M Pérez-Patricio

Abiel Aguilar-González

Jorge-Luis L Camas-Anzueto

Miguel Arias-Estrada

M Perez-

Patricio Tuxtla Gutierrez

Tuxtla Gtz

A Aguilar-Gonzalez

Tuxtla Gutierrez

Luis Enrique Erro

A Fuzzy Logic Approach for Stereo Matching Suited for Real-Time Processing

Keywords: fuzzy logic, dense stereo vision, real-time processing, dedicated hardware, feature-based

published or not. The documents may come

INTRODUCTION

Stereo algorithms recover depth information from a scene by combining two images of that scene. Images are taken at the same time from slightly different viewpoints. In order to retrieve the depth information, primitives that correspond to the same point in the scene should be identified in both images. The correspondence problem consists in defining conjugate pairs of pixels, one from each image, that correspond to the same point of the scene. Because of the different viewpoints, coordinates of each pixel in a conjugated pair may be different. This difference is called the disparity. In order to reduce the complexity of the correspondence problem, images are rectified, i.e. the epipolar lines lie on horizontal lines at the same vertical position in both images. The depth of each primitive can be computed using the disparity value and a standard triangulation technique. Correspondence algorithms can be grouped as feature-based or area-based. In feature-based algorithms, a pre-processing step yields the edges or corners in both images and features in both images are matched. A sparse depth map is obtained while disparity of pixels between edges are computed by interpolation.

In area-based algorithms, a rectangular neighborhood centered on a reference pixel in one of the images is compared to a similar neighborhood of every pixel in the same raster line of the other image. The neighborhoods can be compared using a correlationbased measure such as the Sum of Absolute Differences (SAD). A correlation coefficient is determined for each candidate pixel and the shift that minimizes the correlation coefficient is retained as the disparity. These methods yield a dense depth map, but they are very time consuming. Using these methods, selecting the size of the correlation window is a difficult task. With a large window, used to reveal a maxima of correlation in non-textured areas, edges are blurred and small details or small objects are removed from the disparity map. On the other hand, with a small window, the correlation coefficient is very sensitive to noise. Several adaptive methods have been proposed to improve results in both depth discontinuities and homogeneous areas. Kanade and Okutomi [START_REF] Kanade | A Stereo Matching Algorithm with an Adaptive Window: Theory and Experiment[END_REF] changed neighborhood size and shape iteratively according to the local variation of the intensity and current depth estimates. However, the algorithm was computationally expensive and sensible to the initial depth estimates [START_REF] Scherer | Robust adaptive window matching by homogeneity constraint and integration of descriptions[END_REF]. Veksler [START_REF] Veksler | Stereo Matching by Compact Windows via Minimum Ratio Cycle[END_REF] changed neighborhood size and shape by optimization over a large class of compact windows via minimum ratio cycle. Lotti and Giraudon [START_REF] Lotti | Correlation algorithm with adaptive window for aerial image in stereo vision[END_REF] used edges in the reference image to determine the size of a rectangular window. Yang [START_REF] Yang | Stereo Matching using tree filtering[END_REF] proposed a method where a tree structure is used and the similarity between two pixels is computed using the distance on the tree. Min et al. [START_REF] Min | Joint Histogram-Based Cost Aggregation for Stereo Matching[END_REF] proposed the cost aggregation process from a perspective of a histogram, reducing the complexity of this process. In an article proposed by Chatterji [START_REF] Chatterji | Fuzzy Compactness Based Adaptive Window Approach for Image Matching in Stereo Vision[END_REF], a measure called the fuzzy compactness is used to determine whether or not the intensity variation in the window is enough to split the window. In a paper by Zitnick [START_REF] Zitcnick | A cooperative algorithm for stereo matching and occlusion detection[END_REF], an iterative algorithm that uses the uniqueness and smooth assumptions and where the occlusions are explicitly detected is proposed. Due to its high algorithmic complexity, the processing time of these algorithms is high. To simplify the adaptive methods and reduce time processing, efficient multiple windows methods have been proposed. Roberto et al. and Intille and Bobick [START_REF] Fusiello | Symmetric stereo with multiple windowing[END_REF][START_REF] Intille | Disparity-Space Images and Large Occlusion Stereo[END_REF], computed correlation coefficients on nine windows, and the one yielding the lowest value was retained.

