Biomedical Signal Processing and Control 63 (2021) 102241 Available online 8 October 2020 1746-8094/© 2020 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc Level set segmentation with shape prior knowledge using intrinsic rotation, translation and scaling alignment ✩ Cristobal Arrieta a,b,∗ , Carlos A. Sing-Long a,b,c,d,h , Joaquin Mura a,b,e , Pablo Irarrazaval a,b,c,f , Marcelo E. Andia a,b,g , Sergio Uribe a,b,g , Cristian Tejos a,b,f a Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, Chile b ANID – Millennium Science Initiative Program – Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, Chile c Institute for Biological and Medical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Chile d Institute for Mathematical & Computational Engineering, Pontificia Universidad Catolica de Chile, Santiago, Chile e Department of Mechanical Engineering, Universidad Federico Santa Maria, Santiago, Chile f Department of Electrical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Chile g Radiology Department, School of Medicine, Pontificia Universidad Catolica de Chile, Santiago, Chile h ANID – Millennium Science Initiative Program – Millennium Nucleus for Discovery of Structure in Complex Data, Santiago, Chile ARTICLE INFO Keywords: Image segmentation Level sets Prior knowledge Pose invariance Intrinsic alignment ABSTRACT Level set segmentation has been successfully used in several image applications. However, they perform poorly when applied to severely corrupted images or when the object’s boundaries are blurred or occluded. Poor performance can be improved by introducing shape prior knowledge into the segmentation process by considering additional shape information from training examples. This can be achieved by adding a regularization term that penalizes shapes that differ from those learned from a training database. This regularizer must be invariant under translation, rotation and scaling transformations. Previous works have proposed coupling the curve evolution to a registration problem through an optimization procedure. This approach is slow and its results depend on how this optimization is implemented. An alternative approach introduced an intrinsic alignment, which normalizes each shape to be compared on a common coordinate system, avoiding the registration process. Nevertheless, the proposed intrinsic alignment considered only scaling and translation but not rotation, which is critical in several image applications. In this paper we present a new method to incorporate shape prior knowledge based on the intrinsic alignment approach, but extending it for scaling, translation and rotation invariance. Our approach uses a regularization term based on the eigenvalues and eigenvectors of the covariance matrix of each training shape, and this eigendecomposition dependency leads to a new set of evolution equations. We tested our regularizer, combined with Chan–Vese, in 2D and 3D synthetic and medical images, demonstrating the effectiveness of using shape priors with intrinsic scaling, translation and rotation alignment in different segmentation problems. 1. Introduction Image segmentation based on level set algorithms has been suc- cessfully used in several applications. It was introduced by Caselles et al. [1] as geometric active contours. This method moves a curve ✩ Funding: C.A. was partially funded by CONICYT FONDECYT Postdoctorado 2019 #3190763, CONICYT PCI REDES 180090, and ANID – Millennium Science Initiative Program – NCN17_129. C.SL. was partially funded by CONICYT Fondecyt de Iniciación #11160728, CONICYT PCI REDES 180090, ANID – Millennium Science Initiative Program – NCN17_129, and ANID – Millennium Science Initiative Program – NCN17_059. J.M. was partially funded by ANID – Millennium Science Initiative Program – NCN17_129. M.A. was partially funded by CONICYT FONDECYT #1180525 and ANID – Millennium Science Initiative Program – NCN17_129. S.U. was partially funded by CONICYT FONDECYT #1181057 and ANID – Millennium Science Initiative Program – NCN17_129. C.T. and P.I. were funded by ANID FONDECYT #1191710, ANID – PIA – ACT192064, and ANID – Millennium Science Initiative Program – NCN17_129. ∗ Corresponding author at: Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, Chile and ANID – Millennium Science Initiative Program – Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, Chile. E-mail address: ciarriet@uc.cl (C. Arrieta). URL: http://www.mri.cl (C. Arrieta). in the image to enclose an object of interest, isolating it from the background. The curve is implicitly defined as the zero level set of a signed distance function . Therefore, a point  belongs to the curve if ()=0. The motion of the curve is driven by three criteria: (i) https://doi.org/10.1016/j.bspc.2020.102241 Received 11 November 2019; Received in revised form 25 June 2020; Accepted 18 September 2020