François Sarradin
email: sarradin@cerma.archi.fr

Daniel Siret
email: siret@cerma.archi.fr

Gérard Hégron
email: hegron@cerma.archi.fr

Visual Analysis of Urban Environment

Introduction

This paper presents a survey of methods used to model and to analyse visual events in urban scenes. What we call a visual event is an event which occurs in the visual field while we are moving or while the scene is moving. This could be an object appearance or disappearance, or a shape, a colour, or a texture modification. But here, we mainly consider the visual events provided by objects set during a motion.

In the second section, we examine some methods to model the events that come inside our visual field, giving a first interpretation to a urban environment. This is done after showing methods to represent the visual field. In the third section, we focus on different methods used to analyse and to evaluate the visibility in urban environment. Finally, we conclude on the way each of these representations of visual perceptions and each of these visual analysis methods act, and in which way they could be extended.

Visual event representation

Representation of urban scenes can be made by symbolizing buildings, streets, places, etc. We can also add the visual events which appear as observers move in the streets. The visual events generate transitions in the observer visual field like appearance and disappearance of objects, colour changing, shape transformation, etc. They provide important information about the visual effects.

The purpose of this section is about the representation of visual events. First, we show 2D motionless projections of the visual field which can be used in this representation. Second, we present the visual event sequences acting by motion decomposition into pictures. Apart from all projection, Lynch and Thiel proposed a notation to describe the visual perception of space and motion, and the orientation sense. Then, we show 2D and 3D methods to determine visual events and regions where visual informations do not change.

2D projections of the visual field

Here, we study the visual field representations in a motionlessness context. Most of these representations use a geometrical projection in order to imitate what we see or how we record our visual world.

Perspective projection

The perspective projection study began with italian painters from Renaissance. They wished to create an illusion: their goal was to show objects in three dimensions inside their paintings. It is used in architecture or in image synthesis in order to give a realistic representation. It is also used in simulation for architectural and urban project in order to determine the sun lighting time or the incident energy from the sky [START_REF] Groleau | Solene : un outil de simulation des éclairements solaires et lumineux dans les projets architecturaux et urbains[END_REF].

According to Panofsky, the perspective projection is "the aptitude to represent several objects with the part of the space in which they are, so that the concept of material support of the picture is completely driven out by the concept of transparent plan, so that we believe, our glance crosses to plunge into an imaginary external space which would contain all these objects into an apparent succession and which would not be limited but only cut out by the edges of the picture" [START_REF] Panofsky | On the description of shape and spatial configuration inside buildings: convex patitions and their local properties[END_REF].

The main concept in perspective is this notion of transparent plan where the image of the scene is projected. Teller brings a definition to explain the perspective projection principles (Figure 1): "[…] The perspective projection method is defined as the intersection between the visual lines which link observer eye to points of the real world, and a plane staying at a distance D from observer eye and perpendicular to the vision direction." [START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF] Figure 1: Perspective projection for the same object at different distances.

However, Panofsky notices that the perspective representation involves two assumptions: on the one hand, a unique and motionless eye generates our vision; on the other hand, the intersection plane is an appropriate picture of our visual field [START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF]. In fact, the perspective representation is near the retinal image for a sufficient vision angle interval. But, as the retina is curved and not flattened, the perspective projection differs from retinal image for a wide vision angle. Another disadvantage is that the perspective projection is not consistent with the eighth Euclid's theorem which states that the visible difference between two identical objects unequally spaced must not be determine by their respective distance, but by their visual angles [START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF]. On the Figure 1, we can notice the deformation produced by the perspective projection. The observer stands on O point and his eyes is directed to the top of the page; P is the image plane of the perspective projection. For the observer the outer object appears wider than the closer one. This deformation is due to the fact that the perspective projection cuts linearly the solid angle of each object (this is known as the Leonardo's Paradox [START_REF] Weisstein | Concise Encyclopedia of Mathematics CD-ROM[END_REF]).

Thus, the perspective projection can be assimilated to the retinal image for small observation angles. However, it is not adapted for visual field representation with wide angle, which is useful to anticipate on what we will see.