Hirschmüller [START_REF] Hirschmuller | Improvements in real-time correlationbased stereo vision[END_REF] used a central window surrounded by several support windows. The correlation coefficients of the best support windows, i.e. the lowest values, were added to the coefficient computed using the central window. The reduced number of windows used in these methods cannot cover the whole range of different sizes and shapes required in all situations. Using graphics processing units (GPUs), several algorithms can process stereo images at a real-time rate. The GPU is a massively parallel computing device. For example, Wang implemented [START_REF] Wang | Realtime stereo using approximated joint bilateral filtering and dynamic programming[END_REF] an algorithm using adaptive cost aggregation and dynamic programming. The matching cost is aggregated based on both color and geometric proximity. Their implementation improves the speed by one or two orders of magnitude compared to the CPU implementation. Humenberger et al. [START_REF] Humenberger | A fast stero matching algorithm suitable for embedded real-time systems[END_REF] implemented a simplified Census Transform on embedded systems. In [START_REF] Hosseini | Fast implementation of dense stereo vision algorithms on a highly parallel SIMD architecture[END_REF] the multi-window algorithm proposed in [START_REF] Hirschmuller | Improvements in real-time correlationbased stereo vision[END_REF] has been implemented using a massively parallel SIMD architecture. Yang and Pollefeys [START_REF] Yanga | A versatile stereo implementation on commodity graphics hardware[END_REF] implemented a multi resolution scheme and a six shapes support windows method on a graphics card that achieved up to 289 million disparity evaluations per second. Chang et al. [START_REF] Chang | Real-Time DSP Implementation on Local Stereo Matching[END_REF] implemented a 4x5 jigsaw matching template on a DSP architecture for efficient use of the memory. Ambrosch and Kubinger [START_REF] Ambrosch | Accurate hardwarebased stereo vision[END_REF] implemented a modified version of the Census Transform that expanded the Census Transform to be processed over the intensity image and the absolute value of the gradient in x and y direction. In [START_REF] Sun | Real-time local stereo via edge-aware disparity propagation[END_REF], a two step method was proposed where an initial disparity was computed and only reliable disparity values were aggregated to the cost function for the second step. Jin et al. [START_REF] Jin | Fast and Accurate Stereo Vision System on FPGA[END_REF] proposed a cost aggregation method that computed ground control points (GCP) in order to refine disparity values using the GCPs, while [START_REF] Ding | Real-time stereo vision system using adaptive weight cost aggregation approach[END_REF] adapted the support area using assumptions of similarity and proximity values. Using the graphics hardware, real-time processing can be achieved, but the implementation must be efficiently adapted and modifications to that structure will be difficult to carry out. Another choice for hardware implementation of stereovision algorithms are the FPGA-based architectures. These devices are popular because of their inherent parallelism and high computational power. Ttofis et al. [START_REF] Ttofis | Edge-Directed Hardware Architecture for Real-Time Disparity Map Computation[END_REF] first applied an edge detector in order to reduce the space search, and next used a correlation measure only on the edges detected. Area-based algorithms are the most adapted for implementation on FPGA devices because they have a regular structure with fixed execution time. Several systems that use these methods have been described in the literature [START_REF] Zhang | SAD-Based Stereo Vision Machine on a System-on-Programmable-Chip (SoPC)[END_REF][START_REF] Jin | FPGA Design and Implementation of a Real-Time Stereo Vision System[END_REF]. These algorithms use a fixed size window with Census Transform or SAD as similarity measures where the problem of determining the adequate window size is still a challenge. We are interested in stereo matching algorithms that can be implemented on dedicated hardware for real-time processing. In this paper, a novel method is described that uses area and feature information in order to compute similarity between candidates for matching. Reliability of each candidate pixel is evaluated using a fuzzy logic system and the winner-take-all strategy is used to determine disparity. At this time, only three measures are used as similarity criteria, but the algorithm can be efficiently modified to increment the number of measures used. Results on synthetic images show that this algorithm preserves edges while reducing errors in homogeneous areas. Our proposal can be efficiently implemented on dedicated hardware for real-time processing. The rest of this paper is organized as follows : section 2 presents our algorithm. Experimental results with five synthetic stereo pairs and a comparison with similar algorithms is reported in section 3. Finally, section 4 concludes this paper.

THE PROPOSED METHOD

In order to explain the main idea behind this proposal, the image showed in the figure 1a is used. This image shows several objects at different depths, slanted areas and large homogeneous regions. In figure 1b, a zoom of a small region of the figure 1a Our proposal is depicted in figure 2 where several similarity measures are computed for the pixel for matching (I l (x, y)) and a candidate (I r (x, y, s)). All the similarity values are introduced in a fuzzy logic system that computes the reliability of the matching (R(x, y, s)) for each disparity value (s). The argmax of each reliability value R(x, y, s) is retained as the disparity. We can also observe that each data computed on each phase of the proposed algorithm is not dependant of another one, and they can be computed in parallel using dedicated hardware. For demonstration purposes, only three similarity measures are used. Nevertheless, the number of similarity measures used can be efficiently modified to consider other ones. Each similarity measure used in this proposal is described as follows:

The area-based information

One of the similarity measures used is area-based information. It can be computed using SAD or Census Transform. For demonstration purposes, area-based information is computed using SAD which is computed using equation 1.

C l (x, y, s) = i=wx i=-wx j=wy j=-wy |I l (x + i, y + j) - (1)
I r (x + s + i, y + j)|
where I l (x + i, y + j) and I r (x + i + s, y + j) are the gray levels of the pixels within the neighborhood in both images, called the left and right images respectively. (2 × w + 1) 2 is the window size, s is the shift of the neighborhood in the right image and the maximal shift of the correlation window in the right image is s m . Correlation values are computed using small window sizes that preserve discontinuities.

