Imaging and analysis of forensic striation marks - · PDF fileImaging and analysis of forensic...

Imaging and analysis of forensic striation marks

Michael Heizmann, MEMBER SPIEUniversitat KarlsruheInstitut fur Mess- und RegelungstechnikPostfach 698076128 Karlsruhe, GermanyE-mail: [email protected]

Fernando Puente Leo´n, MEMBER SPIETechnische Universitat MunchenLehrstuhl fur Messsystem- und

Sensortechnik80290 Munchen, Germany

Abstract. We present a new image processing strategy that enables anautomated comparison of striation patterns. A signal model is introducedto describe the interesting features of forensically relevant striationmarks. To provide a high image quality, several images of the samesurface area are recorded under systematically varying conditions andthen combined for an improved result by means of data fusion tech-niques. Based on the signal model, the signal of interest is concentrated,and a compact representation of the marks is obtained. To enable anefficient description of the relevant features, even in the cases of de-formed surfaces or curved striation marks, a straightening of the groovesis performed beforehand. Following, a meaningful ‘‘signature’’ describingthe information of interest is extracted using the whole length of thegrooves. This signature is used for an objective evaluation of similarity ofthe striation patterns. © 2003 Society of Photo-Optical Instrumentation Engineers.[DOI: 10.1117/1.1622389]

Subject terms: automated visual inspection; image processing; data fusion; fo-rensic science; striation patterns; image models; groove straightening.

Paper 030164 received Apr. 8, 2003; revised manuscript received May 21, 2003;accepted for publication May 21, 2003.

d aTh

letstwog achfts,the

nthictabf ththewasrgehiveof-es

byerehen to

th

er

e.

egyful

er-ingtex-and.

ffi-ar-ch

inrfulthat

stly. 5.

onithn-ge

heirse-heeffi-theen-blen-

theen

de-

1 Introduction

The analysis and comparison of marks on objects founa crime scene play an essential role in forensic science.groove-shaped marks on the cylindrical surface of bulhave been used for a long time to investigate whetherbullets have been fired from the same gun, thus enablinidentification of firearms. In the case of tool marks, whiare often found in the context of burglaries and thegroove-shaped marks also arise due to the motion oftool relative to the object touched.

Digitizing and archiving of such marks for subsequecomparisons result in enormous image databases, wmay contain some 1,000 marks of the same kind. To eslish a correspondence between two marks, an image oexhibit coming into question has to be compared withentire database. Up to now, however, this comparisonmainly done visually by experts. Because of the laamounts of comparisons necessary to search the arcthe current matching methods for striation patterns areten unable to provide the turnaround times and succrates that law enforcement demands.

Due to these problems, an automated comparisonmeans of image processing techniques is desirable. Hthe computer should not primarily serve to visualize trecorded images, but rather to perform a first comparisoassist the expert. The automated inspection comprisesfollowing steps:

• a recording of high-quality images of each mark undreproducible conditions

• a preprocessing to simplify further steps

• the extraction of suitable features

• a feature-level comparison with the entire databas

Opt. Eng. 42(12) 3423–3432 (December 2003) 0091-3286/2003/$15.00

te

n

h-e

,

s

,

e

Stepping up to this challenge, we present a new stratthat enables a fully automated extraction of a meaningfeature set we call a ‘‘signature’’ from an image. Considing the nature of the marks of interest, every processstep meets the specific requirements of groove-shapedtures. Based on the signatures obtained, an objectiveefficient comparison of striation patterns can be achieved1,2

Since existing feature extraction algorithms lack a suciently high accuracy to permit a reliable processing ofbitrary striation marks, we had to develop a new approato accomplish this task.

Our strategy is based on the signal model introducedSec. 2. Taking the signal properties into account, poweimaging and preprocessing strategies are presentedyield high-quality images of the marks~see Secs. 3 and 4!.Thereafter, the proposed signal model is used to robuextract the signature of the tool mark, as shown in Sec

2 Signal Model

Neither bullets nor tool marks show a random distributiof groove-shaped marks. In fact, such textures comply wdefinite rules that are implicitly met at the time of the geeration of the grooves. Individual features of the tool edor the gun barrel emboss the groove structures by tmotion relative to the surface that bears the mark. Conquently, all fluctuations of the image intensities along tgrooves are bound to represent disturbances that canciently be suppressed by performing an averaging indirection of the grooves. At the same time, such a conctration of the information of interest leads to a consideradata reduction, which contributes to an efficient implemetation of the later comparison algorithms. Regardingclassification of grooves, one has to distinguish betwemarks on pristine bullets on one hand, and marks onformed bullets as well as tool marks on the other hand.

