Differential Binary Encoding Method for Calibrating Image Sensors Based on IOFBs

Abstract

Image transmission using incoherent optical fiber bundles (IOFBs) requires prior calibration to obtain the spatial in-out fiber correspondence necessary to reconstruct the image captured by the pseudo-sensor. This information is recorded in a Look-Up Table called the Reconstruction Table (RT), used later for reordering the fiber positions and reconstructing the original image. This paper presents a very fast method based on image-scanning using spaces encoded by a weighted binary code to obtain the in-out correspondence. The results demonstrate that this technique yields a remarkable reduction in processing time and the image reconstruction quality is very good compared to previous techniques based on spot or line scanning, for example.

Full text

Sensors 2012, 12, 4133-4155; doi:10.3390/s120404133
sensors
ISSN 1424-8220
www.mdpi.com/journal/sensors
Article
Differential Binary Encoding Method for Calibrating Image
Sensors Based on IOFBs
Pedro R. Fernández 1, José Luis Lázaro-Galilea 1,*, Alfredo Gardel 1, Felipe Espinosa 1,
Ignacio Bravo 1 and Ángel Cano 2
1 Department of Electronics, University of Alcalá, Alcalá de Henares, 28871 Madrid, Spain;
E-Mails: pedro.fernandez@depeca.uah.es (P.R.F.); alfredo@depeca.uah.es (A.G.);
felipe@depeca.uah.es (F.E.); ibravo@depeca.uah.es (I.B.)
2 Department of Telecommunications and Electronics, University of Oriente, Santiago de Cuba,
90400, Cuba; E-Mail: acano@fie.uo.edu.cu
* Author to whom correspondence should be addressed; E-Mail: lazaro@depeca.uah.es;
Tel.: +34-918-856-562; Fax: +34-918-856-591.
Received: 3 February 2012; in revised form: 20 March 2012 / Accepted: 22 March 2012 /
Published: 27 March 2012
Abstract: Image transmission using incoherent optical fiber bundles (IOFBs) requires
prior calibration to obtain the spatial in-out fiber correspondence necessary to reconstruct
the image captured by the pseudo-sensor. This information is recorded in a Look-Up Table
called the Reconstruction Table (RT), used later for reordering the fiber positions
and reconstructing the original image. This paper presents a very fast method based on
image-scanning using spaces encoded by a weighted binary code to obtain the in-out
correspondence. The results demonstrate that this technique yields a remarkable reduction
in processing time and the image reconstruction quality is very good compared to previous
techniques based on spot or line scanning, for example.
Keywords: image sensor; image transmission; sensor calibration; optical fiber sensors
1. Introduction
Visual inspection systems based on electronic cameras are widely used these days for quality
control in various industrial processes and for surveillance systems, positioning and identification of
mobile objects and robotics, etc. The majority of systems based on artificial vision have been designed
OPEN ACCESS

Sensors 2012, 12 4134
for a specific application and thus lack the flexibility necessary for use in other environments where
the use of electrical signals or electronic devices may not be possible or suitable. Examples of these
include environments which are difficult to access because they are winding and/or narrow, medical
applications linked to endoscopy, and the inspection of hostile environments exposed to high
temperatures, the risk of explosion, corrosion, the presence of radiation, etc. To transmit images under
these conditions, coherent optical fiber bundles can be used, where the fibers maintain the same spatial
relationship (or position) with respect to one another. In this way, it is possible to achieve more
effective physical access to the target medium, and high galvanic isolation is assured.
In a fiber bundle, any image projected onto the input plane of the bundle is broken down into
different points related to the image plane, appearing at the output as a set of luminous points
transmitted by each fiber. Most present day applications using coherent fiber bundles to transport
images only permit transmission over short distances and at a relatively high cost per meter length,
which can limit their range of uses in remote environments. In contrast, incoherent optical fiber
bundles (IOFBs) are generally used as light guides although under certain conditions they can also be
used to transmit images, and constitute a cheaper medium that can attain a greater working distance.
Since, from a production point of view, fiber distribution in these devices is less exacting, their cost is
considerably lower. Furthermore, in contrast to coherent bundles, the fibers are not subjected to a
fusion process to reduce the interstitial spaces between them. Thus, it is possible to obtain greater
flexibility and less inter-fiber crosstalk, which can be a possible cause of contrast loss in the received
image [1].
A system with these characteristics requires a sensor or camera connected to a processing unit that
“decodes” the information received at the bundle output, since this is naturally “encoded” due to the
random distribution of the fibers. This implies that in order to transmit and reconstruct images with
IOFBs, it is necessary to calibrate the system before transmission in order to estimate the transfer
function necessary between input and output to recover the information captured [2–5]. An image
calibration/transmission system based on IOFBs is generally composed of the elements shown in
Figure 1 [4–6]. Both the sensor and the calibration screen are controlled from a central processing unit
(CPU), which is also involved during the process of capturing and reconstructing the final image.
In brief, the calibration procedure consists of scanning the bundle input end with appropriate pattern
images projected from a screen. In this way, the input-output transfer function of the system is
determined, verifying the effect produced by the set of pattern images on each fiber at the output end.
The pattern images used strongly influence the speed of the calibration process and the quality of the
results obtained, and can be formed by square pixel regions [7], luminous lines [4,6] or encoded
images of the bundle [8] in both vertical and horizontal dimensions.
In [8], a calibration method is presented in which a series of encoded pattern images was used. The
authors stressed the need to previously locate the fibers in order to determine beforehand where the
useful information would be extracted from during the calibration procedure. This problem was solved
using the simple procedure described in [3,4], extending its application to the process of reconstructing
and correcting the transmitted images, which is extremely useful regardless of the scanning method
employed.