The feature-based information

The feature-based information used is the distance to the left and right nearest edges. They are detected in both images using a Sobel filter (figure 3) using only the vertical component of the Sobel filter (G y ).

g 1 = 1, y > 1 0, otherwise (2)
k 1 (x, y, s) = |I (x, y, s) -I (x, y -g 1 + s)| (3)
d 1 (x, y, s) = l = 0, k 1 (x, y, s) < β l = l + 1, k 1 (x, y, s) > β (4)
g 2 = 1, y < Y 0, otherwise (5)
k 2 (x, y, s) = |I (x, y, s) -I (x, y -g 2 + s)| (6)
d 1 (x, y, s) = l = 0, k 2 (x, y, s) < β l = l + 1, k 2 (x, y, s) > β (7)
where takes values of l or r for the left or right images, and β is a threshold value used to determine a pixel as a border. Fig. 4 shows the distance of each pixel to the nearest edge. Black gray levels represent shortest distances while white gray levels represent longest distances. In order to determine similarity between distances of a pixel in the left image I l and a pixel in the right image I r equation 8 can be used:

D k (x, y, s) = |I l (d k (x, y, 1)) -I r (d k (x, y, s))| ( 8
)
where k is [1, 2] , d k is determined by eq.4 and eq.7

The fuzzy logic system

Correlation values C l (x, y, s) and distance to the nearest left and right edges D 1 , D 2 are the inputs for a fuzzy inference system that determine similarity between candidates. For each one of these inputs, the three membership degrees in the corresponding fuzzy sets good , medium and bad are computed. This is realized by the membership functions µ good , µ medium and µ bad :

µ good (x) = 0, γ ≤ x x-γ α-γ , α ≤ x ≤ γ 1, x ≤ α (9)
Fig. 2. The proposed algorithm

µ medium (x) =    x-γ φ-γ , γ ≤ x ≤ φ x-γ α-γ , α ≤ x ≤ γ 0, otherwise (10)
µ bad (x) = 0, x ≤ γ x-γ φ-γ , γ ≤ x ≤ φ 1, φ ≤ x (11)
where α, φ and γ are empirically defined by 0.0, 0.5 and 1.0 respectively.

In this algorithm greatest fuzzy value determines the best candidate. For this purpose, output fuzzy sets good, medium and bad are proposed. Membership degrees are defined by the membership functions ψ good , ψ medium and ψ bad :

ψ good (x) = 0, γ ≤ x x-γ α-γ , α ≤ x ≤ γ 1, x ≤ α (12)
ψ medium (x) =    x-ρ σ-ρ , ρ ≤ x ≤ σ x-ρ σ-ρ , σ ≤ x ≤ ρ 0, otherwise (13)
ψ bad (x) = 0, x ≤ γ x-γ φ-γ , γ ≤ x ≤ φ 1, φ ≤ x (14)
where α, φ, γ, ρ and σ are empirically defined by 0.0, 0.5, 1.0, 0.4 and 0.6 respectively. Rules in the form of IF-THEN and connective AND defined by the Zadeh operator are used. Rules of the fuzzy system are determined as showed in 1 Fuzzy inference is determined by the Mamdani operator RM as:

RM = min (µ n , µ w (x)), ∀x (15)
where µ w , is the membership function of the output set w and µ n is the rule antecedent value for the n-sima rule. Singleton inputs are used and fuzzy inference is simplified as follows:

RM = µ n ( 16
)
Rule aggregation is realized using the sum operator as follows:

µ φ (x) = µ 1 + µ 2 + • • • µ n , ∀x (17)
where µ φ (x) is the membership function of the output and µ 1 , µ 2 , µ n are RM values for n rules of the system. Finally the bisector of area eq.18 is used for the defuzzification process.

R(x, y, z) = z 0 α µ φ (x)dx = β z 0 µ φ (x)dx (18)
where µ φ (x) is the membership function of the output, α = min{x|x ∈ X}, β = max{x|x ∈ X}, X is the output set and z 0 divides the area into two regions with the same area. The maximum of the values of the output determines disparity value according to equation 19

disparity(x, y) = argmax z R(x, y, x) (19)
The output of the fuzzy system is used as a confidence value in order to determine the reliability of the matching procedure and for subpixel matching. A parabolic equation is evaluated with the output of the fuzzy system, and the minimum value of the equation determines the disparity with subpixel accuracy.

EXPERIMENTAL EVALUATIONS

Several stereo pairs have been processed to demonstrate the effectiveness of our algorithm. A left-right validation has been applied to the disparity maps as a post-processing step in order to reduce errors near discontinuities. Disparity maps are presented as gray level images, using a linearly stretched gray level range to improve readability : black for the minimum disparity, white for the maximum one.

For the first experiment, we used the ground truth of the Corridor image showed in figure 5a. In this image there are several objects with different depths, homogeneous areas, and small objects.

The difficulty is to detect small objects and preserve discontinuities, such as the ball in front, and to have robust results in homogeneous areas simultaneously. Figure 5b shows the disparity image obtained with the algorithm that uses a fixed size window and SAD as similarity measure, while figure 5c shows results of our proposal. Both use a small window of 3x3 pixels. As a small window is used, discontinuities are well preserved in both algorithms. Nevertheless, the SAD algorithm yields incorrect disparities in homogeneous areas-areas that appear black in the images, but should appear white. On the other hand, disparity values obtained with our proposal are more accurate and contain fewer errors in these areas. We can conclude that the use of distance of the nearest edge helps in homogeneous areas while correlation values are used in non-homogeneous areas. Nevertheless, several mismatches have occurred. For example, in figure (c) the white line is an error; because the edge is misread it appears as white when it should appear dark. A detailed analysis of the computed data showed that errors occur for photometric distortion and edges that are not well detected. Using one edge is not sufficient for consistent results, it is much better to use both the left and right nearest edges. Figure 6 shows other test images and their corresponding disparity maps computed using our proposed algorithm and a window size of 11x11 pixels. These images were taken from the Middlebury dataset. In the third column, the images show pixels with mismatches in black and pixels correctly matched in white.