3423© 2003 Society of Photo-Optical Instrumentation Engineers

a-heeof

he

rmaysvilyplecrib

ti-hesurotal

toools

s al

llet.theve

nalires

hetoon.allbe

uldpa-

its

veslar

heu-

rste

tly

-ishle,inge toesralfile

res. 2.urve

ingces-re

rdi-l

c-

,

nalnotin-

Heizmann and Puente Leon: Imaging and analysis . . .

2.1 Pristine Bullets

At the time of firing, the kinematics provides for a genertion of straight grooves on the cylindrical surface of tbullet. All individual characteristics of the barrel armapped onto strictly parallel grooves. Due to the twistthe bullet compared to the direction of flightey , the direc-tion ej of the grooves is tilted by the anglec ~see Fig. 1!.Moreover, the direction of a virtual ‘‘tool edge’’ee describ-ing all of the characteristics of the barrel coincides with tglobal directionex .

However, curved grooves may also be found on fireabullets. The assumption of straight grooves is not alwreasonable, especially with bullets that have been headeformed due to the impact. In such cases, more comsignal models are needed, such as those used to destool marks.

2.2 Deformed Bullets and Tool Marks

When dealing with tool marks or deformed bullets, a reclinear model of the grooves is no longer applicable. Tgeneration process of such marks reveals that the 2-Dface structure results from a combined translation and rtion of a 1-D structureg(s), which in the case of toomarks corresponds with the tool edge.~Although tool edgesactually have a spatial character, it is usually sufficientassume a 1-D edge due to the small extent of most tperpendicular to the edge direction.! In the case of de-formed bullets, the motion inside the gun barrel causeprojection of the individual features on a virtual ‘‘tooedge’’ that embosses strictly straight grooves on the buHere, the curvature of the grooves stems rather fromlater deformation of the entire bullet than from the groogeneration process.

For all of these reasons, the application of a sigmodel based on a 1-D, spatially constant profile requsome assumptions.

• First of all, regarding the acquisition of imagesd(x),wherex5(x,y)T denotes the spatial coordinates, tillumination and the direction of observation havebe kept constant with respect to the groove directiConsequently, to record images of different marks,the illumination and positioning parameters shouldadjusted exactly and reproducibly.1

• Second, a sufficiently large area of the marks shobe analyzed to permit a robust estimation of therameters of the model and to take advantage ofcapability of suppressing disturbances.

• It should be assured that no overlaps of the groooccur, i.e., the tool edge should touch each particu

Fig. 1 Signal model for grooves on bullets.

3424 Optical Engineering, Vol. 42 No. 12, December 2003

xe

--

location of the surface only once. With respect to tshape of the grooves, this condition requires continous paths for all grooves.

• The path of the tool should feature a continuous fiderivative. Although this condition may seem to btoo restrictive, due to the mass of the tool, mosdifferentiable tool paths can be expected.

• Finally, the groove profile has to comply with the requirement of local stationarity. The edge profileonly allowed to vary slowly along the grooves. Sucan alteration of the edge profile occurs, for exampwhen the clearance angle of the tool is changed durthe generation of the striae. A reasonable procedurdeal with striation marks showing profile changwould be to split up the entire structure into sevesections and to assume a constant groove prowithin each section.

Various signal models that lead to such groove structuare conceivable. Some examples are depicted in FigEach signal model uses as model parameters the cm(t), with the curve parametert of an arbitrary position onthe edge as well as the width of the edgew. The parametert may be, but does not need to be, identical to the runnlength. Besides, specific model parameters may be nesary, e.g., the center position and the radius of curvaturin the case of circular grooves@see Fig. 2~c!#. Dependingon the signal model, correspondences of the local coonate system (ej ,eh) in the groove direction with the locaedge directionee or the global coordinate system (ex ,ey)are obtained.

With the signal models introduced, the gray-level funtion gII(x) of a striation pattern within an imaged(x) maybe described as follows:

gII~x!ªg~$x2m@ t~x!#%T•ee!•rectS $x2m@ t~x!#%T

•ee

w D ,

~1!

whereg(s) denotes the groove profile in the directionee ofthe edge, and

rect~x!ªH 1 for xP@2 12 ; 1

2#

0 otherwise. ~2!

