K C Santosh
email: santosh.kc@inria.fr

Cholwich Nattee
email: cholwich@siit.tu.ac.th

Bart Lamiroy
email: bart.lamiroy@loria.fr

RELATIVE POSITIONING OF STROKE BASED CLUSTERING: A NEW APPROACH TO ON-LINE HANDWRITTEN DEVANAGARI CHARACTER RECOGNITION

Keywords: Stroke Number and Order Free, Spatial Relations, DTW, Clustering, On-line Devanagari Character Recognition

In this paper, we propose a new scheme for Devanagari natural handwritten character recognition. It is primarily based on spatial similarity based stroke clustering. A feature of a stroke consists of a string of pen-tip positions and directions at every pen-tip position along the trajectory. It uses the dynamic time warping (DTW) algorithm to align handwritten strokes with stored stroke templates and determine their similarity. Experiments are carried out with the help of 25 native writers and a recognition rate of approximately 95% is achieved.

Our recogniser is robust to a large range of writing style and handles variation in the number of strokes, their order, shapes and sizes and similarities among classes.

Introduction 1.Motivation

Pencil and paper can be preferable for anyone during a first draft preparation instead of using keyboard and other computer input interfaces, especially when writing in languages and scripts for which keyboards are cumbersome. Devanagari keyboards for instance, are quite difficult to use.

Devanagari is derived from two roots: 'deva' and 'nagari'. 'deva' means 'deity' and 'nagari' means 'city'. Together, it implies both religion and urbane. Devanagari is a script used to write several Indian languages, including Nepali, Sanskrit, Hindi, Marathi, Pali, Kashmiri, Sindhi, and sometimes Punjabi. Devanagari characters follow a complex structure and may count up to more than 500 symbols.

In our experiments, we take the most common type of discrete characters that are frequently used. Our dataset is composed of 36 classes of consonants and vowels. Fig. 1 shows a few examples of it where a few samples are provided from each class of a few Devanagari handwritten characters. In this paper, we develop a technique to employ strokes spatial relations to build a writer independent on-line Devanagari handwritten character recognition system. The recogniser yields satisfactory results.

Vocabulary Issue

In order to clearly establish the semantics of our reasonment, we first introduce the following vocabulary distinction: the term "character" refers to a token having a lexicographic meaning, independently of its graphic representation. We shall represent it by its printed form, as in the upper-left corners in each box of Fig. 1. "Symbols" are graphical representations of "characters", most often handwritten. A symbol is an visual instance of a specific character, and visually quite different symbols might represent the same character, as shown in Fig. 1. In this illustration, each box contains three symbols representing the same character. When addressing recognition in Section 3, each character will represent a "class".

Structure of Devanagari Characters

Devanagari is written from left to right with a horizontal line on the top which is the shirorekha. Every character requires one shirorekha from which text(s) is(are) suspended. The way of writing Devanagari has its own particularities.

• Many of the characters are similar to each other in structure. Visually very similar symbols -even from the same writer -may represent different characters. While it might seem quite obvious in the following examples to distinguish the first from the second, it can easily be seen that confusion is likely to occur for their handwritten symbol counterparts (к, ), ( , ), ( , Ú), etc. or Fig. 1) • The number of strokes, their order, shapes and sizes, directions, skew angle etc. are writing units that are important for symbol recognition and classification. However, these writing units most often vary from one user to another and there is even no guarantee that a same user always writes in a same way. Proposed methods should take this into account. As a consequence, significant shape variations may occur between symbols representing the same character. Fig. 2 illustrates this. Since we are operating in an on-line framework, pen strokes are the sequences of sampled points between 'pendown' to 'pen-up' events. In this illustration, every initial pen-tip position in each stroke is encircled to show the number of strokes used to complete a symbol. Stroke extraction and the complete handwritten character representation will be explained in Section 2.1.

Related Work

In the state-of-the-art of handwritten character recognition, several different studies have shown that off-line handwriting recognition offers less classification rate compared to on-line [START_REF] Plamondon | Online and off-line handwriting recognition: a comprehensive survey[END_REF][START_REF] Tappert | The state of the art in online handwriting recognition[END_REF] . Furthermore, on-line data offers significant reduction in memory and therefore space complexity. Another advantage is that the digital pen or a digital form on a tablet device immediately transforms your handwriting into a digital representation that can be reused later without having any risk of degradation usually associated with ancient handwriting. Based on all these reasons, one can cite a few examples [START_REF] Boccignone | Recovering dynamic information from static handwriting[END_REF][START_REF] Doermann | Recovery of temporal information from static images of handwriting[END_REF][START_REF] Qiao | A framework toward restoration of writing order from single-stroked handwriting image[END_REF][START_REF] Viard-Gaudin | Recognition-directed recovering of temporal information from handwriting images[END_REF] where they mainly focus on temporal information as well as writing order recovery from static handwriting image. On-line handwriting recognition systems provide interesting results. More specifically, template based approaches have a long standing record [START_REF] Bahlmann | The writer independent online handwriting recognition system frog on hand and cluster generative statistical dynamic time warping[END_REF][START_REF] Connell | Template-based online character recognition[END_REF][START_REF] Hu | Hmm based on-line handwriting recognition[END_REF][START_REF] Santosh | Stroke number and order free handwriting recognition for nepali[END_REF][START_REF] Schenkel | On-line cursive script recognition using time delay neural networks and hidden markov models[END_REF] [START_REF] Joshi | Machine recognition of online handwritten devanagari characters[END_REF] focussed on structural properties and separated shirorekha based on directional code such as east or west. Their work is writer dependent and is limited to natural handwriting where curve sequences can be shirorekha. In the literature, there has been an extensive use of specific unique features but varying according to the nature of the script. Two concrete examples are the use of shirorekha in 20 to make Devanagari difference with other scripts, and hat feature 17 in Urdu handwriting for recognition confidence. Our claim is that integrating relative positioning of strokes by referencing such a unique feature leads to better recognition.

Handling spatial relations between strokes, in on-line handwriting is not a completely new approach [START_REF] Bouteruche | Handwritten gesture recognition driven by the spatial context of strokes[END_REF][START_REF] Luo | A unit decomposition technique using fuzzy logic for real-time handwritten chinese character recognition[END_REF][START_REF] Marukatat | Handling spatial information in on-line handwriting recognition[END_REF][START_REF] Sinha | Machine recognition of devanagari script[END_REF] . But, these existing approaches are not very generic. Swethalakshmi et al., 2007 30 use spatio-structural feature based on zoning information (as explained in [START_REF] ∅ivind Due Trier | Feature extraction methods for character recognition -a survey[END_REF] ) to recognise Devanagari and Tamil scripts, and provides 95% and 92% recognition rates respectively. The approach however, is very sensitive to handwriting strokes with asymmetric structure and symbols having very long ascender and/or descender, for instance. Our approach is different and uses pairwise spatial relations between the strokes by fixing shirorekha as a reference within a symbol as in [START_REF] Namboodiri | Online handwritten script recognition[END_REF] .

Outline of the Proposed Method

This paper is an extension of previous works [START_REF] Santosh | Stroke number and order free handwriting recognition for nepali[END_REF][START_REF] Santosh | Spatial similarity based stroke number and order free clustering[END_REF] . Especially because of the structure of Devanagari, it is necessary to pay attention to the appropriate structuring of the strokes to ease and speed up comparison between the symbols, rather than just relying on global recognition techniques that would be based on a collection of strokes [START_REF] Santosh | Stroke number and order free handwriting recognition for nepali[END_REF] . Therefore, we develop a method for analysing handwritten characters based on both the number of strokes and the their spatial information [START_REF] Santosh | Spatial similarity based stroke number and order free clustering[END_REF] . This work is essentially identical to previous work 27 but extends it by providing an in-depth description of the method and a more developed experimental validation framework. It consists in four main phases. step 1. Organise the symbols representing the same character into different groups based on the number of strokes. For a specific class of character, it is interesting to notice that writing symbols with the equal number of strokes, generally produce visually similar structure and is easier to compare. Stroke representation within the complete symbol will be explained in Section 2.1. step 2. Find the spatial relation between strokes.

The importance of the location of the strokes is best observed by taking a few pairs of characters that often lead to confusion: ( , ), ( , ), ( , ) etc. The first character in every pair has visually two distinguishing features: its particular location of the shirorekha (more to the right) and a small curve in the text. There is no doubt that one of the two features is sufficient to automatically distinguish both characters. However, small curves are usually not robust feature in natural handwriting, finding the location of the shirorekha only can avoid possible confusion. Our stroke based spatial relation technique is explained further in Section 2.3.2. step 3. Agglomerate similar strokes from a specific location in a group.

In every group within a particular class of character, a representative symbol is synthetically generated from pairwise similar strokes merging, which are positioned identically with respect to the shirorekha. It uses DTW algorithm. The learnt strokes are then stored accordingly. In Section 2.4, we explain in detail about stroke clustering and management of the learnt strokes. step 4. Stroke-wise matching for recognition.

We align individual test strokes of an unknown symbols with the learnt strokes having both same number of strokes and spatial properties. Overall, symbols can be compared by the fusion of matching information from all test strokes. We derive the complete recognition process in Section 3.

Structure of the Paper

Until now, we have mentioned our motivations in Section 1.1, defined vocabulary in Section 1.2, explained Devanagari graphical structure in Section 1.3, reviewed literature in Section 1.4 and briefly outlined the proposed method in Section 1.5. The remaining of the paper is organised as follows. Based on the outline presented in Section 1.5, our learning module is developed in Section 2: it includes handwritten character representation, feature selection and dissimilarity measure definition as well as template management. Section 3 covers our recognition module while Section 4 gives an overview of the obtained results and provides an error analysis.

