![Page 1: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/1.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
The Use of Graph Theory in Forensic FootwearAnalysis
Tony Allen
Advisors: Dr. Martin Herman, Dr. Hariharan IyerInformation Technology Lab
Federal and Industrial Relations Office
NIST SURF Colloquium, 2017
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 2: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/2.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Outline
1 Problem StatementBackgroundOur Approach
2 A Crash Course on Graph TheoryDefinitions and Examples
3 An Example
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 3: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/3.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Background
Outline
1 Problem StatementBackgroundOur Approach
2 A Crash Course on Graph TheoryDefinitions and Examples
3 An Example
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 4: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/4.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Background
Motivation
Footwear impressions as forensic evidence
Commonly found in crime scenesOften have distinctive features — sole patterns, wear,imperfections
Current practices are subjective
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 5: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/5.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Background
Motivation
Footwear impressions as forensic evidence
Commonly found in crime scenes
Often have distinctive features — sole patterns, wear,imperfections
Current practices are subjective
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 6: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/6.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Background
Motivation
Footwear impressions as forensic evidence
Commonly found in crime scenesOften have distinctive features — sole patterns, wear,imperfections
Current practices are subjective
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 7: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/7.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Background
Motivation
Footwear impressions as forensic evidence
Commonly found in crime scenesOften have distinctive features — sole patterns, wear,imperfections
Current practices are subjective
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 8: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/8.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
Outline
1 Problem StatementBackgroundOur Approach
2 A Crash Course on Graph TheoryDefinitions and Examples
3 An Example
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 9: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/9.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
GOAL: Develop quantitative measures for footwear impressioncomparison
Three important steps:
1. Develop tool to extract features
2.
3. Build database of impressions for testing and trainingalgorithms
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 10: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/10.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
GOAL: Develop quantitative measures for footwear impressioncomparison
Three important steps:
1. Develop tool to extract features
2.
3. Build database of impressions for testing and trainingalgorithms
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 11: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/11.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
GOAL: Develop quantitative measures for footwear impressioncomparison
Three important steps:
1. Develop tool to extract features
2. Develop methods for computing high performance comparisonscores
3. Build database of impressions for testing and trainingalgorithms
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 12: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/12.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
GOAL: Develop quantitative measures for footwear impressioncomparison
Three important steps:
1. Develop tool to extract features
2. Develop methods for computing high performance comparisonscores
3. Build database of impressions for testing and trainingalgorithms
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 13: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/13.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
GOAL: Develop quantitative measures for footwear impressioncomparison
Three important steps:
1. Develop tool to extract features
2. Develop methods for computing high performancecomparison scores
3. Build database of impressions for testing and trainingalgorithms
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 14: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/14.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
A Comparison Score — Distance
How to compute distance measure:
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 15: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/15.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
A Comparison Score — Distance
1. Find features common in both impressions.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 16: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/16.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
A Comparison Score — Distance
1. Find features common in both impressions.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 17: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/17.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
A Comparison Score — Distance
2. Use these features to align the prints.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 18: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/18.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
A Comparison Score — Distance
2. Use these features to align the prints.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 19: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/19.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
A Comparison Score — Distance
3. Calculate distance between features after alignment.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 20: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/20.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Our Approach
A Comparison Score — Distance
But remember, this process needs to be accurate, repeatable, andreproducible!
That’s where Graph Theory comes in!
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 21: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/21.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Outline
1 Problem StatementBackgroundOur Approach
2 A Crash Course on Graph TheoryDefinitions and Examples
3 An Example
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 22: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/22.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Definition
A graph G = (V ,E ) is comprised of a set of vertices V and a setof edges E , which are 2-element subsets of V .
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 23: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/23.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Definition
A graph G = (V ,E ) is comprised of a set of vertices V and a setof edges E , which are 2-element subsets of V .
V = {a, b, c , d , e, f }E = {}
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 24: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/24.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Definition
A graph G = (V ,E ) is comprised of a set of vertices V and a setof edges E , which are 2-element subsets of V .
V = {a, b, c , d , e, f }E = {ae, bc, bf , cf }
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 25: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/25.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Definition
A graph G = (V ,E ) is comprised of a set of vertices V and a setof edges E , which are 2-element subsets of V .
V = {a, b, c , d , e, f }E = {ab, ac , ad , ae, af , bc, bd , be, bf , cd , ce, cf , de, df , ef }
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 26: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/26.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Example (Social Networks)
Let V = {Alice,Bob,Charlie,David ,Eve,Fred ,Grace} and let uvbe an edge if and only if person u and person v are friends.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 27: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/27.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Definition
A clique is a subset of vertices in which each pair of distinctvertices are adjacent.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 28: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/28.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Definition
A clique is a subset of vertices in which each pair of distinctvertices are adjacent.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 29: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/29.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Definition
A clique is a subset of vertices in which each pair of distinctvertices are adjacent.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 30: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/30.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Definitions and Examples
Definition
A clique is a subset of vertices in which each pair of distinctvertices are adjacent.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 31: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/31.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
How does this apply?
Definiton - Product Graph:
Given two configurations of features,
P = {p1, ..., pn} and Q = {q1, ..., qm},
we construct a product graph with vertex set
V = {p1q1, ..., p1qm, ..., pnq1, ..., pnqm}.
Two vertices piqj and pkq` are connected if and only if thedistance between points pi and pk is equal to (within a margin oferror) the distance between points qj and q`.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 32: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/32.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
A Small Example
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 33: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/33.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
What does a clique in the product graph represent?
A set of features in P that are congruent to a set of features in Q.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 34: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/34.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
What does a clique in the product graph represent?A set of features in P that are congruent to a set of features in Q.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 35: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/35.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
What does a clique in the product graph represent?A set of features in P that are congruent to a set of features in Q.
We can then align the impressions by this congruence.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 36: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/36.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Shoe Example
0. Create product graph.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 37: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/37.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Shoe Example
1. Find a large clique in the product graph.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 38: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/38.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Shoe Example
2. Align the impressions by the clique correspondence.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 39: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/39.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Shoe Example
2. Align the impressions by the clique correspondence.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 40: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/40.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Shoe Example
3. Compute distance between features.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 41: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/41.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Improvements and Future Work
Normalize distance score for comparison
Investigate other similarity scores
Allow for error in classifying characteristics
Implement machine learning to test and develop scoringsystems
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 42: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/42.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Summary
There is a need for forensic footwear comparisons to beobjective and reproducible.
The distance between impressions is just one similaritymeasure.
But Graph Theory is a helpful tool in computing this (andother!) scores.
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis
![Page 43: The Use of Graph Theory in Forensic Footwear Analysisallen450/nist-presentation.pdf · Problem Statement A Crash Course on Graph TheoryAn ExampleSummary The Use of Graph Theory in](https://reader035.vdocuments.us/reader035/viewer/2022071217/604dce812110fe406713e9ae/html5/thumbnails/43.jpg)
Problem Statement A Crash Course on Graph Theory An Example Summary
Questions?
Special Thanks to:
Dr. Martin HermanDr. Hari Iyer
and to you for listening!
Tony Allen National Institute of Standards and Technology
The Use of Graph Theory in Forensic Footwear Analysis