Sensors 2012, 12 4135
Figure 1. Diagram of an image calibration/transmission system based on IOFBs.
Calibration of IOFBs by Means of the Space Encoding Technique
For calibration, in [8] the input end of the bundle was scanned with pattern images composed of
areas of high contrast (black and white) consisting of vertical or horizontal lines, in such a way that
with each scan, approximately half of the fiber bundle was illuminated. This technique, known as
space encoding, is frequently employed to reconstruct 3D environments [9,10]. The pattern images are
generated using a binary code, and this is an efficient form of scanning the input end of the bundle.
When the behavior of each fiber at the bundle output in response to each of the pattern images is
known, the corresponding positions at the input end can be calculated and this information is stored in
a reconstruction table (RT). The input/output relationship is achieved with a notable reduction in
processing time compared to square region scanning techniques [7] or luminous line techniques [6],
and the number of images required is also notably reduced.
Figure 2 gives an example of pattern images as proposed in [8], but only shows six different images
for each dimension (x and y). The pattern images consist of multiple black and white lines, the
structure of which (width and position) is determined by a weighted binary code. Each space
dimension of a discrete scan is subdivided by “n” areas of excitation. Therefore, given that the base
which generates the pattern images for the horizontal and vertical dimensions is binary, a total of
2log2(n) images are required. For example, in [8], a bundle of approximately 256 × 256 fibers was
used, requiring a total of at least 16 encoded images; eight to scan the horizontal dimension and
another eight to scan the vertical one.
The degree of focus, aberrations and the resolution of the optic used in the input subsystem can all
produce some blurring on the images which impacts on the input and therefore can decisively affect
the quality of calibration. If these questions are not taken into account, the incident energy may be
scattered. For example, when the focus of the input optic is incorrect, the incident energy in those
regions where abrupt changes of intensity should occur (dark to light or vice versa) will be scattered
toward adjoining areas, rendering estimation of the state of the fibers in response to a given pattern
image complicated. Furthermore, as the image appears disordered at the output, the focusing process

Sensors 2012, 12 4136
implies another additional difficulty since the real structure of the transmitted image is lost;
consequently, some traditional focus methods are not applicable. In [2], a focus methodology is
proposed which uses simple metrics and ensures a notable improvement in calibration results.
Figure 2. An example showing a set of pattern images according to the space encoding
scan described in [8].
In the present article, we describe a novel calibration procedure for remote visual inspection
systems based on IOFBs which employs a scanning method with differentially encoded images
(differential space encoding—DSE) and yields short processing times and guarantees fewer of the
calibration errors fundamentally generated by the problems mentioned above.
2. Experimental Section
2.1. Model of the Scanning Space and the RT Structure
Before presenting the proposed method, it is necessary to define a model for the calibration space
required. Given that fiber distribution at the input is irregular, the input is subdivided into different
square regions which we will call cells. This set of cells comprises a kind of imaginary grid (see
Figure 3) that defines a 2D space of discrete scanning. It is on this plane that the set of appropriately
selected pattern images will impact, being projected from the calibration screen. Any scanning
procedure should be capable of generating a sequential set of unique and predefined images that will
pass through and excite all the cells in the imaginary grid. Each side (l) of a cell has a length almost
equivalent to the average diameter d
fib
of the fibers, such that 3/4 d
fib
 l  d
fib
. This does not it imply

Sensors 2012, 12 4137
that an exact correspondence can be established between each fiber and each cell since the area of
influence of a cell can cover more than one fiber. Nevertheless, a cell can be associated with the fiber
that receives its greatest area of influence (see Figure 3).
Figure 3. Relationship between the imaginary grid cells and their effect on the sensor.
Although fundamentally spatial, this calibration will not only have to take geometric parameters
into account, but should also include an implicit calibration of the fiber responses since the information
that is extracted is always affected by the transfer functions of the fibers themselves (attenuation) or by
the input optic. Therefore, these responses must be compensated for in such a way that all the pixels in
the image to be formed possess equal gray levels. An exhaustive analysis of this problem is given
in [6] and has been applied in the present study.
According to the restrictions imposed by the model, a RT is proposed that has a maximum number
of entries defined by the number of “locatable” fibers in the bundle image captured. In each RT row or
entry, the centroid of a located fiber is associated with the position of a cell at the input end and also
with an equalization factor associated with that fiber. The centroid of each fiber i refers to the 2D
coordinate system of the camera [r(i), c(i)] and represents the discrete position, in the image to be
reconstructed, to which the information extracted from the central region of a determined fiber should
be transferred. The associated cell will be the position with the maximum probability of guaranteeing
that the fiber assigned will attain greatest emittance at the output.
In general, the system response can be considered lineal, and thus only one or two constant factors
per fiber are required to define the correction necessary for the fibers. From a mathematical point of
view, these factors represent the slope and the intersection of the straight line at the source which best
approximates each fiber’s response. For the sake of simplicity, only one correction parameter and
gray-tones image processing will be considered in the present article. The general structure proposed
for the reconstruction table (RT) is shown in Table 1. This structure is that which will be necessary in
order to be able to decode any image captured by the sensor.

