Yun Zeng

Chaohui Wang

Yang Wang

Xianfeng Gu

Dimitris Samaras

Nikos Paragios

A Generic Local Deformation Model for Shape Registration

Keywords: 3D Shape Registration, Riemannian Geometry, High-order Markov Random Fields Recalage de Surfaces 3D, Géométrie Riemannienne, Champs de Markov Aléatoires d'ordre élevé

In this paper, we propose a new surface registration approach using a generic deformation model, which is efficient to compute and flexible to represent arbitrary local shape deformations. From Riemannian geometry, local deformation at each point of a surface can be characterized by the eigenvalues of a special transformation matrix between two canonically parameterized domains. This local transformation specifies all the deformations (i.e., diffeomorphisms) between surfaces while being independent of both intrinsic (parametrization) and extrinsic (embedding) representations. In particular, we show that existing deformation representations (e.g., isometry or conformality) can be viewed as special cases of the proposed local deformation model. Furthermore, a computationally efficient, closed-form solution is derived in the discrete setting via finite element discretization. Based on the proposed deformation model, the shape registration problem is formulated as a high-order Markov Random Field (MRF) defined on the simplicial complex (e.g., planar or tetrahedral mesh). An efficient high-order MRF optimization algorithm is designed in the paper for such a special structured MRF-MAP problem, which can be implemented in a distributed fashion and requires minimal memory. Finally, we demonstrate the speed and accuracy performance of the proposed approach in the applications of shape registration and tracking.

Introduction

The problem of shape registration has become increasingly important in computer vision due to the wide availability of acquisition devices [START_REF] Zhang | Spacetime faces: high resolution capture for modeling and animation[END_REF][START_REF] Shaji | Simultaneous point matching and 3D deformable surface reconstruction[END_REF]1]. Understanding the transformation between two shapes (i.e., shape matching) is a fundamental task in shape analysis (e.g., classification and recognition) and inference (e.g., registration and tracking). Existing methods of matching shapes are often limited by the assumptions of the underlying deformations. In this paper, we present a generic shape deformation model that can represent arbitrary deformations between two shapes.

Our new deformation model is inspired by the basic ideas in Riemannian geometry [START_REF] Manfredo | Riemannian Geometry[END_REF] in which a shape is equipped with a metric tensor at each point in the parametrization domain. The problem of matching two shapes is hence equivalent to finding correspondences between their parameterized domains (Fig. 1). Different parametrizations represent the same surface (modulo the isometric deformation) if and only if for each correspondence, their metric tensors satisfy certain transformation rules. Hence, for surfaces undergoing isometric deformations, the task of matching becomes finding consistent parametrization such that the transformation rules are satisfied. To characterize more general deformations, at a given point, we consider a special canonical parametrization of the shape whose metric tensor at that point is Euclidean. Arbitrary deformations can be described by the local distortion of a circle between each pair of correspondence in the canonical parametrization domain [START_REF] Ahlfors | Lectures on Quasiconformal Mappings[END_REF][START_REF] Stephenson | Introduction to Circle Packing: The Theory of Discrete Analytic Functions[END_REF]. Such distortion can be consequently characterized by the eigenvalues of a canonical transformation relating to the Jacobian matrix between the two canonical parametrization domains (the canonical distortion coefficient). In the discrete setting, we consider the common case that a shape is represented as simplicial complex (e.g., a planar or tetrahedral mesh). By assuming the deformation of the shape in the parametrization domain to be piecewise linear, the problem of computing the canonical distortion coefficient at a point becomes computing it at a face. The canonical parametrization at a point is simply equivalent to mapping each face to the 2D domain. Within this setting, the computation of the canonical distortion coefficient for each face becomes solving linear equations with a closed-form solution.

Given the above shape deformation model, the problem of finding the optimal shape registration result that best fits the deformation prior and the observed data can be formulated using the Markov Random Field (MRF) framework [START_REF] Geman | Stochastic relaxation, gibbs distributions and the bayesian restoration of images[END_REF]. Recent combinatorial methods (e.g., [START_REF] Torresani | Feature correspondence via graph matching: Models and global optimization[END_REF][START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF]) have demonstrated the superiority of discrete optimization with respect to both solution quality and computational speed. Moreover, in our problem, an MRF formulation allows us to take multiple matching criteria into the same optimization framework. Because the deformation model is defined on each facet (e.g., triangle for planar mesh), the MRF optimization involves high-order cliques. Compared to existing approaches, our method has the following advantages:

• The proposed deformation model is generic and flexible to handle arbitrary deformations. Most of the previous geometry-based deformation models (e.g., isometry and conformality) fall into certain special classes of our model. As a result, our model can accurately describe the deviation from those existing models, which is important in characterizing real-world deformations.

• In the discrete setting, the computation of the canonical distortion coefficient for each basic element (e.g., a triangle for a planar mesh) can be computed efficiently by solving linear equations with a closed-form solution.

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• An efficient high-order MRF optimization algorithm is designed and implemented based on the dual-optimization technique ( [START_REF] Werner | Revisiting the linear programming relaxation approach to gibbs energy minimization and weighted constraint satisfaction[END_REF]) which requires minimal memory and achieves a good approximate solution.

In summary, our paper proposes a generic deformation descriptor: the canonical distortion coefficient (CDC), and its use in a high-order MRF framework that allows us to impose the deformation of a template as a prior in a Bayesian setting. The novel formulation of the surface registration problem as an MRF problem with a cell complex structure seamlessly brings together Riemannian geometry and modern graphical model. Furthermore, our algorithm can be implemented in distributed hardware that achieves significant speedup1 . In our experiment, we demonstrate that the MRF optimization technique combined with the generalized deformation model leads to significant improvement for the problem of surface registration and tracking. This paper is organized as follows: In Sec. 2 we review related work on shape deformation models. The mathematical formulation of our general shape deformation model is presented in Sec. 3, where both continuous concepts and discrete counterparts are discussed. A high-order MRF formulation for shape registration is given in Sec. 4, with the design of an efficient optimization algorithm. In Sec. 5 we show the applications of our new deformation model and optimization technique to the problems of shape registration and tracking. Finally, we conclude our work in Sec. 6.

Related work

Accurately modeling surface deformation is a very challenging task due to the large degrees of freedom that arbitrary deformations may present. Previously, the "rigidity" assumption is widely used due to its good approximation to many real-world deformations and simplicity in computation. Existing deformation models either characterize the rigidity in the extrinsic (embedding) space or in the intrinsic (parametrization) space.

Assuming two representations of a shape in the embedding space only differ by a global rigid deformation (i.e., rotation and translation), the iterative closest points (ICP) [START_REF] Besl | A method for registration of 3-D shapes[END_REF] method has been successfully applied for shape registration with various extensions (e.g., [START_REF] Brown | Global non-rigid alignment of 3-D scans[END_REF][START_REF] Hahnel | An extension of the icp algorithm for modeling nonrigid objects with mobile robots[END_REF]). However, global rigidity does not take into account bendable shapes (e.g., garments or rubber bands). Hence the notion of local rigidity has been proposed which assumes that the deformation between two local neighborhoods of each correspondence be rigid. Although this increases the degrees of freedom of the deformation, efficient algorithms have been proposed that achieves local optimality for such deformation energy, e.g., [START_REF] Mathieu Salzmann | Surface deformation models for nonrigid 3D shape recovery[END_REF][START_REF] Sorkine | As-rigid-as-possible surface modeling[END_REF][START_REF] Sumner | Embedded deformation for shape manipulation[END_REF][START_REF] Chao | A simple geometric model for elastic deformations[END_REF].

When the shapes undergo large deformations or are represented in different embedding space, intrinsic methods (e.g., [START_REF] Bronstein | Efficient computation of isometry-invariant distances between surfaces[END_REF][START_REF] Bronstein | Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching[END_REF][START_REF] Wang | High resolution tracking of non-rigid 3D motion of densely sampled data using harmonic maps[END_REF][START_REF] Wang | Conformal geometry and its applications on 3D shape matching, recognition, and stitching[END_REF][START_REF] Zeng | Ricci flow for 3D shape analysis[END_REF][START_REF] Zeng | 3D non-rigid surface matching and registration based on holomorphic differentials[END_REF]) become useful. The basic idea of intrinsic methods is from Riemannian geometry [START_REF] Manfredo | Riemannian Geometry[END_REF], assuming a shape be equipped with a metric measuring the distance between any two points. The notion of rigidity (known as isometry) can be best characterized by assuming the metric does not change across two shapes. Hence matching two surfaces becomes finding consistent parametrization that best match the metric. However, finding a globally consistent parametrization is often too restricted. Recently work ([36, 19, 37, 18, 38]) search among multiple parametrization and use multiple matching criteria (e.g., texture

f Φ1 Φ2
Figure 1: The problem of finding correspondences between two surfaces can be reduced to finding correspondences between their parametrization domain. The problem we solve in this paper is: given a predefined points on the first surface, find the correspondences of only those points on the second one. Efficient candidate selection schemes for surface registration and tracking are described in [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF][START_REF] Zeng | Intrinsic dense 3D surface tracking[END_REF].

or curvature) to improve the matching accuracy, though their underlying deformation model is still based on isometry assumption.

Canonical distortion coefficient

In this section, we present the mathematical formulation of our deformation model in both continuous and discrete settings.

Continuous setting

Riemannian metric and parametrization

Let (M, g M ) denote a surface M equipped with a Riemannian metric g M . In Riemannian geometry ( [START_REF] Manfredo | Riemannian Geometry[END_REF]), a surface is described by its local charts

{(U α }, i.e., M = U α ∪ U β . . . and each open subset U α is in 1 -1 correspondences φ α : U α → R 2 .
Here φ α is the local parametrization. For any p ∈ U α ⊂ M, a metric tensor is associated to p as a symmetric positive definite matrix:

g α (p) = g α 11 (p) g α 12 (p) g α 21 (p) g α 22 (p)
.

(1)

Within such setting, a point on M may be covered by multiple charts. In order for different local representations to describe the same surface, certain transformation rules must be satisfied, i.e., if a point p ∈ U α ∩ U β , we must have

g α (p) = J αβ (p) T g β (q)J αβ (p). (2)

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Here J αβ is the Jacobian matrix of the transformation x α (x β ) (x α (x β ) is the local coordinate system of patch U α (U β )) between charts U α and U β , i.e.,

J αβ =   ∂x 1 α ∂x 1 β ∂x 1 α ∂x 2 β ∂x 2 α ∂x 1 β ∂x 2 α ∂x 2 β   . (3)
Any local representation satisfying this transformation rule is a valid parametrization of the surface. Therefore, since the metric tensor at any point p ∈ M is positive definite, it is always possible to apply a proper linear transformation to its parametrization φ α such that g α (p) is the identity matrix. We call such a parametrization the canonical parametrization for point p:

Definition 1. (Canonical parametrization at a point) For any p ∈ M, a parametrization φ α : U α → R2 is called canonical parametrization for p if the metric tensor at p is the identity matrix.