In some cases, Eq.~1! may be simplified. In particularfor circular grooveseh5ee holds, if the origin is chosen tocoincide with the center of the circle@see Fig. 2~c!#:

m~x!5r •eh~x!. ~3!

With the Euclidean normi . . . i , the following simplifica-tion is obtained:

gII~x!ªg~xT•eh2r !•rect

ixi2r

w. ~4!

Such simplifications can be stated for the first four sigmodels of Fig. 2. However, the resulting equations canbe transferred to any other signal model. Therefore, an


Fig. 2 Model mechanisms for the generation of grooves: (a) straight grooves; (b) pure translation oftool edge; (c) circular grooves; (d) piecewise circular grooves; and (e) arbitrary translation and rotationof tool edge.

henal

ry

atwas

vege

ion

lityToro-

ary.ag

m-

hand

the

b-asenne

im-is

thesys-

to

of

nd

dividual method for the recognition of the course of tgrooves has to be developed explicitly for each sigmodel.

The most general model is the one in which arbitratranslations and rotations of the tool edge are permitted@seeFig. 2~e!#. The only assumption used in this model is ththe striae are generated by a 1-D, solid edge. If oneable to reconstruct the pathm(t) of a particular point on theedge as well as the corresponding angle/(ex ,ee) from therecorded image, then every image point within the groopattern could be assigned to a particular point on the edTo some extent, this method would constitute the inversof Eq. ~1!.

3 Imaging

In forensic science, the requirements concerning the quaof the images to be evaluated are especially high.achieve a reliable comparison of forensic marks, a repducible imaging of even the finest marks is necessTherefore, great strides must be made in the area of imcapture. Ideally, the requirements to be fulfilled by the iage acquisition system comprise:

• a high-quality image acquisition providing for higcontrast, high resolution, high image sharpness,high signal-to-noise ratio~SNR! in the whole image

.

e

• a thorough coverage of the surface containingmarks of interest

• an easily reproducible recording situation

• a mostly automated image acquisition.

Due to the limitations of optical systems, illumination prolems as well as difficulties in imaging all interesting aresimultaneously and with the required resolution, it is oftnot possible to meet all these requirements with only oimaged(x) of the object@see Figs. 3~a! and 3~b!#. Instead,these requirements can be fulfilled by acquiring severalages under different recording conditions. If attentionpaid to a proper choice of the degrees of freedom ofimage acquisition system, and its parameters are variedtematically, the images obtained can then be combinedan enhanced resultr (x) matching all requirements, onwhich the further processing can be based. An examplesuch an image is shown in Fig. 3~c!.

A strategy to generate suitable imagesr (x) is based onrecording a series of images

Dª$d~x,vi !, i 50, . . . ,B21%, ~5!

in which the object distance, the illumination direction, a

3425Optical Engineering, Vol. 42 No. 12, December 2003


Fig. 3 Image acquisition problems: (a) general scheme; (b) example of an inhomogeneous image ofa tool mark according to model Fig. 2(c) obtained with directional lighting; and (c) enhanced imagegenerated by means of fusion techniques.

uen

ht

Oftimuldthete-. Inageiro

be

blethede-al

glee

ndnalhech

is

iesefaceeult

asin

lly

glenennly

to

all

ffi-

of

luch

ose-b-

t-est

n-caninglizeden-

inis-ralbe

m

the object pose are all varied, and performing a subseqmultidimensional fusion of the images.3,4 The image seriesis characterized by a parameter vector

vª~f,u,z,aT, . . . !T, ~6!

describing the recording situation, wheref andu representthe azimuth and the elevation angle of a directional ligsource, respectively,z denotes the object distance, andaT

the object pose with respect to the imaging system.course, additional parameters—such as the integrationof the camera or the wavelength of the light source—cobe varied too, if necessary. For more information onimpact of image acquisition problems as well as on stragies to compensate them, we refer to Refs. 1, 5, and 6some particular cases, more than a single resulting imwill be necessary to describe the marks of interest in thentirety. However, such cases concern constellationsmarks showing a complex geometry, and they will notconsidered in the scope of this work.

3.1 Image Capture

For image striation patterns with high contrast, a suitaillumination has to be chosen. It can be shown thatimage intensities obtained from such surfaces highlypend on the direction of the light source, if directionlighting is used@see Fig. 3~b!#.5 Since a diffuse illuminationpattern can be thought of as a superposition of many sindirectional light sources from different directions, diffuslighting will generally lead to a contrast attenuation, athus to suboptimal results. However, although directiolighting is preferable to illuminate surface structures, tposition of the light source has to be adjusted for ealocation x of the surface, if an optimal local contrastwanted.

