highorder graph matching 20131226 Ilchae Jung Introduction of

high-order graph matching 20131226 Ilchae Jung

Introduction of graph matching • Finding matches between two GRAPHS – yia= 1 if node i in G corresponds to node a in G’ – yia= 0 otherwise Slide from “Learning Graphs to Match”, Minsu Cho, Karteek Alahari, and Jean Ponce, ICCV 13

Introduction of graph matching • Maximizing the matching score S Slide from “Learning Graphs to Match”, Minsu Cho, Karteek Alahari, and Jean Ponce, ICCV 13

Introduction of graph matching • How to measure the matching score S ? – Each node & each edge has its own attribute – Node similarity function Slide from “Learning Graphs to Match”, Minsu Cho, Karteek Alahari, and Jean Ponce, ICCV 13

Introduction of graph matching • How to measure the matching score S ? – Each node & each edge has its own attribute. – Node similarity function – Edge similarity function Slide from “Learning Graphs to Match”, Minsu Cho, Karteek Alahari, and Jean Ponce, ICCV 13

Introduction of graph matching • How to measure the matching score S ? – Sum of SV and SE values for the assignment y Slide from “Learning Graphs to Match”, Minsu Cho, Karteek Alahari, and Jean Ponce, ICCV 13

Introduction of graph matching • Slide from “Learning Graphs to Match”, Minsu Cho, Karteek Alahari, and Jean Ponce, ICCV 13

Tensor-based algorithm for high-order graph matching -O Duchenne, F bach, IS Kweon, Jean Ponce, PAMI 2010

abstract • High-order geometric similarity • Spectral algorithm (power iteration) • New similarity for high order

High order similarity • 1 -order similarity • 2 -order similarity -scale variant -affine variant • 3 -order similarity (High) - scale invariant - affine invariant

Tensor based representation Tensor definition

Spectral algorithm Find main eigenvector for graph cut algorithm Power iteration for finding eigenvector

Spectral algorithm Find main eigenvector for graph cut algorithm

Similarity description for high order • 1. similarity-invariant potentials • 2. affine-invariant potentials • 3. projective-invariant potentials

Similarity description for high order • 1. similarity-invariant potentials -using angles of triangle a) Angle: scale a) Distance : rotation a) 3 Angle: scale+rotation

Similarity description for high order • 2. affine-invariant potentials - Normalizing each triangle into an equilateral triangle - extract features from them • 3. projective-invariant potentials

Similarity description for high order • • 1. similarity-invariant potentials 2. affine-invariant potentials 3. projective-invariant potentials + traditional descriptors

Tensor generation 2. For all tuples t, Choose K nearest tuples from Graph 2

Experiments • House dataset

Experiments

Fast and scalable approximate spectral matching for higher order graph matching - Soonyong Park, Sung-Kee Park, Martial Hebert PAMI 2014

contribution • Fast&approximated tensor generation • Marginalized+bistochastic power iteration

original quantization

Power iteration +marginalization, bistochastic normalization

Experiment

Expermient

Experiment

• Thank you