Convex Non-Convex Segmentation over Surfaces

  • Martin Huska
  • Alessandro Lanza
  • Serena MorigiEmail author
  • Fiorella Sgallari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)


The paper addresses the segmentation of real-valued functions having values on a complete, connected, 2-manifold embedded in \({{\mathbb {R}}}^3\). We present a three-stage segmentation algorithm that first computes a piecewise smooth multi-phase partition function, then applies clusterization on its values, and finally tracks the boundary curves to obtain the segmentation on the manifold. The proposed formulation is based on the minimization of a Convex Non-Convex functional where an ad-hoc non-convex regularization term improves the treatment of the boundary lengths handled by the \(\ell _1\) norm in [2]. An appropriate numerical scheme based on the Alternating Directions Methods of Multipliers procedure is proposed to efficiently solve the nonlinear optimization problem. Experimental results show the effectiveness of this three-stage procedure.


Manifold segmentation Images on manifold ADMM Convex non-convex strategy 



This work was supported by the “National Group for Scientific Computation (GNCS-INDAM)” and by ex60% project by the University of Bologna “Funds for selected research topics”.

Supplementary material

427343_1_En_28_MOESM1_ESM.pdf (208 kb)
Supplementary material 1 (pdf 207 KB)


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Martin Huska
    • 2
  • Alessandro Lanza
    • 1
  • Serena Morigi
    • 1
    Email author
  • Fiorella Sgallari
    • 1
  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly
  2. 2.Department of MathematicsUniversity of PadovaPadovaItaly

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