NISTIR 7932

The Use of ‘Slow Motion’ Lévy 

Stable Fractional Diffusion 

Smoothing In Alternative Methods 

of Latent Fingerprint Enhancement 

Alfred S. Carasso 

http://dx.doi.org/10.6028/NIST.IR.7932 
 

 

 

NISTIR 7932 

The Use of ‘Slow Motion’ Lévy 

Stable Fractional Diffusion 

Smoothing In Alternative Methods 

of Latent Fingerprint Enhancement 

Alfred S. Carasso 

Applied and Computational Mathematics Division 

Information Technology Laboratory 

http://dx.doi.org/10.6028/NIST.IR.7932 

April 2013 

U.S. Department of Commerce 

Rebecca Blank, Acting Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 
THE USE OF ‘SLOW MOTION’ LEVY  ́ STABLE FRACTIONAL

DIFFUSION SMOOTHING IN ALTERNATIVE METHODS OF

LATENT FINGERPRINT ENHANCEMENT

ALFRED S. CARASSO∗

Abstract. Photoshop processing1 of latent fingerprints is the preferred methodology among

law enforcement forensic experts, but that appproach is not fully reproducible and may lead to

questionable enhancements. Alternative, independent, fully reproducible enhancements, using IDL

Histogram Equalization and IDL Adaptive Histogram Equalization, can produce better-defined ridge

structures, along with considerable background information. Applying a systematic slow motion

smoothing procedure to such IDL enhancements, based on the rapid FFT solution of a L ́evy stable

fractional diffusion equation, can attenuate background detail while preserving ridge information.

The resulting smoothed latent print enhancements are comparable to, but distinct from, forensic

Photoshop images suitable for input into automated fingerprint identification systems, (AFIS). In

addition, this progressive smoothing procedure can be reexamined by displaying the suite of progressively smoother IDL images. That suite can be stored, providing an audit trail that allows

monitoring for possible loss of useful information, in transit to the user-selected optimal image. Such

independent and fully reproducible enhancements provide a valuable frame of reference that may be

helpful in informing, complementing, and possibly validating the forensic Photoshop methodology.

Key words. latent fingerprints; dodge and burn; reproducible image enhancement; progressive

L ́evy stable smoothing; fractional diffusion equation.

1. Introduction. This report is a sequel to [1] and a contribution to the research

project Metrics for Manipulation and Enhancement of Forensic Images, sponsored by

a 2012 NIST Forensic Measurement Challenges award. Here, an effective smoothing

technique previously used succesfully in nanoscale imaging [2], is applied to gradually

attenuate background detail in certain kinds of latent fingerprint enhancements discussed in [1]. This smoothing process is accompanied by an audit trail. The aim of

this work is to develop independent, systematic, and easily reproducible alternatives

to forensic Photoshop processing that can yield fingerprint enhancements of comparable quality. Viewed constructively, such alternative approaches provide a valuable

frame of reference that may be helpful in informing, complementing, and possibly

validating the Photoshop methodology.

In recent years, the reliability of fingerprint evidence has come under increased

scrutiny, [3–8]. One area of concern involves the digital enhancement of latent fingerprints left unintentionally at a crime scene. Such prints are generally smudgy,

with poorly defined ridge impressions that may be partially obscured by textured

background structures, together with random noise. There may also be overlapping

prints. The difficulty of isolating ridge impressions from such backgrounds, a key

step in latent print enhancements, has been stressed by several authors, [9–11]. In [8,

Chapter 4], the possibility of misleading artifacts in digital enhancements is discussed,

with guidelines proposed for the proper evaluation and acceptance of enhanced images. These guidelines include validation of the enhancement technology, along with

maintenance of an audit trail of the actual digital procedures used.

Photoshop processing of latent fingerprints is the preferred methodology among

∗Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899. (alfred.carasso@nist.gov). 1Mention of commmercial products or services in this report does not imply NIST appproval

or endorsement of these products or services, nor does it imply that such products or services are

necessarily the best available for the intended purpose.

