R Kassab

S Treuillet

F Marzani

C Pieralli

J C Lapayre

An optimized algorithm of image stitching in the case of a multi-modal probe for monitoring the evolution of scars

Keywords: Scars evolution monitoring, stitching, multi-modal probe, autofluorescence

We propose a new system that makes possible to monitor the evolution of scars after the excision of a tumorous dermatosis. The hardware part of this system is composed of a new optical innovative probe with which two types of images can be acquired simultaneously: an anatomic image acquired under a white light and a functional one based on autofluorescence from the protoporphyrin within the cancer cells. For technical reasons related to the maximum size of the area covered by the probe, acquired images are too small to cover the whole scar. That is why a sequence of overlapping images is taken in order to cover the required area.

The main goal of this paper is to describe the creation of two panoramic images (anatomic and functional). Fluorescence images do not have enough salient information for matching the images; stitching algorithms are applied over each couple of successive white light images to produce an anatomic panorama of the entire scar. The same transformations obtained from this step are used to register and stitch the functional images. Several experiments have been implemented using different stitching algorithms (SIFT, ASIFT and SURF), with various transformation parameters (angles of rotation, projection, scaling, etc…) and different types of skin images. We present the results of these experiments that propose the best solution.

Thus, clinician has two panoramic images superimposed and usable for diagnostic support. A collaborative layer is added to the system to allow sharing panoramas among several practitioners over different places.

INTRODUCTION

Skin cancer is the most common form of human cancer. It is estimated that over 1 million new cases occur annually. The annual rates of all forms of skin cancer are increasing each year, representing a growing public concern. It has also been estimated that nearly half of all Americans who live to age 65 will develop skin cancer at least once [L1, L2].

The most common warning sign of skin cancer is a change in the appearance of the skin, such as a new growth or a sore that will not heal. The term "skin cancer" refers to three different conditions. From the least to the most dangerous, they are either basal cell carcinoma (or basal cell carcinoma epithelioma), or squamous cell carcinoma (the first stage of which is called actinic keratosis) or melanoma.

After eradication operations, the risk of the existence of effected cells is big, and the danger is that these cells could redeploy on the skin, this is why an accurate observation of the scar is required to assure that no cells are still affected anymore. Different optical methods for monitoring have been developed over the time starting from clinical methods of detection and characterization where only the personnel experience of practitioners plays the principle role, to the spectroscopic methods of diagnosis based on the fact that the spectral emission of a tissue returns information about its historical, morphological, and biochemical nature. Fluorescence, elastic scattering and Raman scattering are types of spectroscopic methods of diagnosis.

In terms of imaging, color and gray scale images provide interesting anatomical information; they can be used to compare scar over time. The use of fluorescence images provides very interesting functional information depending on the reaction behavior of certain molecules in the skin, like protoporphyrin. The emission spectrum of this molecule can be used for characterization of infected/carcinogenic cells. For all these reasons we developed an optical probe system that acquires tow images (gray scale and fluorescence one) at the same time. This system consists of a CCD camera, a blue light laser source to acquire florescence images and a white light source to acquire anatomical images.

Because the sensor covers a small area of skin, it is necessary to make several shots to cover the scar with a slight overlap between each pair of images. Image registration algorithms are used to obtain panoramic images of the scar in both modes (white light and fluorescence) starting from the couples of images. Because fluorescence images do not have enough information to be used by registration algorithms, we apply these methods over the white light images to obtain the transformation parameters and apply these parameters over fluorescence as well as they have been taken in same place at the same time.

Panoramic images obtained by our system, especially the fluorescence ones, are used by practitioners to observe and characterize scars and their evolution over the time. New panoramas are required every two weeks. That is why a multiview image registration has to be done over the new panoramas to make them comparable with previous one.

Telemedicine can be then used to share these panoramas among several practitioners over different places using different kinds of devices (PCs, PADs, Cell phones, etc…).

In the next section we present some state-of-the-art of stitching methods. Section 3 explains our contribution with some experiments and results. Then the stitching scenario we propose is given in a collaborative way in section 4. Finally the conclusion is followed by further work ideas.

METHODS OF STITCHING

Image stitching algorithms are common in computer vision. The domains where they are used vary from satellite maps images to mobile applications to have wide angle photos. They are also used for medical applications. For example, standard X-ray images using conventional screen-film technique have a limited field of view and failed to visualize the entire long bone on a single image. To produce images with whole body parts, digitized images from the films that contain portions of the body parts are assembled using image stitching [START_REF] Salbiah | A new approach to medical image stitching using minimum average correlation energy filter and peak to side-lobe ratio[END_REF]. The essential step of the most image stitching methods is to extract required pixels information by using the suitable mathematical models. This information is important to relate the corresponding pixels in one image and the other. Before we explain image stitching algorithms, we mention some basic models that are used to determine required information in image stitching methods.

