recognition as graph matching

RECOGNITION AS

GRAPH MATCHING

Presented By-

Vishakha Agarwal

(Research Scholar)M.Tech, Final Year

Department of Computer Science and Information Technology

OUTLINE

Introduction

Pattern recognition approaches

Graphs in pattern recognition

Graph matching taxonomy

Graph matching algorithms

Graph based recognition: Application taxonomy

Graph based recognition: Application

Discussions and conclusions

References

INTRODUCTION

In many practical problems, there is a need to make some

decision about the content of an image or about the

classification of an object that it contains.

For example, the user of a notebook computer may be able to

give input using hand printed characters.

The classification process might actually fail, either because

the character is badly made, or because the person invented

a new character.

Recognition means “To Know Again.”

A recognition system must contain some memory of the

objects that it is to recognize.

PATTERN RECOGNITION APPROACHES

Traditional subdivision of pattern recognition:

PATTERN RECOGNITION APPROACHES: STATISTICAL APPROACH

Advantages: Theoretically well

founded. Many powerful

algorithms available.

Disadvantages Dimension of feature

vector fixed. Only unary feature

values, but no relations can be modeled.

PATTERN RECOGNITION APPROACHES: STRUCTURAL APPROACH

Advantages Representation size is

variable. Higher representation

power.

Disadvantages: Lack of mathematical

structure in the graph domain.

Lack of algorithmic tools.

GRAPHS IN PATTERN RECOGNITION

In pattern recognition and computer vision, it is

required to measure the similarity of objects.

When graphs are used for the representation of

structured objects, then the problem of measuring object

similarity turns into the problem of computing the

similarity of graphs, which is also known as graph

matching.

If graphs are used for object representation this problem

turns into determining the similarity of graphs.

GRAPHS IN PATTERN RECOGNITION

Standard concepts in graph matching include graph

isomorphism, subgraph isomorphism, and maximum

common subgraph.

However, in real world applications we can’t always

expect a perfect match between the input and one of

the graphs in the database.

Therefore, what is needed is an algorithm for error-

tolerant matching, or equivalently , a method that

computes a measure of similarity between two given

graphs.

GRAPH MATCHING TAXONOMY

In graph matching, we used to consider directed and

labeled graphs, which are sometimes synonymously

referred to as (attributed) relational graphs, or

relational structures.

If we delete some nodes from a graph, together with

their incident edges, we obtain a subgraph g’ ⊆ g.


Graph matching can be done by-

Graph Isomorphism- In this, the exact structural

correspondence is sought: there must be a bijective mapping

between the nodes of the two graphs that preserves the

edges of both graphs.


• Subgraph Isomorphism- It requires the existence of an

isomorphism between one of the graphs and a subgraph of

the other. In other words, one of the graphs may have extra

nodes and extra edges linking these new nodes to the rest.


• Monomorphism- In monomorphism, extra edges in the

larger graph are allowed also between nodes that do have a

correspondent in the smaller graph.


Maximum Common Subgraph- It is the largest

subgraph of one of the two graphs that is isomorphic to a

subgraph of the other. This kind of matching allows both

graphs to have extra nodes and edges, but is also

significantly more expensive from a computational

viewpoint.

Weighted graph matching- Here the edges of the

graphs have a weight, and the goal is to find the common

subgraph with the largest total weight.


Graph Edit Distance- It measures the similarity of two

graphs by computing the minimum-cost set of edit

operations needed to transform one of the graphs into the

other.

The sequence of edit operations that transform g into g’

implies an error-correcting mapping from the nodes of g to

the nodes of g’.

GRAPH MATCHING ALGORITHMS

The standard algorithm for graph and subgraph isomorphism detection

is the one by Ullman , in which Maximum common subgraph detection

has been addressed.

Most of these algorithms are particular versions of the A* search

procedure, i.e., they rely on some kind of tree search incorporating

various heuristic look-ahead techniques in order to prune the search

space.