An important question when recording an image serdeals with the strategy for sampling the parameter spacvwith as few images as possible such that 1. every surlocationx is imaged with high quality in at least one imagof the series, and 2. fusion to an improved resr (x)—such as the example shown in Fig. 3~c!—is possible.This problem greatly depends on the object geometrywell as on the surface texture and cannot be dealt with


t

e

e

f

detail here. However, the following cases of forensicarelevant striation marks are treated in more detail.

• Cylindrical surface, straight grooves: To record animage series of cylindrical surfaces showing a sinband of straight, parallel grooves, like, e.g., pristibullets, it is not necessary to vary the illuminatiospace two-dimensionally, because such surfaces oshow a high contrast if illumination is perpendicularthe grooves.5 Thus, only the elevation angleu has tobe varied. If the interesting surface areas are notin-focus simultaneously, the object distancez shouldbe varied, too.

• Planar surface, curved grooves:In the case of planarsurfaces containing curved grooves, it is usually sucient to record an image series in which the azimuthfis varied. This case is typical for a wide rangemarks generated by screwdrivers and other tools.

• Curved surface, curved grooves:In the most generacase of curved surfaces showing curved grooves, sas deformed bullets, both the elevation angleu and theazimuth f of the light source have to be varied tassure a high quality in at least one image of theries. Additionally, it may be necessary to vary the oject distancez and the object poseaT as well toachieve proper focusing and low distortions.

3.2 Fusion Strategy

After an image seriesD has been acquired, a suitable straegy has to be applied to combine the information of interdistributed over the series to an enhanced resultr (x) show-ing a high quality overall. Such a result is not only advatageous to enable a computerized comparison, but italso be used to support forensic examiners in matchstriae, because a larger area of the surface can be visuawith high contrast simultaneously than when using convtional tools like comparison macroscopes.

In this work, only 1-D illumination series—i.e., serieswhich only one illumination parameter is varied—are dcussed. However, by applying this method in sevestages, multidimensional series of images can alsofused.5 Figure 4 shows the structure of the fusion algorithfor the case of a varying azimuthf.


Fig. 4 Structure of the algorithm to fuse 1-D illumination series.

thelo

ray

n-

ithisurea-

t,

x

he

po-

n

heen

ns ofis

re-

rec-the

n

leinle

The fusion algorithm is based on the selection ofbest illuminated image segments of the series for eachcationx based on the maximization of a local criterionC.Since a high contrast is desired in our case, the local glevel variance and the local entropy are suitable criteraC.The selected illumination direction maximizing the cotrast, which is stored for each locationx in the so-calledillumination map,

f~x!ªarg maxf i

C$d~x,f i !%, ~7!

has to be a spatial function varying slowly, compared wthe signal of interest, i.e., the width of the grooves. Thisnecessary to avoid artifacts in the fusion result. To assthat this condition is satisfied, a smoothing of the illumintion map with a binomial low-pass filter LP$.% isperformed7:

w~x!ª/LP$exp~ jf~x!!%. ~8!

In this step, the cyclicity off has to be taken into accounbecause the equationf5f12pk, kPZ, holds. Conse-

quently, notf(x) itself is to be smoothed, but the comple

pointer exp@jf(x)#. The resulting functionw(x), which de-notes the best-suited local illumination direction, is tangle of the complex result.8

The actual fusion is performed by a weighted supersition of two adjacent imagesd(x,f i) by means of a linearinterpolatorg, taking the best local illumination directiow(x) into account:

r ~x!ª@f l2w~x!#mod 2p

~f l2fk!mod 2pd~x,fk!

1~w~x!2fk!mod 2p

~f l2fk!mod 2pd~x,f l !, ~9!

-

-

with

lª~k11!modB,

~f l2fk!mod 2p<@w~x!2fk#mod 2p,

whereB denotes the number of images of the series. Tinterpolation takes care of a smooth transition betwef-neighboring images. The narrow extent ofg ensures anaveraging of only similarly illuminated images. Thus, aundesirable contrast loss due to destructive interferencelight and shadow in different images of the seriesavoided.

Three properties of the proposed fusion method aresponsible for its good performance: 1. the fusion resultr (x)resembles locally the best illuminated imaged(x,f i) of theseries; 2. the smoothness of the selected illumination dition w(x) guarantees that no artifacts are generated inresult r (x); and 3.r (x) achieves globally good results ithe sense of maximizing the local contrastC.