Homography

Image alignment and stitching between two images obviously require determining the similar parts or pixels in the common area between those images. The general idea is that when the camera takes one photo and turns to take the second one, certain kinds of transformation happens that makes us in need to remap pixels coordinate from one image to the other. The parameters of these transformations can be regrouped in a matrix called homography H [START_REF] Bradski | Learning OpenCV[END_REF]. The complexity of this matrix relates to the different kinds of transformation. H is a 3x3 matrix and its general form is:

H = ( ). (1)
So all pixels X in one image can be remapped in the other X' by the general equation:

(

where ( ) , ( ).

In our case, a simple 2D transformation (Fig. 1) is enough to determine image stitching parameters [START_REF] Dubrofsky | Homography Estimation[END_REF][START_REF] Szeliski | [END_REF] between each pair of images.

The general form of a homography which is called the projective transform homography also known as a perspective transform is as follows:

( ) (3)
with A = R( )R(-φ)DR(φ). R( ) and R(φ) are the rotation matrices for angles et φ, and D is a diagonal matrix: The key difference between the affine and projective transformation is the vector v, which is null in the affine case. This vector is responsible for the non-linear effects of the projectivity.

( ) , ( ).
Depending on the values of homography parameters transformation could varied from simple translation to projective. After we had a glance over different transformation models that can face us in our research for stitching parameters, we review the different image stitching methods that use these models in order to estimate stitching parameters. The most well-known methods could be regrouped into two wide domains, pixel-based alignment (direct) and feature-based alignment [START_REF] Szeliski | [END_REF].

One approach is to shift or warp the images relative to each other and to look at how much the pixels agree. Approaches that use pixel-to-pixel matching are often called direct methods. To use a direct method, a suitable error metric must first be chosen to compare the images. Once this has been established, a suitable search technique must be devised. The simplest technique is to exhaustively try all possible alignments. In practice, this may be too slow, so hierarchical coarseto-fine techniques based on image pyramids have been developed. Comparing with feature-based registration methods, measuring the contribution of every pixel by direct methods shows better performance over specific images like blurred images where feature-based registration could fail especially. Knowing that this kind of images is rarely occurred in our work and that feature-based methods like SIFT show a robust performance for changing in scale and lighting, we focus more over the feature-based alignment.

Feature-based registration

While there are technical differences between different feature-based registrations, most of them share the same essential steps depending over the mathematical models explained previously. These common steps are explained in Fig. 2, where detecting points with characteristic features in images are the two first steps. Then these features are used to find the matching between successive pairs of images. Finally, depending on the matching, the transformation parameters are processed to register images and stitch them together.

Figure 2. Feature-based stitching steps.

SIFT Algorithm

Detecting key points was primarily designed for robotic applications in order to recognize objects within a captured image using a visual database as a reference. Lowe and Brown [START_REF] Winder | Learning local image descriptors[END_REF][START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF] also showed a practical application of image registration for automatic panorama recognition. The four major stages of computation used to generate the panorama in the SIFT algorithm [START_REF] Ozuysal | Fast keypoint recognition in ten lines of code[END_REF][START_REF] Martins | Spatio-Temporal Resolution Enhancement of Vocal Tract MRI Sequences Based on Image Registration[END_REF][START_REF] Brown | Automatic panoramic image stitching using invariant features[END_REF] are: Scale-space extrema "key-point" detection: the first stage of computation seeks these points over all scales and image locations. It is efficiently implemented by using a difference-of-Gaussian function to identify potential interest points that are invariant to scale and orientation:

D(x, y, σ) = (G(x, y, k σ) -G(x, y, σ))*I(x, y) = L(x, y, k σ)-L(x, y, σ) (4) where σ σ ⁄
. L(x, y, σ) is produced from the convolution of a variable-scale Gaussian G(x, y, ) with an input image I(x, y). The parameter refers to the smooth parameter of Gaussian function and k is the factor that multiplies the smooth between two nearby levels. D(x, y, σ) is the value of at the pixel (x, y) resulted from the subtraction between the two nearby blurred levels. Key-point localization: at each candidate location, a detailed model is fit to determine location and scale. Key-points are selected based on measures of their stability. Orientation assignment: one or more orientations are assigned to each key point location based on local image gradient directions. All future operations are performed on image data that has been transformed relative to the assigned orientation, scale, and location for each feature, thereby providing invariance to these transformations. The scale of the keypoint is used to select the Gaussian smoothed image L with the closest scale, so that all computations are performed in a scale-invariant manner. For each image sample L(x, y) at this scale, the gradient magnitude m(x, y) and orientation (x, y) are precomputed using pixel differences [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF]:

√ , (5)
.

Key-point descriptor: local image gradients are measured at the selected scale in the region around each key-point. These are transformed into a representation that allows for significant levels of local shape distortion and change in illumination [START_REF] Szeliski | [END_REF].

