A Novel Ray Analogy for Enrolment of Ear Biometrics
Alastair H. Cummings, Mark S. Nixon, John N. Carter

Abstract— The ear is a maturing biometric with qualities
that give it superiority over other biometrics in a number ofsituations; in particular the ear is relatively immune to variation
due to ageing. Successful ear biometrics rely upon a wellenrolled dataset, with ears normalised for position, scale androtation. We present a novel ear enrolment technique using theimage ray transform, based upon an analogy to light rays. The
transform is capable of highlighting tubular structures such as
the helix of the ear and spectacle frames and, by exploiting theelliptical shape of the helix, can be used as the basis of a method
for enrolment for ear biometrics. The presented techniqueachieves 99.6% success at enrolment across 252 images of
the XM2VTS database, displaying a resistance to confusion
with hair and spectacles. These results show great potential
for enhancing many other already existing enrolment methods
through use of the image ray transform at a preprocessing
stage.

I. INTRODUCTION
Ears are a promising avenue for biometrics research andhave been found to be able to identify subjects with similar performance to face recognition [1]. The ear biometricproblem (as with all biometrics) is split between enrolment
and recognition. Enrolment is the discovery, localisation andnormalisation of the ear image, whilst recognition deals withidentification of a subject by ears. Currently, most enrolment
for experiments is done manually, but in any real world testof ear biometrics, enrolment is just as important a problem
as recognition. Enrolment has not seen the same amountof research as recognition but there is some developmentin the area. Alvarez [2] used active contours and an ovoid
model to find the ear, and in a similar vein Arbab-Zavar andNixon [3] used an elliptical Hough transform. Bustard andNixon [4] developed a method of transforming SIFT featurepoints from an image of an ear to a model, and then usedthe distance to create a biometric that was resilient to posevariation and occlusion. Islam et al. [5] used weak classifiers
based upon Haar wavelets combined using AdaBoost to
create a very successful ear detection method. Prakash et al.
[6] used both colour and shape to achieve 95.2% enrolment
success in a database of 150 side view images, suggestingthat colour can indeed augment the enrolment process.
Physical analogies are an exciting paradigm in computer
vision that enable the creation of novel techniques thatapproach the problems of feature extraction from entirely
different angles [7]. These analogy based techniques have theadvantage of being based on physical properties of natural
phenomena such as water, heat or force fields and so are
A. Cummings, M. Nixon and J. Carter are with the School of Electronics
and Computer Science, University of Southampton, Southampton, SO17
1BJ, UK {ahc08r,msn,jnc}@ecs.soton.ac.uk

more easily understood by those using them. In addition to
the intuitive nature of the algorithms, the parameters thatare used have meanings that are clear and have real world
analogues. Although analogy operators are heavily based
upon a well defined physical concept, the analogies can beadapted outside this definition to increase their effectivenessand flexibility whilst maintaining the strengths provided by
the analogy. These properties are a clear advantage overmany standard techniques for which the mechanics can be
hard to grasp and parameter selection is not clear.
Heat flow has been used as an analogy due to its smoothing properties. Anisotropic diffusion [8] is an edge-awaresmoothing technique that allows heat to flow across areasof low but not high edge strength allowing Gaussian noise
to be eliminated whilst maintaining important edge features.
This is one of the earliest examples of a principled vision
technique based upon an analogy.
Hurley’s force field transform [9] generates a force fieldfrom an image that is analogous to a gravitational or magnetic field. Each pixel is assumed to attract every otherpixel with a force dependent on its intensity and the inverse
square law. The sum of these forces generates a vector
field representing an image. This force field can help infeature extraction and was successfully used to create an ear
biometric. Xie and Mirmehdi [10] also used a force field
analogy, generated from magnetostatic theory and joinedwith an active contour model to enable contour detection.
In their model, the image border and evolving contour are
assumed to have an electric current running through themand the interaction of these currents generates a force field.
This field guides the development of the contour, changing
along with it to guide it to the image border.
We use the image ray transform, a transform based uponan analogy to light rays, to enable ear enrolment. Previously
it has been used to enhance circle detection [11], but wetake advantage of its ability to highlight tubular features.
Other techniques have not used light in such a strongly
analogical sense; however, the Eikonal equation has beenused many times for vision techniques. The Eikonal equation
describes the time a ray takes to travel from the boundaryof an anisotropic medium to a point within it and has beenused in a number of applications [12], none of which fully
take advantage of the possible analogical formulation and it
is most often used as a distance metric.
This paper describes an ear enrolment technique using
the image ray transform. Section II describes the image
ray transform and its properties. Section III describes work
into applying the transform for ear biometric enrolment,
showing how its properties are well matched to the ear’s

θr

θl

θi

Normalm1

m2

Reflected

Refracted

Fig. 1.