The Tsukuba image has small objects, homogeneous areas, and several repetitive patterns, while the other ones present large homogeneous areas and slanted objects. Only the Venus, Cones, and Teddy images have subpixel disparities information. For our proposal, subpixel accuracy was achieved using the computed fuzzy value.

We can observe that errors in homogeneous areas are reduced, while an more accurate result is achieved near discontinuities. We can also observe that the fuzzy value can be efficiently used for obtaining subpixel accuracy results. Using images in the third column, it can be observed that a lot of mismatches are present on the left or right borders where there is not border information. In the Venus image, errors can be observed in the bottom-middle of the image caused by incorrect border information. Errors are also detected near discontinuities because this algorithm does not include an explicit discontinuity correction method.

For quantitative analysis, we present table 2 where each image of the dataset has been analyzed using several window sizes and for β = 20. Disparity maps have been compared using the method proposed in [?], in which the percentage of pixels with a disparity error greater than one is computed. Three percentages are computed, one for all non-occluded pixels, one for all pixels which includes the half-occluded regions, and one for non-occluded pixels near depth discontinuities. It can be observed that the percentage computed in the all column reduces with the greater window sizes. Detailed analysis of data shows that for several pixels there is not enough information using small windows and distance to nearest edges information and larger windows are required in this areas. On the other hand, in the disc column, error grows while window size also grows. So, performance of this proposal is similar to SAD algorithm, but the error rate is smaller. Nevertheless, the difference between errors obtained with largest and smallest windows are very similar (less than 1 percent of difference) in the Tsukuba image, and this proposal can be efficiently used with small windows. The importance of this remark is that the use of smaller windows reduces time processing in a CPU implementation and reduces hardware resources and memory requirements in a FPGA implementation. An additional post-processing step to left-right validation can be used in order to reduce errors using the fuzzy value as a confidence measure. As previously mentioned, results depend also on border detection. In order to determine an adequate β value, we evaluate performance of the algorithm for different values of β and for w = 2. Results are shown in figure 7.

We can observe that for values of β smaller than 20 and greater than 40, performance of the algorithm are worse, and better results can be obtained for β values between 20 and 40. We can conclude that a small β value produces a lot of edges that can produce errors of multiple similar edges. On the other hand, larger values of β reduce the number of edges, which are necessary in homogeneous areas.

In order to compare our proposal with other similar real-time stereo algorithms, we present table 3, where the Tsukuba image has been analyzed. In this table, the column P latf orm describes the target hardware architecture, while the Algorithm column shows the type of algorithm used and the Error r ate column describes the percentage of error obtained in the all column of the Middlebury dataset.

Results obtained show that our proposal is only outperformed by algorithms that use adaptive cost aggregation algorithms that require a more complex implementation. Adaptive cost-aggregation algorithms perform better near discontinuities because they only use pixels with the same disparity in the matching procedure, while our proposal includes pixels with different disparity values in the support windows that introduce errors. Nevertheless, the proposed algorithm outperforms algorithms that use a fixed-window size. This

  is presented. This figure shows a pixel for matching and their support area, which is placed in an homogeneous area. The correlation function presents several minimals and the selection of a candidate is difficult. It is well known that the use of only correlation value in the matching procedure is not adequate in homogeneous areas. Nevertheless, the distance d of this pixel versus the left nearest edge must remain equal in the other image as observed by Yang [?]. This observation is valid except in presence of occlusion areas and for slanted regions. So, we propose the use of several similarity measures simultaneously in the matching procedure, ones that can help for homogeneous areas and other ones suited for non-homogeneous areas. a) Corridor image b) a small region

Fig. 1 .

 1 Fig. 1. Corridor image

Fig. 3 .

 3 Fig. 3. Sobel filter G y

Fig. 4 .

 4 Fig. 4. Images of distance to nearest edges

Fig. 5 .

 5 Fig. 5. Comparison of disparity maps

Fig. 6 .

 6 Fig. 6. Comparison of disparity maps using test images

Fig. 7 .

 7 Fig. 7. Effect of β values

Table 1 .

 1 Rules of the fuzzy system

	Correlation	D 1	D 2	output
	good	good	none	good
	good	medium	none	good
	good	bad	none	medium
	medium	good	none	medium
	medium	medium	none	bad
	medium	bad	none	medium
	bad	good	none	medium
	bad	medium	none	medium
	bad	bad	none	bad
	good	none	good	good
	good	none	medium medium
	good	none	bad	medium
	medium	none	good	bad
	medium	none	medium medium
	medium	none	bad	medium
	bad	none	good	medium
	bad	none	medium	bad
	bad	none	bad	bad

Table 2 .