A fusion of an image series in which the elevation angu of the illumination direction is varied can be performedan analogous manner. However, since the elevation anguis not cyclic, instead of Eq.~9!, the following simplifiedexpression is obtained:

r ~x!ª(i

d~x,u i !g@q~x!2u i #

5u l 112q~x!

u l 112u ld~x,u l !1

q~x!2u l

u l 112u ld~x,u l 11!, ~10!

with

q~x!ªLP$u~x!%, u~x!ªarg maxu i

C$d~x,u i !%.


hed inturssherc-tese

reere

in

onin-too

ks,imhe

reof

the. Itent

ionnotthe, axact

chs ofr tofa

eds

us-a

y ofvi-

htento

there.

theucevehehe

tine

epro-.g.,he

heon-ge

ioncedbletion


4 Preprocessing

After having generated a high-quality image showing tmarks of interest by means of the approach presenteSec. 3.2, a preprocessing is performed to suppress texinhomogeneities that arise from the illumination proceand from the object shape. At the same time, the furtprocessing steps will be simplified. To this end, a diretional Gaussian high-pass filter is used that eliminaslowly varying gray-level fluctuations perpendicular to thgrooves and provides for a homogenization of first deg~in image processing literature, this step is sometimesferred to as a shading correction!, i.e., of the local averagegray level, without generating undesirable artifacts.9,10 Fig-ure 5 shows an example of the preprocessing.

Alternatively, a homogenization of second degree,which the local contrast is equalized as well,9 has also beentested. However, since this powerful homogenizatimethod leads to a significant alteration of the signal ofterest, it appeared to be a less indicated preprocessingfor quantitative image comparison.1

5 Extraction of a Signature

To enable an efficient computerized comparison of marthe database matching should not be performed at theage level. Instead, a data reduction should be accomplisfirst to extract from the image asignature, i.e., a 1-D ‘‘fin-gerprint’’ of the striation pattern. The resulting signatucan be considered characteristic for a certain specimentool or firearm.

The signal model proposed in Sec. 2 is based onkinematics imposed during the generation of grooveswould be ideal—if one was able—to infer the 1-D edgdirectly from an image of the marks. This would represe

Fig. 5 Example of the preprocessing of a tool mark: (left) originalimage; (right) homogenization result.


e

-

l

-d

a

the inversion of the kinematics of the groove generat~see Fig. 6!. However, such an immediate strategy doesseem to be feasible, since usually the kinematics ongroove generation cannot be determined. Thereforemethod is needed to extract the signature without an eknowledge of the process that generated the striae.

Many of the strategies applied up to now to extract susignatures are based on sampling the image intensitiethe groove structure along a straight line perpendiculathe striations direction.11,12 Sometimes, a small amount oprofiles specified interactively is averaged. However,computerized optimization of the parameters determinthereby~e.g., the angle to the local direction of the groove!is generally not performed.

The main drawback of these strategies is their high sceptibility to all kinds of disturbances. The texture ofstriation pattern may appear degraded by a large varietfactors, including scratches, and soiling, but also by caties and inclusions when castings are used~see, e.g., Fig.5!. For this reason, a robust strategy to trace and straigthe grooves is proposed next. The underlying idea isconsider the whole length of the grooves to suppressinfluence of local disturbances on the resulting signatuSince such disturbances only affect minor regions ofmarks, a suitable filtering along the grooves can redtheir influence. Filtering the gray values along a grooyields a single point of the signature. By repeating tgroove tracing for all grooves of a striation pattern, tdesired signature is obtained.

5.1 Pristine Bullets

The proposed strategy can easily be illustrated with prisbullets. As shown in the applicable signal models@Figs. 1and 2~a!#, the anglec describes the global direction of thgrooves. This angle has to be estimated to perform thejection in the direction of the striae. This can be done, ebased on the analysis of a radial projection of tperiodogram.1,13

5.2 Deformed Bullets and Tool Marks

If the local orientation of the grooves changes within tarea of interest, it turns out to be more complicated to csider the whole length of the grooves. Here, every imapoint has to be assigned individually to a particular positon the unidimensional edge. The grooves have to be traalong the whole area of the mark. In this case, suitastrategies to generate a signature include a local orientaanalysis and model-based methods.

Fig. 6 Groove straightening and generation of a signature.