Refraction and reflection of light.

structure. Finally section IV draws conclusions and describes
future work: both expanding on the applications previously
described and others that have yet to be investigated.
II. THE IMAGE RAY TRANSFORM
The image ray transform is a novel technique for extracting tubular and circular features that are not often found byother methods. It uses a pixel based ray tracing technique anda subset of the laws of optics to trace rays through an image.
These then react to certain structural features to emphasise
them. Whilst the transform is based on the principles of
optics, the details of the technique can be adjusted to suit
successful feature extraction rather than accurate simulationof the natural phenomenon. The implementation capitalises
only on the basis of the analogy; we do not simulate intricate
details of light propagation.
A. Laws of Optics
Rays are a method of modelling the propagation of waves,most often light, with specific regard for the direction of the
wave as it interacts with its environment and ignoring wavelike interactions such as diffraction. The path of a light ray
will be altered when it crosses the boundary with a medium
of different refractive index, refracting and/or reflecting (seefigure 1). Light crosses the boundary between the media at
an angle of θi between the light direction and the normalof the boundary (the dotted line). If reflection occurs, thenθl = θi . If refraction occurs, the light refracts at an angle ofθr to the normal where θr is calculated from the refractive
indices of n1 and n2 of the media m1 and m2 . Refractive
indices are the ratio of the speed of light in a vacuum to the
speed of light within the media, and in nature 1 ≤ n / 4.
The angle of the refracted light θr is found by Snell’s Law
assin θin2=(1)
sin θrn1
If n1 < n2 , then light bends towards the normal, so θr < θi .
If n1 > n2 , then light bends away from the normal, as long as
it is below the critical angle θc . This is the angle for which
θr would be greater than 90◦ and is therefore physically
impossible and is calculated as
 
n2
−1
θc = sin(2)
n1

In this case, the light is totally internally reflected in an
identical manner to normal reflection. In the natural world,
the amount of refraction and reflection that occurs depends
on the media and in most cases is a combination of the two,some part passing through, and some being reflected back.
These rules form the basis of the image ray transform.
B. The Image Ray Transform
The image ray transform takes the laws of optics described
previously and applies them to the problem of feature extraction. The transform operates by tracing a number of rays
through an image. The paths of these rays are then usedgenerate a new image, with tubular and circular featuresemphasised. The image is analogised to a matrix of two
dimensional glass blocks, each representing a pixel whoserefractive index is related to the intensity of the pixel in theimage. One method to assign a refractive index to a pixel
with intensity i is shown in equation 3, where nmax defines
the maximum possible refractive index. The indices are thenspaced evenly between 1 and nmax .
i· (nmax − 1)(3)ni = 1 +255
The splitting of rays into reflected and refracted parts is notconsidered in order to reduce computational complexity.
In this matrix of blocks, a ray is created with the position(x and y) and the direction (φ) drawn from a uniform
distribution (U ). For an image of size w × h,x ∼ U [0, w), y ∼ U [0, h), φ ∼ U [0, 2π)(4)

φ is converted into a unit vector, V, representing the directionof the ray (this is more convenient for calculations, butcannot be directly generated from a uniform distribution):V = (cos φ, sin φ)T(5)

The ray function r traces the course of the ray and updates
an accumulator A. I is the image from which refractive
indices and the normals at each pixel are derived. d is the
maximum number of reflections or refractions which the ray
can undergo before tracing ceases, also known as the depth.
A0 = r(A, I, x, y, V, d, nmax )(6)

The position vector p initialises the ray at:
p<0> = (x, y)T(7)

p<i+1> = p<i> + V(8)and at iteration i:

At each pixel through which the ray passes, A is updated toshow that the ray has passed through:A0 (p<i+1> ) = A(p<i+1> ) + 1(9)A(p) is only increased once per ray, so as to prevent
small loops in the ray’s path repeatedly increasing a single
pixel and excessively emphasising noise or other undesirable
features. When crossing a pixel boundary between media ofdiffering refractive indices, a new path must be calculated

N

B0

E

E

B1
F

D

C
A
Fig. 2.
The normals that could be used to calculate reflections andrefractions.

using a vector formation of the laws described in section
II-A.
If N is the normal and n1 and n2 are the refractive indicesof the first and second media respectively, then the angle ofincidence ,θi , can be found:.
cos θi = N · V(10)

If n1 > n2 , we have to test whether we should internallyreflect or refract. The critical angle θc is found from equation
2 and if n2 > n1 or θi < θc and assigning n = nn21 then the
direction of refraction Rr is, from [13]:Rr = nV + (n(N · V) − cos θr )N(11)

where cos θr iscos θr =p

1 − n2 (1 − N · V)(12)

If n1 > n2 and θi > θc , then the ray totally internallyreflects. The direction of reflection Rl is thenRl = V − 2(N · V)N
Rl or Rr are then assigned to V(
Rl if n1 > n2 ∧ θi > θc0V =Rr otherwise

(13)

(14)

The ray is traced in this manner until it has either undergone
d reflections or refractions, or the ray exits the image. Thisis repeated for N rays or until a stopping condition (section
II-C.2) is reached, and the normalised accumulator gives thetransformed image. The values of the normals (N) used to
calculate the new directions of rays are always set to thenormal of the edge direction found by the Sobel operator
at that point. In figure 2, this normal is shown orthogonal
to the edge direction E, as well as the normals of the pixel
boundaries B1 and B2 . N is used rather than B1 or B2 as it
is more representative of the information within the image.

G

B
H

Fig. 3. An example of the course a ray might take in a simple 4x4 image.

Currently, we only perform refraction when moving fromhigher to lower refractive indices as this tends to improve
the quality of the transform result, and we are working to
improve this further.
Figure 3 shows the path of a ray as it travels through asimple image. The edge direction at each pixel is horizontal,
and hence the normal at each point is vertical. The ray
is initialised at position A with a random direction andadvances to position B. The intensity of the pixels indicates
their refractive index. At B, the refractive indices of thecurrent and next pixel are compared (n1 and n2 respectively),
and as n1 = n2 the ray continues with no change indirection. At C, n1 < n2 , and so the ray bends towards thenormal, whereas at D n1 > n2 so the ray bends away fromthe normal. At E, total internal reflection occurs, because
n1 > n2 and θi > θc . At F and G, the occurrences at C and
D are repeated in reverse order, whilst at H the ray exits theimage and the trace terminates.
C. Refinements
In addition to the basic transform, a number of additionalparameters and processes can be performed with the transform to give a wider range of results and to extend the rangeof circumstances in which the transform is useful.
1) Intensity and Refractive Index: The transform will
only extract features that have larger refractive indices than
the surrounding area because total internal reflection only
prevents rays from passing from materials with higher tolower refractive indices, and not vice versa. As the refractive
index is proportional to intensity, this has the effect of
extracting features that are lighter than their surroundingarea. Depending on what is known about the properties ofthe features to be extracted different measures can be taken
to improve the result of the transform.
If the approximate intensity of the desired features isknown then the image can be easily transformed to makethe target intensity have the largest value. This can be done
by finding the difference from the target intensity t to theoriginal intensity io for each pixel, as in equation 15.
it = |io − t|(15)