1
2 ALFRED S. CARASSO

law enforcement forensic analysts. A variety of ‘dodge and burn’ and ‘brush’ tools

are freely applied to lighten or darken selected areas within the image, and remove

unwanted background information. The multiplicity and diversity of the individual

steps used in this process are not fully documented, and the procedure may not be

reproducible. For these reasons, forensic Photoshop latent fingerprint enhancements

have occasionally been found questionable.

2. Behavior in alternative latent print enhancements. In [1], several fingerprint enhancement approaches independent of Photoshop are discussed, along with

the software routines necessary to implement them. All of these methods aim at bringing into better visual range potentially significant structures that are present in the

original image, but not easily discernible. Each of these enhancement methods is

based on the use of a single command from such widely used scientific image analysis packages as MATLAB [12], IDL [13], and PV-WAVE [14]. Such enhancement

commands are applied to the whole image at once, are executed in seconds, and are

obviously reproducible. In addition, [15] provides a thorough discussion of the theoretical ideas underlying these various techniques. All images appearing in this report,

and expected as input or returned as output in the software routines, are 8 bit grey

scale tiff images.

While more generally applicable software is discussed in [1], we now list for the

reader’s convenience a simple routine, ‘IDLHist.pro’, for performing either histogram

equalization, or adaptive histogram equalization. These two distinct IDL techniques

exhibit better-defined ridge structure, along with considerably more background detail than is generally the case in forensic Photoshop enhancements, and they are the

primary focus of the present study. The routine below is to be applied to an 8 bit grey

scale original latent print image with white ridge impressions. The routine returns

the enhanced image with white ridge impressions, as well as the reversed enhanced

image with black ridge impressions.

;pro-file IDLHist.pro

;SIMPLE IDL CODE FOR ENHANCING IMAGES

;SELECT EITHER Simple or Adaptive histogram equalization

;APPLY BY TYPING ‘.run IDLHist’ in IDL

;ASKS USER TO PROVIDE INPUT 8bit GREYSCALE TIFF IMAGE

;ASKS USER TO SPECIFY X size and Y size of INPUT TIFF IMAGE

;RETURNS ENHANCED IMAGE IN FILE "sharp.tiff"

;RETURNS REVERSED ENHANCED IMAGE IN FILE "revsharp.tiff"

file1=’ ’

read,’enter filename: ’,file1

openu,1,file1

x1=0

y1=0

read,"enter xsize of image: ",x1

read,"enter ysize of image: ",y1

window,0,xsize=x1,ysize=y1

a = assoc(1,bytarr(x1,y1,/nozero))

image = a(0)

close, 1

;ACTIVATE DESIRED COMMANDS BY DELETING ‘ ; ’ SYMBOLS BELOW

;image=hist equal(image)
LEVY  ́ STABLE SMOOTHING OF LATENT FINGERPRINT ENHANCEMENTS

3

Original latent print

MATLAB contrast adjust

Reversed original print Forensic Photoshop

IDL Hist Equalization IDL Adaptive Hist Equalzn

 FOUR DISTINCT ENHANCEMENTS OF LATENT PRINT 1 Fig. 2.1. Four distinct enhancements of latent fingerprint 1. Possibly significant background structures are suppressed in Forensic Photoshop and MATLAB contrast adjusted images. IDL Histogram images produce better defined ridge impressions, along with considerable background information. As shown in Figure 2.2, L ́evy stable smoothing of IDL images can attenuate background detail while preserving ridge information.
4	 ALFRED S. CARASSO

image=adapt hist equal(image)

reverseimage=255-image

;tvscl, image

tvscl, reverseimage

write tiff, ’idlsharp.tiff’, image

write tiff, ’idlrevsharp.tiff’, reverseimage

end

As was the case in [1], the two original latent prints used in this study, latent

prints 1 and 2, together with their accompanying Photoshop enhancements, were

culled from a ‘before and after’ database made available to NIST by law enforcement

forensic experts. An instructive display of four distinct enhancements of latent print

1 is shown in Figure 2.1. That original print, shown in the top left hand corner, is

the input data into the various enhancement methods. The resulting enhanced prints

are shown as reversed images with black ridge impressions. Clearly, the forensic Photoshop image appears to be a credible reconstruction of a fingerprint that is almost

invisible in the reversed original print image. Remarkably, the single MATLAB command imadjust [1], applied to the same original print, produces the equally good

reconstruction shown in the bottom left hand corner. The IDL Histogram Equalized

and Adaptive Histogram Equalized images, in the bottom row of Figure 2.1, were obtained using the single IDL commands hist equal and adapt hist equal respectively,

in the above ‘IDLHist.pro’ routine. An examination of Figure 2.1 leads to the following observations.