Fig. 7 Model-based groove straightening algorithm.

of-or-to

llyed

nx-

ro-ntos towth.of

nferiaelgo-a

herb

etele odgethislllly,

nal

e

ly.id-ex-thheallly

frpo--he: the

cu-uc-er-

i-inte.

k. Inanes-

id-

aloveto

vesti--

5.2.1 Local orientation analysis

These methods allow us to determine the local directiona texture~e.g., of a striation pattern! based on local features, such as the variance or gradients of gray values,local Fourier analysis.1,14 In the context of textures on technical surfaces, local orientation methods have provenperform satisfactorily.13 They have also been successfuapplied to the processing of striation marks on deformbullets.1

However, a reliable identification of the local striatiodirection requires that the directionality of the surface teture is locally sufficiently pronounced. Concerning the pcessing of tool marks, a segmentation of the texture iregions containing grooves and background regions habe performed first. Moreover, tool marks often do not shsufficiently pronounced grooves over their whole widThis leads regularly to errors that constrain the usabilitythis approach considerably.

5.2.2 Model-based groove tracing

Model-based strategies according to Sec. 2 allow us to ithe path of the tool edge from the arrangement of the stin the image. The corresponding groove straightening arithm is illustrated in Fig. 7, with marks generated bypure translation of the tool edge. Marks described by otsignal models and their corresponding parameters cantreated analogously.

Starting from the preprocessed imaged(x), an adequatesignal model has to be chosen. The selected model dmines the parameters needed. Concerning the exampFig. 7, the assumption of a pure translation of the tool e@Fig. 2~b!# seems to be reasonable. One may object thatsimplifying assumption holds only for a relatively smaclass of striation patterns. However, when applied locathe corresponding model depicted in Fig. 2~b! has proven toyield both satisfactory results and a good computatio

a

o

r

e

r-f

performance in most practical cases. In this case, anedgeline g1(s) describing the direction and the width of thedge as well as aguiding groovem(t) are required asmodel parameters. The argumentss and t describe the po-sition on the edge and the curve parameter, respective

First of all, both model parameters—edge line and guing groove—are estimated interactively by the forensicaminer@see Fig. 8~a!#. The edge line is defined as the widof the interesting region of the mark in the direction of tedge~points 0, 1!. To estimate the guiding groove, severpoints on a particularly pronounced groove are manuamarked ~points 2 to 4!. To comply with the postulate osmoothness for the marked groove, the points are intelated by means ofsplines. However, it should be emphasized that an interactive estimation of the path of tgrooves does not seem to be adequate for a few reasonsprecision of the method would suffer in the case of inacrate user input; and for reasons of reliability and reprodibility, any unsupervised adoption of data determined intactively should be avoided.

To cope with these difficulties, a computer-aided optimzation of the path of the guiding groove is performedwhich the interactive estimation is used as the initial staSeveral approaches are available to accomplish this tasthe following, an algorithm is presented that performsoptimization of the position of all points configuring thdiscrete guiding groove by maximizing the local croscorrelation coefficient.

An alternative approach consists in regarding the guing groove as an active contour orsnake.15 With someslight adaptation concerning the definition of the internenergy, such a snake can be fitted to the optimal gropath. Furthermore, the application of snake algorithmsthe control points of a spline describing the guiding grooconstitutes another possibility to enhance the initial emate of the guiding groove.16 The advantage of those ap



Fig. 8 Groove straightening: (a) interactive estimation of the guiding groove; (b) respective correlationimage; and (c) extraction of the signals g1(s) and g2(s).

ideseex-

lso

r-

he

e-

dfol-

the

asthethe

ori-ryala

proaches based on snakes consists of the implicit consation of continuity conditions. On the other hand, themethods entail a significantly increased computationalpense.

The cross-correlation function~CCF! is a well-knowntool to detect linear correspondences.17 In forensic science,its application to matching striation patterns has aproven to provide successful and robust results.1,18 TheCCF is defined as

k12~t!ªg1~s!~g2~s!5E2`

`

g1~s!•g2~s2t!ds, ~11!

where both signalsgi(s) have been normalized by centeing them around their mean valuesmgi and dividing themby their standard deviationssgiª(var$gi(s)%:)1/2

gi~s!ªgi~s!2mgi

sgi. ~12!

The value of the maximumr12ªmax$k12(t)% indicatesthe degree of similarity between both signalsg1(s) and


r-g2(s). The nearerr12 lies to the maximal value 1, thestronger their resemblance will be. The location of tmaximum of the CCF

t0ªarg maxt

$k12~t!%, ~13!

supplies the information on how to choose the shift btween both signals to achieve the best possible match.