Sensors 2012, 12 4138
Table 1. General structure of the RT.
r(i) c(i) i R(i) C(i)
where:
(r(i), c(i))  Coordinate pairs of the fibers located by the sensor.
i  Intensity equalization factors.
(R(i), C(i))  Position of the cell that best excites a fiber in (r(i), c(i)).
The first two elements of the RT, r (i) and c (i) are obtained through a method for locating circular
pattern images applied to a bundle image when it is homogeneously illuminated without reaching
saturation. The results of this search are the first data to be included in the RT, together with the
correction factor (i). A fast and simple method that obtains good results has been described in [6].
The values R (i) and C (i) in Table 1 are obtained from subsequent processing of all the images
captured by the sensor during the input scanning procedure. This operation implies verifying and
analyzing the state of all the fibers in each image captured by the camera, respecting their order of
appearance.
If each of the points contributed by the fibers relocated, according to the RT, we would obtain an
image which we will call the primitive image (Ip). This image, although intelligible, will present a
large number of empty regions that correspond to regions without fibers at the input (interstices), and
to a lesser extent to the omission of some real fibers due to possible failures in location (see Figure 3).
Depending on the scanning method used, a specific decodification procedure should be applied. We
know that each cell at the input end occupies a determined area. This is a discontinuous representation
of the input exploration domain. In other words, one, and only one cell from the imaginary grid will be
assigned to each fiber at the input end of the IOFB, according to its degree of proximity and influence.
The number of cells to take into account in the scanning space depends on the maximum number of
fibers (theoretical) that can be aligned in both dimensions, and their area is related to the nominal
diameter of the fibers (dfib). The width w of the smallest line projected should satisfy the following
expression:
(1)
where wmin refers to the minimum width of a line projected onto the input that is capable of exciting a
fiber sufficiently (it has been empirically determined that this should cover at least more than 50% of
its area). This working range guarantees that the response of any illuminated fiber can be distinguished
from an unexcited state. Furthermore, a line with a width greater than that specified does not guarantee
greater excitation because the radiance Ri that a particular fiber can transmit depends directly on the
degree of superimposition of the line on the facet of the fiber more than on its width, such that:
(2)
where Afibi represents the area of the fiber and Wf is the width of the line projected onto the fiber. The
size of the final reconstructed image is defined by the range of the scanning space and this, in turn,
depends on the maximum number of fibers (nfibmax) that can appear aligned in any dimension. To
determine the integer value, the following equation is used:
minfib ww d tt
ffibi WA: R i

Sensors 2012, 12 4139
(3)
where B
diam
is the diameter of the bundle and F
diam
is the nominal diameter of the individual fibers.
This value is approximate given that the fibers are considered perfectly aligned.
2.2. Proposal for Scanning Using Differential Binary Space Encoding (DBSE)
Below, we describe the necessary procedures proposed for calculating the parameters included in
the RT. The structure of each pattern image generated for scanning is conditioned by a base weighted
binary code. However, in this study an alternative is proposed aimed at minimizing the problems
discussed in Section 1 arising from the optical resolution of the system. The method, which we will
call Differential Binary Space Encoding (DBSE), carries out differential processing of the images
captured without implying an excessive increase in the number of images to process. Differential
processing of the images implies that for each base pattern image, another, complementary pattern
image is generated (see Figure 4). This ensures that a fiber illuminated by a base pattern image will be
extinguished by its complementary image. If a fiber maintains its excitation slightly in the presence of
both pattern images, it is considered extinguished since it has not undergone an appreciable change of
state and the condition analyzed is not conclusive.
Figure 4. Pattern images for a DBSE scan with a number of bits nbit = 3. Note that the last
image (LSB) of each dimension is subdivided into two.
diam
diam
F
B
nfib |
max

Sensors 2012, 12 4140
To understand this situation, the following example may help. Supposing that a region with light-
dark transitions originating from the pattern image impacts on a fiber in such a way that nearly half the
diameter of its nucleus is covered. In this case, the level of excitation registered in the fiber will be
very similar both for the base image and for its complementary image. Therefore, the fiber is not
considered to have changed its state. Another change that has been introduced concerns the structure of
the last image of the sequence. This is associated with the least significant bit in the code and is formed
by the thinnest lines (of alternate color) in the sequence, thus presenting the greatest frequency of
change compared to the remainder of the images. Under these conditions, it is probable that the optical
resolution of the system will be compromised and will not be appropriate for this type of scanning. In
this case, the optical system can project a gray tone onto the IOFB rather than an image formed by
lines, affecting the decoding process of the least significant bit in the code. To solve this problem, we
opted to subdivide the pattern image corresponding to the least significant bit of each dimension into
two images with their respective complementary images (see Figures 4 and 5).
Figure 5. Subdividing the LSB pattern image constitutes an artificial means of using an
optical system with lower optical resolution.
As regards the method described in [8], where before for 256 × 256 fibers 16 images were required
for the two dimensions, now 36 images will be required. Of these, nine are differential pairs for each
dimension (18 + 18 = 36 images). Although the number of images rises, it remains lower than the
number required for the line scan described in [6] for which, under the same conditions, the same scan
space required a minimum of 512 (2 × 256) high resolution images for decodification.
2.3. Calculation of the RT
The RT construction process is similar to the calibration method using lines described in [6] and the
structure of the tables remains the same. To complete the RT, the images captured by the camera are