The paper is concluded with a brief generalisation of the method in Section 5 along with a few steps to go further.

Learning

Handwritten Character Representation

The digitiser captures a series of strokes during pen movement as soon as it starts to move over the tablet. A string of coordinates (pen-tip positions) from pen-down to pen-up events represents a stroke. Along the pen trajectory, the initial pen-tip position represents the first coordinate of the particular stroke. Similarly, the last point is taken as soon as pen-up event takes place. Depending on the user and/or writing style, a same symbol can be written with a varying number of strokes.

Since the digitiser capture a string of coordinates on a temporal basis, there is no segmentation problem. A symbol S is composed of a set of m strokes, in which each stroke s j consists of a string of coordinates p j k , S = [s 1 , s 2 , . . . , s m ] (1)

s j = [p j 1 , p j 2 , . . . , p j l ] (2)
where p j k = (x j k , y j k ) for j ∈ [1 : m] and k ∈ [1 : l]. Strokes directly collected from users are often incomplete and noisy. Different systems use a variety of different pre-processing techniques before feature extraction [START_REF] Blumenstein | A novel feature extraction technique for the recognition of segmented handwritten characters[END_REF][START_REF] Verma | A feature extraction technique for on-line handwriting recognition[END_REF] . The techniques used in one system may not exactly fit into the other because of different writing styles and nature of the scripts. We utilise repeated coordinates deletion, noise elimination and normalisation.

Co-occurrence Coordinates Deletion

As in 1 , we delete co-occurrence of coordinates p k = p k+1 when they occur for consecutive coordinates of a particular stroke, along the pen trajectory.

Noise Elimination

Sequences with no information about the symbol need to be eliminated in order to enhance recognition accuracy and speed. Elimination of noisy sequences in cursive writing is a difficult task and there exist no robust noise elimination algorithms that can be applied in all situations. Besides, they vary from one script to another. In our case, the following filters have been applied. Deletion of short sequences. We identify unnecessarily written sequences for deletion. We delete short sequences (≤ 5 coordinates) as they do not give any information about the character. It is based on empirical knowledge. If we change it to 10 coordinates, for instance, there may be a chance to delete stroke with important information. Considering the employed dataset, such sequences are often written at the end as re-writing strokes. An example is shown in Fig. 3.

Chopping of undesirable hook or cusp. We chop undesirable hooks or cusps at both the ascender and descender of sequences. This is done by the use of tangent angles along the trajectory path of 5 -10 2D coordinates related to the ascender and descender. The sequence is chopped from the point where the trajectory path turns sharply (angle changes drastically i.e., 80 • -100 • ) as shown in Fig. 3.

Size Normalisation

Many authors demonstrate the use and importance of normalisation [START_REF] Chun | The role of size normalization on the recognition rate of handwritten numerals[END_REF][START_REF] Guerfali | Normalizing and restoring on-line handwriting[END_REF] . Because of variable size of writing strokes, it is necessary to transform a complete symbol into a standard window. In our case, we map the symbol S into a [0, 1] × [0, 1] unit square as shown in Fig. 3 before computing the strokes' spatial relations.

Feature Selection and Dissimilarity Measure

Feature Selection

Appropriate feature selection can greatly decrease the workload and simplify the subsequent design process of the classifier. Features should contain sufficient information to distinguish between classes, be insensitive to irrelevant variability of the input, allow efficient computation of discriminant functions and be able to limit the amount of training data required [START_REF] Lippmann | Pattern classification using neural networks[END_REF] . However, they vary from one script to another [START_REF] Blumenstein | A novel feature extraction technique for the recognition of segmented handwritten characters[END_REF][START_REF] Namboodiri | Online handwritten script recognition[END_REF][START_REF] Okumura | An hmm implementation for on-line handwriting recognition -based on pen-coordinate feature and pen-direction feature[END_REF][START_REF] Verma | A feature extraction technique for on-line handwriting recognition[END_REF] .

In this work, a feature vector sequence of every j th stroke is expressed as in [START_REF] Okumura | An hmm implementation for on-line handwriting recognition -based on pen-coordinate feature and pen-direction feature[END_REF][START_REF] Santosh | Stroke number and order free handwriting recognition for nepali[END_REF] :

F j = p j 1 , α p j 2 ,p j 3 , p j 2 , α p j 2 ,p j 3 , . . . , p j l , α p j l-1 ,p j l (3)
where, α p j l-1 ,p j l = arctan

y j l -y j l-1 x j l -x j l-1
. Our feature includes a sequence of both pentip position and tangent angles sampled from the trajectory of the pen-tip, preserving the directional property of the trajectory path. It is important to remind that stroke direction (either left -right or right -left) leads to very different features although they are geometrically similar. To efficiently handle it, we need both kinds of strokes or samples for training and testing. This does not mean that same writer must be used.

Dissimilarity Measure -Matching Score using DTW

Distance computation between the symbols expresses how similar or dissimilar they are. Given representation explained in Section 2.2.1, how can distance between two feature sequences be measured? Since our features are non-linear sequences of potentially different lengths, the use of a simple distance metric is not appropriate. Following the idea presented in [START_REF] Kruskall | The symmetric time warping algorithm: From continuous to discrete[END_REF] , we employ DTW.

D(a, b) = min [D(a -1, b -1), D(a -1, b), D(a, b -1)] + δ(a, b) (5)
with an initial condition D(1, 1) = δ(1, 1) such that it allows warping path going diagonally from starting node (1, 1) to end (A, B). The main aim is to find the path for which the least cost is associated. The warping path therefore provides the difference cost between the compared signatures. Formally, the warping path is,

W = {w q } q=1...Q where max(a, b) ≤ Q < a+b-1 and q th element of W is w(a, b) q ∈ [1 : A]×[1 : B] for q ∈ [1 : Q].
The optimised warping path W satisfies the following three conditions:

c1. boundary condition:

w 1 = (1, 1) and w Q = (A, B), c2. monotonicity condition: a 1 ≤ a 2 ≤ • • • ≤ a A and b 1 ≤ b 2 ≤ • • • ≤ b B and c3. continuity condition: w q+1 -w q ∈ {(1, 1)(0, 1), (1, 0)} for q ∈ [1 : Q -1].
c1 conveys that the path starts from (1, 1) to (A, B), aligning all elements to each other. c2 forces the path advances one step at a time. c3 restricts allowable steps in the warping path to adjacent cells, never be back. Note that c3 implies c2.

We then define the global distance between F A and F B as

∆ (F A , F B ) = D(A, B) Q . ( 6
)
This means that the last element of the A × B matrix gives the DTW-distance between two vector sequences. It can be normalised by the Q, the number of discrete warping steps along the diagonal DTW-matrix. This is called the DTW-matching score in our recognition processes, and measures similarity between shapes. It also allows ranking between stroke sequences with respect to a reference sequence.

The warping path can be computed with the help of back-tracking along the minimum cost index pairs (a, b) starting from (A, B). As shown in Fig. 4, the backtracking procedure following the optimal warping path is handled with the help of Dynamic Programming (DP).

w q-1 =    (1, b -1) if a = 1 (a -1, 1) if b = 1 argmin{D(a -1, b -1), D(a -1, b), D(a, b -1)} otherwise, (7)
where we take the lexicographically smallest pair in case 'argmin' is not unique.

Fig. 4 shows a DTW-matrix between two continuous time series signatures having different lengths. In this illustration, note that the warping path makes easier to take the average similarity of two non-linear feature sequences. The process of averaging is explained in Section 2.4.1.

Recognition

From a purely combinatorial point of view, measuring the similarity or dissimilarity between two symbols S 1 = s i 1 i=1...n and S 2 = s j 2 j=1...m composed, respectively, of n and m strokes, requires a one by one matching score computation of all strokes s i 1 with all s j 2 . This may not always be sufficient, and these approaches generally need a final, global coherence check to avoid matching of strokes that shows visual similarity but do not respect overall geometric coherence within the complete handwritten character. In order to reduce both combinatorial complexity and enhance global coherence, we introduce a stroke representation, based on the shirorekha and relative positioning of the strokes with respect to the former. To handle this however, we need to identify the shirorekha.

Shirorekha and its identification

As said in Section 1.3, Devanagari is written from left to right with a horizontal line on the top which is the shirorekha. Every character requires one shirorekha from which text(s) is(are) suspended. Sometimes there may be two (Fig. 5 -) but this usually depends on users' writing style. In natural handwriting, the shirorekha may not always be strictly horizontal and exactly on the top. It may be a small curve and may intersect text. Since locations of both shirorekha and text vary, it is difficult to build a general rule to compute spatial relations. In general, the location of the shirorekha is assumed to be on the top and the text(s) is(are) determined with respect to the shirorekha. In Fig. 5, it is clearly seen that every symbol has at least two kinds of strokes: straight and curve. Naturally, straight strokes are more likely to represent the shirorekha. To identify whether a stroke is a straight one, we check the straightness property S t for every j th stroke,

St = δ p j 1 , p j l l-1 1 δ p j k , p j k+1 = 0.8 ≤ St ≤ 1 :straight otherwise :curve (8)
where δ(p j k , p j k+1 ) = (x j kx j k+1 ) 2 + (y j ky j k+1 ) 2 . It is important to notice that St = 1 for completely straight sequences. This is however, not possible in case of natural handwriting. Now, let us check whether the provided St range in equation (8) can classify straight sequences by taking real-world samples. To handle this, we have measured St over handwritten shirorekha. We found that 98% of shirorekha from all training symbols are lying within the range. While, remaining 2% of the shirorekha are still curved sequences. The distribution of St values is shown in Fig. 6. If we increase its range (i.e., reduces the lower limit), remaining 2% can be included with an increased risk of detecting real curve sequences. But, note that these remaining strokes are still located on the top with respect to other strokes. Thus, there is still a chance to correctly identify them as the shirorekhas with the help of their location.