SURF Algorithm

The approach for interest point detection uses a very basic Hessian-matrix approximation, because of its reliable accuracy. More precisely, blob-like structures at locations where the determinant is optimum are detected. In contrast to the Hessian-Laplace detector by Mikolajczyk and Schmid [START_REF] Mikolajczyk | Indexing based on scale invariant interest points[END_REF], the SURF algorithm also relies on the Hessian determinant for scale selection, as performed by Lindeberg [START_REF] Lindeberg | Feature detection with automatic scale selection[END_REF]. The major steps of image feature detection of SURF and SIFT are similar, but SURF lends itself to the use of integral images as made popular by Viola and Jones [START_REF] Viola | Rapid object detection using a boosted cascade of simple features[END_REF], thus reducing the computational time drastically. Integral images fit in the more general framework of boxlets, as proposed by Simard et al [START_REF] Simard | Boxlets: A fast convolution algorithm for signal processing and neural networks[END_REF]. The major goal of using integral images in SURF is to decrease the time of computing key-points [START_REF] Bay | Speeded-Up Robust Features (SURF)[END_REF]. They allow for fast computation of box type convolution filters. An integral image, denoted i(x, y) at location (x, y) contains the sum of the pixel values above and to the left of (x, y). Formally, we have:

∑ . ( 7
)

ASIFT Algorithm

This algorithm depends essentially on SIFT and proposes a crucial parameter for evaluating the performance of affine recognition, the transition tilt [START_REF] Morel | ASIFT: a new framework for fully affine invariant image comparison[END_REF]. The transition tilt measures the degree of viewpoint change from one view to another, giving a first intuitive approach to absolute tilt and transition tilt. It illustrates why simulating large tilts on both compared images proves necessary to obtain a fully affine invariant recognition. Indeed, transition tilts can be much larger than absolute tilts. In fact they can behave like the square of absolute tilts.

CONTRIBUTION

System overview

Our acquisition system consists of different parts: a CCD camera + lenses, two sources of light with automatic switch on/off (one of white light and one at 406 nm for fluorescence excitation), and a high pass filter at 420 nm to reflect laser light and to let fluorescence emission passes to the camera. Reflected light from skin covers the same area and is captured by the camera. The probe we use has a special size limited to the size of blue light, so it cannot cover the whole area of a scar. Therefore, we acquire a sequence of pairs of images to cover the requested area of skin. Hence we calculate the registration parameters between each pair of successive images acquired under white light because it is much easier than processing with fluorescence data which have less salient points. Registration parameters describe the transformation (rotation, translation, scale …) and are used to achieve the whole panoramic fluorescence image. This registration is possible if a common area of skin always appears between each pair of successive images.

Transformations which have to be determined with our system are mainly based on rotation and scale variance. Because rapidity is important to integrate efficiently our work in a collaborative system, we chose to base our stitching process on feature-based registration. So, we apply several tests over several well-known methods in this domain to achieve best scenario of work depending on the results that we had. Giving a sight over the state-of-the-art of feature-based methods, we finally decided to apply our tests over SIFT, ASIFT, and SURF algorithms, which are the methods that look like to deal with the closest problems to ours.

Experiments and results

Two types of tests are required: the pretest "objective" that makes us able to predict the situation and the limits between the algorithms, and the "subjective" test at the end of the panoramic process where we check the accuracy of the stitching after transformation. To implement stitching algorithms and related tests, we used C language with the OpenCV libraries.

Depending on elder results in our last researches, we focused over ASIFT algorithms to test the performance of this algorithm over several pre-transformations in different conditions and different images acquired by the probe. These transformations varied from different rotation angles to different scale and projection values.

Fig. 3 discusses the error for estimating the rotation angle according to the real rotation angle and to the percentage of overlapping between the two images. It shows that the error of rotation angle in the estimated homography is less with small angles and still accepted to 35 degrees with good overlapping. If we consider that the number of robust matching points detected between two successive images is a proof of good performance to estimate the right homography, Fig. 5 shows that the performance of ASIFT with our probe images is still good (30-140 matching points) with overlapping between 20% and 40%, rotation between 5 to 30 degrees with projection in second image. These conditions could represent all deformations that we could face with real experiments. Figure5. ASIFT performance depending on matching points number with multiple transformation (OL: OverLapping, Rotation, and Projection)

The second part of our experiments was made over images of the probe without knowing in advance the transformations. The results are judged by observing it by human eyes to determine whether that was good or not (subjective test).

In Fig. 6, we can see that with good overlapping, results can be satisfactory, where transformation parameters estimated from white light images where used in fluorescence ones.

STITCHING SCENARIO IN A COLLABORATIVE WAY

Depending on the results of experiments explained in the previous paragraph, we propose the next stitching scenario which is figured in Fig. 7.

Depending on preliminary information and feedback of the session opened between practitioners:

If speed is important but not an essential condition, we start with SIFT. If the result is not good enough, we apply ASIFT. If speed is not important, we start with ASIFT. In such a way, we can guarantee the robustness for most of the examples in our case study. As well as SURF proved to be always the faster but the less robust we use it only if the speed is essential.

Figure 7. Best method decision.