If the expected intensity is not known then the ray transform can be performed multiple times, with different target
intensities, and the largest value at each pixel used. This isshown in equation 16 where I0 is the final image and Ix
are the results of different transforms with different target
intensities.
I0 = max(I0 , I1 , . . . , Ix )(16)2) Automatic Stopping Condition: Finding the optimal
number of rays that should be traced in order to ensure
the result of the transform is of sufficient quality is achallenge that must be met. Rather than use fixed valuesof N , an improved method for automatically deciding when
the transform should cease is to monitor the resultant image
and stop when it no longer changes significantly between
iterations.
The best method that has been found to do this is tomeasure the difference in the normalised accumulator image
between iterations. We use the root mean squared (RMS)
difference between the intensities:s2
1 X  0 <t><t> 0 <t>0 <t−T > (i)
I
(i)
−
I
D
(I
,T) =
|I0 | 0i∈I(17)where T is the number of iterations between each comparison. Rather than using successive images, the operation ofa transform is sufficiently fast that large intervals should be
used, that is, T  1. The results produced by this method areconsistent with the observed resultant images, with the sizeof D accurately reflecting the change that can be observedin the successive images.
The RMS difference measure is also cheap to calculate
when T is set high enough, as expensive accumulator normalisations are calculated infrequently. It can be used as astopping condition by setting a minimum value (DS ) to stop
the process. From experimentation it has been found that avalue for DS of 1 when T = 1000 allows termination witha stable result.
D. Properties of the Transform
The ray transform is capable of emphasising tubular features within an image. It is able to do this because tubularfeatures in the image which have larger refractive indicesthan the surrounding area can act like waveguides (suchas an optical fibre), guiding rays along the length of thestructure via total internal reflection. Rays that enter tubes
at shallow angles are likely to reflect along the length andconcentrate rays inside it. Evidence of this can be seen in
figure 4. The transform is also adept at highlighting circles
through repeated shallow reflections off the edges, and thishas previously been used to enhance circle detection with theHough Transform [11]. Figure 4(b) shows a single ray as it
passes through an image with the original image faintly in(a) Original(b) Single Ray(c) Ray Transform

Fig. 4. The application of the ray transform to a 480x640 image with atubular feature. For 4(c) N = 10000, d = 256 and nmax = 2.

the background. The ray is initialized above the circle, andtravels towards the curve (approximately 10 pixels wide),
entering it. On reaching the far edge of the curve, it reflects,
as the angle of incidence is above the critical angle. This
continues until it exits the curve and, subsequently, theimage. The final image can be seen in figure 4(c), where
the curve and the circle are more heavily emphasised thanthe box.
Tubular structures are found in many real images. One
example that clearly shows the ray transform’s strength atextracting tubular features is the helix of the human ear. The
helix is the outer section of the ear, which appears from a
profile view as a curved, tubular structure. By applying the
ray transform to such images, it is possible to extract thehelix of the ear and aid enrolment for ear biometrics.
III. EAR ENROLMENT WITH THE IMAGE RAY
TRANSFORM
The image ray transform’s propensity for highlighting
tubular features such as the helix of the ear can be exploited
to create an enrolment technique. This technique uses thetransform to create an image in which enrolment is considerably easier than in any edge or intensity image. Enrolment
then occurs using a simple template matching technique, but
it should be noted that many other enrolment techniques
could be enhanced through use of the image ray transform
as a preprocessing step on the original ear image.
A. Enrolment Technique
The technique used here exploits the image ray transform’s
strength at extracting tubular features to highlight the helixof the ear and then uses a series of simple steps to extractand normalise the ear. It should be noted that the main
contribution of this work is the application of the image
ray transform: without doubt more complex techniques (including some of the alternative enrolment methods describedabove) could be used to increase the success of the enrolment
process.
The initial step is to apply the image ray transform to theear image with the parameters DS = 1, nmax = 40, d = 256.
These parameters are standard values that produce an image
that has had enough rays of sufficient length traced to reduce
the noise to an manageable level, and the high value of nmax

(a) Original(d) Threshold
Fig. 5.