 2 Performance under several windows sizes

	image	ws	nonocc	all	disc
	tsukuba	3x3	5.32	7.31 19.5
		5x5	5.17	7.15 19.0
		7x7	5.03	7.03 18.9
		9x9	4.96	6.99 19.5
		11x11	4.97	6.97 20.3
	venus	3x3	7.89	8.87 32.6
		5x5	6.60	7.61 32.3
		7x7	5.99	6.99 32.7
		9x9	5.67	6.69 33.5
		11x11	5.43	6.40 33.6
	teddy	3x3	22.3	29.3 35.5
		5x5	21.4	28.6 35.1
		7x7	20.8	28.0 34.3
		9x9	20.4	27.6 35.6
		11x11	20.3	27.5 38.3
	cones	3x3	17.6	24.8 29.9
		5x5	16.3	23.5 28.6
		7x7	15.7	23.0 28.3
		9x9	15.6	23.0 28.8
		11x11	15.2	22.6 29.0

Table 3 .

 3 Comparison with other real-time algorithms

performance is achieved by the reduction of the error rate in homogeneous areas where the distance to the nearest edges helps significantly.

CONCLUSION AND OUTLOOKS

We have presented a new fuzzy logic algorithm for stereo matching suited for real-time processing using dedicated hardware. The algorithm uses local and global information in order to reduce errors in homogeneous areas and to preserve edges near discontinuities. At the moment, we only use three similarity measures, but the process can be adapted to increase the number of similarity measures used.

We will analyze other similarity criteria in order to reduce errorrate when dealing with similarity of edges. An empirical value for determining a pixel as edge has been defined in order to improve results, but it's necessary to reduce the dependency of this value using other strategies of edge detection. We also hope to study the implementation of the algorithm using specialized hardware.


domain: sde shs

text:
Aquarium

Aquariums may be analyzed as places of display based on capital and innovations accumulation, taming the underwater otherness by a scenography and an ordering of what is presented.

Even as oceans cover about seventy percent of the Earth's surface and present an important diversity from seashores to abyssal floors in terms of landscape, fauna and flora, they stay mostly unreachable to our terrestrial mammal condition. The underwater experience is limited to few people and to a very limited part of the global ocean, making it one of the last limits of our Earth, along with the outer space.

Aquariums organize an encounter between Humans and non-Humans in conditions that are unique: we may be affected, moved and impressed by animals that are no more indifferent to us. As they unveil a situated vision of the underwater world that we may experience and place it into wider social issues their main function appear to be their capacity to expend the Ecumene (the places we live and practice on Earth as Humans).

More than 200 million visitors pass through the door of the 240 or so worldwide aquariums and marine life centers every year. On the individual side, roughly twenty million households -six million in the United States only-own an average of twenty fishes each, fueling a business of five to six billion dollars for the yearly exchange of fishes. Ornamental fishes follow a global circulation from productive and fishing zones (Singapore, Malaysia, Brazil, Sri Lanka, Porto Rico…) to important markets places (US, Europe -UK, France, Germany-, Japan, Singapore, Malaysia, China) to an ever faster pace as their medium value is almost hundred times the one of fishes as food. The combined attendance of aquariums can measure up with important sport events. Institutions such as the Monterey Bay Aquarium (California) or the Tokyo Sea Life Park attract 3 to 4 million visitors every year.

The practice of keeping alive fishes is acknowledged in the Roman Empire or China, as early as 1000 BCE. At that time, tanks had to be connected to the sea or a waterway. In 1850, the discovery by R. Warington and H. Gosse of a possible equilibrium between animals producing carbon dioxide and plants producing oxygen is implemented allowing aquariums to be constructed afar from open waters. The Regent's Park (1853), Vienna and Paris (1860) or Berlin (1869) aquariums are the firsts of a long series. An aquarium mania is even described among wealthy city dwellers in England and France around 1850-1870 with specific furniture designed to highlight their fish collection, displayed in their living-room.

Aquariums develop a narrative as scientific institutions producing knowledge by ordering species, offering suitable conditions to study rare specimens and even establish a place to protect and reproduce endangered species.

Throughout their spatial organization aquariums display the separation between Humans and non-Humans as they are located on different sides of the tanks. Species limits also become material as they are located in specifics zones. At Monterey's aquarium, all jellyfishes are gathered in a zone standing for the specie as a category and partly presenting its diversity. The discourse on species classification and evolution is thus embodied in the aquarium materiality and practiced by visitors.

Animals and Plants are also organized according to the place they are supposed to be coming from. In the mid-nineteenth century, fishes are mostly local but as transportation technics are developed and a strong network of catchers and animal dealers follows the European colonial expansion, aquariums tend to mimic zoos by gathering exotic animals from abroad.

Many aquariums present a classification based on a miniature of the World. The Lisbon aquarium is based on the idea of a global ocean subdivided in large zones. A huge central tank is surrounded by the Artic World, the Indian Ocean presenting a reef barrier, the North-Atlantic and its jellyfishes and the temperate Atlantic with giant octopuses.

Even as aquariums are supported by scientific practices, they are mostly based on entertainment as they present the spectacular show of non-Human Animals and Plants. Tanks are filled with stones, wreckages, sculptures or buildings that emphasis their exoticism, wilderness and otherness. Contemporary aquariums tend to organize a scenography mimicking a travel for visitors: we are not only looking at fishes but should experience the immersion in a new underwater environment. The Monterey Bay Aquarium uses special tanks whose limits seem to fade thanks to an optical illusion to presents its jellyfishes.