In our case we suppose that the optical probe is manipulated by hospital staff in one place and practitioners located in other different cities. To make this system works well we need an efficient collaborative system that guarantees data sharing in robust and secure ways. The scenario will be as follows: Hospital staff takes the conventional and fluorescence images, and sends them to a web service by any possible connection (internet, mobile, satellite, etc...). The web service receives these images and manipulates them producing the requested panorama of both conventional and fluorescence modes. Then it distributes these two panoramas to all practitioners who are involved in the telediagnosis. In Fig. 8, we can see that the system sends the same panorama to each practitioner. Our first step in collaborative work could involve problems with the quality of service. That's why we propose a solution for adapting data distribution. We suppose that the practitioners could have different types of connections to the system (for example Internet, Wi-Fi or 3G) and as well different terminals with different capabilities. Because they cannot receive the same panorama, we switch to the adapted solution by adding the WAVA, a new "Web service for Automatic Video data flow Adaptation" module, which adapts the previous scenario like this: Practitioners (A, B, C) connect to WAVA to register themselves, transmitting their capabilities as an XML file called VAC (Virtual Adaptation Card) [START_REF] Aupet | Virtual awareness card for adaptability in collaborative virtual environments[END_REF][START_REF] Aupet | Wava: a new web service for automatic video data flow adaptation in heterogeneous collaborative environments[END_REF]. WAVA gives each of them a rank. The web service receives the images from the acquisition component. It applies the process to produce both the panoramic conventional and fluorescence images, making different copies with different qualities, saving them in a database. When practitioners connect to the web service searching for panoramic images, the web service sends a quality request to WAVA, which sends back the adapted data. At the end, the web service sends to each practitioner the adapted panorama, from which he is making his diagnosis (doted gray arrows in Fig. 8).

CONCLUSION AND FURTHER WORK

In this paper we have tested three different image stitching algorithms applied over our optical probe which provides at the same time two types of panoramic images of the same scar: one image acquired under white light (anatomic information) and another one resulting from tissue autoflorescence (functional image). These two images have been stitched by using parameters extracted from a feature-based algorithm processed on images acquired under white light. We have tested three stitching algorithms giving a suitable scenario to use them in a collaborative system. While ASIFT shows a good performance in affine transformation, SIFT and SURF are faster. Then we made some experiments applying ASIFT method on the images acquired by our probe. Results presented that ASIT could be satisfactory with several kinds of affine transformations. In future work we plan to profit of the rapidity of SURF algorithm and the accurateness of ASIFT to build a new algorithm, more robust and quicker. Also we will determine the weak points of our first version of our probe, like the positioning of white light LEDs and the type of CCD and exceed them in new versions.

  as two scaling values. The matrix A is thus a concatenation of a rotation by φ, a scaling by in the x direction, a scaling by in the y direction, a rotation back by -φ, then another rotation by and .

Figure 1 .

 1 Figure 1. Different transformations.

Figure 3 .

 3 Figure 3. Relation between rotation error estimation and real rotation angle, depending on the overlapping between two images.

Fig.

  Fig.4discuses about scale transformations. It shows that with scaling between 80% up to 120%, ASIFT has a good performance to estimate it with overlapping between 20% and 40%.

Figure 4 .

 4 Figure 4. Relation between scale and overlapping with no rotation nor projection.

Fig. 6 (

 6 a) represents grayscale images from where transformation parameters are really estimated, while in Fig. 6(b) fluorescence images are stitched with the same parameters to get the panorama.

Figure6

  Figure6. (a) white light panorama, (b) fluorescence panorama.

Figure 8 .

 8 Figure 8. Collaborative system for images co-interpretation.

  4 discuses about scale transformations. It shows that with scaling between 80% up to 120%, ASIFT has a good performance to estimate it with overlapping between 20% and 40%.

		16%
		14%
	error	12%
	scale	10%
	of	8%					20% Overlapping
	Percentage	4% 6%					30% Overlapping 40% Overlapping
		2%
		0%
		50%	70%	90%	110%	130%	150%
				Percentage of scale

* franck.marzani@u-bourgogne.fr; phone +33 380 39 63 33; fax +33 380 39 59 10; le2i.cnrs.fr

REFERENCE LINKING

[L1] http://www.skincancer.org.

[L2] http://www.medicinenet.com.


M Bouzid

A Khalfallah

A Bouchot

F S Marzani
email: franck.marzani@u-bourgogne.fr

Automatic cell nuclei detection: a protocol to acquire multispectral images and to compare results between color and multispectral images

Keywords: Automatic cell nuclei detection, multispectral imaging, color imaging, acquisition protocol, image calibration

High-throughput screening in histology and analysis need a necessary automatic cell or nucleus counting. Current methods and systems based on grayscale or color images give results with counting errors. We suggest to use multispectral imaging (with more than three bands) rather than color one for nucleus counting.

A traditional acquisition chains uses a source of white light and a CCD camera in addition to the optical microscope. To pass to a multispectral acquisition, we use a Programmable Light Source (PLS) in the place of the white light source. This PLS is capable of generating different wavelengths in the visible spectrum. So, one color image and four multispectral images have been acquired from histological slices. The four multispectral images contain respectively 3 bands, 5 bands, 7 bands and 10 bands.