Sensors 2012, 12 4141
loaded into the memory maintaining their order of appearance, and a subtraction between each pair of
differential images is carried out according to the expression:
(4)
where IRn is the image resulting from the subtraction of the complementary images with subscript “n”
captured by the camera. The subtraction operation enables us to reject the fibers that, in response to a
differential pair of images present an “indeterminate” response because they are physically located in
the middle of a light-dark transition border or vice versa. For example, if it is expected that a fiber
exposed to a determined illuminated area of a base incident image will be illuminated, then it should
be extinguished when presented with the complementary image and vice versa. In contrast, if the fiber
is illuminated both by the base image and its complementary image, it can be stated that it presents an
indeterminate behavior because the state of the fiber is not known with certainty. A case such as this is
indicated with an ellipse in Figure 6.
Figure 6. Example showing the discriminatory effect of the differential pattern images.
The ellipse indicates two apparently illuminated fibers. Due to the ambiguity of their state
they are considered “unlit”.
It can be observed that fibers in an indeterminate state disappear, and only those fibers indicated by
the symbol “+” in IPn are considered excited. The advantage of using a set of differential images is that
it helps to reject these cases where the fiber, despite having attained a certain degree of illumination, is
not considered to have reached optimum excitation in response to a pair of specific pattern images.
For each resulting image, the state of the fibers is verified. In this way, a “position code” (a row or
column, depending on the dimension analyzed) is “constructed” corresponding to each cell and this is
stored in the RT. It should be noted that in order to determine the state of each fiber it is essential to
know beforehand the central positions of the fibers, since it is from these positions that all the
information used in the calibration analysis and for reconstructing the images is extracted. In our case,
the procedure used for location was the FDDT (Fiber Detection using Distance Transform) technique
described in [3,4], considering that all the fibers possessed a similar nominal diameter. To determine
the state of a fiber in each of the resultant images, our proposal is to calculate the median gray level (or
even the average) in the center of the fiber analyzed, using a set of nine pixels (N9 3 × 3 pixels) such that:
¿
¾
½
¯
®


!
PnDPn
PnDPnPnDPn
Rn II
IIII
I,0
,

Sensors 2012, 12 4142
൝ܫொ஽ቀܰଽ൫ݑ௖೔ǡݒ௖೔൯ቁൌܯ݁݀൫ܫሺݑǡݒሻ൯
׊ሺݑǡݒሻǣሼݑ௖೔െͳ൑ݑ൑ݑ௖೔൅ͳǡݒ௖೔െͳ൑ݒ൑ݒ௖೔൅ͳሽ (5)
If the average gray level exceeded a threshold value, the fiber was considered "illuminated" and was
associated with the logical value “1” in the bit position code. The position of the corrected bit also
corresponded to the order of appearance of the image analyzed. If it did not exceed the threshold
mentioned, it was considered "unlit" and associated with the logical value “0” in the bit corresponding
to the position code.
൜Ͳ൏ܫொ஽ ൐ߜீ௅ ՜ͳ՜݈݄݅݃ݐ݁݀
Ͳ൏ܫொ஽ ൏ߜீ௅ ՜Ͳ՜݋݂݂ (6)
To construct the numerical values Ri/Ci, the real state of each fiber was verified (illuminated-
1/unlit-0) in all the images. The binary code corresponding to the row or column position was obtained
from each state, respecting the order in which the images appeared. Having completed the analysis of
all the fibers and all the images, the final result was a preliminary RT. The time taken to construct the
RT is very low and few images are required for the analysis. Note that when 36 initial images (8 bits)
are used, the number of images to store for subsequent analysis can be reduced by half due to the
implicit subtraction operation.
2.4. Refining the RT in DBSE
The RT should be refined to verify the possible occurrence of empty, duplicate entries, or entries
with atypical values (outliers). This is fundamentally due to poor correspondence of the scanning area
at the bundle input, or to errors in determining the state of the fibers that affect a bit during the
construction of the position values Ri/Ci. Outliers are fundamentally due to poor focus or to false fiber
detections, and their number is generally low or nonexistent if, prior to calibration, good focus and
correspondence between the bundle and the calibration monitor has been ensured. Each cell position
registered in the RT should comply with a physical model that is consistent with reality since no fiber
is located outside of the physical limit imposed by the shape of the bundle. For this reason, each pixel
in the primitive image should registered within a circumference, the center of which (u0, v0) is the
center of mass for all the cell positions calculated (Figure 7). Consequently, all values considered
atypical should be eliminated from the preliminary RT. The maximum distance (confidence circle) is
directly related to the maximum number of fibers considered in the scan, such that:
(7)
To analyze the coordinates of redundant cells, it is first necessary to identify them in the RT and
subsequently to determine which is “the best” or “the most appropriate” of the entries which present
conflicts. A simple means to locate them is to order the RT entries by cell position. In this way, the
redundant entries “disputing” over the same cell, are grouped consecutively and are thus easier to
process. Each group of entries is analyzed separately. For each group in conflict, “the best” entry is
chosen. In other words, the entry that is closer to an ideal condition will remain unaltered in the RT.
The remainder should be relocated toward empty, neighboring cells that have not been included in the
RT (if there are any). If any entry cannot be reassigned then it is eliminated from the RT. In order to
22
max )()(2 vovuounfib |