The signalg1(s) is taken directly from the edge selecteinteractively and serves as a reference pattern for thelowing correlation@see Fig. 8~c!#. According to its defini-tion, it is spatially limited and has the lengthL1 . It mightbe reasonable to weight the intensity values aroundmarked groove, e.g., by means of a GaussianG(s,s). Thisway, a higher weight of the central region is obtainedcompared with more distant parts. Since defects ofgroove pattern are more likely to appear at the border ofmark, their influence on the CCF is thus reduced. Thegin of g1(s) is positioned on the guiding groove. For evepoint m(t) of the guiding groove, the corresponding signg2(s) is determined by interpolating the intensities along

Fig. 9 Direct correlation of two signals parallel to the tool edge extracted from the preprocessedimage.


Fig. 10 Experimental results: (a), (c) original images; (b), (d) preprocessed and straightened imagesections.

n-

ge

ece

tery

tedheirs

ofa-n.ngto

ve,lel t-de-the

hehedcis

rdi-lo-theansteme i

an

singof

and

hasthethe

ble, inr-be

ovedis-its.

utthe

gerksisesevelped

toolitnd,n todim-it-uta-at

fo-

r.his

straight line throughm(t) parallel to the edge line. Theorigin g2(s50) is also set on the guiding groove. In cotrast to g1(s), the lengthL2 of the signalg2(s) is notlimited to a defined value but is restricted by the imaboundaries.

The locationt0 of the maximum of the CCF yields thshift leading to the highest similarity between the referenprofile g1(s) and the groove profileg2(s). If t0 differsfrom zero for a certain pointm(t), an unprecise user inpuis assumed, and the guiding groove is shifted at that vpoint by t0 parallel to the edge line to correct this error.

To give an example, Fig. 9 depicts two signals extracfrom a preprocessed image of a tool mark as well as tcorresponding CCFk12(t). In this case, a Gaussian waused before to weight the signalg1(s). The CCF shows astrongly pronounced maximum withr1250.43. Althoughthis value may seem to be too low for other applicationsthe CCF, the only important property in our context isreliable identification of the global maximum. In this respect, the value obtained suffices for a further evaluatio

The CCFs calculated at every position of the guidigroove can be coded as gray values and assembledcorrelation image@see Fig. 8~b!#. The origin of each CCFhas been chosen to coincide with the guiding groowhereas the CCFs themselves have been plotted paralthe edge line. The maximar12 of the CCFs can be recognized as a bright curve in the correlation image. Thus,spite the very inaccurate input of the guiding groove inexample of Fig. 8~a!, the correlation image in Fig. 8~b!faithfully describes its actual path. The final result of tproposed optimization strategy is equivalent to a matccoordinate system that can be used to perform a prestraightening of the grooves.

5.3 Groove Straightening

The optimized model parameters yield a matched coonate system in which the groove direction correspondscally to the ordinate. The abscissa is not affected byoptimization and represents the edge direction. By meof a nonlinear transform of the matched coordinate sysinto a Cartesian coordinate system, a straightened imagobtained~see Fig. 7!. Based on this result, the signature ceasily be computed by averaging the image rows.

a

o

e

s

6 Experimental Results

To substantiate a good performance of the signal processteps proposed in this work, Fig. 10 shows examplestypical tool marks and the results of our preprocessingstraightening strategies. In Figs. 10~a! and 10~c!, an overlaywith the interactive estimation of the model parametersbeen plotted. As stated in Sec. 5.2, a pure translation oftool edge has been found to be suitable to describegroove generation in the case of most tool marks.

Even though both original images show consideradistortions, such as an inhomogeneous illumination andthe case of Fig. 10~c!, dust particles, the processing geneates satisfactorily straightened grooves that can easilyconcentrated into signatures. However, when the grotexture becomes too faint or parts of the grooves arecontinuous, the straightening approach reaches its limThis can be seen in the upper part of Fig. 10~d!, where asufficient overall straightening still can be achieved, bslight deviations from a strictly straight appearance oftexture have to be tolerated.

7 Conclusions

A model-based description of the structure of a wide ranof forensically relevant marks, such as tool marks, maon firearm bullets, and the like, is introduced. Aided by thmodel, a strategy to generate high-quality images of thmarks is proposed. To obtain reliable signatures, a nomethodology to trace and straighten the groove-shamarks is discussed.