To make a proper comparison of data, several considerations have been taken, like camera linearity, intensity difference between the wavebands from the PLS and non uniformity of the light intensity range in the images. So, a set of measures were done for calibrating the system.

An automatic detection method based on segmentation by expectation-maximization and ellipse fitting is used. An extension of this method is proposed in order to be applied to multispectral images. The original and the extended method are then applied to the data previously acquired to have first results regarding the effect of using multispectral images rather than color ones.

INTRODUCTION

Histology is the study of organism's tissues and also cells shape composing these tissues. To achieve this study, tissues must be included in resins such as paraffin or tissue Tek, cut in thin section of about 5µm, and colored (Hematoxyline Eosine stain, Masson's Trichrome stain, ...) or immuno-labeled. Histological analysis is performed by examining these sections of tissue under an optical microscope [START_REF] Saraydin | Antitumoral effects of Melissa officinalis on breast cancer in vitro and in vivo[END_REF]. The study of histology images is implied in the clinical diagnosis of cancers and identification of prognostic, and in the research field in cancer (but not only) model in animals and therapeutic pathways. For cancer diagnosis, histopathologists visually examine the regularities of cell shapes and tissue distributions, then decide whether tissue regions are cancerous, and determine the malignancy level. Such histopathological study has been extensively employed for cancer detection and grading applications [START_REF] Tough | Histological grading in breast cancer[END_REF]. But this manual analysis of histology tissues that is still the primary diagnosis method in the clinical field depends on the expertise and experience of histopathologists. Such manual intervention has the disadvantages of (a) being very time consuming and (b) showing intra-and inter-observation variations among experts. Computer-based image analysis has become an increasingly important field because of the high rate of production and the increasing reliance on these images by the biomedical community. Histology images have a large amount of objects of interest (cells, cell compartments such as nuclei…). The first goal of computer-based image analysis is to have a robust and accurate approach for identifying nuclei. Although, in literature [START_REF] Chen | An improved method for segmenting cell nuclei from microscopy images[END_REF][START_REF] Chan | Leukocyte nucleus segmentation and nucleus lobe counting[END_REF], a rich set of nuclei segmentation methods has been developed, almost none of them is fully sufficient to handle microscopy images where an enormous number of objects of interest may exist in various forms with large variations.

Many color segmentation algorithms can be found in literature. Color being directly and naturally attached to the regions of an image [START_REF] Park | Automatic cell segmentation in microscopic color images using ellipse fitting and watershed[END_REF][START_REF] Kothari | Automated cell counting and cluster segmentation using concavity detection and ellipse fitting techniques[END_REF], color segmentation methods might give better results than monochromatic segmentation methods.

Color segmentation raises problems related to the representation and the processing of color. One can mention the histogram analysis [START_REF] Zheng | A new method for automatic counting of marrow cells[END_REF], the pixel classification [START_REF] Arambula Cosio | Automatic counting of immunocytochemically stained cells[END_REF] and the region-growing methods [START_REF] Lezoray | Cooperation of color pixel classification schemes and color watershed: a study for microscopic image[END_REF]. This paper proposes an efficient method for nuclei segmentation that uses both ellipse fitting and Expectation-Maximization (EM) segmentation. It is first applied on color images.

Multispectral imaging is a new technique; it uses precise measurements of optical spectra at each pixel of an image. Compared to the color image, the multispectral image can provide more information for each pixel.

The multispectral dimension can be achieved by placing many filters between the sample and the monochromatic sensor. Each filter provides specific information about the sample in the spectral band considered. Such a device can sample the visible spectrum with a higher resolution than a color camera, and avoid the subjectivity of color imaging. The spectral dimension comes from a filter system positioned in the optical path of light. Therefore, a multispectral acquisition can be done by using filters between the light source and the sample or between the sample and the sensor. The technology we used to perform the filtering is based on the use of a Programmable Light Source (PLS).

The method developed and used for nuclei segmentation based on color images has been extended to be applied to multispectral images. Its results, both on color and multispectral data, are compared.

The remainder of this paper is structured as follows. In section 2, we present on one hand the protocol and the acquisition system used, and on the other hand the method chosen to detect the nuclei both on color and multispectral images. In section 3, the experimental results for real images are presented in detail. Finally, we give conclusions in section 4.

MATERIAL AND METHOD

Data acquisition

Cell imaging platform (CellImaP) of SFR 100, University of Burgundy, currently has a conventional acquisition of cell images (Cell Observer station from Zeiss). This system is essentially composed of an optical inverted microscope equipped with a white light source illuminating the sample (halogen source) and a CCD camera for the acquisition. We use a Programmable Light Source (PLS) that we place in the excitation part of the station. Unlike liquid crystal filters, the PLS is capable of generating rays of the visible spectrum with flexibility (amplitudes and widths of the bands).