Finding straight strokes does not necessarily mean that shirorekhas are detected. For the two-stroke symbols, it is easy to separate the straight and curve sequence. But, ambiguity occurs when the symbol is composed of more than two strokes, since there may exists many straight sequences. In such a case, we need to determine the shirorekha from these straight stroke candidates. Therefore, we check the following conditions one after another: • spatial relation between the straight sequences, • width of the sequence i.e., w = x maxx min , and • global stroke direction from initial to the end coordinate i.e., θ p1,p l = arctan y l -y1

x l -x1 × 180 • π .

We select the stroke as the shirorekha which is located on the top with respect to others. We may find a few cases having two strokes on the top due to re-writing shirorekha, for instance. In the latter case, we take the one which has largest width. It is quite rare to get first two conditions identical. If it happens, then we check minimum global stroke direction.

Once the shirorekha is identified, we use it as reference stroke to compute spatial relations between remaining strokes within the symbol. This is explained in the following section.

Relative Positioning of Strokes

To handle relative positioning of strokes, we use six spatial predicates i.e., 2 × 3 relational regions:

R = top-left (T-L) top (T) top-right (T-R) bottom-left (B-L) bottom (B) bottom-right (B-L) .
To confirm the location of the stroke, we use the projection theory: minimum boundary rectangle (MBR) [START_REF] Papadias | Relation Based Representations for Spatial Knowledge[END_REF] model combined with the stroke's centroid. Based on 10 , we start with checking fundamental topological relations such as disconnected (DC), externally connected (EC) and overlap/intersect (O/I). Considering two strokes s j = p j k k=1...l and s

j ′ = p j ′ k ′ k ′ =1...l ′
as follows,

s j ∩ s j ′ = 1 if (p j k ∩ p j ′ k ′ = ∅) ⇒ EC, O/I 0 otherwise ⇒ DC.
We then use the border condition from the geometry of the MBR. It is straightforward for disconnected strokes while, is not for externally connected and overlap/intersect configurations. In the latter case, we check the level of the centroid with respect to the boundary of the MBR. For example, if a boundary of the shirorekha is above the centroid level of the text stroke, then it is confirmed that the shirorekha is on the top. This procedure is applied to all of the six previously mentioned spatial predicates. Note that use of angle-based model like bi-centre [START_REF] Miyajima | Spatial organization in 2D segmented images: representation and recognition of primitive spatial relations[END_REF] and angle histogram [START_REF] Wang | Human-based spatial relationship generalization through neural/fuzzy approaches[END_REF] are not the appropriate choice due to the cursive nature of writing. On the whole, assuming that the shirorekha is on the top, the locations of the text strokes are estimated. This eventually allows to cross-validate the location of the shirorekha along with its size, once texts' locations are determined. Fig. 7 shows a real example demonstrating relative positioning between the strokes for a twostroke symbol к. Besides, symbols with two shirorekhas are also possible to treat. In such a situation, the first shirorekha according to the order of strokes is taken as reference.

Templates

In this section, we explain how we represent handwritten characters using stroke templates. These known representative templates are used for unknown stroke alignment to do recognition. To obtain them, stroke clustering is used.

Stroke Clustering

Basically, clustering is a technique for collecting items which are similar in some way. Items of one group are dissimilar with other items belonging to other groups. Consequently, it makes the recognition system compact. To handle this, we present spatial similarity based stroke clustering. As mentioned in Section 1.5, our clustering scheme is a two-step process. The first step is to organise symbols representing a same character into different groups, based on the number of strokes used to complete the symbol. Fig. 8 shows an example of it for a class of character a. In the second step, strokes from the specific location are agglomerated hierarchically within the particular group. Once relative position for every stroke is determined as shown in Fig. 8, single-linkage agglomerative hierarchical clustering is used. This means that only strokes which are at a specific location are taken for clustering. This applies to all groups within a class. In agglomerative hierarchical clustering, we merge two similar strokes and find a new cluster. The distance computation between two strokes follows Section 2.2. The new cluster is computed by averaging both strokes via the use of the discrete warping path along the diagonal DTW-matrix. This process is repeated until it reaches the cluster threshold. The threshold value yields the number of cluster representatives i.e., learnt templates. Consider T G is the total number of number of templates (learnt strokes) in one group from a class of character. It consists of a templates in all relative positions described in Section 2.3.2 i.e.,

T G = T top-left + T top + T top-right T shirorekha + T bottom-left + T bottom + T bottom-right Ttext .
Our clustering threshold is based on the number of strokes in the particular relative positions. For instance, if there exists 'shirorekhas' in three different positions such as top-left, top and top-right, clustering happens individually. For 'shirorekha', we develop a single template for each location. In case of text strokes, we still keep importance of relative position while threshold is determined based on the number of strokes. Now, we have

T bottom-left = (T G -T shirorekha ) × N bottom-left N total , T bottom = (T G -T shirorekha ) × N bottom N total and
T bottom-right = (T G -T shirorekha ) × N bottom-right N total ,
where N R represents the number of strokes in the particular relative position and N total = N bottom-left + N bottom + N bottom-right . Since number of templates are always in fixed number, we round-up (and round-down) by giving importance to stroke relative positioning. Following Fig. 9, overall concept can be provided when T G = 5. Overall, let us emphasise the spatial similarity in stroke clustering. Since clustering is applied for those strokes which have identical relative positions, a single shirorekha which is on the top never merges with others. This brings an impression that the location of the shirorekha is important otherwise ambiguities may be introduced for very similar pairs of characters such as ( , ), ( , ), ( , ) etc. as mentioned in Section 1.5.

Template Management

Following Section 2.4.1, stroke templates are taken by averaging similar strokes. In every class of character, there are variable groups of clusters according to the number of strokes used to complete symbol. Each of them is representative of other strokes in every particular location. For instance, the stroke representatives from two-stroke symbols, three-stroke symbols and four-stroke symbols are respectively labelled as first, second, and third group. Fig. 10 shows a sample of our template management technique by taking a few groups for a vowel a. This procedure is applied for all classes.

Weight Determination

Our approach allows for the determination of the probability that strokes are at specific location in a specific group. The probability of occurrence of a template (stroke representative) in every specific location can be obtained by using the proportion of strokes in the training set. Consider the first group having two-strokes a only in Fig. 10 to realise the weights for all possible locations a .

• for shirorekha: → bottom-left = 5 6 = 83.4% → bottom = 1 6 = 16.7% and → bottom-right = 0 6 = 0%. We shall use this probability information as a weight in Section 3 for template matching in order to find the test strokes for recognition. It gives a trend of the global writing style in the training set by showing, for example, how often the shirorekha is exactly on the top position.

→ top-left = 0 6 = 0% → top = 1 6 = 16.

Classification

In the previous sections we have described how to represent handwritten characters based on templates, and how to compare individual strokes. Combining those together, we can now proceed to developing our recognition method. The aim is to verify a given unknown handwritten test symbol with respect to the corresponding character class label.

Let S be an unknown test symbol composed of n strokes; S = s i i=1...n . Let T be the set of template strokes coming from the cluster representing the symbols a For clarity, the presented weights correspond to the stroke example shown in Fig. 10, is a representative but small illustration. In our real dataset, the sample set is large.

with same number of strokes as S. We use simple template matching on a stroke-bystroke basis via DTW. Each stroke s i from symbol S is matched with the templates independently. The stroke is said to be similar with the template for which the lowest distance is produced. The following algorithm gives a complete idea of how test strokes are matched with the templates. a. Find the number of strokes n in the test symbol S. Separate the shirorekha from the text parts and determine each stroke's spatial relation with respect to it. b. For each known character c, the strokes s i are matched with the corresponding ones (i.e., those positioned similarly with respect to their shirorekha) from the templates in T c . Thus the set of corresponding templates is T c | s i = τ t c,i . Every matching produces a matching score that is represented as,

M =      D 1 D 2 . . . D n     
where D i = {∆ t i }, ∆ t i is the matching score between s i and the appropriate templates τ t c,i of T c | s i . These matching scores ∆ t i are obtained via DTW as explained in equation (6). c. Each matching score is divided by the weight of the corresponding template τ t c,i as described in Section 2.4.3. Finally, the weighted matching score is,

∆ t c,i = ∆ t c,i /weight(c, i). (9)
Once we have obtained these weighted matching scores, we can compute an overall matching score for each character c by computing n i=1 min t ∆ t c,i . The classification candidate is the character having obtained the lowest value. The template matching is straightforward when spatial information is not considered.