Please note that although there exists infinite number of such a canonical parametrization for a surface, the parametrization at the particular point is unique. In the following we shall show that focusing on the parametrization only at one point at a time allows us to characterize arbitrary deformations between two surfaces while regardless of both the intrinsic and extrinsic representations of the surface, which is the main advantage of our new deformation model.

Diffeomorphisms between two shapes

Now we consider arbitrary diffeomorphisms between the parametrization domains of two surfaces (Fig. 1). For any correspondence p ∈ U α ⊂ M → q ∈ U β ⊂ N , the change of metric g α (p) → J αβ (p) T g β (q)J αβ (p) reflects how locally a circle is deformed into an eclipse (Fig. 2(a)) 2 . In particular, under canonical parametrization for points p and q, the matrix J T pq J pq accurately characterizes such local deformation, where J pq is the Jacobian at point p. If we only consider the change of shape, i.e., how a circle is deformed into an eclipse regardless its orientation, the eigenvalues λ 1 , λ 2 of J T pq J pq can best describe such change. Therefore, the local deformation between two surfaces can be characterized by the eigenvalues λ 1 , λ 2 for each correspondence. Formally, we define:

Definition 2. (Canonical distortion coefficient)

The eigenvalues of the Jacobian transformation matrix J T pq J pq between any canonical parametrization at p and q are the canonical distortion coefficients between the two points.

We call the Jacobian matrix J pq between the two points p and q under the canonical parametrization the canonical Jacobian. The significance of using canonical Jacobian is that it allows us to characterize arbitrary deformation by considering the parametrization of the surface at a single point. Some special cases of deformations can be characterized by the canonical distortion coefficient as follows:

1. In the case of the isometric deformation, a unit circle is mapped to a unit circle, i.e., λ 1 = λ 2 = 1.

2. In the case of the conformal deformation, a unit circle can be mapped to a circle with arbitrary radius [START_REF] Stephenson | Introduction to Circle Packing: The Theory of Discrete Analytic Functions[END_REF]. Thus, The finite element method assumes the transformation between facets to be piecewise linear and

λ 1 = λ 2 .
f ( ab) = a ′ b ′ , f ( ac) = a ′ c ′ .
Under the linearity assumption, the Jacobian can be computed in a closed form for each triangle pair △abc → △a ′ b ′ c ′ .

To further connect the canonical distortion coefficient to a general class of diffeomorphisms defined in the complex plane f : U α → U β , between any canonical parametrization x α and x β for p and q respectively, we define

∂f ∂z = 1 2 ( ∂x 1 α ∂x 1 β + ∂x 2 α ∂x 2 β ) + i 2 ( ∂x 2 α ∂x 1 β - ∂x 1 α ∂x 2 β ) ∂f ∂z = 1 2 ( ∂x 1 α ∂x 1 β - ∂x 2 α ∂x 2 β ) + i 2 ( ∂x 2 α ∂x 1 β + ∂x 1 α ∂x 2 β ),
The notion of quasi-conformality [START_REF] Ahlfors | Lectures on Quasiconformal Mappings[END_REF] can be characterized by the following Beltramicoefficient:

µ(z) ≡ ∂f ∂z / ∂f ∂z ,
which gives us all the information about the conformality of f . Suppose

λ 1 ≥ λ 2 , it can be shown that |µ(z)| = ( √ λ 1 - √ λ 2 )/( √ λ 1 + √ λ 2 ). In particular, f is called holo- morphic if µ(z) = 0 ([ 12
]), i.e., λ 1 = λ 2 , coinciding with the fact that holomorphic function is another description of conformal mapping. Hence the Beltrami-coefficient generalizes conformal mapping and can be partially determined using the canonical distortion coefficient. However, the Beltrami-coefficient is for surface parametrization, where scaling factor is lost. The proposed canonical distortion coefficient preserves the scale information which is important for shape matching. Besides, the canonical distortion coefficient is directly extendable to nD. In this paper, we propose an efficient approach to compute the local deformation based on the canonical distortion coefficient in the context of shape registration.

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Finite element discretization

The basic assumption in finite element analysis [START_REF] Brenner | The Mathematical Theory of Finite Element Methods[END_REF] is that the continuous space can be approximated using a set of basic elements (e.g., polynomial functions defined on each face). Meanwhile, consistencies must be preserved at the boundaries among the basic elements. In this paper, we consider the most common representation of a continuous surface -a triangular mesh, whose basic finite element is a triangular face. In this discrete setting, the canonical distortion coefficient (CDC) is assumed to be constant for each basic element (i.e., △abc shown in Fig. 2).

Thus, the concept of canonical parametrization (Sec. 3.1.1) can be expressed in the following manner: a parametrization of a point p is locally Euclidean at p if the images of any two tangent vectors have the same angle and length. In the discrete setting, this means a triangle △abc keeps all its angles and lengths in its parametrization, which can be achieved by simply mapping the face △abc onto a 2D domain by keeping all its edge lengths.

Finally, we consider the computation of the canonical Jacobian (Sec. 3.1.2). In the continuous setting, the Jacobian matrix at a point p is a linear operation that transforms tangent vectors at p to tangent vectors at q. Given a basic element △abc in the discrete setting, the tangent space at p is equivalent to the linear space spanned by △abc. Hence the linear mapping J(•) between two canonical domains should satisfy J( ab) = a ′ b ′ and J( ac) = a ′ c ′ . The Jacobian of a linear transformation between two triangles is a 2 × 2 matrix and can be computed in closed-form. Since J(•) is linear, J( bc) = b ′ c ′ must be satisfied as well, i.e., Jacobian for mapping p → q ⇔ Linear transformation matrix for mapping ab → a ′ b ′ , ac → a ′ c ′ For clarity, Alg. 1 summarizes the algorithm for computing the canonical distortion coefficient. Note that the computation is in analogy with previous work for surface parametrization (e.g., [START_REF] Pinkall | Computing discrete minimal surfaces and their conjugates[END_REF][START_REF] Polthier | Computational aspects of discrete minimal surfaces[END_REF][START_REF] Sander | Texture mapping progressive meshes[END_REF]) since both are based on the same piecewise linear assumption. However, here we derive it from a different continuous setting in the context of shape deformation estimation. Also note that when the shape is n-manifold, the computation of CDC becomes solving n linear equations and eigenvalues.

Algorithm 1: Algorithm for computing the canonical distortion coefficient (CDC) for each triangular face.

Input : △abc and its mapping △a ′ b ′ c ′ Output : CDC for mapping from △abc to △a ′ b ′ c ′ .

Step One: Map the triangles △abc and △a ′ b ′ c ′ to 2D and keep their orientation.

Step Two: Compute the 2 × 2 linear transformation J mapping ab to a ′ b ′ and ac to a ′ c ′ .

Step Three: Compute the eigenvalues, λ1 and λ2 of J T J.

Step Four: Output λ1 and λ2 4 High-order MRF-based shape registration

MRF formulation for shape registration

Given the canonical distortion coefficient (CDC) defined for each basic element, i.e., the triangular face, one can either deform the original shape (e.g., [START_REF] Sorkine | As-rigid-as-possible surface modeling[END_REF]), or find the correspondences between two shapes combined with other matching cues (e.g., [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF]).

Here we consider the problem of finding the mapping f between two shapes M and N . Similar to [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF], we assume a set of n points V = {p u |p u ∈ M, u = 1, . . . , n} are sampled on the surface M and a triangulation of these points are constructed (Fig. 1). Hence the task of shape registration becomes finding the correspondences for the set V ⊂ M on shape N .

To formulate the shape matching problem using graphical models, we construct a graph G = (V, F) where V is a set of vertices and F ⊂ V × V × V is a set of faces. For each u ∈ V, let the random variable x u ∈ L = {1, . . . , L} denote the discrete labeling of all the possible matching candidates of vertex u ∈ M on shape N . In the rest of this paper, we use x u to denote the labeling of vertex u or the point on shape N when it is clear from the context.

Firstly, let fea(•) be the feature vector (e.g., texture or shape context) at each point on the shape. We define the cost function θ u (x u ) of matching u to x u :

θ u (x u ) = |fea M (u) -fea N (x u )| 2 . Next, we denote by λ M (u, v, w) = λ 1 (u, v, w) λ 2 (u, v, w)
as the prior knowledge of CDC that characterizes the deformation for the face (u, v, w) and

λ N (x u , x v , x w ) = λ 1 (x u , x v , x w ) λ 2 (x u , x v , x w )
as the CDC computed from deforming △uvw to △x u x v x w (Alg. 1). Hence we define:

θ uvw (x u , x v , x w ) = d(λ M (u, v, w), λ N (x u , x v , x w ))
as the deformation energy. Here d(•, •) is the distance function that is defined according to the application.

Finally, given the feature function fea(•) and the deformation prior λ M (•, •, •) for each vertex and face, the problem of shape registration becomes solving the best configuration x that minimizes the following energy:

min x E(x) = u∈V θ u (x u ) + (u,v,w)∈F θ uvw (x u , x v , x w ). (4)
To reduce the search space L and avoid local minima, we adopt a hierarchical optimization scheme in solving the energy function [START_REF] Brenner | The Mathematical Theory of Finite Element Methods[END_REF]. Inspired by [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF], sparse feature points are first selected to compute the initial matching with the global constraint λ 1 = λ 2 = 1 for each triangle (u, v, w) ∈ F. Then, a small set of candidates L are selected to find the best local match by minimizing the energy function (4).

An efficient high-order MRF optimization

The high-order potential of Eq. 4 presents the difficulty for solving our surface registration problem. Existing algorithms either transform high-order cliques into pairwise ones (e.g., [START_REF] Ishikawa | Higher-order clique reduction in binary graph cut[END_REF]) or decompose the original problem into a union of sub-problems (e.g., [START_REF] Komodakis | Beyond pairwise energies: Efficient optimization for higher-order MRFs[END_REF]). However, these algorithm are designed for general problems and requires extra memory to store the transformed problem or the dual variables that relates the subproblems. For the problem of high-order MRF inference, memory efficiency is an important issue since a poorly designed optimization algorithm can easily reach the limit of current hardware. In this paper, we follow the framework by Thomas [START_REF] Werner | Revisiting the linear programming relaxation approach to gibbs energy minimization and weighted constraint satisfaction[END_REF] to design a fast and memory efficient MRF optimization algorithm using the linear programming (LP) relaxation technique. The first step in the LP relaxation of Eq. 4 is to introduce the indicator variables. For any u ∈ V and i ∈ L, we define

τ u;i = 1 if x u = i 0 otherwise .
Also for any (u, v, w) ∈ F and (i, j, k) ∈ L × L × L, we define

τ uvw;ijk = 1 if x u = i, x v = j, x w = k 0 otherwise .
Similarly, we define θ u;i = θ u (i) and θ uvw;ijk = θ uvw (i, j, k). Hence we have the integer LP formulation of the problem of Eq. 4:

min τ u∈V i∈L θ u;i τ u;i + (u,v,w)∈F (i,j,k)∈L 3 θ uvw;ijk τ uvw;ijk s.t. i τ u;i = 1, ∀u ∈ V i,j,k τ uvw;ijk = 1, ∀(u, v, w) ∈ F j,k τ uvw;ijk = τ u;i , ∀(u, v, w) ∈ F and i ∈ L τ u;i , τ uvw;ijk ∈ {0, 1}.
By relaxing the variables to the domain [0, 1], we obtain the dual form of the above LP problem as

max M u min i θ u;i + (u,v,w)∈F min i,j,k θ uvw;ijk (5)
s.t. θ u;i = θ u;i + (u,v,w)∈F M uvw;u:i , ∀u ∈ V and i ∈ L θ uvw;ijk = θ uvw;ijk -M uvw;u:i -M uvw;v:j -M uvw;w:k , ∀(u, v, w) ∈ F and (i, j, k) ∈ L × L × L.
Here M uvw;u:i is the dual variable (message) corresponding to the constraint j,k τ uvw;ijk = τ u;i . (Fig. 3).