•	 Much of the background detail evident in the two IDL Histogram images has

been filtered out in the forensic Photoshop and MATLAB contrast adjusted

images. This may be desirable in facilitating subsequent processing using

Automated Fingerprint Identification Systems (AFIS) software. However, the

ridge impressions in the Photoshop image are less clearly defined than they

are in the two IDL images. Conceivably, the Photoshop ’dodge and burn’

process that eliminated significant portions of the background, may have also

adversely affected the ridge structure. Such unintended collateral damage is

not uncommon in image processing. Viewed in isolation, the forensic Photoshop image provides no clues as to whether valuable information may have

been inadvertently discarded in the process of enhancing the original print.

•	 The original latent print in Figure 2.1 is susceptible to a multiplicity of distinct useful enhancements. The two IDL Histogram processes extract significantly more useful information from the original latent print, than do the

other techniques discussed in [1]. Note that the ridge structure in the Adaptive Equalized image is relatively free of the obscuring smudges that occur in

the other three enhancements in Figure 2.1. The background details in the

two IDL Histogram images include lines, streaks, and texture, in addition to

noise. This may be valuable contextual information in some circumstances.

2.1. Progressive smoothing of IDL Histogram images. An enhancement

strategy based on applying specifically designed smoothing to the IDL Histogram

images, is the main object of this report. This smoothing process is applied to the

enhanced image with white ridge impressions, and it is applied to the whole image.
LEVY  ́ STABLE SMOOTHING OF LATENT FINGERPRINT ENHANCEMENTS 5

 

Forensic Photoshop MATLAB contrast adjust

Smoothed IDL HistEq Smoothed IDL AdaptHistEq

LEVY STABLE SMOOTHING OF IDL IMAGES LEADS TO

COMPARABLE ENHANCEMENTS OF LATENT PRINT 1

Fig. 2.2. L ́evy stable fractional diffusion smoothing of IDL Histogram images, developed in

Sections 3-5, leads to fully reproducible enhancements of latent fingerprint 1 that are comparable to,

yet distinct from, the AFIS-ready forensic Photoshop image.
6 ALFRED S. CARASSO

It can preserve ridge structure while gradually attenuating background detail. As

shown in Figure 2.2, this leads to enhanced images that are comparable to, yet distinct

from, AFIS-ready forensic Photoshop images. A software routine to implement this

smoothing procedure, ‘IDLLevy.pro’, written in IDL language, is included in Section

4.

A significant aspect of the above smoothing process is that it can be implemented

in slow motion. The progressive evolution from the original IDL Histogram images

to the user-selected final smoothed versions shown in Figure 2.2, can be monitored,

stored, and displayed. That stored evolution serves as an audit trail, allowing the user

to verify whether significant information has been lost in transit. Indeed, the smoothing process can be reconsidered with different parameters, and contextual background

detail can be retrieved, if desired. These ideas are fully developed in Sections 3, 4,

and 5, and illustrated in Figures 4.1 through 5.3, where they are applied to enhancing

latent fingerprint 2.

3. L ́evy stable fractional diffusion smoothing. Given an enhanced latent

print image f(x, y), the smoothing procedure used on the bottom two images in Figure

2.2 results from solving an initial value problem for a special type of diffusion equation,

with the image f(x, y) as initial data. Such smoothing is applied to the whole image,

and not just to a selected portion of the image. For fixed p with 0 < p ≤ 1, consider

the linear fractional diffusion initial value problem in L2(R2),

(3.1) wt = −(−Δ)pw, t > 0, w(x, y, 0) = f(x, y),

where Δ denotes the 2D Laplacian. This reduces to the classical heat conduction

equation when p = 1. However, our smoothing procedure uses the fixed value p = 0.1.

