

    minima in signal curvature has been presented. Thisalgorithm, which allows manual detection of any feature inthe first beat of a hemodynamic signal, followed byautomatic detection of this feature in subsequent beats, hasthe potential for wide applicability in time-domain analysisof hemodynamics.

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    [3] R. Kelly, C. Hayward, A. Avolio, and M. O'Rourke, "Noninvasivedetermination of age-related changes in the human arterial pulse,"Circulation , vol. 80, pp. 1652-1659, 1989.

    [4] I. B. Wilkinson, H. MacCallum, P. C. Hupperetz, C. J. van Thoor, J.R. Cockcroft, and D. J. Webb, "Changes in the derived central

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    [6] A. Rosenfeld and E. Johnston, "Angle detection on digital curves," IEEE Transactions on Computers , vol. C22, pp. 875-878, 1973.

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