The stability of the overall matching score can be significantly improved by taking into account the potential risk of having mismatched individual strokes. Indeed, the value of min t ∆ t c,i can be weighted by the number of other strokes having a very similar matching score. In that case, e. Count the number of matching scores close to the minimum, upto a threshold ǫ c,i = min t ∆ t c,i + ε i , for every stroke s i and every character c. This number determines how many similar strokes are available as templates:

W c,i = t l=1 C ∆ l c,i , ǫ c,i , (10)
where

C(z 1 , z 2 ) = 1 if z 1 <

Experimental Results

We compare our approach to two different methods: one does not use spatial information of the strokes 1 and another uses a spatio-structural feature based on zoning information [START_REF] Swethalakshmi | Spatiostructural features for recognition of online handwritten characters in devanagari and tamil scripts[END_REF] . It is important to notice that the method mentioned in [START_REF] Santosh | Stroke number and order free handwriting recognition for nepali[END_REF] is an extension of the method presented in 1 . Table 1 shows the experimental results for both training and test datasets and recognition speed. In order to check the training quality, it makes sense to confront training symbols to the recognition system. In case of the training set, recognition rates for all methods do not provide notable difference. For the test set, our method provides error rate of approximately 5% which is less than by more than 7% from the method where spatial information is not used 1 and by 11% from the method that uses spatio-structural information of the strokes [START_REF] Swethalakshmi | Spatiostructural features for recognition of online handwritten characters in devanagari and tamil scripts[END_REF] .

Besides the recognition rate, performance also depends on recognition speed. In average, recognition speed of our method is less than 4 seconds per character, compared to approximately 32 seconds from 1 and 17 seconds from [START_REF] Swethalakshmi | Spatiostructural features for recognition of online handwritten characters in devanagari and tamil scripts[END_REF] . The huge difference between our method and 1 is due to the fact that the latter does not include spatial information and the categorisation of the symbols while learning. Besides, we have controllable stroke matching, thanks to our template management, due to which, stroke matching is made only with those which have identical relative position from the same group (cf. Section 3).

Overall, our method provides significant improvement in recognition performance (both recognition rate and speed) over provided benchmarking methods.

Experimental Error Analysis

This section investigates the recognition performance based on the observed errors. We first study the origin of errors and then analyse them one by one. Table 2 shows the origin of the errors that are occurred in our experiments. As said in Section 1.3, these are mainly due to 1. structure similarity, 2. reduced and/or very long ascender and/or descender stroke, and 3. others such as re-writing strokes and mis-writing.

In our experiment (see Table 1 and2), we observe that spatio-structural feature based on zoning information 30 simply does not provide complete shape information of the strokes when their sizes vary widely -which is obvious in natural handwriting. This means that the approach is very sensitive to handwriting strokes with asymmetric structure and symbols having very long ascender and/or descender, for instance. In such a situation, DTW (used in 1 ) can absorb the varying strokes' features. Additional use of spatial relations information in our method, provides better recognition performance. In what follows, we discuss origin, cause and effect of different error types, one by one. As discussed in Section 1.3, Devanagari has a structural tendency to produce confusions between the characters. However, most of the similar character pairs such as ( , ), ( , ), and ( , ) are correctly recognised, thanks to stroke spatial information. Fig. 11 gives an example between and . In this illustration, cusp elimination described in Section 2.1, has been integrated with spatial relation information. However, some of the characters do not have such distinguishing features. Symbols representing them cannot be correctly classified, as is shown in Fig. 12 (a) for , and . Sometimes, we have observed that user introduces one-way confusions between classes of characters as shown in Fig. 12 (b). One-way confusion refers to confusion of symbol S 1 to symbol S 2 i.e., S 1 → S 2 but not vice versa. In a similar manner, there are two-way confusions (S 1 ↔ S 2 ) as shown in Fig. 12 (c). Due to lack of skill in writing with a digitiser, some strokes are too long and sometimes too short. Having very long or small stroke sequences causes problems in classifying the symbol as shown in Fig. 13. However, most of these cases are correctly recognised in our method as well as in CSDTW 1 , while more mis-recognitions are found to be in [START_REF] Swethalakshmi | Spatiostructural features for recognition of online handwritten characters in devanagari and tamil scripts[END_REF] .

Fig. 13. Confusion between characters (even for human eyes) due to reduced descenders.

Others

Symbols with re-writing strokes as well as mis-writing symbols come under this.

Re-writing strokes. Users often add corrections to their writings by adding strokes to complete the previous ones. In an off-line context, such re-written strokes are helpful in giving a complete graphical interpretation, but they are close to nothing in case of on-line context. We have not implemented an explicit method to eliminate or treat these extra re-written strokes, since they are extremely delicate to identify or distinguish from regular strokes. Usually, however, re-writing strokes are small, and are eliminated during pre-processing. Fig. 14 shows two samples of characters having re-writing strokes, which are mis-recognised.

Mis-writing and Miscellaneous. A collection of strokes giving no supplementary information about the characters is grouped under mis-writing. These symbols are often rejected. These are usually occurred in cursive handwriting. The worst drawings are found in the miscellaneous category.

In both cases, in contrast, our method does not suffer much. Overall, compared to all methods mentioned in Table 1, our method provides interesting results. Following Table 2, Table 3 presents class-wise experimental results from our method in order to provide closer analyse.

Conclusion and Extensions

In this paper, we have established an approach, and validated its efficacy for online natural handwritten Devanagari character recognition. It uses the number of strokes used to complete a symbol and their spatial relations. Considering such a dataset, our approach outperforms state-of-the-art character recognition systems, by providing notable difference in recognition performance. Overall, the success rate is approximately 95% in less than 4 seconds per character on average. The proposed approach is able to handle handwritten symbols of any stroke and order. Moreover, the stroke-matching technique is interesting and completely controllable. It is primarily due to our symbol categorisation and the use of stroke spatial information in template management. However, the relational model based on MBR cannot handle huge skew-angle orientation since it is simply based on the orthogonal projection. In this situation, more elaborative spatial relation model can be used [START_REF] Santosh | Symbol recognition using spatial relations[END_REF] . In our dataset, we do not have strokes of more than 30 • . On the other hand, size variation of the strokes does not affect. However, it is sensitive to tremor handwriting, symbols with re-writing strokes and mis-writing. To extend the work, we are going to increase the size of the dataset so that we can adequately apply cross-validation evaluation protocol. This can avoid possible confusions between the characters having structure similarity (more specifically oneway confusions) happened in dichotomous classification of dataset. On the other hand, in our current method, we do not yet integrate the recognition of Devanagari at syllable level (see Fig. 15). Syllable composition accounts for the major part of the 500 symbols used in Devanagari. Therefore, we are inspired to extend our approach up to that level.

Fig. 1 .

 1 Fig. 1. A few sample images from each class of a few Devanagari natural handwritten characters.

Fig. 2 .

 2 Fig. 2. A few possible variations in writing units for a consonant к.

Fig. 3 .

 3 Fig. 3. Stroke pre-processing: noise and cusp elimination, and normalisation.

  DTW Algorithm. Let us consider two feature sequences F A = {f a } a=1,...,A and F B = {f b } b=1,...,B of size A and B respectively. The aim of the algorithm is to provide the optimal alignment between both sequences. At first, a matrix M of size A × B is constructed. Then for each element in matrix M, local distance metric δ(a, b) between the events e a and e b is computed. δ(a, b) can be expressed as, δ(a, b) = (e ae b ) 2 , (4) where e a = f a and e b = f b for a ∈ [1 : A] and b ∈ [1 : B]. Let D(a, b) be the global distance up to (a, b),

Fig. 4 .

 4 Fig. 4. DTW distance between two non-linear sequences -an example.

Fig. 5 .

 5 Fig. 5. Straight sequence(s) plus curve sequence(s) in a symbol.

Fig. 6 .

 6 Fig. 6. Straightness calculation for all shirorekhas in training dataset.

  (a) Two-stroke к. (b) MBR + Centroid model. (c) Model realisation.

Fig. 7 .

 7 Fig. 7. Pairwise spatial relation for a two-stroke к taken from Fig. 3.

  (a) Two-stroke a.(b) Three-stroke a.

Fig. 8 .

 8 Fig. 8. Relative positions of strokes for a class a in two different groups i.e., two-stroke and three-stroke symbols.

Fig. 9

 9 illustrates a simple example of stroke clustering.

  (a) text strokes. (b) shirorekha.

Fig. 9 .

 9 Fig. 9. Stroke clustering for two-strokes vowel a based on relative positions. These strokes are taken from Fig. 8 (a) where six users are employed.

Fig. 10 .

 10 Fig. 10. Cluster management for a class a, following Fig. 8 and 9.

  7% and → top-right = 5 6 = 83.4%. • for text:

4. 3 . 1 .

 31 Structure similarity

Fig. 11 .

 11 Fig. 11. Effect of stroke pre-processing and spatial information in recognition. The location of the shirorekha after cusp elimination can distinguish and even though texts are similar.

  (a) Three characters: , and with similar handwritten representations. (b) One-way confusion: ( → ).(c) Two-way confusion: ( ↔ ).

Fig. 12 .

 12 Fig. 12. Two examples of confusion pairs -( → ) and ( ↔ ).

4. 3 . 2 .

 32 Reduced and/or elongated ascenders and/or descenders

Fig. 14 .

 14 Fig. 14. Two examples of re-writing strokes from class and к -every third stroke is used to complete the first stroke.

Fig. 15 .