Define the 2D Fourier transform of the image f(x, y) by

 

(3.2) F{f} = f

ˆ(ξ, η) ≡ f(x, y) exp{−2πi(ξx + ηy)}dxdy.

R2

Eq.(3.1) has the unique Fourier domain solution

 p (3.3) wˆ(ξ, η,t) = exp{−t (2πξ)

2 + (2πη)2 }f

ˆ(ξ, η), t > 0,

from which w(x, y,t) can be found by inverse Fourier transformation

 p (3.4) w(x, y,t) = exp{2πi(ξx + ηy)} exp{−t (2πξ)

2 + (2πη)2 }f

ˆ(ξ, η)dξdη.

R2

As is evident from Eq.(3.4), w(x, y,t) becomes increasingly smoother as t increases.

However, for small p, and over a short time interval, the smoothed image may be

expected to retain many of the essential features present in the initial data f(x, y).

In Eq. (3.3), the function

ˆ (3.5) h(ξ, η,t) = exp{−t

 

(2πξ)

2 + (2πη)2 p

}, t > 0,

is the Fourier transform of the Green’s function for the linear fractional diffusion

equation in Eq. (3.1). For each fixed t > 0, the function in Eq. (3.5) is also the Fourier

transform of an isotropic L ́evy stable probability density function with exponent 2p,

[16]. When p = 1, Eq.(3.5) corresponds to a Gaussian distribution. For p « 1,

Eq.(3.5) corresponds to a heavy-tailed density in physical (x, y) space. Unlike a
LEVY  ́	 STABLE SMOOTHING OF LATENT FINGERPRINT ENHANCEMENTS 7

Gaussian, that L ́evy density is not known in closed form in the physical variables

(x, y), and it has infinite mean and infinite variance.

Smoothing an image by convolution with a Gaussian is equivalent to using p =

1, and solving the heat conduction equation in Eq.(3.1). The significance of L ́evy

stable fractional diffusion smoothing with p = 0.1 can be inferred from Eq. (3.3).

Clearly, attenuation of high frequency information, corresponding to large (|ξ| + |η|),

is dramatically more severe when p = 1, than it is when p = 0.1. In [2], such

fractional diffusion smoothing preserved important morphological surface detail, while

attenuating background noise in nanoscale Helium Ion microscope imagery. Likewise,

in the present application, we expect important ridge information to be preserved

over short time intervals.

4. FFT L ́evy fractional diffusion smoothing of 2N ×2N pixel images. Latent print images g(x, y) are often rectangular. Such rectangular images are accepted

and enhanced by routine ’IDLHist.pro’ in Section 2. However, post-processing and

prior to L ́evy smoothing, the enhanced rectangular image is required to be centered

in a larger 2N ×2N array f(x, y), with zero pixel values surrounding the original rectangular image. This process is illustrated in Figure 4.1, where the original 1151×1600

pixels latent print 2 image is enhanced, using the single IDL commmand hist equal

in the routine ‘IDLHist.pro’. This results in an image of the same size, with white

ridge impressions. Using zero padding, that enhanced image is then centered in the

larger 1900 × 1900 pixel square array, in preparation for smoothing. The smoothing

software routine ‘IDLLevy.pro’ listed below, assumes a square input image of even

dimension, and returns a square smoothed image of the same size. The smoothed

image can subsequently be cropped to the original rectangular size.

Given the 2N × 2N pixels image f(x, y) as initial data, ‘IDLLevy.pro’ computes

the solution w(x, y,t) in Eq. (3.1) at any given t > 0, by using the forward and inverse

FFT to implement the operations in Eq. (3.3) and Eq. (3.4) respectively. In order to

render mathematical formulae more transparent, we use the same notation, f

ˆ(ξ, η),

for both discrete and continuous Fourier transforms. In the discrete FFT case, the

frequencies 2πξ and 2πη are understood to be integer-valued and to range from −N

to N. After selecting a tentative maximum smoothing time Tmax at which to terminate the smoothing process, Eq.(3.4) can be evaluated at finitely many intermediate

times 0 = t0 < t1 < t2 < t3 < · · · = Tmax, to create a suite of progressively smoother

images. In ‘IDLLevy.pro’ where p = 0.1, a total of six images are displayed at times

tm = {(m − 1) ∗ Tmax}/5, m = 1, 6. The first image is the original unsmoothed

IDL Histogram image, while the sixth image is the smoothest image at the final time

