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 Table of Contents  
ORIGINAL ARTICLE
Year : 2018  |  Volume : 4  |  Issue : 4  |  Page : 192-196

Fast fourier transform: A Niche, but critical strategy in optimizing impression evidence


Department of Forensic Science, Laurentian University, Sudbury, Canada

Date of Web Publication27-Dec-2018

Correspondence Address:
Dr. Brian Dalrymple
Department of Forensic Science, Laurentian University, Sudbury, Ontario
Canada
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/jfsm.jfsm_35_18

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  Abstract 


The evolution from film to digital as the recording medium for forensic imaging has extended the reach of forensic photographers, both in original capture and postphotography processing. Images of fingermarks and footwear impressions are routinely obstructed by substrates displaying intrusive color and pattern. Such backgrounds are frequently sufficiently intrusive as to prevent the analysis and comparison of the images to known exemplars. Digital techniques such as Fast Fourier Transform (FFT) in postphotography processing can optimize the signal-to-noise ratio to a greater degree than was ever possible when film was the recording standard. Occasionally, unwanted backgrounds can be removed or diminished in Photoshop with techniques such as background subtraction and channel blending. These strategies, however, are dependent on either physical removal of the evidence impression to obtain a second image of the obstructive pattern or on differences in color between the impression and the offending substrate. FFT is unique in its ability to optimize the image signal to noise ratio by suppressing the obstructive background, in that it is not reliant on color, and is not applied in the spatial domain.

Keywords: Fast Fourier Transform, image pro premier, postphotography digital optimization


How to cite this article:
Dalrymple B. Fast fourier transform: A Niche, but critical strategy in optimizing impression evidence. J Forensic Sci Med 2018;4:192-6

How to cite this URL:
Dalrymple B. Fast fourier transform: A Niche, but critical strategy in optimizing impression evidence. J Forensic Sci Med [serial online] 2018 [cited 2019 Jan 16];4:192-6. Available from: http://www.jfsmonline.com/text.asp?2018/4/4/192/248701




  Fast Fourier Transform Top


To understand the process of FFT, it is helpful to characterize impression evidence (fingermarks, shoeprints) as visible “signal,” and anything else appearing in the field of view as “noise.” The sequential process of developing and photographing such evidence, with the ultimate goal of (analysis and comparison to exemplars) can be stated as optimizing the signal-to-noise ratio.

All conventional photographs are captured and displayed in the spatial domain. The use of FFT requires that the image be converted from the spatial to the frequency or periodic domain, in which the image data are represented as a function of frequency, rather than position in space. The component frequencies (sinusoids) in the image are separated and appear as spikes in the periodic display.[1]

An interesting analogy is made by Joseph.[1] The image is likened to a cake containing multiple ingredients, and the impossibility of removing one of these components after the cake has been baked. This is likened to a fingerprint and periodic noise, both present in a grayscale image and inseparable in the spatial domain.

Stated another way, the respective data of fingerprint and obstructive pattern that are inseparably overlaid in a grayscale image appear in different areas of the periodic display as energy spikes if their amplitude and frequency are different. This separation renders them amenable to editing. The signature spike(s) of a repetitive pattern will be in a different location from those occupied by the fingerprint data and consequently can be removed without altering the ridge detail. When the edited frequency display is converted back to the spatial domain, the obstructive pattern will be diminished or removed. Conversely, if the ridge detail and pattern have similar direction and frequencies, their respective signatures in the periodic display will be too close together for effective editing.


  History Top


FFT was first used forensically (to the writer's knowledge) in 1971, pursuant to a homicide in San Diego, California.[2] A ridge detail impression recorded in blood on a bedsheet was potentially key evidence; however, the impression could not be effectively analyzed and compared due to interference from the weave of the cloth. The Jet Propulsion Laboratory in Pasadena, California, used cutting-edge technology (FFT) to diminish the weave pattern of the cloth and reveal the impression more clearly. It was ultimately compared with and associated to the palm impression of the suspect. A chart was prepared for court presentation; however, the court ruled the process and the resulting image inadmissible, on the grounds that the technology was not generally accepted by the peer group within forensic science.

Twenty years would elapse before two almost identical situations emerged, and FFT technology would again be presented in court and with significantly different results. In each case, FFT editing was the subject of a Frye Hearing and was upheld.[3] Roughly concurrent with these cases, FFT was used effectively but sporadically in the United States and Canada.[4],[5],[6]


  Software Top


There are several options for FFT software available, including the following.