RR n°7676

Algorithm 2: Min-sum diffusion algorithm. repeat for each M uvw;u:i do M uvw;u:i -= 1 2 [θ u;imin j,k θ uvw;ijk ] and reparameterize θ u;i and θ uvw;ijk according to the constraints in Eq. 5.

end for until convergence

The dual problem of Eq. 5 can be solved by the simple min-sum diffusion algorithm [START_REF] Werner | Revisiting the linear programming relaxation approach to gibbs energy minimization and weighted constraint satisfaction[END_REF] as shown in Alg. 2 (Note that in [START_REF] Werner | Revisiting the linear programming relaxation approach to gibbs energy minimization and weighted constraint satisfaction[END_REF] their optimization problem is a maximization so the algorithm is called max-sum). It has been shown that at convergence, the solution satisfies J-consistency condition as introduced in [START_REF] Werner | Revisiting the linear programming relaxation approach to gibbs energy minimization and weighted constraint satisfaction[END_REF]. Since after each update of the message, reparameterization is performed, no extra memory is needed for storing all the dual variables M uvw;u:i . Hence the memory requirement for the Alg. 3 is the storage for the primal variables, i.e., O(|V ||L| + |F||L|3 ), which can not be avoided by any algorithm.

Each update of the message in Alg. 2 only involves the parameters in a triangle. Also within each face △uvw, the update of each label M uvw;u:i , i = {1, . . . , L} is independent. Hence the algorithm can be significantly accelerated using distributed hardware.

In order to explore the parallelism of the min-sum Algorithm 2, we define the concept of independent face set:

Definition 3. (Independent face set) Given a graph G = (V, F), a subset F k ⊂ F is called independent face set if for any f i , f j ∈ F k , f i ∩ f j = ∅.
The decomposition of a set F into subsets of independent face sets F = ∪ i F i can be efficiently computed in polynomial time by a simple greedy algorithm. Hence we can implement Alg. 2 in parallel as shown in Alg. [START_REF] Besl | A method for registration of 3-D shapes[END_REF]

Performance evaluation

We implement Alg. 3 using the NVIDIA CUDA architecture [START_REF] Keane | CUDA (compute unified device architecture)[END_REF] 3 . In approximation algorithms [START_REF] Vazirani | Approximation Algorithms[END_REF], the approximation error (AE) is defined as the gap between the optimal integral solution and the solution obtained by the algorithm. The gap between the result by the LP relaxation and the optimal integral solution is often used to upper bound the approximation error. Here we aim to test the true approximation error, as well as the speedup, by designing the test inputs as follows: Given any input mesh, we randomly assign a default labeling l u for each node u ∈ V. We define the singleton potentials of Eq. 4 as

θ u (x u ) = 0 if x u = l u rnd(1) otherwise ,
where rnd(1) is a random number between [0, 1]. Also we define the high-order potentials as

θ uvw (x u , x v , x w ) = 0 if (x u , x v , x w ) = (l u , l v , l w )
rnd(1) otherwise .

In such case, the optimal solution of Eq. 4 should be {l u |u ∈ V}. Fig. 4 (a) shows the result of our algorithm using the above designed test cases for different mesh and label size. Note that although the total energy increases with mesh size, the average energy per term (vertex and face) remains significantly low (< 0.01 for all cases). Fig. 4 (b) shows the comparison on average time taken per iteration, between the implementations with and without GPU accelerations. The total number of iterations depends on the energy. In our experiment the algorithm converges within 3000 iterations. Hence our algorithm is both memory and computational efficient, which is important for shape tracking.

Experimental results

In this section, we apply our deformation model and optimization technique to the problems of shape registration and tracking. The input to our algorithm is two 3D shapes M and N , and a triangulated sampling point set G = (V, F) on M (Fig. 6 (a)). The output is the registered result on N for each point in V (Fig. 6 (c)). We implement our algorithm on an Intel Core(TM)

Estimation of deformation prior:

In our experiment, we assume that the deformation priors are similar across different shapes of the same type (e.g., human faces [START_REF] Vlasic | Face transfer with multilinear models[END_REF]). The ground truth deformation prior can be obtained by 3D scanning systems with reliable texture information (e.g., markers). As shown in Fig. 5, the two 3D data in (a) and (c) are captured with markers using the system introduced in [START_REF] Wang | High resolution tracking of non-rigid 3D motion of densely sampled data using harmonic maps[END_REF]. Here we select two frames with the largest expression difference to measure the maximal possible change of CDC. Fig. 5 (b), (d), (f) and (g) show the visualization of the distribution of CDC. From the above data set we obtain the allowed bound for human face expression changing from neutral to large deformation as I 1 = [0.7, 5.66], I 2 = [0.1, 4] for λ 1 and λ 2 , respectively. For the problem of surface registration, we define a Potts-like energy for the high-order terms in Eq. 4 as follows:

θ uvw (x u , x v , x w ) = 0 if λ 1 ∈ I 1 and λ 2 ∈ I 2 10 otherwise , (6)
where λ 1 and λ 2 are the CDCs obtained by matching △uvw to △x u x v x w .

Shape registration

Fig. 6 shows one of our shape registration results and its comparison with the results of Zeng et.al [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF]. The singleton terms are defined similarly as in [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF]. To obtain enough matching candidates, re-sampling is made near its original candidates. The high-order graph matching formulation in [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF] assumes the two surfaces are isometrically deformed so they have consistent conformal mapping if three correspondences are found. Hence when the deformation is not isometric, the registered points can be significantly distorted (Fig. 6 (b) and (c)). Besides, the optimization technique in [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF] requires reducing high-order terms into pairwise ones so the memory required is huge and it only handle label size < 5. In contrast, our method poses deformation constraint onto each triangle and guarantees the consistency condition for the final solution. As a result, unlikely matching is avoided and the results are visually plausible (Fig. 6 (e) and (f)). More quantitative comparisons are given in Table 1. It can been seen that the unnatural deformations presented in [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF] are significantly reduced.

To test the accuracy achieved by using a anisometric deformation prior, defined as the canonical distortion coefficient (CDC) in our paper, we design the following experiment. The 3D scan of a highly deformable toy is captured by the system introduced in [START_REF] Wang | High resolution tracking of non-rigid 3D motion of densely sampled data using harmonic maps[END_REF] before and after a large deformation, as shown in Fig. 7 Outliers are pruned off using the selection tool provided by the MeshLab software 4 . An original set of points and their candidates are selected using the method described in [START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF]. To establish the ground truth and estimate the deformation prior, we manually select 20 facets and their matches based on the texture information. The two shapes are then matched without using the texture information, i.e., in Eq. 4 of in the paper, we use curvature as the singleton term (data likelihood) and the learnt deformation prior as the high-order term (the deformation prior). Fig. 8(b) shows the result using isometric assumption (λ 1 , λ 2 ) = (1, 1) and Fig. 8(c) shows the result using the learnt CDC prior (λ 1 , λ 2 ) = (1.028, 0.993). To compare the accuracy achieved by the two assumptions, we compare the average texture difference between the original area covered by the matching points (the blue mesh in Fig. 8) and the matched area.

Shape tracking

To apply our method to tracking dynamic 3D scanned data, we consider both interframe consistency and the consistency between the current frame and the first frame.

For the singleton term in Eq. 4, we use the robust metric defined in the paper of [START_REF] Zeng | Intrinsic dense 3D surface tracking[END_REF].

To impose inter-frame consistency, we use the same data set (here we select two con- Table 2: Comparison between results with and without isometric assumption. The matching is done without using the texture information. The comparison is based on the average texture difference (the gray level is normalized in [0, 1]), by warping the source mesh to the matched target mesh.

respectively. Also we handle drift error by imposing the consistency between the first frame and the current frame, using the same face deformation prior learnt in Fig. 5.

Fig. 9 shows tracking results on the BU-4DFE database [START_REF] Yin | A highresolution 3d dynamic facial expression database[END_REF]. A template is constructed in the first frame and tracked in the subsequent frames (same as in [START_REF] Zeng | Intrinsic dense 3D surface tracking[END_REF]. Because of the temporal continuity in consecutive frames, sufficient matching candidates can be obtained by only looking at the neighborhood of each point. In this data set, the texture information is noisy so relying on texture information only can lead to erroneous results. By imposing a simple prior on the bound of the deformation, we have achieved plausible tracking results as shown in Fig. 9.

Conclusion

We have presented a generic, geometry-inspired deformation model for characterizing arbitrary diffeomorphisms between shapes. An efficient and accurate algorithm to compute the canonical distortion coefficients (CDCs) is proposed based on finite element analysis in the discrete setting. Searching for the optimal shape registration result given such model is made possible with a high-order MRF framework. An efficient optimization algorithm is designed for such problem. We demonstrated the speed and accuracy performance on 2-manifold shape registration. However, both the deformation model and the optimization algorithm can be easily extended to high-dimensional space.

Tangent space, inner product and metric tensor

In Riemannian geometry, the concept of tangent space is the vehicle for studying the intrinsic properties of the geometric shape such as isometry, conformality and diffeomorphism. Intuitively, this is because the tangent space gives us the first-order information of the surface which is linear and hence easy to handle. Definition 4. A tangent vector at p ∈ M, call it X, assigns to each coordinate patch (U α , x α ) holding p, and n-tuple of real numbers

(X i α ) = (X 1 α , . . . , X n α ) (7
)

such that if p ∈ U α ∩ U β , then X i β = n j=1 [ ∂x i β ∂x j α (p)]X j α (8)
Here the matrix (

∂x i β ∂x j α
) is the Jacobian matrix between the two charts U α and U β , as defined in Eq. 8. Hence a tangent vector can be represented by different coordinates under different parametrizations as long as Eq. 8 is satisfied. Also at each point, all the tangent vectors form a linear space, which can be represented by a coordinate basis under any parametrization U α . Definition 5. The tangent space to M at the point p ∈ M is the real vector space consisting of all tangent vectors to M at p. If x α = {x 1 , . . . , x n } is a coordinate system holding p, then the n vectors

∂ ∂x 1 , . . . , ∂ ∂x n (9)
form a basis of this n-dimensional vector space and the basis is called a coordinate basis. We denote by T p (M) as the tangent space at a point p ∈ M.