To connect the PLS, we designed a mechanical part between the optical fiber end of the PLS and the optical inverted microscope. The dimensions of this piece were taken with good precision for securing the fiber center and then the light beam. Unfortunately, this system degrades image quality. The degradation is mainly due to the weakness of the light energy from the PLS and more, to the illumination of the sample in reflection and not in transmission. We decided to take a 3-bands multispectral image (MS3) to simulate the color image. Then we decided to acquire 5-bands multispectral images (MS5), 7-bands multispectral images (MS7) and 10-bands multispectral images (MS10) covering the visible spectrum.

To interpret the results and provide data acquisitions in conditions similar to the existing professional system, we had to characterize the system.

Linearity of the camera:

To analyze the linearity of the camera, we made acquisitions without any sample with integration times ranging from 300 ms to 10,100 ms (with 200 ms steps). To this end, 50 images were performed. For each image, an area of 100 by 100 pixels in the center was taken and averaged, plotted as a function of integration time. The linearity of the camera is clearly proved in Figure 2.

PLS calibration:

To ensure a good response with the Programmable Light Source, we conducted some series of tests on the PLS at rates of different times in a perfectly dark room in our lab (Le2i-France). The measurements were made using a perfect white patch and a spectrophotometer. Figure 3 shows the curves of repeatability of the PLS. These curves represent measurements taken at different moments simulating the real acquisitions. The x-axis represents the wavelength and the y-axis represents the amplitude of the signal. The measurements showed that the response of PLS is stable but not linear.

y = 6,745x + 396,19 0,0E+0 2,0E+3 4,0E+3 6,0E+3 8,0E+3 1,0E+4 1,2E+4 0,0E+0 1,0E+4 2,

Uniform Light Range (ULR)

After acquisition of images by our system, we noted that these images have an intensity distribution default of light and may affect future treatments. So to have a Uniform Light Range (ULR), images acquired are corrected by a correction matrix, one coefficient per pixel. The coefficients of this matrix are computed using acquired images by our system in absence of sample. This correction is a kind of normalization which allows images acquired in absence of sample to become uniform after correction. In figure 4, we can see that the dark part of the image (top left corner) has been lightened.

a. acquired image b. image after correction Figure 4. Impact of Uniform Light Range.

For PLS, measures taken by our system allowed us to prepare the set command, to verify the stability and the nature of the signal emitted during the image acquisition time. They also allowed us to determine the amplitude of signal emitted in each band which still enables us to calculate multiplicative coefficients. These coefficients can serve in case we want to compare the bands of a multispectral image.

For the camera, measures taken have allowed us firstly to check the linearity of the camera, and on the other hand to compute the coefficients of the correction matrix described previously.

Method

In the literature there are many methods for counting cell nuclei; among these methods we decided to follow the one proposed by Park et al. [START_REF] Park | Automatic cell segmentation in microscopic color images using ellipse fitting and watershed[END_REF]. The principle of this method relies on the use of 3-bands RGB color images. Image segmentation is one of the key processes in the field of cell nuclei counting. The choice of the segmentation method can affect the counting results. Our method is based on Expectation-Maximization (EM) segmentation and ellipse fitting for edge detection and contour selection.

In our study we are interested in multispectral images. To apply this nuclei detection algorithm on multispectral image, a pre-treatment phase is necessary to enhance the multispectral image quality.

Pre-treatment

The different results for the pre-treatment phase are illustrated in figure 5. In fact, the acquired image are too dark, too noisy (figure 5.a) and seems difficult to use for cell nuclei detection algorithm. The pre-treatment phase is released in 4 steps. The first one is the adaptive histogram equalization: it consists on modifying the image intensity in order to have a uniform histogram. It leads to an improvement in the quality of the processed image by increasing the contrast thus facilitating the distinction between the background and the objects contained in the image (Figure 5.b). The second step is the image intensity values adjustment. This operation consists in modifying the image histogram to let it covering the entire range of intensity. This is realized by a linear change of pixel intensities (Figure 5.c). The third step is a median filtering. It reduces noise without significantly affecting the signal provided by the stained cells (Figure 5.d) [START_REF] Forero | Image Processing Methods for Automatic Cell Counting In Vivo or In Situ Using 3D Confocal Microscopy[END_REF][START_REF] Forero | A DeadEasy Caspase: Automatic counting of apoptotic cells in Drosophila[END_REF].

Finally, the fourth step is the Wiener filtering. It attempts to minimize the impact of noise deconvolution at frequencies which have a poor signal-to-noise ratio (Figure 5.e). The wiener method is based on statistics estimated from a local neighborhood of each pixel [START_REF] Sarder | Deconvolution methods for 3-D fluorescence microscopy images[END_REF].

Automatic cell nuclei detection algorithm

The principle of our approach of automatic nuclei detection is shown in Figure 6. For each band, we apply the segmentation through the Expectation-Maximization (EM) algorithm. From this segmentation we isolate the class relative to the nuclei. We apply on this region a morphological gradient to extract contours. The extracted contours are classified using the ellipse fitting. The selected contours are returned in two categories: contours of single nuclei (RCS) and contours of multiple nuclei (RCM). This process is applied to all bands. Finally, we fuse single nuclei separately from multiple nuclei. This merging is based on the logical OR operator.