Other approaches are based on neural networks such as the Hopfield

network or the Kohonen map.

Also genetic algorithms have been used in many approximate method

based on maximum flow . However, all of these approximate methods

may get tracked in local minima and miss the optimal solution.

GRAPH BASED RECOGNITION:APPLICATION TAXONOMY

At least six application areas in which graph matching

techniques have been successfully employed can be

individuated:

2D and 3D image analysis and processing

Document processing

Biometric identification

Image databases

Video analysis

Biological and biomedical applications

GRAPH BASED RECOGNITION: APPLICATION

Automatic Transcription of Handwritten Medieval TextDigitization of historical documents has become a focus of intensive research.


Challenges in the Transcription of Handwritten

Historical Documents

Layout analysis and extraction of text

Decorations

Decay of paper or parchment

Faded ink

Bleed through

Various other artifacts

Lack of language model etc.


Problems with the conventional approach-

Two dimensional shape of the characters is not

adequately modeled; no structural relations.

Possible Solution:

Use skeletons to represent the handwriting by a graph.

Transform the graph of a handwritten text into a

sequence of feature vectors.

Apply HMMs and RNNs to sequence of feature vectors.

GRAPH BASED RECOGNITION: APPLICATION Graph Extraction-

Apply a thinning operator to generate the skeleton of the image.

Nodes: Key points: crossings, junctions, end points, left-most points of

circular arcs. Secondary points: equidistant points on the skeleton between

key points; distance d is a parameter. Edges:

Nodes that are neighbors on the skeleton are connected by edges.


Comments-

In this application, graph-matching based feature

extraction could reduce the error rate by about 50%

compared to a standard set of features.

Because the graphs are rather small, the additional

computational cost is moderate (compared to HMM

decoding)

Recent experiments with alternative graph distance

measures have given good results.

DISCUSSIONS AND CONCLUSIONS

Recognition and learning of patterns are subjects of

considerable depth and interest to cognitive psychology,

pattern recognition, and computer vision.

A wide spectrum of graph matching algorithms have

become available meanwhile.

They range from deterministic approaches, suitable for

finding optimal solutions to problems involving graphs

with a limited number of nodes and edges, to approximate

methods that are applicable to large-scale problems.

DISCUSSIONS AND CONCLUSIONS

It is conjectured that there are many applications in

pattern recognition and computer vision where the full

representational power of graphs may not be needed.

Restricting the focus on special subclasses of graphs may

result in more efficient matching procedures.

Other promising areas of future research include the

automatic inference of edit costs from a set of sample

graphs, and the combination of optimal and approximate

graph matching methods.

REFERENCES

http://www.cse.nd.edu/Fu_Prize_Seminars/bunke/slides.pdf.

Valiente G.,et. al,An Image Similarity for Graph Matching,0-

7695-0746-8/00 ©2010 IEEE.

http://www.nptel.ac.in/courses/117104069/chapter_1/1_10.html.

Wachinger C.,et.al, Structural Image Representation for Image

Registration , 978-1-4244-7028-0/10/ ©2010 IEEE.

Conte D.,et.al, Graph Matching Application in Pattern Recognition

and Image Processing, 0-7803-7750-8/03 ©2003 IEEE.

Bunke H.,et.al,Graph Matching: Theoritical foundations,

Algorithms ,and Applications.

REFERENCES

Wiskott L.,et.al,Face Recognition by Elastic Bunch graph

Matching,7th intern conference, on Computer Analysis on

Images and Patterns, Keil, Germany, September 1997.

International Master of Research in Computer Science: Computer

Aided Decision Support, Graph for Pattern Recognition, Author:

Romain Raveaux , Zeina Abu-Aisheh, in the RFAI groups at the

University of Tours ,October 2013.

Caetano T.,et.al,Learning Graph Matching,IEEE Transactions on

Pattern Analysis and Machine Intelligence, VOL 31, NO. 6, June

2009.

THANK YOU FOR

YOUR ATTENTION!

recognition as graph matching

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