Both the tangent vector and the tangent space are defined at a single point on the surface. If we consider the "bundle" of tangent vectors defined at every point, we can define a vector field on an open set U to be the differentiable assignment of a vector X to each point of U ; in terms of local coordinates

X = n j=1 X j (x) ∂ ∂x j . (10)
Given the vector field defined on each point p ∈ M, we can define a basis in the tangent space {e 1 (p), . . . , e n (p)}. Hence we can define the inner product •, • that measures the distance between two tangent vectors at each point.

v, w p = i e i v i , j e j w j p = i j v i e i , e j p w j (11)
If we define the matrix G = (g ij ) p with entries then v, w = vGw. The matrix (g ij ) is called the metric tensor. Note that here G is a function defined at each point on the surface. A Riemannian metric tensor (g ij ) is required to be symmetric positive definite at every point. Hence it is always possible to apply a linear transformation to (g ij ) at a given point p such that the new metric tensor (g ′ ij ) = J T p (g ij )J p is the identity matrix I, where J p is an non-degenerate matrix. Therefore, given any coordinate chart {U α , x α }, we can define a new coordinate chart {U ′ α , x ′ α } where x ′ α = J p x α . It can be easily verified that at point p e ′ i , e ′ j p = J p e i , J p e j p = e T i J T p (g ij )J p e j = δ j i .

g ij := e i , e j p (12)
Consequently, the new coordinate chart is called the canonical parametrization as defined in Definition 1.

Diffeomorphisms, isometries and conformal maps

Given a diffeomorphism f : M → N , the mapping between two tangent spaces df : T p (M) → T q (N ), where q = f (p), is a linear mapping [START_REF] Manfredo | Differential Geometry of Curves and Surfaces[END_REF]. The mapping f can be fully characterized by its differential df at each point on the surface given an initial correspondence [START_REF] Evans | Lectures on Quasiconformal Mappings[END_REF]. The advantage of studying the mapping f from its first-order derivative is its simplicity since df is defined on a linear space. Within this setting, the change of the tensor metric, i.e., v, w → df (v), df (w) q

is determined by the linear transformation df . Hence, under this the linear transformation, a unit circle in T p (M) is mapped into an eclipse in T q (N ). Under canonical parametrization (Def. 1), such change of metric tensor can be represented as I → J T pq J pq . Since J T pq J pq = O T diag(λ 1 , λ 2 )O, this deformation represents both scale change information and angle change information. Here λ 1 and λ 2 represents the scale change along the two axes and the (rotational) orthogonal matrix O represents the angle change. Equivalently, such changes can be fully characterized by the distortion of a unit circle in the tangent space at p into an eclipse in the tangent space at q (Fig. 10). In the following, we show that the canonical distortion coefficient can fully characterize two deformation models that is prevalent in computer vision, i.e., isometry and conformality. Definition 6. A diffeomorphism f : M → N is an isometry if for all p ∈ M and all pairs of tangent vectors v, w ∈ T p (M), we have v, w p = df (v), df (w) q (15)

INRIA Hence, under canonical parametrization, the mapping must satisfy

J T pq J pq = I, (16)
i.e., λ 1 = λ 2 = 1. Definition 7. A diffeomorphism f : M → N is called a conformal map if for all p ∈ M and all pairs of tangent vectors v, w ∈ T P (M), we have

df (v), df (w) q = λ 2 (p) v, w p , ( 17
)
where λ 2 is a nonwhere-zero differentiable function on M.

Again, under canonical parametrization, we have J T pq J pq = λ 2 (p), implying λ 1 = λ 2 .

Canonical distortion coefficient and quasi-conformal mapping

The above discussion established the link between the popular deformation models (i.e., isometry and conformality) and the canonical distortion coefficient. In fact, the canonical distortion coefficient is also closely related to the more general quasi-conformal mapping [START_REF] Ahlfors | Lectures on Quasiconformal Mappings[END_REF]. The quasi-conformal mapping studies the deformation between two planes w = f (z), where z = x + iy and w = u + iv. At a given point z 0 , f induces a linear mapping of the differentials du = u x dx + u y dy (18)

dv = v x dx + v y dy (19)
which we can also write in the complex form:

f z = 1 2 (f x -if y ) and f z = 1 2 (f x + if y ) (20)
Note that this transformation is defined on two charts U α and U β which is assumed to have Euclidean metric. Hence one can write in classical notation

du 2 + dv 2 = Edx 2 + 2F dxdy + Gdy 2 (21)
with

E = u 2 x + v 2 x , F = u x u y + v x v y , G = u 2 y + v 2 y ( 22
)
Under canonical parametrizations at q (f (z 0 )), since it is Euclidean at q, the metric tensor can be represented as du 2 + dv 2 . Hence we can establish

J T pq J pq = E F F G . ( 23
)
In the theory of quasi-conformal mapping, the beltrami-coefficient µ(z) = fz fz can be partially determined by the eigenvalues of the matrix E F F G , which is equivalent to the canonical distortion coefficient. To see this, we first define

D f = |f z | + |f z | |f z | -|f z | . ( 24
)
From

dw = f z dz + f z dz, (25)
we have

(|f z | -|f z |)|dz| ≤ |dw| ≤ (|f z | + |f z |)|dz|. ( 26
)
Hence D f denotes the ratio of the major to the minor axis of the mapping f at z 0 , i.e.,

D f = ( λ 1 λ 2 ) 1 2 (27)
Therefore we can easily obtain

|µ(z)| = √ λ 1 - √ λ 2 √ λ 1 + √ λ 2 . ( 28
INRIA

  Figure 2: The finite element method assumes the transformation between facets to be piecewise linear and f ( ab) = a ′ b ′ , f ( ac) = a ′ c ′ . Under the linearity assumption, the Jacobian can be computed in a closed form for each triangle pair △abc → △a ′ b ′ c ′ .

Figure 3 :

 3 Figure 3: An example of the messages defined for the dual problem of Eq. 5. For each face △uvw, the messages are defined from the high-order clique (u, v, w) to each of the nodes u, v and w.

Figure 4 :

 4 Figure 4: Performance analysis of our MRF optimization algorithm. (a) shows the optimality using the test cases described in Sec. 4.3. (b) shows the speedup using the parallel implementation of Alg. 3. We show the runtime per iteration since different inputs would result in different iteration counts.

  Fig.6shows one of our shape registration results and its comparison with the results of Zeng et.al[START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF]. The singleton terms are defined similarly as in[START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF]. To obtain enough matching candidates, re-sampling is made near its original candidates. The high-order graph matching formulation in[START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF] assumes the two surfaces are isometrically deformed so they have consistent conformal mapping if three correspondences are found. Hence when the deformation is not isometric, the registered points can be significantly distorted (Fig.6 (b) and (c)). Besides, the optimization technique in[START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF] requires reducing high-order terms into pairwise ones so the memory required is huge and it only handle label size < 5. In contrast, our method poses deformation constraint onto each triangle and guarantees the consistency condition for the final solution. As a result, unlikely matching is avoided and the results are visually plausible (Fig.6 (e) and (f)). More quantitative comparisons are given in Table1. It can been seen that the unnatural deformations presented in[START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF] are significantly reduced.To test the accuracy achieved by using a anisometric deformation prior, defined as the canonical distortion coefficient (CDC) in our paper, we design the following experiment. The 3D scan of a highly deformable toy is captured by the system introduced in[START_REF] Wang | High resolution tracking of non-rigid 3D motion of densely sampled data using harmonic maps[END_REF] before and after a large deformation, as shown in Fig.7(a) and (b), respectively.

INRIA

Figure 5 :

 5 Figure 5: Expression deformation prior is obtained by 3D scanned data with markers. (a) and (b) show the 3D scan of the onset and peak of a facial expression with large shape deformations respectively. (c) and (d) are the corresponding triangular meshes constructed from the 3D scan data. The color coding in (d) shows the deformation intensity as illustrated in (e). The histogram of the canonical distortion coefficient values are shown in (f) and (g).

Figure 6 :

 6 Figure 6: Shape registration result. (a) shows the input mesh with triangulated discrete samples obtained by the method described in [37]. The matching result and its closeup is shown in (b) and (c).

Figure 7 :Figure 8 :

 78 Figure 7: The 3D scan of a highly deformable toy.

Figure 10 :

 10 Figure 10: The deformation of a unit circle into an eclipse is defined in the tangent space.

) 7 . 2 Bτ

 72 . Details of high-order MRF optimization algorithm7.2.1 Derivation of dual optimizationIn linear programming (LP), a general form of primal-dual relation is the followingmin c T x max b T y(29)s.t. Ax = b ⇔ s.t. A T y ≤ c x ≥ 0Here c and b are two vectors and A is a matrix. Now let us consider the LP relaxation of the problem of Eq. 4 as derived in Sec. 4:min τ u∈V i∈L θ u;i τ u;i + (u,v,w)∈F (i,j,k)∈L 3 θ uvw;ijk τ uvw;ijk(30) s.t.i τ u;i = 1, ∀u ∈ V i,j,k τ uvw;ijk = 1, ∀(u, v, w) ∈ F j,k τ uvw;ijk = τ u;i , ∀(u, v, w) ∈ F and i ∈ Lτ u;i ≥ 0, τ uvw;ijk ≥ 0, uvw;ijk = τ u;i → M uvw;u:i ,

Algorithm 3 :

 3 . The maximal speedup achieved Parallel min-sum diffusion algorithm.

	end for
	until convergence
	in Alg. 3 is max i (|F i ||L|).

Decompose F into independent face sets ∪ i F i repeat for each Independent face set F i , in parallel for all (u, v, w) ∈ F i and k ∈ L do Update the message M uvw;u:k , M uvw;v:k and M uvw;w:k and do reparameterization (Alg. 2).

Table 1 :

 1 Comparison with[START_REF] Zeng | Dense non-rigid surface registration using high-order graph matching[END_REF]. Here (•, •, •) denote the average, minimal and maximal area ratios between the original facets and the matched facets.an NVIDIA Geforce 9800GTX+ graphics card with 128 CUDA cores. The number of labels L (matching candidates) is set to be 2 n for best hardware performance. In most of our experiments, we set L = 64. The computation of all the L 3 possible CDCs for one face takes only 2.0ms on average on GPU. Hence the computation of the energy term θ uvw;ijk for a mesh with 165 vertices and 272 faces takes only 0.5s.