Tmax. A user may select an image at some tm ≤ Tmax as the optimal image, or may

elect to try a different value of Tmax. The routine ‘IDLLevy.pro’ is applied as follows:

•	 At the prompt, the number 2N should be entered for image size. For final

time of smoothing Tmax, a number between 0.2 and 0.5 should be entered as

a good first choice. Exploring several values of Tmax is useful.

•	 For each choice of Tmax, the associated suite of progressively smoother images

is computed and displayed in a matter of a few seconds. The user is then

prompted to select the optimal smoothed image by entering a picture number

between 2 and 6. Several trial choices can be explored. For each trial selection of optimal image, the original unsmooth image and the selected optimal

image are displayed side by side.
8	 ALFRED S. CARASSO

•	 When a final selection is made, the number -1 is entered to quit ‘IDLLevy.pro’.

The suite of six progressively smoother images corresponding to the last choice

of Tmax, is in the file ‘LevyEvol.tiff’. The final selection of optimal image in

that suite, is in the file ‘Levysmooth.tiff’.

;pro-file IDLLevy.pro

;LEVY FRACTIONAL DIFFUSION IMAGE SMOOTHING

;APPLY BY TYPING ‘.run IDLLevy’ in IDL

;ASKS FOR INPUT 2Nx2N 8bit GREYSCALE TIFF IMAGE

;RETURNS USER SELECTED OPTIMAL SMOOTH IMAGE IN FILE ‘Levysmooth.tiff’

;RETURNS PROGRESSIVELY SMOOTHER 6 IMAGE SUITE IN FILE ’LevyEvol.tiff’

file1 = ’ ’

sz= ’ ’

time= ’ ’

read,’enter filename (e.g. Unsmooth.tiff): ’, file1

read,’enter image size, (e.g. 1600; Square image assumed):’,sz

read,’enter final time of smoothing, (e.g. 0.5 ): ’, time

close,1

openu,1,file1

a	 = assoc(1,bytarr(sz,sz,/nozero))

B=a(0)

SB=Size(B,/dimensions) & N=SB[0] & M=SB[1]

u=(Findgen(N)-N/2)#Replicate(1,M)

v=(Findgen(M)-M/2)##Replicate(1,N)

window,0,xsize=1800, ysize=1200

DEVICE, DECOMPOSED=0

LOADCT,0

B=Reverse(B,2)

BB=CONGRID(B,600,600)

BB=255-BB

p=0.1

r2=u*u+v*v

r2p=(r2 ^ p)

dt=time/5.0

AF=FFT(B)

AFS=Shift(AF,N/2,M/2)

TV, BB, 0

;SELECT APPROPRIATE TITLE FOR INPUT UNSMOOTH IMAGE

XYOUTS,300,1160, ’IDL HistEq; Time=0’, Alignment=0.5,$

;XYOUTS,300,1160,’IDL AdaptHistEq; Time=0’,Alignment=0.5,$

CHARSIZE=4.0, CHARTHICK=5.0, /DEVICE, color=0

for i=1,5 do begin

h=exp(-i*dt*r2p)

AFH=h*AFS

BH=Abs(FFT(AFH,/Inverse))

BBH=CONGRID(BH,600,600)