The resulting representation describes the entireedge faithfully. Consequently, it is straightforward to usefor a subsequent comparison at a signal level. To this eapproaches based on correlation methods have showprovide satisfactory results.17 Furthermore, the presentestrategy can also be combined with existing systems toprove their performance and reliability. Together with suable comparison approaches, a highly robust and comptionally efficient comparison framework is obtained thprovides the turnaround times and success rates that arensic identification of marks demands.

Acknowledgments

The authors would like to thank Mr. Andreas Kapp and MThao Dang for valuable comments on a draft version of twork.


n

’’

sor

ci-

n

om

to-

ica-

ur

ar

in


References

1. F. Puente Leoń, Automatische Identifikation von Schußwaffen, VDIVerlag, Dusseldorf~1999!.

2. F. Puente Leoń and J. Beyerer, ‘‘Automatic comparison of striatioinformation on firearm bullets,’’Proc. SPIE3837, 266–277~1999!.

3. J. J. Clark and A. L. Yuille,Data Fusion for Sensory InformationProcessing Systems, Kluwer Academic Publishers, Boston~1990!.

4. X. E. Gros,NDT Data Fusion, Arnold, London~1997!.5. F. Puente Leoń, ‘‘Enhanced imaging by fusion of illumination series,

Proc. SPIE3100, 297–308~1997!.6. G. H. Tarbox and S. N. Gottschlich, ‘‘Planning for complete sen

coverage in inspection,’’Comput. Vis. Image Underst.61~1!, 84–111~1995!.

7. B. Jahne,Digital Image Processing: Concepts, Algorithms, and Sentific Applications, Springer-Verlag, Berlin~1993!.

8. K. V. Mardia,Statistics of Directional Data, Academic Press, London~1972!.

9. J. Beyerer and F. Puente Leoń, ‘‘Suppression of inhomogeneities iimages of textured surfaces,’’Opt. Eng.36~1!, 85–93~1997!.

10. T. Lindeberg,Scale-Space Theory in Computer Vision, Kluwer Aca-demic Publishers, Boston~1994!.

11. W. Deinet, ‘‘Studies of models of striated marks generated by randprocesses,’’J. Forensic Sci.26~1!, 35–50~1981!.

12. Z. Geradts, J. Keijzer, and I. Keereweer, ‘‘A new approach to aumatic comparison of striation marks,’’J. Forensic Sci.39~4!, 974–980~1994!.

13. J. Beyerer, ‘‘Model-based analysis of groove textures with appltions to automated inspection of machined surfaces,’’Measurement15, 189–199~1995!.

14. M. Kass and A. Witkin, ‘‘Analyzing oriented patterns,’’Comput. Vis.Graph. Image Process.37~3!, 362–365~1987!.

15. M. Kass, A. Witkin, and D. Terzopoulos, ‘‘Snakes: active contomodels,’’ Int. J. Comput. Vis.1~4!, 321–331~1987!.

16. R. Cipolla,Active Visual Inference of Surface Shape, Springer-Verlag,Berlin ~1995!.

17. F. Puente Leoń and M. Heizmann, ‘‘Strategies to detect non-line


similarities by means of correlation methods,’’Proc. SPIE4572, 513–524 ~2001!.

18. M. Heizmann, ‘‘Strategies for the automated recognition of marksforensic science,’’Proc. SPIE4709, 68–79~2002!.

Michael Heizmann received his MS de-gree in mechanical engineering in 1998from the University of Karlsruhe, Germany.Since September 1998, he has been a re-search assistant with the Institut fur Mess-und Regelungstechnik of the University ofKarlsruhe. His research interests includeimage processing, automated visual in-spection, and their applications in industryand forensic science.

Fernando Puente Leoń is a professor inthe Department of Electrical Engineeringand Information Technology at the Tech-nische Universitat Munchen, Germany. Hereceived his MS degree in electrical engi-neering in 1994 and his PhD degree in au-tomated visual inspection in 1999, bothfrom the University of Karlsruhe, Germany.From 2001 to 2002, he was employed byDesign of Systems on Silicon (DS2), Va-lencia, Spain. From 2002 to 2003, he was

a postdoctoral research associate at the Institut fur Mess- undRegelungstechnik of the University of Karlsruhe, where he headedthe Information Fusion Group. His research interests include imageprocessing, automated visual inspection, information fusion, mea-surement technology, and communications.

Imaging and analysis of forensic striation marks - · PDF fileImaging and analysis of forensic...

Documents

Transcript of Imaging and analysis of forensic striation marks - · PDF fileImaging and analysis of forensic...