Least-Squares Object Matching (LSOM)

Introduction

The goal of cross-domain object matching (CDOM) is to find correspondence between two sets of objects in different domains in an unsupervised way. Photo album summarization is a typical application of CDOM, where photos are automatically aligned into a designed frame expressed in the Cartesian coordinate system. CDOM is usually formulated as finding a mapping from objects in one domain (photos) to objects in the other domain (frame) so that the pairwise dependency is maximized.

Main Idea

It solves the CDOM problems via maximizing the squared-loss mutual information (SMI) between matched pairs:

pi^* := mathop{textnormal{argmax}}_{pi in Pi_n} widehat{textnormal{SMI}}_pi(X, Y_pi).

where Pi_n in {0,1}^{n times n} is a permutation matrix.

Features

  • All the model parameters are automatically tuned by cross-validation.

  • Optimization of LSOM is carried out via solving the linear assignment problem (LAP) O(n^3).

Download

Usage

  • Download & compile the source code.

  • mex hungarian.cpp

  • Run the script (main_usps.m).

Photo Album Summarization

  • Color image

PAS1 
  • Face

PAS1 
  • Digit

PAS1 

Acknowledgement

I am grateful to Prof. Masashi Sugiyama for his support in developing this software.

Contact

I am happy to have any kind of feedbacks. E-mail: textnormal{yamada@sg.cs.titech.ac.jp}

Reference

Yamada, M., & Sugiyama, M.
Cross-Domain Object Matching with Model Selection.
AISTATS 2011 [paper]