Image J is a free software program, developed by the National Institutes of Health and the Laboratory for Optical and Computational Instrumentation (https://imagej.nih.gov/ij/).

Clear ID, a product of Ocean Systems (www.oceansystems.com), offers a series of three sliders, which allow the user to review in real time, the results of a three-stage adjustment process in removing pattern.

ImagePro Premier (Media Cybernetics, www.mediacy.com) was used for the illustrations in this article, for the following reasons:

  1. Unlike some other software options, the periodic display features a black matrix, against which the signature spikes, weak ones in particular, are much more visible
  2. The brightness of the periodic display can be adjusted. This can be important when some of the noise signatures are difficult to see and consequently, difficult to edit
  3. Editing of the noise can be done by selecting one area of the overall image at a time. When the entire background pattern creates a complex periodic signature, it is much easier to edit in stages. Even when the background pattern is uniform, transforming the image one area at a time, can render the signature of the fingerprint (signal) easier to identify and hence, easier to preserve
  4. The shape of the selected area can be rectangular, polygonal, circular or elliptical, depending on the area to be edited. This flexibility further facilitates the clear display and editing of noise in the periodic domain.


Example 1

Effective use of FFT is reliant on understanding the periodic display and correctly interpreting the data. A repeating pattern consisting of diagonal lines is seen in [Figure 1]a. The lines are of uniform width, spacing, direction, and gray value. When this image is converted to the periodic domain, the resulting signature is quickly seen – a line of focused white spikes along an axis that is at 90 degrees to the direction of lines in the original image and passing through the dynamic center of the display [Figure 1]b. This signature is a mirror image and consequently, editing done on the one side of the center line will automatically be applied to the other.
Figure 1: (a) Image of parallel diagonal lines (b) signature as it appears in periodic display

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Other repetitive patterns that differ in the size of the repeating elements, distance apart, direction, and tonal value will each reveal individual signatures when converted to the periodic display.[7]

Example 2

A mechanical dot pattern is depicted in [Figure 2]a. The pattern elements are relatively uniform in size, direction, frequency, and tonal value. When the image is converted to the frequency domain, the data pertaining to the pattern are manifested as focused white spikes against a black matrix [Figure 2]b. These spikes are the pattern data.
Figure 2: (a) Mechanical dot pattern (b) corresponding signature in periodic display

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When a fingerprint is placed in black ink on the dot pattern [Figure 3]a, it displays a separate signature in the frequency domain [Figure 3]b, in stark contrast to the uniformity of the dot pattern. This signature is donut-shaped, consistent with the changing direction of the ridges through 360 degrees. It is also seen as a soft haze of spikes, reflecting the variability of ridge detail in width and frequency, as the imprint of an organic entity rather than a mechanical pattern, the elements (dots) of which are repeated without significant variation.
Figure 3: (a) Fingerprint superimposed on dot pattern (b) signatures of both dot pattern and fingerprint in periodic display

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In [Figure 4]a, the upper-right sector of the fingerprint is delineated and converted to the periodic domain. The soft arcing signature of the ridges in that quadrant is clear [Figure 4]b and is left intact. The spikes associated with the dot pattern are removed [Figure 5]a. When the edited periodic display is converted back to the spatial domain [Figure 5]b, the dot pattern has been considerably diminished, and the ridge detail of the fingerprint remains clear. [Figure 6] displays the final result when the signature spikes pertaining to the dot pattern in all four quadrants of the image have been edited.
Figure 4: (a) Upper-right quadrant selected and (b) signature in periodic display

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Figure 5: (a) Data pertaining to dot pattern edited (b) result of editing

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Figure 6: Result after editing in all four quadrants

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Example 3

A fingerprint was deposited in black ink on a textured plastic fabric [Figure 7]a, which has obstructed the ridge detail, limiting the analysis, comparison, and evaluation of the impression. The impression was transformed, quadrant by quadrant and edited, in the same manner as for Example 2. [Figure 7]b displays the effect of the editing.
Figure 7: (a) Fingerprint on textured plastic (b) result of editing by Fast Fourier Transform