Picture: The jellyfish tank, Monterey Aquarium, 2008, Jean Estebanez

Most aquariums present important exotic collections and ornamental fishes mostly come from tropical environments. They also focus on local fauna and flora. Brest Océanopolis in France has about a third of its surface inviting to dive off the Brittany coasts. The Monterey Aquarium is about animals and micro-environments from the Bay area. Even local underwater animals are very different from us: fishes have no faces and coral or jellyfish body is radically different from ours. The local otherness is strong enough to be worth displaying and made esthetic enough to be attractive and to enable a form of bond between them and us.


Raul Moreno Flores

Enrique Escobedo

David Antonio

Gómez Jáuregui

Masha Smit

Victor Manuel

Ramirez Rivera

R Moreno-Flores

D A Gomez-Jauregui

V Ramirez

Stack performance optimization of low power PEM Fuel Cell

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCION

The fuel cell proton exchange membrane (PEMFC) is an electrochemical device that transforms the chemical energy of a reaction into electrical energy with high efficiency. The high power density at low temperatures and long life makes it attractive to DC to be used in stationary, mobile and portable systems, such as for backup systems energy, automotive and electronic entertainment equipment industry, respectively. The fuel cell is mainly composed of five parts: end plates, current collector plates, gaskets, bipolar plates and membrane electrode assembly. The union of anode-membrane-cathode is known as MEA, it is considered the heart of the cell because it is in the catalytic layer where the electrochemical reactions take place. On the surface of the anode hydrogen is oxidized, while oxygen is reduced at the cathode. The catalytic layer is basically the joining of a catalyst, a carbonaceous support and ionic conductor; typically this layer can be applied on the membrane or on the gas diffuser. Generally the most used materials for the MEA is carbon supported platinum catalyst, Nafion, electrolyte membrane, paper or carbon cloth as a gas diffuser. There are several ways to apply the catalytic layer as a liquid mixture of catalyst and solvent in the electrolyte solution through the dropping technique that involves depositing ink, with a micropipette, drop by drop to the diffuser; Another way is by electrospray technique of applying the same way that ink dropping but applying a potential difference (10 to 11 kV) between metal needle pipette and the diffuser surface. Arrangements FC connections in series are to raise a potential difference and put this potential for practical use. Such connections are provided and are improved by bipolar plates. Other functions of the plates are: being a way by which the heat is removed and water, provide mechanical support to the 1 CONACYT Research Fellow -Centro de Investigación Científica de Yucatán, A.C. Mérida, México, correo electrónico: victor.ramirez@cicy.mx, 2 Centro de Investigación Científica de Yucatán, A.C., 3 ESTIA Institute of Technology, Bidart, France, cells, provide a thermal contact between the coolant, driving electrons generated in the reactions, the reactant gases lead to all cells and all your work surface through channels [START_REF] Dihrab | Review of the membrane and bipolar plates materials for conventional and unitized regenerative fuel cells[END_REF] [START_REF] Antunes | Corrosion of metal bipolar plates for PEM fuel cells: A review[END_REF]. It is important that the materials plates have high electrical conductivity such as metals, polymers or composite graphite whit flow channels of different configurations for conducting the fuel and oxidant. Individual PEMFC is characterized by delivering direct current at low potential difference, relatively, this means that to get a potential to use in conventional electrical equipment is required series connection of the cells. Each cell produces a voltage of 1.23V theoretically, this potential is ideal, in a real cell performance losses are various causes, under standard operating conditions and may be increased if more cells connected in series are added [START_REF] Dicks | Fuel Cell Systems Explained[END_REF] to learn the electrical performance of the electrochemical cell operation polarization curve technique is used.

II. MATERIALS Y METHODS

The materials used were diffusers carbon cloth BASF Fuel Cell Inc. A6NCV2.1 ELAT and carbon paper EC-TP1-060T, Nafion membrane (DuPont), Nafion Solution 5% (SIGMA ALDRICH), catalyst Pt/C 20% and 2-propanol (reagent grade). The only known diffusers carbon cloth have Teflon coated fabric, a microporous carbon layer vulcan and measured 0.36mm thick; carbon paper is treated with 30% Teflon and 0.19mm thickness, these data are given by the manufacturer [START_REF] Pfrang | X-ray computed tomography of gas diffusion layers of PEM fuel cells: Calculation of thermal conductivity[END_REF]. The electrochemical characterization made to all cells in all tests were through a polarization curve using the testing station (FCT-50, BioLogic) for controlling the operating conditions and the potentiostat / galvanostat (VSP BioLogic ) with booster 10 A -20 V (BioLogic, VMP3B-10) for the polarization curves, they were conducted with a scan rate of 10mV / s OCP to 0V and operating conditions, which we will call conditions standard in this work, were 60 C, 50 ML / min / cm2 flow of gases (H2 / O2) to 100 % relative humidity (RH).

III. MATERIALS COMPARISON FOR DIFFUSERS

Two MEAs of 1cm2 were prepared with platinum loading of 0.5 mg/cm2, both with parameters membrane electrode assembly EROSA(2011) [START_REF] Renovable | Centro de Investigacin Cientfica de Yucatn[END_REF], temperature 120C, 4 minutes pressing time and 1814.4 kgf / cm2 (4000 lbf / cm2), a diffuser MEA carbon cloth and the other of carbon paper. The obtained MEAs were placed in the hardware with flow field single serpentine configuration, both cells under standard conditions for evaluation by polarization curve operated.

