Adventures of a Physicist: Computational and Laboratory ... posters... · Computational and Laboratory Investigations of a Model of Blood Droplet Flight for Forensic Applications

Adventures of a Physicist:

Computational and Laboratory Investigations of a Model

of Blood Droplet Flight for Forensic Applications

Raquel Murray

UOIT

August 23, 2012

Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 1 / 35

Introduction

At a crime scene, the reconstruction of bloodletting events can be a keyplayer in solving crimes.


Methods

The most common method for reconstructing bloodletting events is theString Method.

Can be time consuming

Neglects gravity and drag

Cannot accommodate downwardmoving drops

Figure: Using the String Method to reconstruct a bloodletting event [2]


Methods Software Packages

Programs like HEMOSPATTM[6, 7] and BACKTRACKTM[1, 2, 3] also usestraight line geometric reconstructions for bloodletting events.

Use virtual strings Do not account for the forceof gravity or the e↵ects ofdrag


Methods BACKTRACK

Figure: Top view from BACKTRACK related to downward moving drops. Theintersections correspond to the blood source location in the plane of the floor [2]


Methods BACKTRACK

Figure: Side view from BACKTRACK related to downward moving drops. Threevirtual strings were added from upward moving drops. [2]


Methods HEMOSPAT

Figure: HemoSpat Software interface [5]


The Problem

What about laws of physics?!


Early Laboratory Experiment

Figure: A single camera experiment. The high-speed camera is orientedperpendicular to the path of the projectile to capture the motion of the dropletsin a vertical plane.



Figure: Still shot from single high-speed camera experiment video.



Figure: Manual tracking of a single droplet. Here, a single droplet is observed in10 frames from a single camera and the position was marked by the user. TheMegaspeedTM [8] software takes those ten points and applies polynomialinterpolation to reconstruct the path.



Figure: An approximation of a blood droplet trajectory using the Verlet Algorithm.



Looks great right?!

This is only a two-dimensional model.

This model is not telling us anything about the parameters involvedwith the flight of blood droplets.

There’s still work to be done...


Laboratory Experiment

The laboratory procedure used to generate videos of simulatedbloodletting events is as follows:

1 Prepare mock crime scene and recording equipment.

2 Calibrate the recording equipment.

3 Run the laboratory experiment.

4 Document and verify the experiment.


Laboratory Experiment Experimental Setup

Figure: Placement of lab jack and paintball gun within the crime scene. A)paintball gun used as a weapon. B) Lab jack on which the ballistics gel is placedin front of the paintball gun. C) Halogen 500W work light.


Laboratory Experiment Experimental Setup

Figure: The full laboratory setup.


Camera Calibration

Before shooting the ballistics gel, calibration videos needed to be captured:

1 Capture the moving checkerboard calibration video

2 Capture the moving laser dot calibration video

3 Verify the accuracy of the calibration

4 Capture the riot ball calibration video


Camera Calibration


Movies

Show stereo videos of pig blood experiment.


The Droplet Tracker

Figure: Automated tracking of a full experiment using the Droplet Tracker [9].


Reconstructed Blood Droplet Paths

!0.1 0 0.1 0.2 0.3 0.4 0.5

!0.2

!0.15

!0.1

!0.05

0

0.05

0.1

x

y

!0.2 !0.15 !0.1 !0.05 0 0.05 0.1 0.15

!0.2

!0.15

!0.1

!0.05

0

0.05

0.1

z

y!0.2 !0.15 !0.1 !0.05 0 0.05 0.1 0.15

!0.1

0

0.1

0.2

0.3

0.4

0.5

zx

Figure: Visualisation of the tracked trajectories from the Droplet Tracker.


Documenting the Experiment

(a) A digital photograph of a transfer bloodstain in the field of view ofCamera A.

(b) A digital photograph of a transfer bloodstain in the field of view ofCamera B.


Our Model Purpose

We are looking to achieve the following:

Using a set of initial conditions, produce ODE-based trajectories

Fit those ODE-based trajectories to the experimental pathreconstructions

Estimate the radius, direction, and initial speed of an individual blooddroplet

Investigate the resulting Reynolds number and drag coe�cients fromthese droplets


Our Model Dynamic ODE Model

Y

XFg

Fd

directionof motion

Figure: The forces acting upon a single droplet as it flies through the air. Thedrag force (Fd) will oppose the direction of motion and the force of gravity (Fg)acts only in the y direction, pulling the droplet downward.