 15 Fig. 15. A few samples of Devanagari syllables.

  . Our approach is inspired by the cluster generative statistical dynamic time warping (CS-DTW) technique 1 but varies distinctly where the clustering technique itself is concerned. As mentioned in Section 1.3, Connell et al., 2000 7 also highlighted the difficulties associated with the cursive nature of Devanagari writing. Due to its structural complexity, Niranjan et al., 2005

  In this work, we have used a Graphite tablet (WCACOM Co. Ltd.), model ET0405A-U, which captures the pen-tip position in the form of 2D coordinates at the sampling rate of 20 Hz. The data set is composed of 1800 symbols representing 36 characters, coming from 25 native speakers. Each writer was given the opportunity to write each character twice. No other directions, constraints, or instructions were given to the users. Our dataset can be downloaded from the IAPR tc-11 website http://www.iapr-tc11.org.In our test, 15 writers are used for training and the remaining 10 are for testing. For our experiment, we have used MATLAB 7.0.4 on a 1.81 GHz, 1.00 GB RAM, PC running Microsoft Windows XP professional.

	f. Finally, the test symbol is classified by the character's label,
	L = argmin c	n i=1	min t ∆ t c,i W c,i	for c = 1, . . . , κ.	(11)
	4. Experiments
	4.1. Dataset
				z 2
			0 otherwise.

Table 1 .

 1 Error rates for both training and test data and running time (per character) from different methods.

			# of	# of	Avg.	Time
	Method	Dataset Misrecog. Reject Error % sec.
	M1. Swethalakshmi Training et al., 2007 30 Test	16 91	13 26	03.0 16.0	16
	M2. CSDTW 1	Training Test	19 71	07 19	02.0 12.5	32
	M3. Our Method	Training Test	10 33	03 08	01.0 05.0	04

Table 2 .

 2 Error types (test data).

		# of Chars.
	Error type	M1 M2 M3	Index
	1. Structure similarity	52 43 19	M1. Swethalakshmi
	2. Reduced and/or very long ascender and/or descender stroke	18 13 09	et al., 2007 30 M2. CSDTW 1
	3. Others	47 42 28	M3. Our Method

Table 3 .

 3 Class-wise experimental results (test data) for both consonant and vowel.

		# of	# of	# of		# of	# of	# of
	Class Recog. Confusion Rejection	Class Recog. Confusion Rejection
	к	17	2 ( )	2	х	20	0	0
		18	2 ( )	0		20	0	0
	Ê	19	1 ( )	0		20	0	0
	я	20	0	0		13	5( )	2
		20	0	0		20	0	0
	Ú	20	0	0		20	0	0
		18	1( ), 2( )	0		18	1( ), 1(Ê)	0
	Ú	16	2( ), 1( )	1		19	1 ( )	0
		18	1( ), 1( )	0		20	0	0
		19	2(к)	0	º	19	0	1
		19	2( )	0		19	2( )	0
		18	1( ), 1( )	0		20	0	0
		19	1( )	0		19	1( )	0
		18	1( ), 1( )	0	ш	20	0	0
		20	0	0		20	0	0
		20	0	0	a	18	1( )	1
	e	18	1( )	1	u	19	0	1
	i	18	2(Ú)	0		20	0	0

K.C.Santosh et al.

K.C.Santosh et al.

Acknowledgement

Authors would like to thank to the anonymous reviewers for their clear guidance, comments and suggestions to improve manuscript.


MD Fernando Lopez-Rios
email: flopezrios@hospitaldemadrid.com

Elena Garcia-Garcia

Carlos Gomez-Martin

Barbara Angulo

Esther Conde

Ana Suarez-Gauthier

Magdalena Adrados

Cristian Perna

Jose Luis Rodriguez-Peralto

Manuel Hidalgo

Elena García-García

Carlos Gómez-Martín

Bárbara Angulo

Ana Suárez-Gauthier

José Luis Rodríguez-Peralto

Fernando López-Ríos

Hybridization for HER2 testing in gastric carcinoma: a comparison of fluorescence in situ hybridization with a novel fully automated dual-color silver in situ hybridization

Keywords: HER2, FISH, SISH, gastric carcinoma, dual-color hybridization HER2, FISH, SISH, gastric carcinoma, dual-color hybridization

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

Abstract

Aims: Amplification of the human epidermal growth factor receptor 2 (HER2) gene has been reported in gastric carcinoma (GC). Accordingly, trastuzumab plus chemotherapy has recently become the new standard treatment for HER2 positive advanced GCs.

Methods and results:

We sought to compare the alleged gold standard for hybridization (FISH) with a novel fully automated bright-field dual-color silver enhanced in situ hybridization (SISH) in a series of 166 GC samples.

Additionally, tumors with discordant results obtained by FISH and SISH were analyzed by real-time quantitative PCR with the LightMix kit HER2/neu. 17.5% and 21% of the samples were amplified by FISH and SISH, respectively.

Heterogeneity was identified in up to 52% of the cases. In 96.4% of cases FISH showed the same results as SISH. All six discordant cases were positive by SISH and negative by FISH. On review of the FISH slides, all contradictory cases were polysomic and were confirmed as negative for amplification by realtime PCR. Interestingly, all ratios in this latter group were between 2.06 and 2.50 so setting the cut-off for amplification at ≥ 3 resulted in a perfect concordance.

Conclusions: Dual color SISH represents a novel method for the determination of HER2 status in GC.

Deleted: 6

Deleted: to be

Introduction

In 1987, Slamon et al. described the relationship between the amplification of the HER2 gene and a group of of breast carcinomas [START_REF] Slamon | Human breast cancer: correlation of relapse and survival with amplification of the HER-2/neu oncogene[END_REF] for the first time. The development, in later years, of a specific treatment for this alteration, the antibody trastuzumab, has been one of the greatest successes of solid tumor oncology. Naturally, there have been attempts to reproduce this success in other neoplasias which can also show amplification of HER2 (carcinomas of the stomach, bladder, lung etc.). [START_REF] Bang | Trastuzumab in combination with chemotherapy versus chemotherapy alone for treatment of HER2-positive advanced gastric or gastro-oesophageal junction cancer (ToGA): a phase 3, open-label, randomised controlled trial[END_REF][START_REF] Laé | Assessing HER2 gene amplification as a potential target for therapy in invasive urothelial bladder cancer with a standardized methodology: results in 1005 patients[END_REF][START_REF] Ross | Randomized phase II multicenter trial of two schedules of lapatinib as first-or second-line monotherapy in patients with advanced or metastatic non-small cell lung cancer[END_REF] Finally, in the year 2009, results were presented of the ToGA trial in patients with advanced gastric carcinoma. [START_REF] Bang | Trastuzumab in combination with chemotherapy versus chemotherapy alone for treatment of HER2-positive advanced gastric or gastro-oesophageal junction cancer (ToGA): a phase 3, open-label, randomised controlled trial[END_REF] The ToGA trial was a prospective randomized multicenter phase III trial conducted in 24 However, since trastuzumab was first approved for breast cancer, there have been notable inconsistencies in procedures for studying HER2.. This "cancer biomarker problem" significantly affected the specific method: immunohistochemistry (IHC), FISH or the various types of brightfield in situ hybridization (ISH). Similarly it affected the concordance between techniques; the cut-off point and the work-flow algorithm although IHC has traditionally been considered the primary testing modality. [START_REF] Tubbs | Discrepancies in clinical laboratory testing of eligibility for trastuzumab therapy: apparent immunohistochemical false-positives do not get the message[END_REF][START_REF] Mass | Evaluation of clinical outcomes according to HER2 detection by fluorescence in situ hybridization in women with metastatic breast cancer treated with trastuzumab[END_REF][START_REF] Arena | Fluorescent in situ hybridization for human epidermal growth factor receptor 2 assessment in breast cancer: is it applicable as a primary test?[END_REF] The fact that the first ASCO/CAP consensus was not published until 2007 [START_REF] Wolff | American Society of Clinical Oncology/College of American Pathologists guideline recommendations for human epidermal growth factor receptor 2 testing in breast cancer[END_REF] and the lack of consensus among different national guidelines (reviewed in 9) undoubtedly contributed to the problem.

Further fuelling the controversy was the subtle recommendation of initial FISH in specific settings (core-needle biopsies) [START_REF] Chivukula | Clinical importance of HER2 immunohistologic heterogeneous expression in core-needle biopsies vs resection specimens for equivocal (immunohistochemical score 2+) cases[END_REF] and the direct suggestion of "FISH as the primary HER2 testing modality for women with breast cancer who are candidates for HER2 targeted therapies". [START_REF] Sauter | Guidelines for human epidermal growth factor receptor 2 testing: biologic and methodologic considerations[END_REF] This latter paradigm shift has remained largely unnoticed despite publication in a high impact journal and the fact that Slamon was among its authors more than 20 years after his initial discovery. The situation that we have outlined above has recently been termed "the HER2 testing conundrum" and the result is that as many as one in five HER2 tests give the wrong answer. [START_REF] Phillips | Clinical practice patterns and cost effectiveness of human epidermal growth receptor 2 testing strategies in breast cancer patients[END_REF][START_REF] Allison | The HER2 testing conundrum[END_REF] However, it must be pointed out that the clinical benefit of trastuzumab in the ToGA trial seems to be restricted to patients IHC 2+ and FISH positive or IHC 3+, when compared with patients IHC 0 or 1+ and FISH negative. [START_REF] Bang | Trastuzumab in combination with chemotherapy versus chemotherapy alone for treatment of HER2-positive advanced gastric or gastro-oesophageal junction cancer (ToGA): a phase 3, open-label, randomised controlled trial[END_REF] With the above controversies in mind, we sought to compare the alleged gold standard (FISH) with a novel fully automated brightfield dual-color approach in a series of gastric carcinoma samples. [START_REF] Nitta | Development of automated brightfield double In Situ hybridization (BDISH) application for HER2 gene and chromosome 17 centromere (CEN 17) for breast carcinomas and an assay performance comparison to manual dual color HER2 fluorescence In Situ hybridization (FISH)[END_REF] Our aim was to provide robust analytical and post-analytical information in the setting of gastric

Material and methods

Tumor samples

A randomly selected total of 166 gastric adenocarcinomas from several Spanish institutions were collected for HER2 status analyses. The study was approved by a centralized ethics committee. Before paraffin embedding, tissues were fixed in buffered formalin. We have no data regarding how concentrated the fixative was or the time of fixation. Fifty (30.1%) were endoscopic biopsies and 116 (69.9%) surgical specimens of which 15 (9%) were distant metastases. All cases were diagnosed according to the Lauren´s classification [START_REF]The two histological main types of gastric carcinoma: diffuse and so-called intestinal-type carcinoma. An attempt at a histo-clinical classification[END_REF] : 86 (51.8%) intestinal type, 47 (28.3%) diffuse type and 33 (19.9%) indeterminate type.