BBH=255-BBH

TV, BBH, i
LEVY  ́ STABLE SMOOTHING OF LATENT FINGERPRINT ENHANCEMENTS 9

if (i le 2) then begin

XYOUTS, 300+i*600, 1160, $

’Smoothed; Time=’+strsub(si(i*dt),0,4),$

Alignment=0.5, CHARSIZE=4.0, CHARTHICK=5.0, /DEVICE, color=0

endif

if (i ge 3) then begin

XYOUTS, 300+(i-3)*600, 560, $

’Smoothed; Time=’+strsub(si(i*dt),0,4),$

Alignment=0.5, CHARSIZE=4.0, CHARTHICK=5.0, /DEVICE, color=0

endif

sidt= si(i*dt)

endfor

GB=TVRD(0,0,1800,1200)

write tiff, ’LevyEvol.tiff’, GB

i=0

read,’enter picture number [2..6 to select image, or -1 to quit]: ’,i

while (i ne -1) do begin
 

print,’picture number: ’,i
 

j=i-1
 

h=exp(-j*dt*r2p)
 

AFH=h*AFS
 

BH=Abs(FFT(AFH,/Inverse))
 

BB=CONGRID(B,1200,1200)
 

BB=255-BB
 

BBH=CONGRID(BH, 1200,1200)
 

BBH=255-BBH
 

window,0,xsize=2400, ysize=1200
 

TV, BB, 0
 

XYOUTS, 600,1130, ’Unsmoothed; Time=0’, Alignment=0.5,$
 

CHARSIZE=9.5, CHARTHICK=5.0, /DEVICE, color=0
 

TV, BBH, 1
 

XYOUTS, 1800,1130, ’Smoothed; Time=’+strsub(si(j*dt),0,4),$
 

Alignment=0.5, CHARSIZE=9.5, CHARTHICK=5.0, /DEVICE, color=0
 

read,’enter picture number (-1 to quit): ’,i
 

endwhile
 

BH=255-BH

write tiff, ’Levysmooth.tiff’, BH

close,1

end

5. Applying fractional diffusion smoothing to latent fingerprint 2. Latent print 2 is distinctly different from latent print 1, although both prints share

similar characteristics. In Figure 4.1, the original 1151 × 1600 latent print shows

little visible structure, but IDL Histogram Equalization brings out considerable information. Even more information results from IDL Adaptive Equalization. Both these

enhanced images, with white ridge impressions, were embedded in a larger 1900×1900

array prior to processing using ‘IDLLevy.pro’.

After some preliminary exploration, a final smoothing time Tmax = 0.5, was
10 ALFRED S. CARASSO

Original latent print IDL Hist Equalization

Embedding in square array prior to smoothing

PRE PROCESSING FOR SMOOTHING OF IDL HISTOGRAM EQUALIZED LATENT PRINT 2 Fig. 4.1. Rectangular original 1151 × 1600 latent fingerprint 2 image is enhanced, using single command ‘hist equal’ in routine ‘IDLHist.pro’, resulting in same size IDL HistEq image, with white ridge impressions. Using zero padding, IDL HistEq image is then centered in 1900 × 1900 array prior to input in smoothing routine ‘IDLLevy.pro’.
LEVY  ́ STABLE SMOOTHING OF LATENT FINGERPRINT ENHANCEMENTS 11

chosen for both IDL Histogram images, resulting in the ‘slow motion’ smoothing

displays shown in Figures 5.1 and 5.2. The image at t = 0.4 was selected as optimal

in Figure 5.1, while an earlier image, at t = 0.3, seemed best in Figure 5.2.

Figure 5.3 displays the reversed forensic Photoshop enhancement of latent fingerprint 2, bracketed by the two L ́evy smoothed IDL Histogram images. That figure, as

well as other figures in this report, is more informative when viewed on a high resolution device, such as an active matrix, backlit, LCD monitor. Noteworthy features

in the on-line Figure 5.3 include the following:

•	 Some type of writing appears at the very top of the leftmost image in Figure

5.3. This writing is also present, but somewhat less visible, in the rightmost

image. However, that feature must have been deemed irrelevant in the Photoshop image, as it appears to have been eliminated by the ‘dodge and burn’

process. Further down the image, there appears to be additional writing

across the print. This is again more visible in the two IDL Histogram images,

than it is in the Photoshop image. Also, the streaks near the bottom left

edges in the two IDL Histogram images are more clearly defined than they

are in the Photoshop image.

•	 Near the bottom right corner in the leftmost image in Figure 5.3, there is

an unmistakeable horizontal smearing of the lower fingerprint, from left to

right. Such smearing is somewhat less well-defined in the righmost IDL image.