	Data	Zeng et.al. [37]	Our method
	Face_Smile	(2.26, 0.19, 67.83)	(1.24, 0.86, 4.2)
	Face_Laugh (1.75, 0.12, 111.11) (1.36, 0.82, 11.0)
	Face_Sad	(1.87, 0.19, 78.62) (1.48, 0.87, 7.52)

2 Duo 3.16G PC with 4G RAM and

RR n°7676

The source code and executable for the CUDA implementation of the high-order MRF optimization can be downloaded from http://www.cs.sunysb.edu/~yzeng/software_HighorderMRF.html RR n°7676

A rigorous formulation can be found in the Appendix.RR n°7676

The source code for CUDA implementation of the MRF optimization algorithm and the executables used in our comparison between CPU and GPU implmentations can be downloaded from http://www.cs.sunysb.edu/~yzeng/software_HighorderMRF.html.INRIA

http://meshlab.sourceforge.net/ RR n°7676

Appendix 7.1 A. Theoretical analysis of the canonical distortion coefficient

In this section, we give the rigorous definitions for characterizing arbitrary diffeomorphisms between two surfaces using Riemannian geometry. Specifically, we give the precise meaning of "deformation of a unit circle into an eclipse" mentioned in the paper and explain why it is able to represent arbitrary deformations. We also connect our canonical distortion coefficient to the Beltrami-coefficient defined in quasi-conformal mapping theory. Most of our notations and definitions are adapted from the classic textbooks [START_REF] Manfredo | Differential Geometry of Curves and Surfaces[END_REF], [START_REF] Frankel | The Geometry of Physics-An Introduction[END_REF] and [START_REF] Ahlfors | Lectures on Quasiconformal Mappings[END_REF].

INRIA by following the primal-dual formulate of Eq. 29, we have the dual problem of the LP problem (Eq. 30):

If we define the reparametrization

we have for any u ∈ V

and for all (u, v, w) ∈ F

Hence the dual optimization problem of Eq. 34 can be equivalently formulated as

s.t. θ u;i = θ u;i + (u,v,w)∈F M uvw;u:i , ∀u ∈ V and i ∈ L θ uvw;ijk = θ uvw;ijk -M uvw;u:i -M uvw;v:j -M uvw;w:k , ∀(u, v, w) ∈ F and (i, j, k) ∈ L × L × L.

An efficient algorithm for finding independent face sets

Alg. [START_REF] Brenner | The Mathematical Theory of Finite Element Methods[END_REF] shows the algorithm that decomposes a third-order graph G = (V, F) into subsets of independent face sets defined in Sec. 4.2 in the paper. To see to complexity of this algorithm, for each iteration of step two, it take O(| max(V, F)|) to traverse all the faces to construct a new independent face set. The total number of iterations depends on the total number of decomposed sets (< O(|F|)). Hence the worst case complexity of this algorithm is O(|V||F|). However in practice the number of iterations is expected to be very small.

Algorithm 4:

Greedy algorithm for independent face sets.

Input : A third-order graph G = (V, F ). Output : Decomposition of F into independent face sets ∪iFi.

Step One: Initialization.

Step Two: Find maximal independent face set among the un-visited faces.


Keywords: MALT-type lymphoma of the urinary bladder, primary lymphoma of the bladder, urinary bladder neoplasms, ultrasonography of the urinary bladder MALT-type lymphoma of the bladder; urinary bladder neoplasms, ultrasonography of the urinary bladder

Incidental sonographic detection of mucosa-associated lymphoid tissue lymphoma

Introduction

Primary MALT (mucosa -associated lymphoid tissue) -type lymphomas of the urinary bladder are extremely rare. Only four cases have been found in the medical records of the University of Toronto in a 30 year period [1]. Six cases were registered in the Scotland and Newcastle lymphoma group database [2]. Seven patients were identified in the Mayo Clinic's Tissue Registry records between 1940 and 1996 [3]. We present another case of the rare MALT-type lymphoma of the urinary bladder, found incidentally on ultrasonography. This is the first such case to be diagnosed in our department of urology within its 14 years of experience.

Case report

A 17-year-old woman was referred to our department of urology for the treatment of her urinary bladder tumour, which was incidentally discovered in the course of diagnostic tests performed in a paediatric hospital for hypertension. As part of the investigations of hypertension, abdominal ultrasonography was performed, and showed a small atrophic right kidney -measuring 56x22 mm -with irregular outlines and segmental lack of parenchyma (Fig. 1). It was associated with compensatory hypertrophy of the left kidney, which measured 132x67 mm along its long axis (Fig. 2). Dynamic scintigraphy confirmed atrophy of the right kidney, showing it to have only 8% of the normal kidney function. The renal scintigraphy curve for this organ was flat. The GFR of the right kidney was 46-48 ml/min, while that of the left kidney was 564-589 ml/min.

The decision was made to perform right nephroureterectomy. Before the operation, in the aim of obtaining a fuller evaluation of the urinary tract, urinary bladder ultrasonography was done; this showed an exophytic, hypoechoic lesion, located on the posterior wall of the bladder, medially to the left ureteral orifice. The patient was completely asymptomatic. The lesion, measuring 36 x 15 mm, had a broad base, a solid echotexture, and a nodular surface, with 3 nodules being visible (Fig. 3). Cystoscopy revealed a submucosal lesion with a nodular surface upon a wide base, covered by normal epithelium (Fig. 4). Transurethral resection (TUR) of the lesion was performed. Specimens obtained by transurethral biopsy were diagnosed as extranodal marginal zone B-cell lymphoma of the MALT-type. Immunohistochemical staining was specific for a MALT-type lymphoma, being DES -, LCA+, CD3+, CD20+, Ki 67 in 25% of the cells, and BCL 2 + (Fig. 5AB). An abdominal CT, apart from the small atrophic right kidney and the compensatory hypertrophy of the left, did not reveal any other pathologies in the abdominal cavity. The bone marrow biopsy and spinal fluid analysis were normal, all together confirming the diagnosis of so-called localized bladder disease [1]. TUR of the tumour was followed by adjuvant treatment, with the patient undergoing 8 courses of chemotherapy -the regimen consisting of vincristine, cyclophosphamide, and prednisolone (COP). The patient underwent follow-up sonography and cystoscopy 3, 9, 12 and 24 months after completing chemotherapy, and had no signs nor symptoms of recurrence. A follow-up CT of the abdomen and pelvis was performed 3 and 12 months after the chemotherapy, and also did not reveal any lymphatic abnormalities. The patient was then referred for right laparoscopic nephroureterectomy, as treatment of her hypertension.

Discussion

Bladder ultrasonography allows for the visualization of 95% of exophytic changes with a diameter > 0,5 cm within the urinary bladder (4). This holds incredible significance, as currently the majority of neoplastic changes of the urinary tract are asymptomatic (5). This was true of the presented case of the very rare MALT-type lymphoma, found incidentally upon urinary bladder ultrasonography. The few cases of MALT-type lymphomas reported in the scientific literature, occurred mostly in women between the ages of 22 and 83 years (mean 65.5) [1,3,[6][7][START_REF] Takahara | Primary mucosa-associated lymphoid tissue (MALT) lymphoma of the urinary bladder[END_REF][START_REF] Fujimura | Regression of mucosa-associated lymphoid tissue lymphoma of the bladder after antibiotic therapy: a case report[END_REF][START_REF] Ueno | Mucosa-associated lymphoma of the bladder with relapse in the stomach after successful treatment[END_REF][START_REF] Gallardo | Malt lymphoma of the bladder: report of a case[END_REF]. Our 17-year-old female was therefore the first such young patient described with this type of malignancy. The tumour was asymptomatic, although the most common presenting symptom of this disease in patients described in the literature was heamaturia [START_REF] Gallardo | Malt lymphoma of the bladder: report of a case[END_REF]12]. Less frequently reported signs or symptoms were: recurrent urinary tract infections, dysuria, malaise, weight loss, and urinary retention [7,[START_REF] Takahara | Primary mucosa-associated lymphoid tissue (MALT) lymphoma of the urinary bladder[END_REF][START_REF] Gallardo | Malt lymphoma of the bladder: report of a case[END_REF]. As far as we know, only one other team had reported an asymptomatic MALT-type bladder lymphoma, incidentally diagnosed in the course of diagnostic tests for ovarian cancer [START_REF] Ueno | Mucosa-associated lymphoma of the bladder with relapse in the stomach after successful treatment[END_REF].

In our case, the broad-base tumour was very well visualized on urinary bladder ultrasonography. However, sonography is not a very specific examination, and the diagnosis is always determined from a histopathological assessment of specimens obtained from transurethral bladder tumour biopsy.

It is unknown what is the best treatment approach for a low -grade MALT lymphoma of the urinary bladder, and the topic remains controversial [2,3]. Taking into consideration the therapeutic efficacy of systemic chemotherapy and the quality of life of our young 17 year-old patient, TUR of the lesion was followed by adjuvant chemotherapy, and resulted in complete remission of the mass. Two years after the diagnosis of MALT lymphoma, she remains disease-free. Ultrasonography, aside from the preliminary diagnosis, was a sensitive diagnostic tool in the follow-up examinations.

In summary, the presented case of an incidentally-found MALT -type lymphoma of the urinary bladder by urinary bladder sonography, along with the more frequently encountered asymptomatic neoplastic changes of the urinary tract, would support making sonographic examination of the urinary system-including the urinary bladder-an integral part of the abdominal cavity ultrasound.

Abstract

We present yet another a rare case of a MALT-type (mucosa-associated lymphoid tissue) lymphoma of the bladder, incidentally found on vesical sonography of a 17-year-old woman.

The tumour was incidentally found during preoperative abdominal sonography.The diagnosis was determined based upon histopathological assessment of specimens obtained from transurethral tumour biopsy. Transurethral resection of the bladder tumour and subsequent chemotherapy has turned out in our case to be a successful treatment. In the context of reports published so far, this is the youngest case, and an asymptomatic one, of a MALT-type lymphoma of the urinary bladder. The tumour was an incidental finding upon urinary bladder sonography, which in light of the more frequently encountered asymptomatic neoplastic changes of the urinary tract, would indicate the need to include sonographic examination of the urinary system-in this of the urinary bladder-as an integral part of the abdominal ultrasound.

. Key words: MALT-type lymphoma of the bladder; primary lymphoma of the bladder; urinary bladder neoplasms, ultrasonography of the urinary bladder Newcastle lymphoma group database [2]. Seven patients were identified in the Mayo Clinic's Tissue Registry records between 1940 and 1996 [31]. We present another case of the rare MALT-type lymphoma of the urinary bladder, found incidentally on ultrasonography. This is the first such case to be diagnosed in our department of urology within its 14 years of experience.

Case report

A 17-year-old woman was referred to our department of urology for the treatment of her urinary bladder tumour, which was incidentally discovered in the course of diagnostic tests performed in a paediatric hospital for hypertension. As part of the investigations of hypertension, abdominal ultrasonography was performed, and showed a small atrophic right kidney -measuring 62 x 28 x 37 mm -with irregular outlines and segmental lack of parenchyma (Fig. 1). It was associated with compensatory hypertrophy of the left kidney, which measured 14 cm along its long axis (Fig. 2). Dynamic scintigraphy confirmed atrophy of the right kidney, showing it to have only 8% of the normal kidney function on scintigraphy.

