The element used to display the input images in the experimental device that performs this calibration is a flat-panel LCD screen. To address a chromatic aberration problem generated by the optical device composed of conventional lenses, diaphragms are used. These diaphragms have the additional effect of reducing the emitted light, thus also resolving the CCD saturation problem in the camera. Unfortunately, this results in non-uniform illumination in the output images, creating noise in the reconstructed images.
This paper presents and compares three methods for correcting the non-homogeneous illumination present in the system, using the CIFO and its subsequent calibration, showing the results obtained with each method.
Keywords: Image transmission, incoherent fiber optic cable, non-homogeneous illumination correction. 

An alternative for image transmission is the use of coherent fiber optic cables, in which spatial correlation between each fiber is maintained. These are used over short distances for endoscopies in medicine. With this type of cable, any image at one end of the cable is transferred directly to the other end, allowing the use of this technology in the visible range [3, 4]. However, coherent fiber optic cables are considerably expensive and have limited practical applications. To overcome this drawback, the use of incoherent fiber optic cables (IFOCs) has been proposed [5, 6]. IFOCs lack spatial correlation between the fibers. Therefore, calibration is necessary before their use for image transmission, establishing a relationship between the positions of the input and output points, which allows the reconstruction of the images obtained at the output [5, 6, 7].

In our case, for the calibration stage and the reconstruction of the output images, the input image is projected onto the CIFO (Central Optical Fiber Optic) and its output onto the CCD sensor. Diaphragms are necessary to improve the definition of the transmitted images by reducing aberrations, which results in the attenuation of the transmitted light. This chromatic aberration problem arises because different wavelengths of light do not converge at a single point when passing through different lenses. As a result, light is split around bright objects (this phenomenon could also be corrected by adding special lenses or glass). The optical system, combined with the fact that the optical fiber transmits 60% of what it receives at the input, produces an output image with non-homogeneous illumination losses, which generates noise in the reconstructed images. To improve
this image transmission, several methods for correcting the resulting non-homogeneous illumination are proposed and compared.

Operating Principle:
First, and prior to illumination correction, a CIFO calibration method proposed and described in [5, 6] is selected. In short, this method consists of projecting a block of white pixels onto a black background as the input image, which is then projected onto the CIFO input plane. At the output, the resulting image is projected onto the CCD plane where it is captured. For each position of the white pixel block, a set of illuminated fibers is obtained at the output. A lookup table is thus created, recording the coordinates of the illuminated fibers in correspondence with the coordinates of the pixel block. Once this lookup table is obtained, the output image can be reconstructed by calculating the average value of the fibers illuminated by a given position.
The three methods described in the following sections treat each pixel of the output images, assuming that the illumination is non-homogeneous. The non-homogeneous illumination present in the system is illustrated in Figure 1. The response at the cable output when a uniform gray level is sent at the input is represented.

Correction using a multiplicative factor.
The operating principle of the first proposed method is to output a white image as input and calculate, for each pixel and each color component, a multiplicative factor that corrects the intensity level for that pixel, restoring it to the value 255 (the value of white). Thus, for each pixel i, the following is obtained:

a (i).Routage (i) = Rentrada (i) = 255
aG (i).Goutage (i) = Gintrade (i) = 255 (1)
aB (i).Boutage (i) = Bintrade (i) = 255

Where a is the multiplicative factor for each component R, G, and B (red, green, and blue).
To correct the illumination of a pixel i in the following output images, each color component is multiplied by its associated a.

Correction using the YIQ color space.
The YIQ color space (I stands for “in-phase” and Q for “quadrature”), like the RGB color space, is represented by a three-dimensional matrix. Unlike RGB, it presents color information decoupled from luminance information. The first matrix corresponds to luminance, while the other two are color information called chrominances. The YIQ space was the color space used in NTSC standard televisions. The luminance matrix contains values ​​in the range [0, 1].
To modify the color intensity of a pixel, and thus affect the luminance, the luminance value is raised to g. This variable g is calculated according to the following equations:

g = 1-b, if 1 > b > 0
(for a brighter image).
g = 1
1+b , if -1 < b < 0 (2)
(for a darker image).

To correct for non-homogeneous illumination, the value of the variable b(i) is chosen to be the difference between 1 and the intensity value of a pixel in the luminance matrix (values ​​in the range [0, 1]) of the YIQ color space. The new value of pixel i is calculated by raising it to the power
g(i), as shown in the following system of equations.

Rcorrected(i) = Routput(i)g(i)
Gcorrected(i) = Goutput(i)g(i) (3)
Bcorrected(i) = Boutput(i)g(i)

It is then possible to increase the illumination by applying the same g value to the entire image.

Lighting calibration-assisted correction:
The third method allows correcting the output image using information obtained after a lighting calibration step. The calibration process is as follows:

• First, a uniform image is output to the input. Each generated input image consists of a single grayscale level (with equally spaced levels between 0 and 255).
• For each pixel, each color component, and each output image, the output value is correlated with the homogeneous input value.
• Once the process is complete, an independent register is available for each pixel and each RGB color space component, relating a value of that component at the input to the output value.
• For each of these registers, a polynomial approximation of the resulting function is performed.
• The resulting coefficients are stored in a correction matrix.