(b) Ray Transform(e) Detection

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(c) Smoothed(f) Extraction

Example of the steps taken to achieve successful ear enrolment.

makes rays conform strongly to structural features within theimage. This produces an image in which the helix of theear is highlighted (figure 5(b))(in addition to other tubularfeatures such as spectacles). Due to the non-deterministic
nature of the transform, it is then necessary to apply Gaussiansmoothing to the result (figure 5(c)) to reduce noise. The
image is then thresholded (figure 5(d)) to produce an image
with a strong helix as its focus. Histogram equalisation isused to allow a consistent threshold (of 249) across all
images to be used. Simple template matching is then usedwith an elliptical template across a range of rotations andscales (figure 5(e)) and then the matched section is thennormalised and extracted (figure 5(f)).
B. Results
Enrolment was performed on 252 images (4 per subject)from the XM2VTS database [14] using the technique above.
This is a section of the database that has been used earlier,and provides basis for comparison. The mean computation
time for each ear for the entire technique was 5.45s, whilst
the ray transform alone took only 1.47s and required approximately 19000 rays to be traced. In figure 6, a range of images
after the thresholding stage are shown. The propensity of thetechnique to extract the helix strongly in all images is shown,as well as cases where spectacle frames (figures 6(a),(b) and(c))or other features are highlighted (light hair in figure 6(a)and part of the forehead in figure 6(d)). The extent to whichfeatures are highlighted depends strongly upon their intensity(as discussed in section II-C.1), primarily highlighting ear
helices due to their high intensity skin surrounded by low
intensity shadows. Other structures such as some spectacle
frames, and, more rarely, hair, are highlighted through thismechanism as well. In general it was found that these extra
features retained through smoothing and thresholding do notaffect the enrolment results in most cases, because they are
rarely of an elliptical shape of the type that would be foundin the template matching stage.
The results of the extraction were encouraging. Out of
252 images, 99.6% of extracted images contained the subject
ear. 98.4% of these images had the ear correctly normalised,

Fig. 6. Selection of transformed images before and after smoothing andthresholding.

with the incorrectly normalised images having small scale orrotation errors. This is a performance similar to that achieved
earlier [3]. It is possible that the enrolment process is morerefined by our new approach, but certainly it appears thatthe preprocessing here could be of advantage in the othertechnique, which used edge detection.
The successful performance of the technique and small
number of failed enrolments has prevented meaningful ROC
analysis. Further experiments in which peaks which were not
the maximal value in images were extracted and classified
would allow the discriminatory power of the technique to be
more accurately characterised.
Shown in figure 8 is the image in which ear extraction
failed completely. The ear was extracted perfectly in all otherimages of this subject. The ear has not been extracted due
to both a streak of white hair and the subject’s spectacle
frames being strongly extracted in addition to the ear. The
combination of these features has created a structure that
responds more strongly in the template matching phase thanthe ear. This situation could be successfully prevented byfiltering out straight features that are very unlikely to be partof the ear, such as the spectacle frames, before matchingoccurs.
IV. DISCUSSION AND FUTURE WORK
We have shown how the image ray transform is a noveland powerful technique that can be used to enhance detectionof structural features. In particular, the transform’s aptitude
for highlighting tubular features has been employed in orderto create an effective technique for ear enrolment. Further,targeted ray initialisations; drawing initial ray positions froma probability distribution with peaks at likely ear positions.
Further work could be done on enhancing enrolment with
an improved matching algorithm, or, alternatively, creatinga recognition technique based upon the transformed ear.
The ray transform may also be appropriate for use in gait
biometrics, as legs act as tubular features that the transform
is adept at extracting. The transform could also be extended
to work upon 3D images, both spatial and spatio-temporal,
for 3D biometrics or object tracking.
ACKNOWLEDGEMENTS
We gratefully acknowledge Alastair Cummings’ EPSRC
CASE studentship funded by the National Physical Laboratory (NPL).
R EFERENCES
Fig. 7.

Extracted and normalised ears for a selection of subjects

Fig. 8.

The ear image that failed to be extracted correctly

the computational complexity is such that it appears to be aninteresting contender for a choice as a preprocessing stage.
The transform has an inherent ability to strongly highlight thehelix of the ear in all cases, and only rarely highlights otherfacial features in similar ways, making extraction simple andreliable. Clearly, we have a low-level feature extraction technique, which can be specifically tuned to ear extraction. The
technique shown here concentrates on exhibiting the potentialof the image ray transform for enhancing enrolment andrelies only upon simple thresholding and template matching.
It is likely that through use of a more complex elliptical
Hough transform, such as the one utilised by Arbab-Zavar
and Nixon [3], these results could be improved upon further.
There are many directions in which the image ray transform and its application to ear biometrics could be expanded. The transform itself could be improved with more

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