Analytical Phase

Sections of tumoral tissue samples 4µm-thick were cut and placed on charged polylysine-coated slides for analysis.

FISH

HER2 copy number was investigated by FISH, using the PathVysion HER2 DNA probe kit (Vysis Inc, Abbot Laboratories, IL), with the DAKO Histology FISH Accessory kit. The manufacturer´s instructions were modified using DAKO Histology kit in order to optimize the technique (decreased laboratory processes). [START_REF] Tubbs | Fluorescence in situ hybridization (FISH) as primary methodology for the assessment of HER2 Status in adenocarcinoma of the breast: a single institution experience[END_REF] Sections were incubated at 56ºC overnight, desparaffinized in two series of xylol followed by rehydratation with an ethanol series. Slides were Enzymatic digestion was carried out with Ready-to-Use Pepsin for three minutes at room temperature (endoscopic biopsies) or six minutes at 37ºC (surgical specimens). After dehydratation with graded ethanol series, 10µl of HER2/CEP17 probe mix was applied to each tissue section. The slides and probe were denaturalized at 80ºC for five minutes and hybridized at 37ºC overnight in a Dako Hybridizer. On the second day, the sections were washed with Stringent Wash Buffer at 65ºC for ten minutes in a water bath. Next, the slides were dehydrated using graded ethanol series and 10µl of fluorescence mounting media containing 4´-6-diamino-2-phenylindole (DAPI) was applied.

Dual-color SISH

Automated SISH was performed on Ventana Benchmark XT (Ventana Medical Systems, Tucson, AZ). INFORM HER2 DNA Probe and INFORM Chromosome 17 Probe was visualized on the same slide following manufacturer´s protocols with a few variations. Assay conditions were modified for optimal results. The entire assay procedure (deparaffinization, pretreatment, hybridization, stringency wash, signal detection and counterstaining) was fully automated. [START_REF] Nitta | Development of automated brightfield double In Situ hybridization (BDISH) application for HER2 gene and chromosome 17 centromere (CEN 17) for breast carcinomas and an assay performance comparison to manual dual color HER2 fluorescence In Situ hybridization (FISH)[END_REF] Pretreatment was performed with Reaction Buffer and enzyme digestion with ISH Protease 3 for 12 minutes. HER2 probe was denatured at 95ºC for 15 minutes and hybridized at 56ºC for six hours. Chromosome 17 centromere probe was denatured at 95ºC for 12 minutes and hybridized at 44ºC for three hours. Stringency washes for HER2 probe were performed at 72ºC for eight minutes (three steps) and incubated with anti-DNP (dinitrophenol) antibody for 20 minutes. Next, tissue slides were incubated with HRP-conjugated anti-rabbit and Bluing Reagent for four minutes. The slides were covered with Cytoseal mounting media. Some of the slides had to be stained once or twice. We were not able to identify the cause of these failures, which other authors have also experienced. [START_REF] Bartlett | Chromogenic in situ hybridization: a multicenter study comparing silver in situ hybridization with FISH[END_REF]

Real-time PCR

Although FISH is still considered the gold standard for HER2 amplification in the clinical setting, we sought to study our discordant cases (see below) by a third technique. [START_REF] Layfield | Monoplex LightCycler polymerase chain reaction quantitation of the HER2 gene for quality assurance of HER2/neu testing by immunohistochemistry and fluorescence in situ hybridization[END_REF]

Post-analytical Phase (Interpretation)

The slides were analysed by two observers. All the preparation was previously evaluated (10x and 40x objectives in the case of SISH and 100x objective in the case of FISH) to identify areas for scoring and to avoid the bias of tumor heterogeneity. For FISH, a total 20 nuclei were scored from two different areas using an epifluorescence microscope (Olympus BX61) equipped with a DAPI, a Spectrum Orange, Spectrum Green and double-filter set, using a 100x oil immersion objective lens. The scoring of SISH was similarly conducted with the use of a bright-field microscope (Olympus BX41) with a 40x objective. Positivity for HER2 gene amplification was considered when ISH ratio was ≥ 2; negativity when ISH ratio was < 2. Chromosome 17 polysomy was defined as ≥ 3 CEP17 signals on average per cell. [START_REF] Hofmann | Assessment of a HER2 scoring system for gastric cancer: results from a validation study[END_REF] Amplification patterns in clusters versus double minutes were considered according to published criteria. [START_REF] Kanta | Topoisomerase II alpha gene amplification in gastric carcinomas: correlation with the HER2 gene. An immunohistochemical, immunoblotting, and multicolor fluorescence in situ hybridization study[END_REF] For data analysis in the real-time assay, we used the LightCycler 480 Relative Quantification software (version 1.5) provided by Roche Diagnostics. We used the Second Derivative Maximum method to calculate the value of the crossing point for target and reference genes of each sample. The HER2 copy number was calculated automatically as the ratio between HER2 and the reference gene. The ratio HER2/Reference for each sample was normalized to one of the non-amplified tumors (determined either by FISH or SISH) included as positive controls in the PCR experiment. According to the manufacturer, a ratio between HER2 and the reference gene of < 2 is regarded as negative for HER2 gene amplification while a ratio of ≥ 2 indicates amplification of the HER2 gene.

Statistical analysis

The agreement between FISH and SISH was estimated by the percentage of agreement and by kappa statistics. One sample Z test was performed in order

Results

FISH

FISH was successfully performed on all samples. The quality of the hybridization was good (Figure 1). 17.5% were amplified, 55% had double minutes amplification and 45% cluster amplification. Heterogeneity (focal amplification) was observed in 52% of the amplified cases. Interobserver agreement was perfect. For one observer, the median of the ratios was 5.25 and the range 13.26. For the other observer, the median of the ratios was 5 and the range 17.9. HER2 amplification was significantly associated with the intestinal histological subtype when compared with the other categories of the Lauren classification (86% versus 14%, p<0.0001).

Dual-color SISH

SISH was successfully performed on all samples. The quality of the hybridization was good (Figure 2). 21% were amplified, 34% had double minutes amplification, 46% cluster amplification and 20% mixed amplification pattern. Heterogeneity (focal amplification) was observed in 29% of the amplified cases. Interobserver agreement was perfect. For one observer, the median of the ratios was 5.75 and the range 14.64. For the other observer, the median of the ratios was 5.65 and the range 9.01. In 96.4% of cases FISH showed the same results as SISH. All 6 discordant cases were positive by SISH and negative by FISH (sensitivity=1, specificity=0.956, concordance=0.964, kappa=0.884; Table 1). Upon review of the FISH slides, all contradictory cases were polysomic and were confirmed to be negative for amplification by real-time PCR (see below). Interestingly, all ratios in this latter group (including those of the two observers) were between 2.06 and 2.50 so setting the cut-off for amplification at ≥ 3 would result in a perfect concordance (sensitivity=1, specificity=1, concordance=1, kappa=1; Table 2). All the ratios (including those of the two observers) of the SISH concordant cases were greater than 3 (median=8.1 and 6.02, range=13.66 and 8.02).

Real-time PCR

Six tumors with discordant results obtained by FISH and SISH were analyzed by real-time quantitative PCR with the LightMix kit HER2/neu (Roche Diagnostics) in order to classify them as amplified or non-amplified for the HER2 gene (Table 3). Samples amplified by FISH and SISH, considered as a positive control for HER2 gene amplification, were all found to be amplified using the real-time quantitative approach. Similarly, samples assessed as negative for HER2 gene amplification by both FISH and SISH gave a normalized ratio of HER2/RPL23 ~1 (range from to 0.836 to 1.0) which is below the cut-off limit of two and confirms the absence of amplification. All samples with discordant results show no amplification of the HER2 gene by real-time quantitative PCR. After normalization of the ratio target/reference gene for each

Discussion

In the present study we have compared for the first time a novel fully automated dual color SISH with FISH for the assessment of HER2 amplification in a large series of gastric carcinoma samples. There follows discussion of the different phases of the procedures. Firstly, ISH is not affected by the unavoidable variability of the preanalytical phase in pathology laboratories worldwide as long as buffered formalin is used as fixative. In our experience as a referral laboratory for FISH HER2 testing, only 3% were considered non-informative due to pre-analytical aspects (F. López-Ríos, unpublished data). Expanded decalcification protocols even permit ISH in bone marrow biopsies (E. García-García, unpublished data).