IV. CATALYTIC INK DEPOSITION METHOD COMPARISON

The method of dropping was selected to be simple to implement in very small cells and electrospray by to be controlled deposition. Two MEAs were prepared with platinum loading 0.5 mg/cm2, one for each method, using hot-pressing parameters (temperature, pressure and time) proposed by EROSA (2011) whit carbon paper diffusers. Two MEAs obtained were placed on the same hardware in the previous section and is operated under standard conditions. The electrochemical characterization was by a polarization curve.

V. COMPARISON OF METHOD OF MEMBRANE-ELECTRODE

ASSEMBLY

To carry out the comparison of two methods of membrane assembly electrode with optimized parameters for each author, two MEAs of 4 cm2 were prepared with platinum loading of 0.5 mg/cm2, one with each method, was used electrospray to apply the catalyst ink in the diffuser of carbon paper. The membrane electrode assembly parameters of OKUR(2013) [START_REF] O. Okur | Optimization of parameters for hot-pressing manufacture of membrane electrode assembly for PEM (polymer electrolyte membrane fuel cells) fuel cell[END_REF] are: temperature 97 C, 3.6 minutes, 66 kg/cm2 (145.5051 lbf/cm2) of pressure press and the method of EROSA(2011) are: temperature 120C, 4 minutes pressing time and 1814.4 kgf/cm2 (4000 lbf/cm2) For electrochemical characterization of obtained MEAs, was used a hardware with flow field single serpentine configuration and were electrochemically characterized by polarization curve, both cells operated at standard conditions.

VI. COMPARISON OF ELECTRICAL CONTACT RATIO

To know the effect of the electrical contact ratio (ECR) variation of the flow field in the cell performance, mainly resistance electrical contact and diffusion of gases, were evaluated electrochemically two designs of flow fields with two different reasons of electrical contact. ECR for plates were 0.2 and 0.5, the depth of channel designs were both 1 mm, the channel width and rib were variable in both designs according to the limitations of the tools and materials used for the manufacture of plates. Cells were characterized electrochemically by polarization curves operated at standard conditions.

VII. CHARACTERIZATION OF OPTIMIZED MEAS IN THE

STACK

Graphite diffuser plates were made (two end plates and two bipolar plates), and three MEAs and the others components were made to use in the stack according the results of this work. The polarization curves were run simultaneously to all cells in the stack to standard operating conditions. The range was from open circuit potential to 0 V at a scan rate of 10 mV/s, were performed graphs current density versus potential (I-V).

VIII. RESULTS AND DISCUSSION

A. Carbon cloth and carbon paper as diffusers

In the first part of this work was to study what diffuser which offered higher power density, as shown in the polarization curve in Figure 1 a) the MEA made with carbon cloth diffuser showed better performance than MEA paper diffuser, showing that the peak power density of the MEA with carbon cloth and the MEA with carbon paper was 214 and 208 mW/cm2, respectively. Likewise, it can be seen that the performance of the MEA with paper falls faster than the MEA with cloth, especially in the region of higher current density. This could indicate a problem of diffusion of gases through the diffuser of the MEA with paper and attributed to the highly disorganized, irregular and compact structure of carbon paper severely limits mass transport when the cell operates at high relative humidity; in addition, its relatively smooth surface makes the water drop separating harder, resulting in water on the cover surface so therefore increased waste mass transfer [START_REF] Wang | Elucidating differences between carbon paper and carbon cloth in polymer electrolyte fuel cells[END_REF]. Some studies report that the high porosity of the material used as diffusers are necessary to improve the operation of the FC [START_REF] Millington | The effect of materials on proton exchange membrane fuel cell electrode performance[END_REF], others report that diffusers with low amounts of Teflon in its structure are best to increase cell performance [START_REF] Wikander | On the influence of Pt particle size on the PEMFC cathode performance[END_REF][10] [START_REF] Antolini | Effects of the cathode gas diffusion layer characteristics on the performance of polymer electrolyte fuel cells[END_REF] [START_REF] Lobato | Influence of the Teflon loading in the gas diffusion layer of PBI-based PEM fuel cells[END_REF].

B. Dropping and electrospray

In the results of the comparison of deposition techniques catalyst ink, in Figure 1 b), it can be seen that the MEA made with the ink by electrospray shows the best performance with maximum power density of 266 mW/cm2 compared to the value obtained by the drooping method was 208 mW/cm2. Also, the potential of the MEA-DROP falls faster than the polarization curve in areas of higher current densities (from 400 mA/cm2). This behavior could be due to a lower gas diffusion more sites of the catalytic layer, it mean, greater charge transport resistance, the porosity of the structure of the catalyst layer could be a factor that causes the variation of the operation, other words, it is possible that deposits made by dropping clusters exist that block catalytic active sites.