CT of the abdomen delineated right renal atrophy On voiding cystography, grade I vesicoureteral reflux was seen bilaterally. Abdominal ultrasound examination performed before planned right laparoscopic nephroureterectomy showed a nodular, exophyticr The decision was made to perform right nephroureterectomy. Before the operation, in the aim of obtaining a fuller evaluation of the urinary tract, urinary bladder ultrasonography was done; this showed an exophytic, hypoechoic lesion, located on the posterior wall of the bladder, medially to the 3 left ureteral orifice. The patient was completely asymptomatic. The lesion, measured 36 mm, measuring 36 x 15 mm, had a broad base, a solid echotexture, and a nodular surface, with 3 nodules being visible 3 nodules were seen (Fig. 23). Cystoscopy revealed a submucosal lesion with a nodular surface upon a wide base, covered by normal epithelium (Fig. 43).

Transurethral resection (TUR) of these lesions was performed. Specimens obtained by transurethral biopsy were diagnosed as extranodal marginal zone B-cell lymphoma of the MALT-type. Immunohistochemical staining was specific for a MALT-type lymphoma, being DES -, LCA+, CD3+, CD20+, Ki 67 in 25% of the cells, and BCL 2 + (Fig. 35AB). An abdominal CT, apart from the small atrophic right kidney and the compensatory hypertrophy of the left, did not reveal any other pathologies in the abdominal cavity. The bone marrow biopsy and spinal fluid analysis were normal, all together confirming the presence of so-called localized bladder disease [1]. TUR of the tumour was followed by adjuvant treatment, with the patient undergoing 8 courses of chemotherapy -the regimen consisting of vincristine, cyclophosphamide, and prednisolone (COP). After completing chemotherapy, the patient was readmitted for cystoscopy which has not revealed any suspicious lesions, and cold cup biopsy was taken from a scar tissue following the previous intervention. Histopatological examination of tissue obtained by TUR was negative.

The patient underwent follow-up sonography and cystoscopy 3, 9, 12 and 24 months after completing chemotherapy TUR, and had no signs nor symptoms of recurrence. A follow-up CT of the abdomen and pelvis was performed 3 and 12 months after the chemotherapy, and also did not reveal any lymphatic abnormalities. The patient was then referred for right laparoscopic nephroureterectomy, as treatment of her hypertension.

Discussion

Bladder ultrasonography allows for the visualization of 95% of exophytic changes with a diameter > 0,5 cm within the urinary bladder (4). This holds incredible significance, as currently the majority of neoplastic changes of the urinary tract are asymptomatic (5). This was true of the presented case of the very rare MALT-type lymphoma, found incidentally upon urinary bladder ultrasonography. The few cases of MALT-type lymphomas described in the scientific literature, occured mostly MALT-type lymphomas of the bladder usually occured in women between the ages of 22 and 83 years (mean 65.5) [1,3,[6][7][START_REF] Takahara | Primary mucosa-associated lymphoid tissue (MALT) lymphoma of the urinary bladder[END_REF][START_REF] Fujimura | Regression of mucosa-associated lymphoid tissue lymphoma of the bladder after antibiotic therapy: a case report[END_REF][START_REF] Ueno | Mucosa-associated lymphoma of the bladder with relapse in the stomach after successful treatment[END_REF][START_REF] Gallardo | Malt lymphoma of the bladder: report of a case[END_REF]. Our 17-yearold female was therefore the first such young patient described with this type of malignancy.

The tumour was asymptomatic, although the most common presenting symptom of this disease in patients reported in the literature was heamaturia [START_REF] Gallardo | Malt lymphoma of the bladder: report of a case[END_REF]12]. Less frequently reported signs or symptoms are were: recurrent urinary tract infections, dysuria, malaise, weight loss, and urinary retention [7,[START_REF] Takahara | Primary mucosa-associated lymphoid tissue (MALT) lymphoma of the urinary bladder[END_REF][START_REF] Gallardo | Malt lymphoma of the bladder: report of a case[END_REF]. As far as we know, only one other team had reported an asymptomatic MALT-type bladder lymphoma, incidentally diagnosed in the course of diagnostic tests for ovarian cancer [START_REF] Ueno | Mucosa-associated lymphoma of the bladder with relapse in the stomach after successful treatment[END_REF].

In our case, the broad-base tumour was very well visualized on urinary bladder ultrasonography. However, sonography is not a very specific examination, and the diagnosis is Preoperative differential sonographic diagnosis most commonly includes transitional cell bladder carcinoma [3], however in our young patient rhabdomyosarcoma was rather suspected I zawsze diagnosis was always determined from a histopathological assessment of specimens obtained from transurethral bladder tumour biopsy.

It is unknown what is the best treatment approach for a low -grade MALT lymphoma of the urinary bladder, and the topic remains controversial [2,3]. ]. Some limit their management to observation alone [3], others perform the TUR of the tumor only, or administer chemotherapy

8 .

 8 Fig.1. Ultrasonography shows an atrophic right kidney in the longitudinal plane. The organ is

Fig. 2 .

 2 Fig. 2. Hyperthropic left kidney measuring 132x67 mm along its long axis.

Fig. 3 .

 3 Fig. 3. Urinary bladder sonography shows an exophytic, nodular lesion upon a broad base,

Fig. 4 .

 4 Fig. 4. Cystoscopy presents a nodular submucosal lesion covered by normal epithelium.

7 Fig. 5 .

 75 Fig. 5. Immunostaining shows (A) neoplastic cells presenting LCA (Leucocyte Common

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 . 1

 12341 Fig.1. Ultrasonography shows an atrophic right kidney in the longitudinal plane. The organ is small, measuring 56x22 mm, segmentally lacks parenchyma, and has increased echogenicity compared to the liver.

  mucosa -associated lymphoid tissue) -type lymphomas of the urinary bladder are extremely rare. Only four cases have been found in the medical records of the University of Toronto in a 30 year period[13]. Six cases were registered in the Scotland and

5 or

 5 local radiotherapy, or chemotherapy with whole bladder irradiation, as well as innovative treatment with antibiotics to eradicate possible co-pathogenic Helicabacter pylori, sometimes combined with diathermy[1,2,5,[START_REF] Fujimura | Regression of mucosa-associated lymphoid tissue lymphoma of the bladder after antibiotic therapy: a case report[END_REF]. Taking into consideration the therapeutic efficacy of systemic chemotherapy and the quality of life of our young 17 year-old patient, TUR of the lesion was followed by adjuvant chemotherapy, and resulted in complete remission of the mass. Two years after the diagnosis of MALT lymphoma, she remains disease-free.Ultrasonography, aside from the preliminary diagnosis, was a sensitive diagnostic tool in the follow-up examinations.In summary, the presented case of an incidentally-found MALT -type lymphoma of the urinary bladder by urinary bladder sonography, along with the more frequently encountered asymptomatic neoplastic changes of the urinary tract, would support making sonographic examination of the urinary system-including the urinary bladder-an integral part of the abdominal cavity ultrasound.

Fig. 1 .

 1 Fig.1. Ultrasonography shows an atrophic right kidney in the longitudinal plane..The organ is

Fig. 2 .

 2 Fig. 2. Hyperthropic left kidney measuring 132x67 mm along its long axis.

Fig. 3 .

 3 Fig.3. Urinary bladder sonography shows an exophytic, nodular lesion upon a broad base,

Fig. 4 .

 4 Fig. 4. Cystoscopy presents a nodular submucosal lesion covered by normal epithelium.

Fig. 5 .

 5 Fig. 5. Immunostaining shows (A) neoplastic cells presenting LCA (Leucocyte Common

John Wiley & SonsJournal of Clinical Ultrasound


Dr Emmanouil Galanakis

Sofia Maraki

George Samonis

Keywords: antimicrobial resistance, children, clinical isolates, Greece, Streptococcus pneumoniae, pneumococcal vaccine coverage

All Streptococcus pneumoniae strains isolated from paediatric clinical samples at Heraklion University General Hospital in the 10-year period 2000-2009 were tested for serotype and susceptibility to antimicrobials. Among a total of 258 strains, 159 were isolated in the 5-year period 2000-2004, before the heptavalent pneumococcal conjugate vaccine (PCV7) introduction and 99 in the post-PCV7 5-year period [2005][2006][2007][2008][2009]. Prevalence of PCV7-included serotypes decreased in the post-PCV7 period (p=0.0002), but increase was observed for serotypes 7F (p=0.002) and 19A (p=0.004). Pan-susceptibility rates and susceptibility to cotrimoxazole increased in the post-PCV7 period (p=0.01 and p=0.008, respectively), but serotype 19A emerged as a contributor to multiresistance (p=0.007). PCV7 was followed by decreased S. pneumoniae resistance and prevalence of vaccine-related serotypes but increased prevalence of serotypes 7F and 19A. Continuing surveillance is required after the recent introduction of PCV10 and PCV13.

List of responses, Ms. No. EJCMID-D-10-00179

Serotypes and susceptibilities of paediatric clinical isolates of Streptococcus pneumoniae in Crete, Greece before and after the heptavalent pneumococcal conjugate vaccine Reviewer #1: Comment. This study examines the occurrence of individual pneumococcal serotypes and emergence of antimicrobial resistance, or not, before and after the introduction and widespread use of the pediatric seven-valent protein conjugated pneumococcal vaccine (PCV-7) on the Island of Crete. The group of invasive strains, blood, cerebrospinal fluid (CSF) and middle ear fluid, is only one-fourth of the total 258 strains reported and the respiratory tract strains represent more than one-half of the strains. It is difficult to judge whether a strain recovered from the respiratory tract is the pathogen or not. Thus, in published studies, PCV-7 vaccine efficacy has been estimated only using invasive strains. In this manuscript, analyzing invasive and non-invasive strains together distorts the effect of PCV-7 on invasive strains. Comment? Response. We agree that up to date PCV-7 efficacy studies have mainly focused on invasive strains; however important studies investigating seroprevalence and resistance rates nasopharyngeal rate have appeared as well. In any case, in response to this comment we added (Results and Discussion, last paragraph, sentence 3): "The study included all clinical isolates rather than invasive strains or nasopharyngeal carriage samples alone, and this limitation did not allow for a reliable comparison of the PCV-7 efficacy results to previously reported findings."

Comment. The number of invasive strains recovered seems very low for ten years of surveillance. I estimated the pediatric population of Crete about 200,000 or about onethird of the total population. The low rates raises the question of whether all (or nearly all) patients admitted to hospital or treated in an emergency department for serious respiratory disease have blood cultures done. Comment? Response. We do understand this comment; however the child population in Crete is actually 130,000. It is also true that the frequency of obtaining blood cultures does vary from country to country, but our study focused on the seroprevalence trends rather than the precise incidence per se. Nevertheless, following this comment we added data about the child population in Crete (Patients and Methods, paragraph 1, sentence 2): "The Hospital is the referral centre for the island of Crete with a coverage population of 631,000, of whom 130,000 are children aged less than 14 years."