Our Model Dynamic ODE Model

We start o↵ our model with Newton’s Second Law of motion:

F = Fd + Fg, (1)

Substituting the drag force (also used by Liu et. al. in [4])

Fd = �1

2⇢airAkuk2u, (2)

and the gravitational force

Fg = �mg. (3)

We obtain

u = �3

8

r

⇢air

⇢dropkuk2u� g. (4)


Objective Function

Therefore, the objective function, f , is written as

f(r, u0, ✓0,�0) =kX

t=1

kvt �wtk2 . (5)

The decision parameters are:

radius: r

initial speed: u0

angles: ✓ and �


Visual Verification

0 0.05 0.1 0.15 0.2 0.25

!0.16

!0.14

!0.12

!0.1

!0.08

!0.06

!0.04

!0.02

0

x

y

0 0.01 0.02 0.03 0.04 0.050

0.05

0.1

0.15

0.2

0.25

z

x0 0.01 0.02 0.03 0.04 0.05

!0.15

!0.1

!0.05

0

zy

Figure: The red data points are the spatial coordinates of a transfer blood droplettracked by DT. The black line is the ODE-based trajectory with optimisedparameters to reduce the Euclidean norm between the DT trajectory and theODE trajectory.


Visual Verification

!0.1 0 0.1 0.2 0.3 0.4

!0.5

!0.4

!0.3

!0.2

!0.1

0

0.1

x

y

Figure: An xy view of the DT trajectories (red data points) and each of theirODE-based trajectories (black line). The riot ball is plotted in green, moving inthe positive x direction.


Conclusion

Collect stereo video data of simulated bloodletting events

Blood droplets are tracked

Successfully fit ODE-based trajectory to experimental pathreconstructions

Retrieves the initial speed, directional angles, and radius


Future Work

Backward integrationOscillations or radial distortions of a droplet during its flightHow blood droplets impact di↵erent surfaces

Figure: A digital photograph of the resulting bloodstain pattern formed on acardboard surface from the porcine blood experiment.


My Future

Research changed the course of my life for the better :)


Acknowledgements

THANK YOU


References

A. L. Carter.The directional analysis of bloodstain patterns theory andexperimental validation.Canadian Society of Forensic Science, 34(4):173–189, 2001.

M. B. Illes, A. L. Carter, P. L. Laturnus, and A. B. Yamashita.Use of the backtrack computer program for bloodstain patternanalysis of stains from downward-moving drops.Canadian Society of Forensic Science, 38(4):213–218, 2005.

International Association of Bloodstain Pattern Analysts.Ballistic Trajectories of Blood: Computer Applications and Workshop,Reno, Nevada, October-November 1990.

Alex B. Liu, Daniel Mather, and Rolf D. Reitz.Modeling the e↵ects of drop drag and breakup on fuel sprays.Sae technical paper series, University of Wisconsin, Masidon EngineResearch Center, March 1993.


References

Andy Maloney and Kevin.Hemospat bloodstain pattern analysis software, 2009.

Andy Maloney, Celine Nicloux, Kevin Maloney, and Franck Heron.One-sided impact spatter and area-of-origin calculations.Journal of Forensic Identification, 61(2):123–135, August 2011.

Kevin Maloney, Jim Killeen, and Andy Maloney.The use of hemospat to include bloodstains located on nonorthogonalsurfaces in area-of-origin calculations.Journal of Forensic Identification, 59(5):513–524, April 2009.

Mega Speed.High-Speed B/W & Color CMOS Camera Model MS50K & MS55K,2.9 edition, 2010.


References

Luis Zarrabeitia, Dhavide Aruliah, and Faisal Qureshi.Extraction of blood droplet flight trajectories from videos for forensicanalysis.Algarve, Portugal., February 2012. International Conference onPattern Recognition Applications and Methods.


Documents

Adventures of a Physicist: Computational and Laboratory ... posters... · Computational and Laboratory Investigations of a Model of Blood Droplet Flight for Forensic Applications