C. EROSA and OKUR and Okur

The effects of varying the parameters of the hot-pressing technique are shown in Figure 1 c), the OCP obtained MEA-OKUR is 1.008 V and the MEA-EROSA is 0.98 V, a higher OCP is one result of a better contact between the catalyst layer and the membrane [START_REF] O. Okur | Optimization of parameters for hot-pressing manufacture of membrane electrode assembly for PEM (polymer electrolyte membrane fuel cells) fuel cell[END_REF]. Furthermore, the power density of the MEA-OKUR show be greater than the MEA-EROSA, 310 mW/cm2 for the first and 270 mW/cm2 for the second; the maximum current density of MEA-OKUR 1413 mA/cm2, while the MEA is 1113 EROSA mA/cm2. The highest value of the current density and maximum power is presented by the MEA-OKUR that can result in a more porous structure of the catalyst layer of the MEA-EROSA, however, other factors may be influencing that behavior. The decay of the power density may be due to a change in the structure of the MEA caused by high temperatures and pressures when preparing them. High pressures affecting the catalytic structure, which reduces the electron conductive network and causes mass transport problems [START_REF] O. Okur | Optimization of parameters for hot-pressing manufacture of membrane electrode assembly for PEM (polymer electrolyte membrane fuel cells) fuel cell[END_REF], in other words, a higher pressure will result in the compaction of the porous structure, which affect the cell performance by mass transport problems, limiting the flow of the reactant gases through the active sites of the catalyst layer. D. Electrical contact ratio, ECR 0.5 and ECR 0.2

In comparing of the electrical contact ratios in the flow field of graphite plates, the results shown in fig. ?? d) which shows that the single cell with ECR 0.2 provides better performance than obtained of the ECR 0.5, particularly at low potential (mass transfer losses). The maximum power density of ECR0.2 increased 11%, from 261 to 290 mW/cm2 compared to 0.5 ECR design, it increases with decreasing electrical contact ratio, in other words, to increase the area of gas contact with the diffuser, a smaller channel area means a wider rib, and gas diffusion behind the ribs becomes more difficult, it is also possible that water retention is higher.

E. Characterization in the stack of optimized MEAs

In fig. ?? the polarization curves of the three cells in the first two loss zones (ohmic and activation) are very similar; the difference between cells highest OCP is 0.008 V (8 mV), while at 500 mA/cm2 the difference is 0.022 V (22 mV); cell C1 has the highest potential and the cells C2 and C3 of less at 500 mA/cm2, these values can be seen in table 1. Furthermore, in the concentration loss zone behave very different, the difference between the highest potential cell at 800 mA/cm2 and the less is 0.170 V (170 mV), the cell potential was greater C1, followed by C2 and C3 in the same order from highest to lowest. In the table ??, the potential cell and stack are observed in three different points of each curve, OCP, 500 mA/cm2 and 800 mA/cm2. Different behavior between the performances of the three cells at high current densities is observed, particularly, in the concentration losses zone. The inputs of both gases of the stack were sided in one side, near to C1; there could be within the stack has bad distribution gas flow that difficult the arrival of one or both gases to the cells, causing an absence of fuel or the oxidant. Linked to poor gas distribution, it could also be added, low elimination of water produced by reactions in cells that do not arrive gases; that reason affect the pores of electrode surface, obstructing the gases flow through the catalytic layer. Another reason that can be attributed that difference is the lack of standardization of manufacturing and assembling the components of the cell, starting from the MEA, diffusers graphite plates, seals, etc; emphasizes that in developing the MEAs, to press them with heat, the membranes were dehydrated and loss their original shape.

IX. CONCLUSI ÓNES

The electrospray technique allowed depositing catalytic layer on the diffuser homogeneous and scalable compared to the dropping technique. In addition, it was possible to increase the maximum power density only by varying the deposition technique from 208 to 270 mW/cm2, the optimized method OKUR (2013) for the development of MEAs allowed improving yields of these, the reduction of electrical contact ratio of the flow field allowed to increase the maximum power by 11Stack maximum power was 762 mW/cm2, and each one of its cells was 270, 254 and 243 mW/cm2. The potential in the polarization curves of the three cells of the stack at 500 mA/cm2 were 0.50, 0.48, 0.48 V, a difference of potential between the highest and lowest cell of 22 mV. The cells in the stack had a very similar behavior due to the selection of materials and methods suitable for preparation of homogeneous cell components.

Fig. 1 .

 1 Fig. 1. Curves of current density-potential and current density and power density, operated under standard conditions of monocells: (a) of 1 cm2 with cloth and paper diffuser, (b) of 1 cm2 made by the dropping and electrospray techniques, (c) made by EROSA and OKUR method, (d) made by two plates diffuser designs, ECR0.2 ad ECR 0.5.

Fig. 2 .

 2 Fig. 2. Polarization curves measures to stack and its three cells simultaneously. The tests were conducted under standard operating conditions

TABLE I .

 I

	Component	Value
	L	5 µH
	R	1000 Ω
	C	100 µF
	switching frequency	30 KHz

POTENTIAL STACK AND POTENTIAL CELLS AT THREE DIFFERENT CURRENT DENSITIES REPRESENTATIVE OF LOSSES ZONES (ACTIVATION, OHMIC AND MASS TRANSPORT) OF THE POLARIZATION CURVE.

ACKNOWLEDGMENT Authors thanks to ESTIA and Proyecto de Desarrollo Cientfico para Atender Problemas Nacionales foundings No. 2015-01-786.