After that, we clean the result from isolated regions of small surface areas and combine regions of multiple nuclei with regions of single nuclei to correct the distribution of contours of both single nuclei and multiple nuclei.

-EM segmentation algorithm Usually, image intensity is considered as a mixture of Gaussians randomly generated. In our case, the application of EM segmentation algorithm in n classes is based on the histogram of the image. This algorithm is an iterative process which is widely used and based on the maximum likelihood. This is achieved by computing a likelihood factor V(x, i) specific to each Gaussian (i=1..n) and pixels x which allows, at each iteration, to recalculate the parameters of the Gaussians [START_REF] Forero | Image Processing Methods for Automatic Cell Counting In Vivo or In Situ Using 3D Confocal Microscopy[END_REF][START_REF] Sarder | Deconvolution methods for 3-D fluorescence microscopy images[END_REF][START_REF] Yonghong | EM algorithm with improvement for color image segmentation in multiple color spaces[END_REF].

The nuclei are seen as dark spots. Based on this difference in brightness, we use the EM algorithm to separate the nuclei from the tissue background. So, we opted for a classification into two classes through the EM algorithm. The obtained results did not allow a good identification of nuclei. To bypass this problem, we actually process a classification into three classes (n=3) where nuclei are located in class 1 with the darkest levels. This change allows efficient localization of nuclei. Finally, the detected edges are computed by morphological operators to extract the contours.

-Ellipse fitting This step allows computing the characteristic equation of the ellipse relative to a given distribution of points (contours). It allows extracting the parameters of the ellipse passing by the maximum number of points of the given distribution. Among these parameters, we are interested in the lengths of the major and minor axis of the ellipse and its eccentricity.

Applying the ellipse fitting to the contours given by the segmentation and basing on the parameters of the ellipse, we report if the contour may be a single nucleus contour (RCS), a multiple nuclei contour (RCM) or an invalid contour. A RCS contour means that our algorithm has detected one nuclei, a RCM contour means that our algorithm has detected more than one nuclei and 'invalid' contour signifies that the contour given by the segmentation will be eliminated. So, we fixed some thresholds on eccentricity, major and minor axis to sort the contours.

RESULTS AND DISCUSSION

As a first assessment of our hardware and our technique for nuclei detection, we chose three areas of a rat brain sample. Capture is made by our multispectral system. So, we got 3-bands, 5-bands, 7-bands and 10-bands multispectral images (MS3, MS5, MS7 and MS10) for each area. To judge our approach, we compared our results with a manual selection done by a biologist.

In figure 7b and7c, an area with a single nucleus is marked by a green color and an area with multiple nuclei by a blue color. By comparing these figures, we can deduce that a detection technique analysis can rely on 3 major criteria: detecting defects, labeling defects and valid detection. Detection defects can be divided in two classes:

• False detection: a portion of tissue (background) is considered as nuclei by our algorithm.

• Double detection: a nucleus is marked by more than one contour.

Labeling defects affect mainly the qualification of the detected nuclei. Indeed, the area may have portions for single nucleus and other portions for multiple nuclei. Labeling defects can be divided in two classes too: • A single contour (green color) including more than one nucleus.

• A multiple contour (blue color) containing a single nucleus.

On the other hand, the algorithm successfully detects nuclei. This detection can be described in two ways:

• General detection is the percentage of nuclei (really existing in the tissue) detected by our automatic detection algorithm (without taking into account the single or multiple nature), compared to the ground truth (manual selection).

• A perfect detection is the percentage of nuclei detected by our algorithm and respecting their nature (single or multiple nuclei), compared to the ground truth. To evaluate the performance of our acquisition system and detection algorithm and to highlight the effect of the multispectral extension, we use the three criteria previously defined. As mentioned, this study is established on 3 areas of a histological slice of rat brain, each of them containing around fifty single nuclei and some multiple nuclei.

The obtained results are shown in the tables below. Tables 1 and2 illustrate respectively for MS3 and MS10 images, the wrong detection average (background defects and double detection defects), the wrong labeling average and the valid detection average (perfect detection and general detection) obtained using our automatic nuclei detection algorithm. The average is calculated for the three studied areas (area 1, area 2 and area 3). The results are similar for the other MS5 and MS7 images; for simplicity reasons we chose not to show all tables. By analyzing these results, it is clear that some bands have good general and perfect detection; however others show many defects due to background wrong detection (Table 1, band 2). To have a better exploitation of these multispectral images, we decided to fuse the automatic nuclei selection of all bands in same image (MS3 or MS5 or MS7 or MS10). But this merging may increase the wrong detection rate due to background defects. To decrease this effect, we defined a selection criterion of multispectral image bands before starting the fusion process. We take as a reference the MS3 multispectral image which is close to the traditional RGB system. According to the performance of our automatic nuclei selection on MS3 image (Table 1), we set a wrong background detection threshold that selection in bands should not exceed. The band 2 of the MS3 image presents the worst wrong background detection (13.8%) so we set the wrong background detection threshold as 15%.