Comment. Were physicians more likely to test for invasive pneumococcal strains in the five-year period after the introduction of vaccine as the numbers of strains were more in the second five-year period compared with the first five-year period even though the total number of strains recovered in the second five-year period was less than in the first fiveyear period? Response. It is true that broad introduction of a vaccine increases awareness of the disease but we do not find that this awareness would only lead to increase of invasive strains and not of strains as a total. In order to stress this point and to avoid confusion we added (Results and Discussion, last paragraph, sentence 6): "Invasive disease and otitis media isolates appeared to be more common in the vaccine period, but it is questionable Authors' Response to Reviewers' Comments Click here to download Authors' Response to Reviewers' Comments: S pneum-EJCMID-Responses.doc

whether this increase should be attributed to the small sample size or to increased awareness of pneumococcal disease following the introduction of PCV7, rather than to a real increase in disease."

Comment. Abstract, page 2: In my copy of the manuscript, the notations between p and the value are missing. For example, line 9, p 0.0002, is p=0.0002 meant here? Also, even though the authors note that "susceptibility rate increased for erythromycin," the p value of 0.08 is not significant. Comment?

of data from Crete and there are few data on this topic from Greece or other Mediterranean areas. The other unique aspect is the apparent increase in isolation of pneumococcal isolates after the introduction of PCV7. However the authors provide no information to explain this apparent increase which may be an artefact. Response. Following this point and a similar point by Reviewer#1, we added (Results and Discussion, last paragraph, sentence 6): "Invasive disease and otitis media isolates appeared to be more common in the vaccine period, but it is questionable whether this increase should be attributed to the small sample size or to increased awareness of pneumococcal disease following the introduction of PCV7, rather than to a real increase in disease."

Comment. The first main limitation of this study is that the overall sample size from 10 years is small (n=258) and the proportion of the isolates that came from invasive isolates is very small (28) so most of the data are from non-invasive isolates about which no clinical data is provided. Response. We agree that this is a major limitation of our study; to accommodate this issue, we added (Results and Discussion, last paragraph, sentencew 2 and 3): "Limitations of this study include the small cohort of isolates and the retrospective design which did not allow for investigation of factors potentially affecting seroprevalence and susceptibility besides the introduction of PCV7. The study included all clinical isolates rather than invasive strains or nasopharyngeal carriage samples alone, and this limitation did not allow for a reliable comparison of the PCV-7 efficacy results to previously reported findings."

Comment.

The second main limitation is that no demographic information is provided about the pediatric population on Crete, no clinical data is provided and there is no explanation of clinical and laboratory practices related to the collection of non-invasive specimens. So the reader cannot understand if the numbers of isolates obtained were influenced by any factors besides the introduction of PCV7. Response. In response to this comment, we added information about the child population in Crete (Patients and Methods, paragraph 1, sentence 2): "The Hospital is the referral centre for the island of Crete with a coverage population of 631,000, of whom 130,000 are children aged less than 14 years." On the other hand it is true that the retrospective design does not allow for investigation of confounding factors potentially affecting pneumococcal seroprevalence besides the introduction of PCV7 and, as already mentioned, this was acknowledged in Results and Discussion, last paragraph, sentence 2): "Limitations of this study include the small cohort of isolates and the retrospective design which did not allow for investigation of factors potentially affecting seroprevalence and susceptibility besides the introduction of PCV7." Some specific comments include the following: Comment. Page 3/line 34. Do the authors have any data on PCV7 vaccination rates on Crete? Response. No published data exist on PCV7 vaccination rates in Crete; however given the nationwide implementation of the vaccine we do believe that the rates from other areas of Greece apply to Crete. In response to this comment we modified the text (Introduction, first paragraph, sentence 3) to: "In Greece, PVC7 became available in 2004 and was introduced for all children younger than 5 years of age in January 2006. Vaccination compliance has been high nationwide with reported rates of up to 98% [START_REF] Grivea | Impact of heptavalent pneumococcal conjugate vaccine on nasopharyngeal carriage of penicillinresistant Streptococcus pneumoniae among day-care center attendees in central Greece[END_REF]."

Comment. Page 3/line 44. How were "children" defined? The results include and age range from 15 days to 14 years of age. What was the upper limit of age? Response. Age definition was added (Patients and Methods, first paragraph, sentence 2): The Hospital is the referral centre for the island of Crete with a coverage population of 631,000, of whom 130,000 are children aged less than 14 years.

Comment. Page 3/line 49ff. What were the clinical and laboratory practices related to collection of both invasive and non-invasive specimens over the course of the study and were there any changes? In addition, what was the trend in population of children on Crete during the study. Although this study does not report disease rates and is not population-based, the authors note the near doubling of invasive isolates in the period after PCV7 introduction compared with before (18/99 vs 10/159) as well as an increase in isolates from middle ear fluid (24/99 vs 15/159). Could these apparent increases be related to changes in clinical or laboratory practices, or population, as opposed to reflecting a real increase in disease? Are there clinical data about the children from whom the isolates were obtained? Response. Due to the retrospective design of the study and due to the fact that specimens originated from more than one health care facilities we could not reliably investigate changes in collection of invasive and non-invasive specimens. In order to stress this uncertainty which was also noted by Reviewer#1, we added (Results and Discussion, last paragraph 4, sentence 6): "Invasive disease and otitis media isolates appeared to be more common in the vaccine period, but it is questionable whether this increase should be attributed to the small sample size or to increased awareness of pneumococcal disease following the introduction of PCV7, rather than to a real increase in disease." Furthermore, as already stated, these limitations were appropriately stressed in Results and Discussion, last paragraph 4, sentence 2): Limitations of this study include the small cohort of isolates and the retrospective design which did not allow for investigation of factors potentially affecting seroprevalence and susceptibility besides the introduction of PCV7.. 2. It is incorrect to state that "rates of nonsusceptibility in the vaccine period were lower for the majority of antibiotics assayed..." There was a statistically significant (P<0.05) change for only one antibiotic (cotrimoxazole) and near-significant changes for 4 others. Response. Following this comment we modified the text (Results and Discussion, paragraph 3, first sentence) to: "Non-susceptibility rates were significantly lower in the vaccine than in the pre-vaccine period for cotrimoxazole (20.2% vs. 36.5%; p 0.008; OR 0.44; 95% CI 0.24-0.79) and near-significantly lower for erythromycin (p 0.081)." 2 Abstract All Streptococcus pneumoniae strains isolated from paediatric clinical samples at Heraklion University General Hospital in the 10-year period 2000-2009 were tested for serotype and susceptibility to antimicrobials. Among a total of 258 strains, 159 were isolated in the 5-year period 2000-2004, before the heptavalent pneumococcal conjugate vaccine (PCV7) introduction and 99 in the post-PCV7 5-year period 2005-2009. Prevalence of PCV7-included serotypes decreased in the post-PCV7 period (p=0.0002), but increase was observed for serotypes 7F (p=0.002) and 19A (p=0.004). Pan-susceptibility rates and susceptibility to cotrimoxazole increased in the post-PCV7 period (p=0.01 and p=0.008, respectively), but serotype 19A emerged as a contributor to multiresistance (p=0.007). PCV7 was followed by decreased S. pneumoniae resistance and prevalence of vaccine-related serotypes but increased prevalence of serotypes 7F and 19A. Continuing surveillance is required after the recent introduction of PCV10 and PCV13.

Comment. Page 7/line 31 and Table

Introduction

The introduction of heptavalent pneumococcal conjugated vaccine (PCV7) has resulted in decrease of pneumococcal infections, but reports on increase of potentially invasive and resistant strains necessitate the surveillance of S. pneumoniae isolates [START_REF] Isaacman | Burden of invasive pneumococcal disease and serotype distribution among Streptococcus pneumoniae isolates in young children in Europe: impact of the 7-valent pneumococcal conjugate vaccine and considerations for future conjugate vaccines[END_REF].

Information on the impact of the implementation of PCV7 into the immunization programs comes mainly from the USA and Canada, and in a lesser degree from Europe [START_REF] Maraki | Antimicrobial resistance and serotype distribution of Streptococcus pneumoniae isolates from Crete, Greece[END_REF][START_REF] Zissis | Serotype distribution and antimicrobial susceptibility of Streptococcus pneumoniae causing invasive infections and acute otitis media in children[END_REF][START_REF] Paraskakis | National Surveillance Network for Pneumococcal Resistance (2006) Serotypes and antimicrobial susceptibilities of 1033 pneumococci isolated from children in Greece during 2001-2004[END_REF][START_REF] Grivea | Impact of heptavalent pneumococcal conjugate vaccine on nasopharyngeal carriage of penicillinresistant Streptococcus pneumoniae among day-care center attendees in central Greece[END_REF][START_REF] Grivea | Interaction of the heptavalent pneumococcal conjugate vaccine and the use of individual antibiotics among children on nasopharyngeal colonization with erythromycin-resistant Streptococcus pneumoniae[END_REF][START_REF] Whitney | Effectiveness of seven-valent pneumococcal conjugate vaccine against invasive pneumococcal disease: a matched case-control study[END_REF][START_REF] Fenoll | Temporal trends of invasive Streptococcus pneumoniae serotypes and antimicrobial resistance patterns in Spain from 1979 to 2007[END_REF]. In Greece, PVC7 became available in 2004 and was introduced for all children younger than 5 years of age in January 2006. Vaccination compliance has been high nationwide with reported rates of up to 98% [START_REF] Grivea | Impact of heptavalent pneumococcal conjugate vaccine on nasopharyngeal carriage of penicillinresistant Streptococcus pneumoniae among day-care center attendees in central Greece[END_REF]. Crete is the southernmost point of Europe and the second major island in the Eastern Mediterranean basin. In this study we investigated the circulating S. pmeumoniae serotypes and the trends in antimicrobial susceptibility of clinical isolates form children pre-and post the PCV7 introduction.

Patients and methods

This study included all paediatric S. pneumoniae specimens which were cultured, serotyped and tested for susceptibility to antimicrobials in the Laboratory of Microbiology at the University General Hospital, Heraklion, Greece for the 10-year period January 2000 through December 2009. The Hospital is the referral centre for the island of Crete with a coverage population of 631,000, of whom 130,000 are children aged less than 14 years. Invasive pneumococcal disease isolates were recovered from blood or CSF, and otitis media isolates from middle ear fluid. One isolate per patient was identified and tested. Samples were immediately plated after collection on chocolate agar and Columbia agar plates (Becton Dickinson, Sparks, MD) supplemented with 5% sheep blood and incubated at 35ºC in an atmosphere of 5% CO 2 in air for 24-72 hours. For blood cultures, the automated BacT/Alert system pneumoniae ATCC 49619 (penicillin-resistant) were used as control strains. Data were compared using Fisher exact probability test. Odds ratios (OR) and 95% confidence intervals (CI) were calculated. Statistical significance was set at two-tailed p<0.05.