Although the role of the new rapid fixatives remains to be determined, it must be emphasized that alcohol-based fixation is not appropriate for ISH procedures. In the present series, in spite of studying samples of different sizes (endoscopic versus surgical specimens, etc...) and sources (community hospitals versus large university hospitals, etc...), both methods showed very low failure rates (data not shown). These results are consistent with previous reports on failure rates for EGFR SISH versus FISH. [START_REF] Gaiser | Comparison of automated silver enhanced in situ hybridization and fluorescence in situ hybridization for evaluation of epidermal growth factor receptor status in human glioblastomas[END_REF] Secondly, manual ISH (that is, FISH) remains the gold standard in this setting and will continue to be until proven otherwise. Nevertheless, new automated ISH alternatives may improve the reproducibility of the analytical phase if the technical platforms, reagents and protocols are fully standardized. In the past, there were two main limitations to the widespread use of ISH techniques: 1) FISH has traditionally been perfomed in central or referral laboratories, with lack of community acceptance or experience, and 2) brightfield ISH has not, until recently, been a dual color procedure. [START_REF] Nitta | Development of automated brightfield double In Situ hybridization (BDISH) application for HER2 gene and chromosome 17 centromere (CEN 17) for breast carcinomas and an assay performance comparison to manual dual color HER2 fluorescence In Situ hybridization (FISH)[END_REF][START_REF] Mayr | Chromogenic in situ hybridization for Her-2/neu-oncogene in breast cancer: comparison of a new dualcolour chromogenic in situ hybridization with immunohistochemistry and fluorescence in situ hybridization[END_REF][START_REF] Hoff | Visualization of FISH Probes by dual-color chromogenic in situ hybridization[END_REF] The new, fully automated, dual color SISH overcomes both limitations but appropriate training is essential to perform the post-analytical phase (interpretation) of the procedure adequately. This is somewhat easier and quicker for brightfield ISH than for FISH. [START_REF] García-Caballero | Determination of HER2 amplification in primary breast cancer using dual-color chrmogenic in situ hybridization is comparable to fluorescence in situ hybridization: a European multicentre study involving 168 specimens[END_REF][START_REF] Papouchado | Silver In Situ Hybridization (SISH) For Determination of HER2 Gene Status in Breast Carcinoma: Comparison With FISH and Assessment of Interobserver Reproducibility[END_REF] It is beyond the scope of this study to establish the predictive value of the different ISH modalities in gastric carcinoma patients who are candidates for HER2 targeted therapies but the use of automated ISH techniques may enable rapid screening of thousands of patients in order to find out the real predictive cut-off for clinical benefit (ie, polysomy, degree of HER2 amplification).

Discrepancy between the FISH and SISH occurred in six out of 166 cases, all of them positive for SISH (all ratios between 2.06 and 2.50) and negative for FISH. All discrepant cases were polysomic by FISH and negative for HER2 amplification by real-time PCR. These results are consistent with previous studies reporting on both EGFR and HER2 brightfield ISH, both using single color [START_REF] Bartlett | Chromogenic in situ hybridization: a multicenter study comparing silver in situ hybridization with FISH[END_REF][START_REF] Papouchado | Silver In Situ Hybridization (SISH) For Determination of HER2 Gene Status in Breast Carcinoma: Comparison With FISH and Assessment of Interobserver Reproducibility[END_REF][START_REF] Dietel | Comparison of automated silver enhanced in situ hybridization (SISH) and fluorescence ISH (FISH) for the validation of HER2 gene status in breast carcinoma according to the guidelines of the American Society of Clinical Oncology and the College of American Pathologists[END_REF][START_REF] Carbone | Delineation of HER2 gene status in breast carcinoma by silver in situ hybridization is reproducible among laboratories and pathologists[END_REF][START_REF] Francis | Bright-field in situ hybridization for HER2 gene amplification in breast cancer using tissue microarrays: correlation between chromogenic (CISH) and automated silver-enhanced (SISH) methods with patient outcome[END_REF][START_REF] Shousha | Evaluation of automated silver-enhanced in situ hybridization (SISH) for detection of HER2 gene amplification in breast carcinoma excision and core biopsy specimens[END_REF][START_REF] Yoo | Reliability of chromogenic in situ hybridization for epidermal growth factor receptor gene copy number detection in non-small-cell lung carcinomas: a comparison with fluorescence in situ hybridization study[END_REF] and dual-color [START_REF] Nitta | Development of automated brightfield double In Situ hybridization (BDISH) application for HER2 gene and chromosome 17 centromere (CEN 17) for breast carcinomas and an assay performance comparison to manual dual color HER2 fluorescence In Situ hybridization (FISH)[END_REF][START_REF] Mayr | Chromogenic in situ hybridization for Her-2/neu-oncogene in breast cancer: comparison of a new dualcolour chromogenic in situ hybridization with immunohistochemistry and fluorescence in situ hybridization[END_REF][START_REF] García-Caballero | Determination of HER2 amplification in primary breast cancer using dual-color chrmogenic in situ hybridization is comparable to fluorescence in situ hybridization: a European multicentre study involving 168 specimens[END_REF][START_REF] Pedersen | The correlation between dual-color chromogenic in situ hybridization and fluorescence in situ hybridization in assessing HER2 gene amplification in breast cancer[END_REF] approaches. However, it must pointed out that, in some series, the brightfield ISH results are "false" negatives not "false" positives, a consideration with potential clinical consequences. [START_REF] Nitta | Development of automated brightfield double In Situ hybridization (BDISH) application for HER2 gene and chromosome 17 centromere (CEN 17) for breast carcinomas and an assay performance comparison to manual dual color HER2 fluorescence In Situ hybridization (FISH)[END_REF][START_REF] Mayr | Chromogenic in situ hybridization for Her-2/neu-oncogene in breast cancer: comparison of a new dualcolour chromogenic in situ hybridization with immunohistochemistry and fluorescence in situ hybridization[END_REF][START_REF] Pedersen | The correlation between dual-color chromogenic in situ hybridization and fluorescence in situ hybridization in assessing HER2 gene amplification in breast cancer[END_REF] Interestingly, polysomy has been reported as the major cause of response to trastuzumab in FISH negative breast carcinoma patients. [START_REF] Hofmann | Central HER2 IHC and FISH analysis in a trastuzumab (Herceptin) phase II monotherapy study: assessment of test sensitivity and impact of chromosome 17 polysomy[END_REF] In our series, no cases showing gene amplification by FISH were considered negative by SISH. When we raised the SISH cut-off for amplification (≥ 3), the concordance was 100%, demonstrating that SISH is a valid testing method for HER2 testing in gastric carcinoma patients and that a higher cut-off (≥ 3) should be considered even for dual-color SISH in order to increase the concordance rate. It is also necessary to take into account that polysomy may be the cause of interobserver differences. [START_REF] Carbone | Delineation of HER2 gene status in breast carcinoma by silver in situ hybridization is reproducible among laboratories and pathologists[END_REF] A very recent report using a similar methodogy to the one reported herein (fully automated SISH assay with a single color locus detection on two separate slides) has arrived at the same conclusions: chromosome 17 counts are the main source of discrepancy between SISH and FISH ratios. [START_REF] Papouchado | Silver In Situ Hybridization (SISH) For Determination of HER2 Gene Status in Breast Carcinoma: Comparison With FISH and Assessment of Interobserver Reproducibility[END_REF] Another potential source of disagreement between ISH techniques is heterogeneity. [START_REF] Gaiser | Comparison of automated silver enhanced in situ hybridization and fluorescence in situ hybridization for evaluation of epidermal growth factor receptor status in human glioblastomas[END_REF][START_REF] Mayr | Chromogenic in situ hybridization for Her-2/neu-oncogene in breast cancer: comparison of a new dualcolour chromogenic in situ hybridization with immunohistochemistry and fluorescence in situ hybridization[END_REF][START_REF] Dietel | Comparison of automated silver enhanced in situ hybridization (SISH) and fluorescence ISH (FISH) for the validation of HER2 gene status in breast carcinoma according to the guidelines of the American Society of Clinical Oncology and the College of American Pathologists[END_REF] Although heterogeneity occurred in up to 52% of our amplified cases, it did not cause the discrepancies because, before scoring, screening of the entire slide took place.