Sensors 2012, 12 4143
correct the RT, all the gray levels registered in response to each pair of pattern images must be
analyzed again for each fiber.
Figure 7. Confidence positions and atypical values (outliers) in a primitive image.
The “best entry” from a group disputing over the same cell is the one closest to an ideal condition.
However, what is an ideal condition? We considered that ideal fiber excitation (or an ideal condition)
existed when each time the fiber was illuminated from the input, it attained its maximum level of light
transfer and, on the other hand, when it was unlit it reached the minimum degree of intensity at the
output. If these ideal conditions always occurred in the fiber, this would indicate that each fringe
exciting produced the maximum superimposition on its nucleus at the input, and, in contrast, when it
was unlit it would indicate that it was not receiving any influence.
Normally, this does not always occur; a fiber is more or less illuminated depending on the degree of
the fringe superimposition on its nucleus. However, bearing in mind the sequence of gray levels that
should be obtained under ideal conditions and comparing it with the real sequence, an idea is obtained
of the extent to which the result obtained resembles that sought. In other words, the ideal condition
serves as a reference for comparing the different entries of a group in dispute and defining which is the
best candidate for that cell.
When the maximum gray level (݃
௠௔௫
௜
) reached by each fiber during the scan is known, a pattern
values vector (or pattern chain) can be constructed from n bits by means of:
(8)
where b
k
is the weight ሼ׊݇ൌͲǡͳǡǤǤǡ݊ሽ which has the value of 1 for the “illuminated” fiber and 0 for
the “unlit” fiber, and ݃
௠௔௫
௜
is the maximum level of gray that has been registered for the fiber i by the
sensor. This representation is analogous for rows and columns, and thus each fiber will have its own
pair of ideal sequences. Similarly, considering ݃
௞
௜
as the average real level of gray reached by the fiber
i in the image p = {0, 1, 2, n  1}, then, for each redundant entry we obtain the vector:
(9)
>@
max0max1max2max1 ,,,....... gibgibgibgibCp no 
>@
00112211 ,,,...... gibgibgibgibCr nn o 

Sensors 2012, 12 4144
To analyze the degree of similarity between the pattern and redundant chains, the quadratic
error produced is calculated. The root of the mean quadratic error for each real code compared to the
pattern is:
(10)
The combination giving the least error out of the redundant cell combinations is chosen and remains
in the TR. The remainders of the redundant entries are relocated toward the positions of neighboring
cells not registered in the RT, where errors between pattern chains Cp (row and column) and Cr are
also minimized. These values are temporarily stored and verified again to check whether new
redundancies appear when all entries are verified again. If, after a specific number of iterations, not all
cases have been solved, these are definitively eliminated from the RT, since they may be associated
with false fiber detection, and where these arise, their number is very low compared to the remainder
of validated entries.
2.5. Experimental Setup and General Considerations
The results reported in this article were obtained using a software application built in Matlab
containing all the operations necessary to conduct a spatial calibration of the system and to evaluate
both the line scan method and the DBSE. The application was run on a Pentium Core 2 Duo 3 GHz
4 GB RAM PC. A monochrome BCi4-6600 camera was used with a 6.6 megapixel CMOS sensor and
a 2,208 × 3,000 pixel matrix. The optics used was a 19–35 mm optical zoom from Cosina. The sensor
and the screen were isolated into a dark box to prevent external influences (for example: sunlight,
artificial lighting variations and reflections on the screen, etc.) Camera resolution was established
based on the assumption that each fiber occupied an effective area of around 7 × 7 pixels, in order to
ensure adequate location of the fiber in the output image.
An AOC TFT screen (17'') was used with a resolution of 1,280 × 1,024 and pitch size of 0.064 mm.
This device should be perpendicular to the bundle input end in order to avoid errors and distortions in
the calibration caused by inadequate perspective. All experiments were conducted using a plastic fiber
bundle 2.8 m in length and containing approximately 50,000 fibers with a nominal fiber diameter of
50 μm [11]. Given these characteristics, nfibmax in Equation (7) was approximately 256 fibers in both
dimensions.
In accordance with the geometry of the installation, an active screen area of 768 × 768 pixels was
chosen, which implies that w in Equation (1) was 3 pixels wide.
Figure 8 depicts a general overview of the experimental setup used. This study has been based
on [2,3,6], the algorithm for fast fiber location (FDDT), the focus method using fvar measurement and
the line scan method employed as a reference scan method.

