A Novel Parametric Deformable Model Based on Calculus of Variations for QRS Detection

  • Mahdi Saadatmand-Tarzjan
  • Niloofar Rashidi
  • Mozafar Iqbal
Technical Note


In this paper, a novel single-dimensional parametric deformable model based on calculus of variations is proposed for automatic QRS detection in electrocardiogram (ECG) signal. It is inspired by the active contours, conventionally used for image segmentation. Primarily, the Shannon envelop of the ECG signal is obtained by a preprocessing algorithm. The proposed parametric deformable model includes a chain of consecutive points, randomly spread along the temporal domain. These points should be collected at local maxima of the Shannon envelop. For this purpose, the proposed energy functional consists of internal and external energy terms. By minimization of the former, all model points are pushed towards the peaks of their probability density function, while by minimization of the later, every peak of the probability density function is fitted on the corresponding local maximum of the Shannon envelop. The whole energy functional is minimized, in the light of the Euler–Lagrange equation, using the gradient descend and finite difference methods. After convergence of the deformation process, for R-peak detection, it is sufficient to extract the point clusters of the optimal deformable model. Experimental results demonstrated superior/comparable performance of the proposed algorithm compared to a number of well-known methods.


Calculus of variations Euler–Lagrange equation Parametric deformable models QRS detection ECG signal 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Medical Imaging Lab, Department of Electrical Engineering, Faculty of EngineeringFerdowsi University of MashhadMashhadIran

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