Results and discussion

A total of 258 clinical isolates were collected from 140 boys and 118 girls. Children age ranged 15 days to 14 (mean, 3.16; median, 2.0) years. Isolates represented blood (23), cerebrospinal fluid (5), middle ear fluid (39), nasopharyngeal swabs (132), ocular secretions (43), sputum [START_REF] Grivea | Interaction of the heptavalent pneumococcal conjugate vaccine and the use of individual antibiotics among children on nasopharyngeal colonization with erythromycin-resistant Streptococcus pneumoniae[END_REF], bronchoalveolar lavage [START_REF] Grivea | Interaction of the heptavalent pneumococcal conjugate vaccine and the use of individual antibiotics among children on nasopharyngeal colonization with erythromycin-resistant Streptococcus pneumoniae[END_REF], and pus (4). 159 (61.6%) isolates were collected during the pre-vaccine 5-year period 2000-2004 and 99 (38.4%) during the vaccine 5-year period 2005-2009. Blood and CSF isolates were more common in the vaccine period (18/99 vs. 10/159; 18.2% vs. 6.29%; p 0.004; OR 3.31, 95% CI 1.46-7.51) as were middle ear fluid isolates (24/99 vs. 15/159; 24.2% vs. In the vaccine period decrease was observed for serotypes included in the PCV7 (Table 1), but increase was observed for the PCV10-included 7F, the PCV13-included 19A, and for the total of serotypes not included in PCV7, PCV10, or PCV13 (25 vs. 21 isolates; 25.3% vs. 13.2%; p 0.019; OR 2.22, 95% CI 1.16-4.23). Coverage by PCV7 was 69.2% for the pre-vaccine period, but coverage for the vaccine period by the 7valent, 10-valent, and 13-valent PCV were 45.5%, 56.6%, and 75.5% of clinical isolates, respectively. Prevailing serotypes for invasive infection were 19F (3/10) in the pre-vaccine and 7F (7/18) in the vaccine period. The prevailing serotype for otitis media was 19F both in the in the pre-vaccine (4/15), and in the vaccine period (10/24). Non-susceptibility rates were significantly lower in the vaccine than in the prevaccine period for cotrimoxazole (20.2% vs. 36.5%; p 0.008; OR 0.44; 95% CI 0.24-0.79) and near-significantly lower for erythromycin (p 0.081). 124/258 isolates (48.1%) were susceptible to all antibacterials tested, and this pan-susceptibility was more common in the vaccine than in the pre-vaccine period (58/99 vs. 66/159; 58.6% vs. 41.5%; p 0.01, OR 1.99, 95% CI 1.20-3.32). The overall high-level resistance rates were 17.1% for penicillin, 26.4% for cefuroxime and 0% for cefotaxime and ceftriaxone.

Among 91 isolates resistant to erythromycin, phenotypes M, cMLS B, and iMLS B were detected in 62, 25, and 4 isolates respectively. Invasive and non-invasive isolates had similar susceptibility patterns. Ocular strains were more penicillin-sensitive than invasive and middle ear strains (72.1% vs. 52.2%; p 0.01; OR 2.36, 95% CI 1.04-5.47).

Ultrahigh penicillin resistance (MIC 4 g/mL) was observed in 11/258 isolates (4.28%), of whom 9 were serotyped as 19F. Ciprofloxacin MIC of >3 mg/L was observed in 6 13/258 isolates. Among common serotypes in the vaccine period, serotype 19A was often non-susceptible to penicillin, cefuroxime, and erythromycin (84.6%, 69.2%, and 76.9%, respectively), but serotype 7F was sensitive to all antimicrobials tested. Multiresistance (penicillin, erythromycin, cotrimoxazole and tetracycline) rates were similar in the pre-vaccine and the vaccine period (13.8% and 15.2%, respectively). The principal multiresistant serotype in the pre-vaccine period was 19F (16/22, 72.7% deceasing to 7/15, 46.7% in the vaccine period). Serotype 19A was a significant contributor to multiresistant strains in the vaccine as compared to the pre-vaccine period (5/15 vs. 0/22, 33.3% vs. 0%; p 0.007).

The introduction and the high uptake of PCV7 in the study area and the ability to centrally test clinical isolates provided the tools to investigate the effects of vaccine introduction in a well-defined population. Limitations of this study include the small cohort of isolates and the retrospective design which did not allow for investigation of factors potentially affecting seroprevalence and susceptibility besides the introduction of PCV7. The study included all clinical isolates rather than invasive strains or nasopharyngeal carriage samples alone, and this limitation did not allow for a reliable comparison of the PCV-7 efficacy results to previously reported findings. Serotypes of S. pneumoniae isolates were similar to these reported elsewhere in Greece [START_REF] Maraki | Antimicrobial resistance and serotype distribution of Streptococcus pneumoniae isolates from Crete, Greece[END_REF][START_REF] Zissis | Serotype distribution and antimicrobial susceptibility of Streptococcus pneumoniae causing invasive infections and acute otitis media in children[END_REF][START_REF] Paraskakis | National Surveillance Network for Pneumococcal Resistance (2006) Serotypes and antimicrobial susceptibilities of 1033 pneumococci isolated from children in Greece during 2001-2004[END_REF][START_REF] Grivea | Impact of heptavalent pneumococcal conjugate vaccine on nasopharyngeal carriage of penicillinresistant Streptococcus pneumoniae among day-care center attendees in central Greece[END_REF][START_REF] Grivea | Interaction of the heptavalent pneumococcal conjugate vaccine and the use of individual antibiotics among children on nasopharyngeal colonization with erythromycin-resistant Streptococcus pneumoniae[END_REF]. In the pre-vaccine era, PCV7 coverage was 69.2% in the study area, but following decrease in vaccine-included serotypes, coverage by PCV7 in Crete dropped to 36.5% during the last 3 study years. Invasive disease and otitis media isolates appeared to be more common in the vaccine period, but it is questionable whether this increase should be attributed to the small sample size or to increased awareness of pneumococcal disease following the introduction of PCV7, rather than to a real increase in disease. Reports on invasive pneumococcal disease due to non-PCV7 serotypes have been controversial [ . Non-susceptibility rates of S. pneumoniae isolates were similar to rates already reported elsewhere in Greece [START_REF] Zissis | Serotype distribution and antimicrobial susceptibility of Streptococcus pneumoniae causing invasive infections and acute otitis media in children[END_REF][START_REF] Paraskakis | National Surveillance Network for Pneumococcal Resistance (2006) Serotypes and antimicrobial susceptibilities of 1033 pneumococci isolated from children in Greece during 2001-2004[END_REF]. No resistance was observed to fluoroquinolones, and third-generation cephalosporins were active throughout the study. The introduction of PCV10 and PCV13 will reasonably necessitate continued monitoring of S. pneumoniae seroprevalence, replacement of isolates by non-vaccine serotypes, and susceptibility patterns.

4 (

 4 BioMérieux, Durham, NC, USA) was used. S. pneumoniae isolates were identified on the basis of colonial and microscopic morphology, haemolytic activity on sheep blood agar medium, optochin susceptibility and bile solubility. All isolates were serotyped by the Quellung reaction using pooled and selected factor antisera from Statens Seruminstitut (SSI, Copenhagen, Denmark). Nineteen antimicrobial agents including 7 -lactams (penicillin, cefuroxime, cefotaxime, ceftriaxone, cefepime, imipenem and meropenen), 3 macrolides (erythromycin, clarithromycin, and roxithromycin), 4 quinolones (ciprofloxacin, moxifloxacin, levofloxacin, and sparfloxacin), clindamycin, cotrimoxazole, tetracycline, chloramphenicol, and vancomycin were assayed by E-test (AB Biodisk, Solna, Sweden). Results were interpreted according to the 2008 Clinical and Laboratory Standards Institute criteria. S. pneumoniae ATCC 6305 (penicillin-sensitive) and S.

and susceptibilities of paediatric clinical isolates of Streptococcus pneumoniae in Crete, Greece before and after the heptavalent pneumococcal conjugate vaccine

	1
	2 2
	3 3
	4 4
	5 5
	6 6
	7 7
	8 8
	9 10 11 12 13 14 15 16 17 18 19 20 9 10 11 12 13 14 15 16 17 18 19 20	Serotypes S. Maraki • G. Samonis • E. Galanakis
	21 21
	22 22
	23 23
	24 25 24 25	S. Maraki
	26 26
	27 27
	28 28
	29 29
	30 30
	31 31
	32 32
	33 33
	34 34
	35 35
	36 36
	37 37
	38 38
	39 39
	40 40
	41 41
	42 42
	43 43
	44 44
	45 45
	46 46
	47 47
	48 48
	49 49
	50 50
	51 51
	52 52
	53 53
	54 54
	55 55
	56 56
	57 57
	58 58
	59 59
	60 60
	61 61
	62 62
	63 63
	64 64
	65 65

  OR 3.31, 95% CI 1.62-6.78); by contrast non-invasive isolates were more common during the pre-vaccine period (134/159 vs. 57/99; 84.3% vs. 57.6%; p <0.0001, OR 3.95, 95% CI 2.20-7.08).

	5
	9.43%; p 0.001;
	1
	2
	3
	4
	5
	6
	7
	8
	9
	10
	11
	12
	13
	14
	15
	16
	17
	18
	19
	20
	21
	22
	23
	24
	25
	26
	27
	28
	29
	30
	31
	32
	33
	34
	35
	36
	37
	38
	39
	40
	41
	42
	43
	44
	45
	46
	47
	48
	49
	50
	51
	52
	53
	54
	55
	56
	57
	58
	59
	60
	61
	62
	63
	64
	65

  7,

	1
	2
	3
	4
	5
	6
	7
	8
	9
	10
	11
	12
	13
	14
	15
	16
	17
	18
	19
	20
	21
	22
	23
	24
	25
	26
	27
	28
	29
	30
	31
	32
	33
	34
	35
	36
	37
	38
	39
	40
	41
	42
	43
	44
	45
	46
	47
	48
	49
	50
	51
	52
	53
	54
	55
	56
	57
	58
	59
	60
	61
	62
	63
	64
	65

Table 1

 1 Serotype distribution of 258 clinical isolates of Streptococcus pneumoniae from children in Crete, 2000-2009 isolates in the period 2005-2009 as compared to isolates during 2000-2004; b serotype included in the PCV10; c serotype included in the PCV13; na, not appropriate; ns, not significant

	8
	1
	2
	3
	4
	5
	6
	7
	8
	9
	10
	11
	12
	13
	14
	15
	16
	17
	18
	19
	20
	21
	22
	23
	24
	25
	26
	27
	28
	29
	30
	31
	32
	33
	34
	35
	36
	37
	38
	39
	40
	41
	42
	43
	44
	45
	46
	47
	48
	49
	50
	51
	52
	53
	54
	55
	56
	57
	58
	59
	60
	61
	62
	63
	64
	65

a