The Average Mixing Kernel Signature

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12365)


We introduce the Average Mixing Kernel Signature (AMKS), a novel signature for points on non-rigid three-dimensional shapes based on the average mixing kernel and continuous-time quantum walks. The average mixing kernel holds information on the average transition probabilities of a quantum walk between each pair of vertices of the mesh until a time T. We define the AMKS by decomposing the spectral contributions of the kernel into several bands, allowing us to limit the influence of noise-dominated high-frequency components and obtain a more descriptive signature. We also show through a perturbation theory analysis of the kernel that choosing a finite stopping time T leads to noise and deformation robustness for the AMKS. We perform an extensive experimental evaluation on two widely used shape matching datasets under varying level of noise, showing that the AMKS outperforms two state-of-the-art descriptors, namely the Heat Kernel Signature (HKS) and the similarly quantum-walk based Wave Kernel Signature (WKS) .


Shape representation Shape analysis Quantum walks 



Luca Cosmo was supported by the ERC Starting Grant No. 802554 (SPECGEO) and the ERC Consolidator grant No. 724228 (LEMAN).

Supplementary material

504476_1_En_1_MOESM1_ESM.pdf (181 kb)
Supplementary material 1 (pdf 181 KB)


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Sapienza University of RomeRomeItaly
  2. 2.University of LuganoLuganoSwitzerland
  3. 3.Università Ca’ Foscari VeneziaVeniceItaly
  4. 4.Imperial College LondonLondonUK
  5. 5.TwitterLondonUK
  6. 6.Queen Mary University of LondonLondonUK

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