A particular case of the perspective projection is used in architecture and called axonometry. This projection consists in setting the observer to infinite distance so that visual lines are parallel. As a result, the axonometry preserves neither area nor angle but only distance. It is often used for solar simulation purposes -the sun is supposed to be at the infinite.

Spherical projection

The spherical projection is used in cartography for Earth representation. Thiel used it for representing luminous sources in its notation [START_REF] Thiel | La notation de l'espace, du mouvement et de l'orientation[END_REF], and the LEMA for solar access decision-making [START_REF] Teller | Townscope II -A computer system to support solar access decisionmaking[END_REF]. In order to analyse urban scenes, Teller worked with three kinds of spherical projections.

The spherical projection can be defined as the intersection between visual lines, which link observer eye to points of the real world, and a sphere centred at observer eye. It allows a visual world representation in all directions at a time (above, below, in front, etc.) This panoramic representation is closed to our perception of the visual world which is composed by a snapshot series of our visual field [START_REF] Dupagne | A multidisciplinary survey of visibility[END_REF]. As this snapshot is senseless, our visual world image is persistent and stable (see [START_REF] Gibson | The Perception of the Visual World[END_REF]). Unlike perspective projection, all dimensions depend on distance to the observer [START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF]. It comes from the fact that the spherical projection acts by cutting the solid angles of objects with a sphere. Suppose that the projection is made on a sphere which radius is 1; then, the projection function is (Figure 2) :

÷ ÷ ø ö ç ç è ae M M M D z D y D x M z y x M , , ' ) , , ( a
Where 2 2 2 z y x D M + + =
is the distance between the observer and the point M which coordinates are ) , , ( z y x . However, a spherical projection is a three-dimensional representation and it is not directly exploitable. It is necessary to apply another transformation that projects the spherical image on a plane. There are several kinds of transformations to flatten the sphere. Their deformations provide to spherical projection specific characteristics which allows to adapt spherical projection for particular cases. For urban morphology study, Teller works around three flattening functions shown in Figure 3. • Stereographic projection (Figure 4). The stereographic projection is a "map projection in which great circles are circles and loxodromes1 are logarithmic spirals" [START_REF] Weisstein | Concise Encyclopedia of Mathematics CD-ROM[END_REF]. Its main property is to conserve tangential angles. According to Teller, the stereographic projection preserves visual aspect of 3D shapes rather well [START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF]. The flattening function is given below [START_REF] Teller | Townscope II -A computer system to support solar access decisionmaking[END_REF]: • Orthogonal projection. The orthogonal projection preserves the vertical angles. Thus, the radial distances inside the projection is proportional to the observable height. However, it does not preserve neither area nor angle. The equidistant projection is useful to compare the visual height. Its flattening function acts by a substitution of the height [START_REF] Teller | Townscope II -A computer system to support solar access decisionmaking[END_REF]]: ) , ( ) , , ( y x z y x a • Isoaire projection. With the isoaire projection, the surfaces projected on the image are representative of the solid angles intercepted on the sphere. The flattening function is given below [START_REF] Teller | Townscope II -A computer system to support solar access decisionmaking[END_REF]:

÷ ø ö ç è ae + + z y z x z y x 1 , 1 ) , , ( a
÷ ÷ ø ö ç ç è ae + - + - 2 2 2 2 1 , 1 ) , , ( y x z y y x z x z y x a
The spherical projection is an interesting representation of the visual world as it is relatively consistent with our representation. Although it can not be exploited directly, a map projection (i.e. stereographic projection, equidistant projection, isoaire projection) applied to the spherical projection produces deformations which highlight scene characteristics like height ratio, area shape ratio or angle ratio. From a certain viewpoint, the spherical projection is adaptable. However, it presupposes that we have a unique eye, and, as it is a projection on a surface, the deepness ratio between objects disappears. The projection of a small and near object can be as important as a bigger but farther one.

We will show in section 3.3 a use of spherical projection in visual analysis of urban scenes by processing sky opening generated by the building shapes.