2
1
0
max
n
gbgib
RMSE
np
p
ppp
¦



Sensors 2012, 12 4145
Figure 8. System setup.
2.6. General Calibration Procedure
In order to obtain the law of correspondence between the input-output of the fibers (decoding), it is
necessary to carry out a set of tasks run in the following sequence:
1. Correctly focus the bundle by means of the fvar metric described in [2] and adjust the position of
the bundle input end, so that, it will completely capture the active area that the pattern images
will occupy, in order to optimize the scanning space.
2. Locate all the fiber positions in an image captured by the camera. This is carried out by means
of a FDDT algorithm and an image of the homogeneously illuminated bundle, which enable
rapid location of the fiber centroids.
3. Determine the equalization factors which will compensate for the fiber responses.
4. Once the entire system has been adjusted, the encoded images should be exposed sequentially
and, at the same time, each image captured by the camera should be captured and stored in
well-differentiated files.
5. For each resultant image, the fibers previously located using FDDT and showing a great
lighting excitation will be stored in a table. This operation makes it possible to generate a
binary position code for each fiber by dimension. These results are stored in a preliminary RT
in the pair (R (i), C (i)).
6. Once the preliminary RT has been built, RT refinement is carried out to eliminate the outliers
and the redundant coordinates. Once the system has been calibrated and the RT refined, it is
necessary to verify that calibration is correct.

Sensors 2012, 12 4146
Figure 9 summarizes the steps listed above, subdividing the entire process into two phases. Each
corresponding step number is also indicated. The first phase focuses on preparation of the system for
calibration (focus, camera adjustment, etc.) and determination of fiber position and equalization factors
based on a white image captured by the sensor without causing saturation. From this phase a
provisional RT is obtained in which associations with cell positions are still to be determined.
Figure 9. Flow chart of the procedure to follow in DBSE.
The second phase consists of scanning with differential images and capturing the resultant images.
Subsequently, all the images are analyzed to complete the RT, outliers are eliminated, and the results
are refined. Once this phase is completed, the definitive RT is ready.

Sensors 2012, 12 4147
3. Results and Discussion
Regarding the previous studies used as a reference, it is difficult to compare some of the results
obtained since not all the information about the original experiments which would be necessary is
available. For this reason, the results reported here were obtained respecting the general ideas
described but adapting them to the specific conditions of the experimental setup.
Before carrying out calibration using the techniques that will be analyzed in this section, we applied
the focus methodology of the optical system proposed in [2], employing a metric based on variance in
the gray levels contributed by the fibers. This step was essential to obtain correct spatial calibration
since calibration methods based on space encoding are especially sensitive to this aspect because, in
contrast to the line scan technique, the light-dark frequency change rises progressively with scanning.
Figure 10 shows the effect that a poorly focused input optic would have on the image obtained by the
sensor (disordered). The input pattern image used corresponds to the least significant bit formed by
alternate black and white lines which are three pixels wide per line on the screen (worst case scenario).
Figure 10. Influence of input focus on the same image formed by alternate black and white
lines captured by the sensor. (a) focused and (b) not focused.
(a) (b)
In Figure 10(a), the image is well focused whereas in Figure 10 (b) it is not, and therefore the image
captured tends to be more homogeneous due to energy scattering at the input, indicating that
significant errors may be produced during RT calculations. In this case, decodification of the least
significant bit would be affected. If an error were produced in the least significant bit, the error in
calculation of position would be much greater.
Table 2 shows a comparison of line scan calibration methods, the space encoding techniques
described by Dujon [8] and the differential method proposed here. These results were obtained under
the same working conditions in terms of camera configuration, hardware, lighting, etc.
As can be seen, the method which requires most time for scanning and processing is the luminous
line scan technique, which requires a much higher number of high resolution images (in our case, 6.6
megapixels) to be processed if the space encoding techniques of Dujon and DBSE were used instead.
This implies massive memory use for image storage, as well as notable use of the system’s operating
memory, both aspects which require adequate management. Nevertheless, the results obtained are very
good, with a high number of entries being validated after the RT refinement procedure.

