Recent efforts in the area of joint object matching approach the problem by taking as input a set of pairwise maps, which are then jointly optimized across the whole collection so that certain accuracy and consistency criteria are satisfied. One natural requirement is cycle-consistencynamely the fact that map composition should give the same result regardless of the path taken in the shape collection. In this paper, we introduce a novel approach to obtain consistent matches without requiring initial pairwise solutions to be given as input. We do so by optimizing a joint measure of metric distortion directly over the space of cycle-consistent maps; in order to allow for partially similar and extra-class shapes, we formulate the problem as a series of quadratic programs with sparsity-inducing constraints, making our technique a natural candidate for analysing collections with a large presence of outliers. The particular form of the problem allows us to leverage results and tools from the field of evolutionary game theory. This enables a highly efficient optimization procedure which assures accurate and provably consistent solutions in a matter of minutes in collections with hundreds of shapes.

Consistent Partial Matching of Shape Collections via Sparse Modeling

COSMO, LUCA;RODOLA', Emanuele;ALBARELLI, Andrea;
2017

Abstract

Recent efforts in the area of joint object matching approach the problem by taking as input a set of pairwise maps, which are then jointly optimized across the whole collection so that certain accuracy and consistency criteria are satisfied. One natural requirement is cycle-consistencynamely the fact that map composition should give the same result regardless of the path taken in the shape collection. In this paper, we introduce a novel approach to obtain consistent matches without requiring initial pairwise solutions to be given as input. We do so by optimizing a joint measure of metric distortion directly over the space of cycle-consistent maps; in order to allow for partially similar and extra-class shapes, we formulate the problem as a series of quadratic programs with sparsity-inducing constraints, making our technique a natural candidate for analysing collections with a large presence of outliers. The particular form of the problem allows us to leverage results and tools from the field of evolutionary game theory. This enables a highly efficient optimization procedure which assures accurate and provably consistent solutions in a matter of minutes in collections with hundreds of shapes.
File in questo prodotto:
File Dimensione Formato  
10.1111-cgf.12796.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Accesso gratuito (solo visione)
Dimensione 3.09 MB
Formato Adobe PDF
3.09 MB Adobe PDF Visualizza/Apri
cgf.12796.pdf

non disponibili

Tipologia: Versione dell'editore
Licenza: Accesso chiuso-personale
Dimensione 3.07 MB
Formato Adobe PDF
3.07 MB Adobe PDF   Visualizza/Apri

I documenti in ARCA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/3677536
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 39
  • ???jsp.display-item.citation.isi??? 23
social impact