This calibration for any given pixel is represented by Figure 2. Each figure shows the output values ​​for a given gray level on the x-axis and the image number for that gray level on the y-axis (in this case, 20 images are used. The first corresponds to a black image, the last to a white image). Figure 2(a) represents the measured responses, while Figures 2(b), (c), and (d) are approximations of Figure 2(a) using a straight line, a second-degree polynomial, and a third-degree polynomial, respectively.
To correct for non-homogeneous illumination, the new value of each color component of pixel i is calculated using the previously calculated polynomials; that is, in the case of a straight line approximation (Fig. 2(b)), by solving the following equations:

aR (i).XR + bR (i) - Rout (i) = 0
aG (i).XG + bG (i) - Gout (i) = 0 (4)
aB (i).XB + bB (i) - Bout (i) = 0

The correction is finalized by adjusting the new value X = 255 x X/number_of_input_images; if X > 255, the value 255 is adjusted, and if X < 0, the value 0 is adjusted.
Experimental Results
Once the image is captured at the CIFO output, the non-homogeneous illumination is corrected, and then the reconstruction process is applied [5, 6]. The results obtained are shown in Figure 3, which displays the original image, the reconstructed image without illumination correction, and the reconstructed image corrected for illumination: using a multiplicative factor, using the YIQ space with subsequent illumination increase (g = 0.6), and using illumination calibration by approximating a line, in Figures 3(a) to (e), respectively.
Conclusions
As can be seen in Figure 3, the most efficient method is illumination calibration (particularly with a first-degree approximation). Indeed, as can be seen in Figure 3(e), compared to reconstruction without lighting correction, this method significantly reduces noise and restores the original colors. However, the method using the YIQ color space has the advantage of processing in a much shorter time (with MATLAB®: 1.6 seconds versus 20 seconds for correction using lighting calibration), but, although it reduces image noise, it has the effect of attenuating the colors. Finally, the method using a single multiplicative factor falls between the other two methods in terms of processing time, but it does not significantly reduce noise; instead, it changes its hue.
Ultimately, this method of non-homogeneous lighting correction could be implemented by many other applications that use cameras, particularly in dark environments or when color information needs to be restored.

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Acknowledgments
This work has been partially supported by the Spanish project SILPAR (System for Absolute Robot Localization and Positioning. Development of an Intelligent Space), National Program for Industrial Design and Production, Ministry of Science and Technology, ref. DPI 2003-05067, and the regional project TIFO (Sensory System for Image Detection and Transmission via Optical Fiber for the Development of an Intelligent Space) of the Community of Madrid, ref. GR/MAT/0720/2004.
References
[1] VI Bovrinev, Jung-Young Son, Seong-Keun Lee, “Two-dimensional spectral multiplexing method for direct image transmission through an optical fiber”, Opt. Eng., 36, 1, 15-21, 1997.
[2] CE Dionne, RA Gonsalves, “Optical incoherent imaging through a thin slab waveguide”, Opt. Eng., 39, 9, 2392-2396, 2000.
[3] Smith JS, Lucas J., “A vision-based system seam tracker for butt-plate TIG welding”, J. Phys. E. Sci. Instrum., 22, 435-440, 1989.
[4] Gamo, J; Horche, PR; Merchan, M.; Rodriguez, M. and Rosales, P, “A neural-network based system for pattern recognition through a fiber-optic bundle”, Proc. SPIE, 4305, pp. 119, 2001.
[5] J. Gamo, O. Demuynck, Ó. Esteban, JL Lázaro, A. Cubillo, “Calibration of incoherent optical-fiber-bundle for image transmission purpose”, Proc. IADAT, 2005.
[6] O. Demuynck, Ó. Esteban, JL Lázaro, J. Gamo, Á. Cubillo, “Image transmission by means of an incoherent optical fiber bundle”, Proc. OPTOEL'05, 2005.
[7] MJ Tsai, JS Smith, J. Lucas, “Multi-fibre calibration of incoherent optical fiber bundles for image transmission”, Trans. Inst. MC, 15, 5, 260-268, 1993.

Author biographies

Olivier Demuynck obtained his degree in Computer Engineering from ISIMA (Institut Supérieur en Informatique, Modélisation et ses Applications) in Clermont-Ferrand, France, in 2001. He is currently pursuing doctoral studies in the Department of Electronics at the University of Alcalá. His research focuses on the disciplines of vision for robotics, smart spaces, image and signal processing, three-dimensional reconstruction using multiple views, and optics.

José Luis Lázaro obtained his degree in Electronics and Telecommunications Engineering from the Polytechnic University of Madrid in 1985 and 1992, respectively, and his PhD in Telecommunications from the University of Alcalá in 1998, where he is currently a professor. His research focuses on sensor and laser systems for robotics, infrared and machine vision applied to smart spaces, and monocular metrology.

Oscar Esteban obtained his Bachelor's degree in Physics and his PhD in Physics, specializing in advanced optics, from the Complutense University of Madrid in 1997 and 2001, respectively. He is currently a professor in the Department of Electronics at the University of Alcalá. His main research interests are related to fiber optic sensors and optoelectronics applied to smart spaces.

Daniel Pizarro obtained his degree in Telecommunications Engineering from the University of Alcalá in 2003. He was a research fellow in the Department of Electronics at the University of Alcalá from 2003 to 2005. Since 2005, he has held a position as an assistant professor in the same department. His research focuses on the disciplines of computer vision, smart spaces, optimization theory, three-dimensional reconstruction using multiple views, visual SLAM, and control theory.

Javier Gamo earned his Bachelor of Science degree in Physics from the University of Zaragoza and his PhD in Science from the Polytechnic University of Madrid in 1993 and 2000, respectively. In 2000, he joined the Research and Development Department of the Spanish Royal Mint (Fábrica Nacional de Moneda y Timbre - Real Casa de la Moneda). Since then, he has also collaborated as an Associate Professor in the Department of Electronics at the University of Alcalá. His main research interests are related to the optical security of valuable and identification documents.

Authors:

O. Demuynck, JL Lázaro, Ó. Esteban, D. Pizarro, J. Gamo

Department of Electronics, Higher Polytechnic School,

University of Alcalá. University Campus, s/n

28871 Alcalá de Henares (Madrid-Spain).

E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.