Sensors 2012, 12 4148
Table 2. Comparison of the different calibration techniques analyzed.
Parameters Method
Line Dujon DBSE (8bits)
Number of fibers located. Initial RT entries 49,127 49,127 49,127
Final validated entries 46,454 (94.5%) 40,241 (81.9%) 42,711 (86.9%)
Corrected entries (redundant) 3,270 1,920 5,867
Eliminated entries 2,672 (5.4%) 6,077 (14.1%) 6,416 (13%)
Mean scan time 7.91 min 2.6 min 5.54 min
Mean RT calculation time 38.94 min 1.3 min 2.2 min
Mean analysis time of redundancies and outliers 13.98 min 2.5 min 5.36 min
Number of images used 522 * 16 36
Final image size [pixels] 261 × 2611 254 × 254 254 × 254
* A scan space of 261 × 261 images in each dimension was considered. This inflated size of the grid is
subsequently corrected in the TR so that the size of the image is not greater than nfibmax = 256 in each
dimension, eliminating those cell positions that do not have an appreciable influence on the fibers.
It can also be observed that the number of entries deleted in the analysis, or entries to which it has
not been possible to assign a coherent position at the input (outliers), is smaller. This question is
related to the fact that position error does not depend on the reconstruction of a binary position code, as
is the case with space encoding, but rather, it depends on the level of certainty about the position of
maximum excitation for each fiber. This error is generally in the range of ±1 positions for each
dimension.
Methods based on space encoding are quantitatively superior to the line technique regarding
processing speed, memory use for storage and post-processing of the images captured, fundamentally
as a result of the reduction in the number of images involved. Both the Dujon and DBSE methods
described above achieve a high number of validated entries compared with the number of initial entries
included in the RT, although, not always as many as the line scan method. Nevertheless, it can be seen
that in both cases the quantity of entries assigned is very high (>80%), and it is possible to reconstruct
good quality images in accordance with the maximum number of bundle fibers.
It is to be expected that in order to obtain good results with space encoding techniques, a higher
resolution optic is required. If the system does not possess the necessary focus and optical resolution,
the number of outliers may increase notably because the number of errors in the position codes
estimated would also rise. It is precisely regarding this aspect where DBSE has proved to be superior
to the technique described by Dujon, and thus can serve as the basis for future research. Differential
image processing provides greater immunity to calibration errors, showing a significant increase in the
number of validated entries compared to the method described by Dujon. This improvement is mainly
due to the usage of complemented patterns images, FDDT and the redundancies analysis, which allow
discarding undetermined states of the fibers during the RT calculation.
Furthermore, in order to reduce the appearance of errors due to this fact without using a very
expensive input optical system, the results can be further improved by creating a subdivision of the
pattern images associated with the least significant bit in the position codes. In this way, a reduction in

Sensors 2012, 12 4149
the frequency of change in the pattern images is artificially obtained. However, this inherently implies
an increase in the number of images to process, although this will always be much lower compared to
the line scan calibration technique.
On the other hand, the method described by Dujon presents an additional difficulty related to the
procedure for determining the state of excitation of the fibers in response to each pattern image. An
excitation threshold is used which is determined by an iterative optimization procedure that can
increase calibration time. In contrast, DBSE discriminates the indeterminate states of fibers, and thus
the optimum threshold that serves as a reference for determining the real state of the fiber is zero (or
very close), implying notable savings in terms of time.
The analysis of redundancies makes it possible to relocate a specific number of positions that share
the same cell in the RT (redundant registrations) toward empty pixels. This is another of the main
characteristics that distinguish DBSE, from Dujon method. Figure 11 shows the evolution of a
primitive image (and therefore, of the RT) corresponding to a totally white input image, when the
redundancy correction analysis is applied using the DBSE method. Figures 11(a) and 11(b) represent,
respectively, the initial state of the primitive image, after a first scan analysis, and following the
redistribution of redundant positions in the RT and elimination of the outliers. This procedure ensures
that each represented pixel is in a “probably optimum” position, and covers a greater area of the
circular shape of the image, facilitating a subsequent inpainting procedure.
Figure 11. (a) Original primitive image, (b) Primitive after RT redundancy correction.
(a) (b)
Inpainting is an essential procedure to achieve correct reconstruction of the final image that is
consistent with the original input structure, and techniques based on calculation of variance, PDEs and
mask convolutions, etc., are usually employed for this purpose. However, this procedure will not be
analyzed in this article as it falls outside the main area of interest, although it is interesting to give
some examples of reconstructed images obtained in uncontrolled environments.
Figure 12 shows an example of the evolution of an image transmitted through a sequence of images.
Initially, the image captured by the camera is shown in (a), subsequently the corrected primitive
image is presented in (b), and finally in (c), the completely reconstructed image using the inpainting

Sensors 2012, 12 4150
technique described by Oliveira is given [12]. The primitive image is formed by extracting the gray
levels contributed by the located fibers, and subsequently reordering and equalizing the information (a)
according to the RT.
Figure 12. Image Progression and details. (a) Sensor Image, (b) Primitive Image,
(c) Inpainted Image.
(a) (b) (c)
Figure 13 shows another two real examples captured by the system. The results were obtained after
carrying out a DBSE calibration; it can be seen that the images present good contrast and the quality is
appropriate for the spatial resolution of the system presented here, where the images did not exceed
254 × 254 pixels.
Figure 13. Real images captured with the experimental system.