However, in the Photoshop image, this smearing effect was not sufficiently

noticeable to attract attention when the Photoshop image was viewed in

isolation. This is one of several examples where features in the Photoshop

image become more clearly understood upon consultation of the adjoining

IDL Histogram images.

6. Concluding remarks. AFIS-ready forensic Photoshop latent fingerprint enhancements typically strive to achieve an image exhibiting black ridge impressions over

a quasi uniform light grey background. However, viewing such enhancements without

some frame of reference, cannot allay the apprehension that potentially significant

information may have been inadvertently eliminated, or artifacts possibly introduced,

by overzealous application of ‘dodge and burn’, ’brush’, and other Photoshop tools.

This report has outlined an auditable, fully reproducible approach, independent

of Photoshop. The methodology begins with single command enhancements of the

original latent print, using IDL Histogram Equalization and IDL Adaptive Histogram

Equalization. These two distinct enhancements techniques produce considerable background information, along with high quality reconstruction of ridge impressions. A

‘slow motion’ progressive smoothing procedure is then applied to gradually attenuate, but not eliminate, background detail. This leads to latent print enhancements

that are comparable to, but distinct from, AFIS-ready Photoshop images. In particular, potentially significant contextual background information remains visible in

these L ́evy-smoothed IDL enhancements, as shown in Figures 2.2 and 5.3. Such reproducible enhancements may provide a valuable frame of reference for evaluating

Photoshop processed latent prints.

A question of major interest is whether the additional information provided in

these smoothed IDL enhancements leads to the same matches obtained using the
12 ALFRED S. CARASSO

 ‘SLOW MOTION’ LEVY STABLE SMOOTHING OF IDL HISTEQ LATENT PRINT 2 Fig. 5.1. Progressive smoothing of IDL Histogram Equalized latent fingerprint 2, using routine ‘IDLLevy.pro’ to solve L ́evy stable fractional diffusion equation Eq.(3.1), from t = 0 to t = 0.5. Smoothed image at t = 0.4 was considered optimal .
LEVY  ́ STABLE SMOOTHING OF LATENT FINGERPRINT ENHANCEMENTS 13

 ‘SLOW MOTION’ LEVY STABLE SMOOTHING OF IDL ADAPTHISTEQ LATENT PRINT 2 Fig. 5.2. Progressive smoothing of IDL Adaptive Histogram Equalized latent fingerprint 2, using routine ‘IDLLevy.pro’ to solve L ́evy stable fractional diffusion equation Eq.(3.1), from t = 0 to t = 0.5. Here, smoothed image at t = 0.3 was considered optimal

.
14 ALFRED S. CARASSO

 Smoothed IDL AdaptHistEq. 

 THREE COMPARABLE AND DISTINCT ENHANCEMENTS OF LATENT PRINT 2

Forensic Photoshop Smoothed IDL HistEq.

at time = 0.4 at time = 0.3 Fig. 5.3. Viewed on-line on high resolution device, smoothed IDL images complement and inform the forensic Photoshop image. Leftmost IDL Adaptive Histogram image shows writing near top, streaks near bottom left edge, and horizontal left to right smearing of lower print near lower right corner, in addition to well-defined ridge structure. To a lesser extent, these features are also present in the righmost IDL Histogram image. However, when the Photoshop image is viewed in isolation, the smearing in the lower print is not immediately evident. Also, the streaks are faint in the middle image, and the writing near the top appears to have been erased.
LEVY  ́	 STABLE SMOOTHING OF LATENT FINGERPRINT ENHANCEMENTS 15

forensic Photoshop process. If that is not the case, how much further smoothing of

the IDL enhancements is necessary to recover the Photoshop induced matches ? Conversely, if the original forensic Photoshop enhancement procedure is reprogrammed,

and aimed towards matching the smoothed IDL enhancements, how would the new

Photoshop enhanced print be processed by the AFIS-software ?

7. Acknowledgements. This work was sponsored by the 2012 NIST Forensic Measurement Challenges grant, Metrics for Manipulation and Enhancement of

Forensic Images.

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