Another interesting aspect to consider is the concordance of ratios between the different ISH techniques. In agreement with some authors [START_REF] Pedersen | The correlation between dual-color chromogenic in situ hybridization and fluorescence in situ hybridization in assessing HER2 gene amplification in breast cancer[END_REF] and in disagreement with others [START_REF] Hoff | Visualization of FISH Probes by dual-color chromogenic in situ hybridization[END_REF][START_REF] García-Caballero | Determination of HER2 amplification in primary breast cancer using dual-color chrmogenic in situ hybridization is comparable to fluorescence in situ hybridization: a European multicentre study involving 168 specimens[END_REF] , there seems to be, in our series, a weak trend toward lower ratios for FISH than for brightfield ISH. This should be taken into consideration if, in the future, the ratio has predictive value, as has been demonstrated in the neoadjuvant setting of breast carcinoma patients. [START_REF] Arnould | Pathologic complete response to trastuzumab-based neoadjuvant therapy is related to the level of HER-2 amplification[END_REF] Interestingly, the HERA trial has failed to confirm that the degree of HER2 amplification influences the benefit from adjuvant trastuzumab. However, it is important to emphazise that central FISH analyses were only available in 61% of the patients randomized and that it was perfomed in two different laboratories. [START_REF] Dowsett | Disease-free survival according to degree of HER2 amplification for patients treated with adjuvant chemotherapy with or without 1 year of trastuzumab: the HERA Trial[END_REF] Following that line of reasoning, in the future, large trials could benefit from the availability of robust automated hybridization assays that allow for a rapid (<24 hours), reliable and permanent ISH technique. An analysis of the literature on ISH in gastric carcinoma is consistent with our results although there is no data yet on the use of dual-color brightfield ISH approaches. A recent publication reviewed this matter. An analysis, combining this information with our literature shows that, in 2513 samples, the mean HER2 positivity rate was 16.5% (range 6.9-42.6%), very similar to the results of our series. [START_REF] Kanta | Topoisomerase II alpha gene amplification in gastric carcinomas: correlation with the HER2 gene. An immunohistochemical, immunoblotting, and multicolor fluorescence in situ hybridization study[END_REF][START_REF] Hofmann | Central HER2 IHC and FISH analysis in a trastuzumab (Herceptin) phase II monotherapy study: assessment of test sensitivity and impact of chromosome 17 polysomy[END_REF][START_REF] Liang | Analysis of EGFR, HER2, and TOP2A gene status and chromosomal polysomy in gastric adenocarcinoma from Chinese patients[END_REF][START_REF] Barros-Silva | Association of ERBB2 gene status with histopathological parameters and disease-specific survival in gastric carcinoma patients[END_REF][START_REF] Marx | HER-2 amplification is highly homogenous in gastric cancer[END_REF] Agreement exists that this alteration is associated with gastric carcinomas of intestinal type but it is controversial whether it is homogeneous or focal. [START_REF] Marx | HER-2 amplification is highly homogenous in gastric cancer[END_REF][START_REF] Bilous | HER-2 amplification is highly homogenous in gastric cancer[END_REF] In the present study, HER2 amplification was indeed more frequent in that histologic type and heterogeneous in up to 52% of the samples. This result emphasizes the need to screen the whole slide before scoring, a post-analytical approach that is easier with SISH than with FISH.

The implementation of FISH in local laboratories

2 Deleted

 2 centers. This study looked for HER2 expression/amplification in 3807 patients with gastric carcinomas (GC) with a positivity rate of 22% (either by FISH or IHC 3+). Five hundred and eighty four HER2 positive GCs were included and randomized between cisplatin plus fluoropyrimidine (5Fu or capecitabine) (Ch) or the same chemotherapy plus trastuzumab (Ch+T). Patients treated with Ch+T showed a clinically and statistically significant improvement in terms of overall survival (13.8 months vs 11.1 months, HR 0.7 95%CI 0.6 -0.9, p= 0.0046). Secondary end points of the study were also met; thus Ch+T significantly improved overall response rate and progression-free survival, compared with Ch alone, without any increase in toxic effects including cardiac events. Therefore, trastuzumab plus 5Fu/cisplatin chemotherapy has become the new standard treatment for HER2 positive advanced gastric cancer.

  the clinical validation of the different assays, as has been suggested.[START_REF] Mandrekar | Clinical trial designs for predictive biomarker validation: theoretical considerations and practical challenges[END_REF]

  -treatment Solution in a water bath at 97ºC for ten minutes.

  minutes. The silver signal for HER2 was revealed by sequential silver reactions (Silver C´s incubation time 4 minutes). For chromosomal 17 centromere probe, three stringency washes were applied at 59ºC for eight minutes. Next, tissue slides were incubated with anti-DNP antibody for 20 minutes and with alkaline phosphatase-conjugated antibody for 12 minutes. The signal of centromere was visualized with Red ISH Naphthol reaction for four minutes. The tissues were counterstained with Hematoxilin II for eight minutes

4 Deleted: 8 Deleted: 4

 484 Real-time quantitative PCR was performed with the LightMix R kit HER2/neu (Roche Diagnostics). A 101bp fragment of the HER-2 gene and a 119 bp fragment of the RPL23 reference gene, both localized on chromosome 17q21, were amplified according to the manufacturer's instructions. Simultaneous quantification of the HER2 gene and of the reference gene was accomplished by using two different LightCycler hybridization probes (LightCycler R Red 640 and LightCycler R Red 670, respectively) enabling dual color detection in a single test tube. A color compensation file generated with the Roche Diagnostics LightCycler R Multicolour Compensation Set was used to correct the fluorescence in the duplex reaction. DNA was extracted from FFPE Deleted: -Deleted: time incubation Deleted: 8 Deleted: were applied Deleted: Deleted: as shown by other authors.

  using a previously described protocol[START_REF] García-García | The pre-analytical phase in the study of KRAS mutations in colorectal carcinoma: a proposal to standardize the pre-PCR procedure through a morphology-based approach[END_REF] and subsequently amplified in triplicate using a LightCycler 480 real-time PCR instrument (Roche Diagnostics). In each PCR experiment, DNA extracted from tumors with known HER2 amplification status (tumors classified as amplified or non-amplified by both FISH and SISH) was included as positive controls: three samples without amplification and three samples with amplification. Moreover, each PCR experiment included a non-template control and standards (from 10 1 to 10 6 equivalents per reaction of HER2 DNA and of reference DNA) supplied with the kit. These standards allow the generation of standard curve for both products to determine the linear range of both PCR reactions and to estimate the quantity of the target sequence in unknown samples. Briefly, for each reaction 2µl of LightCycler HER2 mix, 2µl LightCycler reference mix, 10µl LightCycler 480 probes master mix and 1µl PCR grade water were combined. 5µl of DNA (for samples and standards) or PCR grade water (for negative control) was added to give a total volume of 20µl. PCR was performed as follows: after an initial ten minutes denaturation of DNA at 95ºC, 45 amplification cycles were performed.Each cycle consisted of denaturation at 95ºC for ten seconds, annealing at 60ºC for ten seconds, and extension at 72ºC for ten seconds. The fluorescence signals were measured after each annealing step.

  proportion equality for the two histological subtypes (intestinal versus diffuse and indeterminate).

  found values < 2 for all tumors, confirming the results obtained by FISH.

  has fallen below the initial expectations (approximately 4% of hospitals with < 300 beds), according to a recent CAP survey. 41 Therefore, it is likely that interpretation of gastric HER2 SISH will be performed by pathologists who are not familiar with FISH. SISH has three main advantages over FISH (permanent record, bright-field post-analytical phase and fully automated analytical phase) that are particularly relevant in gastric HER2 assessment: (1) SISH slides are easier to screen at low power (important with heterogeneity, as mentioned above); (2) co-localization of ISH and IHC findings is straightforward with bright-field assays (approximately 8-13% of GCs may exhibit HER2 genetic-protein discordances); 2 and (3) availability of a fully automated SISH that allow for a rapid subgroup analysis of the ToGA trial samples (mining of this database is of great why patients with IHC 0 or 1+ and FISH positive do not seem to benefit from trastuzumab). 2 In summary, we have compared two different ISH approaches for HER2 testing in gastric carcinoma. The excellent concordance and the absence of false negative cases validate this novel automated dual color SISH. The few discrepant results with FISH were caused by polysomy. This shortcoming may be avoided by raising the cut-off for amplification (≥ 3). Global and national consensus are urgently needed in this setting as a framework for analytical (technical) and post-analytical (interpretative) training. The implementation of a new methodology should be based on gastric carcinoma data but take into serious consideration the previous highs and lows in the experience of breast cancer HER2 testing.Disclosure/conflict of interestAll authors declare no conflict of interest. This validation study was funded by Roche.

Figure 1 .

 1 Figure 1. Gastric carcinoma with HER2 amplification. (a) Amplification in

Figure 2 .

 2 Figure 2. In situ hybridation of HER2 in gastric carcinoma. (a) Non-amplified

Figure 1 .Figure 2 .

 12 Figure 1. Gastric carcinoma with HER2 amplification. (a) Amplification in clusters by FISH and (b) SISH. (c) Amplification in a double minutes pattern by FISH and (d) SISH. 177x149mm (96 x 96 DPI)

Table 1 :

 1 Performance of silver in situ hybridization (SISH) with a cut-off ≥ 2

Table 2 :

 2 Performance of silver in situ hybridization (SISH) with a cut-off ≥ 3

Table 3 :

 3 Correlation of HER2 status studied by FISH, SISH and Real-time quantitative PCR

	F o r
	P
	e
	e r
	R
	e
	v i e
	w

Titles and legends to figures

Table 1 : Performance of silver in situ hybridization (SISH) with a cut-off ≥ 2

 1

			FISH		Total
			Positive	Negative
	SISH	Positive	29	6	35
		Negative	0	131	131
		Total	29	137	166

Table 2 : Performance of silver in situ hybridization (SISH) with a cut-off ≥ 3

 2

			FISH		Total
			Positive	Negative
	SISH	Positive	29	0	29
		Negative	0	137	137
		Total	29	137	166

Table 3 : Correlation of HER2 status studied by FISH, SISH and Real-time quantitative PCR

 3 Negative controls: samples 12, 9, 11; positive controls: samples 35, 84, 85; discordant cases: samples 68, 39, 67, 113, 129, 8.

	Real-time quantitative PCR

Published on behalf of the British Division of the International Academy of Pathology Histopathology

Acknowledgements

We would like to thank the Tumor Bank at the 'Laboratorio de Dianas Terapéuticas', Hospital Universitario Madrid Sanchinarro, for handling the samples used in this study. This work was funded by Roche and was presented in part at the 34 th European Society for Medical Oncology Multidisciplinary Congress, Berlin 2009. The authors thank Rebeca Martínez, Luna Muñoz, Pilar Redondo, Ana Rojo and Ismael Sánchez for their excellent technical assistance. Translated into English by Michelle Homden.

Correlation between FISH and SISH