Sensors 2012, 12 4151
In order to demonstrate the improvement achieved by using DBSE compared to the technique
described by Dujon. Figure 14 shows a sequence of images for each technique, corresponding to the
initial primitive images (blank), the corrected images and lastly, a reference image in white. Note the
significant decrease in the number of interstitial spaces and outliers (in magenta) in the primitive
images corresponding to the DBSE, with respect to the Dujon method. So, this indicates the
improvement obtained by DBSE respect to Dujon. Calculating the correlation coefficient (CC
p
)
between the primitives and the reference image, the improvement obtained by DBSE is demonstrated.
Figure 14. Primitive images and reconstructed images decoded using the RT for BSE and
DBSE, respectively.
Primitive image
obtained without RT
correction
Primitive Reference Image CC
p
Dujon
Method
0.65466
DBSE
Method
0.71047
In [7], system calibration was carried out by means of two techniques, the single-mode fiber with
pixel block scanning and that of Dujon. However, this study did not employ fiber location or any
appropriate focus method. The information that was extracted from the fibers was not calibrated for
intensity and the RT was constructed on the basis of the illumination changes present in each image
resulting from scanning; thus it is to be expected that the number of calibration errors would be very
high, generating a large quantity of outliers.
Figure 15 reproduces some of the results obtained in [7] with respect to those obtained in this study
using the logo of Matlab ® and the Lena image. The advantage of using fiber location and differential
pattern images is clearly evident. Unfortunately, it is not possible to present comparative results that
better illustrate these differences.

Sensors 2012, 12 4152
Figure 15. Comparison of results obtained using the method described in [7] and
a modified version using DBSE. (a) Dujon method implemented and discussed in [7],
(b) Reconstruction using DBSE.
Matla
b ®
logo
Lena
(a)(b)
Figure 16 shows some primitive images obtained by means of the techniques analyzed in Table 2.
In order to quantify the quality of the results, two correlation coefficients were calculated. The former
(CC
p
), estimates the similitude between each primitive and its original image. The second one (CC),
calculates the correlation between an inpainted image and the original one (not shown). CC has been
calculated only for DBSE method, because it would be practically the same for the rest of the methods
due to the reduction of the number of interstitials interpolated by the inpainting procedure. This value
is really near to 1 indicating a good degree of similitude between the inpainted image and the original
one. Note the significant decrease of the number of interstitial spaces in the primitive images
corresponding to the methods of DBSE and Lines, with respect to the method of Dujon. The
coefficients CC
p
clearly demonstrate the improvement reached in the primitive images for DBSE and
Line methods, with respect to Dujon.

Sensors 2012, 12 4153
Figure 16. Images reconstructed using different calibration methods.
Primitive Images
(Dujon Method)
CC
p
0.6845 0.6607 0.6392
Primitive Images
(DBSE Method)
CC
p
0.7301 0.7081 0.6776
Primitive Images
(Line Scan
Method)
CC
p
0.8196 0.8016 0.7389
Inpainted Images
(BSDE)
CC 0.9091 0.9007 0.8370
4. Conclusions
In this article, a new technique has been presented for calibrating image transmission systems based
on IOFBs. We have demonstrated that transmission via IOFBs is an alternative to other,
technologically consolidated fiber-based elements such as coherent bundles. The DBSE calibration
technique presented here is based on the space encoding technique, but the principal contribution is on
the use of differential pattern images. For the purposes of comparison, we have taken the luminous line
scan technique and the method developed by Dujon [8] as references to compare and validate the
proposed calibration model, using a very simple experimental setup.
The experiments showed that all the proposed methodology is valid and that it is capable of offering
good results; however, it is necessary to highlight the need to ensure certain aspects:

Sensors 2012, 12 4154
xAdequate fiber location, an aspect which has been effectively solved using the FDDT technique
described in [3,4].
xCorrect focus of the optic at the input, which can be achieved by means of the fvar metric
described in [2].
xResolution of the input optic can condition the application of space encoding techniques.
From the experiments that have been presented, the following can be concluded:
xDBSE is a valid proposal since it achieves good image quality and is faster than the line scan
method. However, the line scan method achieves better results since it generates less
ambiguous results or outliers. However, DBSE is a strong method whenever sufficient optical
resolution of the system can be guaranteed.
xThe results given in Table 2 show that validation of the RT entries is over 80% compared to the
initial entries obtained with FDDT. This guarantees good quality in reconstruction of the final
and primitive images since less than 1.59% of the information is lost through calibration errors.
xThe redundant coordinate correction procedure enables redistribution of most of the ambiguous
cases towards other, more optimum positions, providing a notable improvement in the active
pixel area of the image formed.
xWe have shown that image focusing strongly influences calibration, and the DBSE method is
the most sensitive to this effect. This problem can be minimized by using other, alternative base
codes to generate the pattern images, and this will be the subject of future research.
xOf the techniques taken as points of reference, the technique described by Dujon presents the
worst results in terms of quality of the reconstruction, discrimination of the state of the fibers
and in the generation of outliers.
xThe luminous line scanning method continues to represent a more accurate alternative to
DBSE. Nevertheless, the results are not very different and in no instance was the quality of the
final image seen to be compromised. With the DBSE method, the reduced use of storage and
processing memory is notable, as is the greater speed.
In future research, the results will be extrapolated to a system with a lower resolution sensor, in
order to be able to conduct high resolution calibration for applications using less expensive sensors
which offer the same functionalities.
Acknowledgements
This research was funded by the Spanish Research Program (Programa Nacional de Diseño y
Producción Industrial, Spanish Ministry of Science and Technology), through the ESPIRA project
(ref. DPI2009-10143).
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distributed under the terms and conditions of the Creative Commons Attribution license
(http://creativecommons.org/licenses/by/3.0/).