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Example 4

Occasionally, fingermarks developed on evidence are superimposed, making evaluation of either more difficult. It is routinely challenging to determine the evidential importance of either impression at this stage, and it is obviously desirable to optimize both to the degree possible for evaluation. [Figure 8]a displays one fingerprint that has been superimposed on another, on white paper. Both fingerprints are recorded in the same medium, black ink, and are of different digits from the same donor. Consequently, their respective signatures in the frequency domain occupy the same location regarding distance from the center of the display, separated only by the direction of the ridge flow. When the entire image is transformed to the periodic display, the signatures are difficult to interpret and edit because the ridge flow of each fingerprint represents almost 360 degrees, although the parallel ridges are not necessarily in the same part of the image [Figure 8]b.
Figure 8: (a) Two fingerprints superimposed (b) periodic display of entire image

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Accurate interpretation and editing in the frequency domain are often easier if they are conducted in stages, one zone at a time. The zone in [Figure 9]a outlined in green reveals two groupings of spikes (signatures) in the periodic display [Figure 9]b, representing the two sets of ridges which are approximately at right angles to each other. As stated previously, recurring pattern elements in an image will generate signatures in the periodic display that are located at 90° to their direction in the image. The horizontal fingerprint is first regarded as signal and the vertical one as noise. [Figure 10]a depicts the outlined signature in the periodic display for the ridges associated to the vertical fingerprint. [Figure 10]b reveals the result of editing this signature. The ridge detail associated to the horizontal fingerprint is now suppressed and the ridges of the horizontal impression are easier to analyze. The remainder of the horizontal fingerprint was divided into three additional zones and edited in a similar fashion [Figure 11]. It is important to overlap each new zone to include part of the preceding one, to ensure unbroken transition.
Figure 9: (a) Highlighted area of superimposition (b) conversion to periodic display

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Figure 10: (a) Signature of ridges in vertical print highlighted for editing (b) result of editing

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Figure 11: Image edited to reveal the horizontal fingerprint

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The image of the superimposition was then reopened, and the vertical fingerprint was treated as signal. Similarly, the area of superimposition was divided and edited in four zones [Figure 12].
Figure 12: Image edited to reveal the vertical fingerprint

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Wherever the ridges of both impressions are flowing in the same direction, their respective signatures in the periodic domain will occupy the same location and editing in FFT will not be possible.


  Conclusions Top


Latent fingermarks obstructed by background pattern and color are occasionally encountered during the process of evidence photography. In some cases, the obstructions can be diminished or removed with postphotography processing strategies in Photoshop or other software, allowing for the evaluation and analysis of the impressions.

On other occasions, however, the obstructions take the form of repeating patterns that are recorded in grayscale or complex colors that cannot be filtered or isolated in an image channel. In these cases, FFT may be the best option for suppressing the obstruction and optimizing the fingerprint detail.

If the frequency and direction of the obstructive pattern are similar to those of the fingerprint, their respective signatures will occupy the same location in the periodic display and editing in FFT will not be possible.

FFT provides the potential to optimize each of two superimposed fingerprints in turn, in the areas where the respective directions of the ridge flow of each are significantly different.

The effectiveness of FFT editing will be limited by several factors including the strength, direction, and complexity of the pattern noise.

The author certifies that all sample collection was in strict accordance with the ethics guidelines of Laurentian University.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.



 
  References Top

1.
Joseph C. Unbaking a Cake – Fourier Series Transforms. Available from: https://www.youtube.com/watch?v=Qm84XIoTy0s.  Back to cited text no. 1
    
2.
Olsen RD Sr. Scott's Fingerprint Mechanics. Springfield, IL: CC. Thomas Publisher; 1978. p. 429-35.  Back to cited text no. 2
    
3.
Dalrymple B, Smith J. Forensic Digital Image Processing: Optimization of Impression Evidence. Boca Raton, FL: CRC Press; 2018. p. 210-2.  Back to cited text no. 3
    
4.
Watling WJ. Using the FFT in forensic digital image enhancement. J Forensic Identif 1993;43:573-53.  Back to cited text no. 4
    
5.
Kaymaz E, Mitra S. A novel approach to Fourier spectral enhancement of laser-luminescent fingerprint images. J Forensic Sci 1993;38:530-41.  Back to cited text no. 5
    
6.
Dalrymple BE, Menzies T. Computer enhsancement of evidence through background noise suppressionl. Forensic Sci 1994;39:537-46.  Back to cited text no. 6
    
7.
Dalrymple B, Smith J. Forensic Digital Image Processing: Optimization of Impression Evidence. Boca Raton, FL: CRC Press; 2018. p. 137-9.  Back to cited text no. 7
    


    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12]



 

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