Wrong detection Wrong labeling Detection

The lowest general detection is 75.4% given by our selection algorithm in the third band of MS3 image. So, we fixed the general detection threshold as 75%. We consider only the bands where general detection exceeds the fixed threshold to the fusion process.

Following these selection criteria, all bands are taken into account for the MS3 images during fusion process. While, for MS5 images only the bands 2, 3 and 4 bands are selected. For MS7 images only the bands 2, 3, 4 and 5 are selected and finally, for MS10 images, the bands 4, 5, 6 and 7 are used (Table 3). We deduce that relevant information is located in the middle frequencies while low and high frequencies are rejected for their background defects rate or for their low general detection.

Wrong detection Wrong Labeling Detection

Background Double Perfect General MS3 (1,2,3) According to Table 3, we notice that the merging step decreases double detection rate and increases the general detection percentage. In addition, we notice that the extension in multispectral MS5, MS7 and MS10 reduces wrong detections and the wrong labeling percentage.

From these results, we infer also that the multispectral image does not ensure a best detection. However, this detection is still more than 80% for the general detection and more than 40% for the perfect detection. In other hand, the multispectral image reduces the background wrong detection percentage compared to the MS3.

When the minimum threshold for general detection is decreased to 70%, the number of bands increases in MS5, MS7 and MS10 images. So, bands 1, 2, 3 and 4 are selected in the fusion process of MS5 image. The merging process for MS7 and MS10 images includes respectively bands 2, 3, 4, 5 and 6 and bands 2, 3, 4, 5, 6, 7 and 8 (Table 4).

Wrong detection Wrong labeling Detection

Background Double Perfect General MS3 (1,2,3) Comparing the results illustrated in Tables 3 and4, we deduce that when we increase the number of bands selected in the fusion process, general detection increases with the background wrong detection. However, the background wrong detection percentage for MS5, MS7 and MS10 image is lower than that obtained for the MS3 image. We note also that the increase of the number of bands improves the perfect detection for MS7 and MS10 images.

We conclude that increasing the number of fused bands boosts the number of detected nuclei but also increases the percentage of background wrong detection.

CONCLUSION

There are two main goals in this work, the first one is to calibrate the acquisition system and the second one is to detect automatically cell nuclei inside histological slices of rat brain.

First, we calibrated all the components of the acquisition system. The programmable light source has been calibrated by doing many measurements and tests (repeatability, stability, linearity). Next, we checked the camera linearity by measuring its response. Finally we acquired 3-bands, 5-bands, 7-bands and 10-bands multispectral images. Because these acquired multispectral images are quite noisy, we proposed some pre-treatments to enhance the image quality. When this step has been finished, we applied the detection algorithm. It is mainly based on expectation-maximization segmentation and ellipse fitting. The results showed that the detection quality of nuclei augments by increasing the number of bands. Also for the same multispectral image, the general detection percentage increases with background wrong detection percentage.

For the future works, we think working towards two main ways to improve the results. First, in terms of software, we must improve the automatic detection method (segmentation method and ellipse fitting) by better adjusting some parameters of changing some parts of the methodology. Secondly, because current multispectral images contain some noise, we have to change the acquisition mode by using transmission process for the light instead of acquiring images by reflection.

Figure 1 .

 1 Figure 1. Acquisition chain.

Figure 2

 2 Figure2shows the linearity curve amplitude grayscale function of time integration.

Figure 2 .

 2 Figure 2. Response curve of the camera.

Figure 3 .

 3 Figure 3. Response curve of the PLS.

  a. image after ULR correction b. image after histogram equalization c. image after intensity adjustment d. image after median filtering e. image after Wiener filtering Figure 5. Image pre-treatment.

Figure 6 .

 6 Figure 6. Detection algorithm.

  a. band 2 of MS3 image b. manual selection of nuclei c. automatic detection of nuclei Figure 7. Comparison between manual selection and automatic detection in a MS3 image.

Table 1 .

 1 Results for MS3 image.

				Double		Perfect	General
	MS3	band 1 band 2	6,5% 13,8%	5,7% 5,9%	27,3% 34,6%	52,0% 43,0%	78,4% 79,6%
		band 3	10,2%	5,5%	29,4%	46,0%	75,4%

Table 2 .

 2 Results for MS10 image.

Table 3 .

 3 Results for band fusion with maximum threshold for wrong detection of 15% and minimum threshold for general detection of 75%.

Table 4 .

 4 Results for bands fusion with maximum threshold for wrong detection of 15% and minimum threshold for general detection of 70%.

		12,8%	0,0%	39,1%	49,8%	88,9%
	MS5 (1,2,3,4)	8,2%	1,0%	36,5%	47,8%	84,3%
	MS7 (2,3,4,5,6)	7,8%	0,6%	30,9%	53,4%	84,3%
	MS10 (2,3,4,5,6,7,8)	10,6%	0,0%	35,8%	48,6%	84,4%