Visual event sequences

A sequence is a series of more or less realistic images ordered in time, which is obtained during a motion (i.e. motion of the visual field, or motion of an object in the visual field). In order to decompose movement into image series, Eadweard Muybridge generated several photographic sequences, between 1884 and 1885, with an apparatus composed of several cameras linearly disposed. This strange apparatus was able to decompose human or animal motions (e.g. walking, running, jumping, etc.) Then, the Lumière's brothers created the Cinématographe in 1894. Its principle was to decompose movement into image sequences.

Much later, some urban designers have argued that movement can be read and understood as a pictorial sequence. Namely, Cullen talked about the approach of architectural objects by using pictorial sequences [START_REF] Cullen | The Concise Townscape[END_REF]. Appleyard, Lynch et al. tried different techniques to record visual sequences in order to analyse it [START_REF] Appleyard | The view from the road[END_REF]. One of them consists in using the motion pictures which record sequences in a permanent form that can be shown to large groups of people. However, they did not keep this technique because of "the inherent difference between the camera and the human eye" [START_REF] Appleyard | The view from the road[END_REF]. Later, Bosselmann tried to represent a walk through Venice by using a sequence of drawings with a text explaining what he saw plus additional informations [START_REF] Bosselmann | Representation of Places[END_REF]. However, the author noticed some disadvantages to this technique. For example, the glance direction in the drawings follows the observer motion direction. Besides, there are no drawing representing the view to the right, to the left, at rear, etc. Thus, no drawing could represent the view which opens on each side of the observer when he is on a bridge for example [START_REF] Bosselmann | Representation of Places[END_REF].

In this section, we will focus on a method, proposed by Panerai, based on pictorial sequences, which record the visual effects.

Sequential analysis

In order to record the motion, the movie cameras decompose it into a series of image. Panerai reused this idea of visual sequence and adapted it to represent visual events on urban routes [START_REF] Panerai | Paysage urbain et analyse pittoresque[END_REF][START_REF] Panerai | Formes urbaines, de l'îlot à la barre[END_REF], 1999]. Inspired by [START_REF] Wolfe | The Italian Townscape[END_REF], this method proceeds by isolating and identifying in a sequence different pictures which refer to a codified and schematic configuration of the scene. These pictures can be named [START_REF] Panerai | Analyse Urbaine. Collection eupalinos[END_REF]:

• Picture illustrating general viewpoints: symmetry or dissymmetry; lateral demarcation or axial demarcation; opening or closure; convexity or concavity.

• Pictures insisting on lateral walls: horizontal or vertical cutting up, undulation; face relation; deference, indifference, or competition.

• Pictures studying lateral walls extension to vanish point and beyond: narrowing, strangling, or wings effect; open or hidden highlighting; deflection; demarcation.

• Pictures characterizing the front closure of the visual field: centring or diaphragm. A sequence is composed of a particular picture suite configuration that can be called a linkage2 . A picturesque scene results in accumulation in short distances of breaks in the logic of the linkage. For monumental effects, the sequence consists of relatively slow successions with superpositions of pictures.

In order to complete sequential analysis, it is necessary to collect pictures and linkages in order to get set of linkages and to process entire sequences. A first solution consists in assembling pictures linked to an object. In this case, landmarks and monuments play a primary role and sequences are generated by these objects. A second solution consists in assembling pictures by theme, then to introduce the cuts when the theme changes; a sign or a mark allows sometimes to determine a cut.

The sequential analysis method was tested by Dupagne and Teller, with pictures produced by stereographic projection, in order to study routes in open spaces [START_REF] Dupagne | A multidisciplinary survey of visibility[END_REF] (see section 2.1). Following their point of view, it is not really a tool for decisionmaking. They describe it as a basic tool to serve in reflection or in presentation of project intents.

Visual event notation

The view from the road

As we walk in the street or drive on the road, we see all kind of visual informations which reveal our motion. They are based on our knowledge of architectural objects. In the United States, during 1950s, it is possible to drive on expressways through the cities at accelerated speed. On these quick axis, the visual informations are numerous and stream quickly. In answer to the confusion that could be generated by this evolution, Appleyard, Lynch and Myer have created a notation in a view to provide an 'artistic' sense for highway because: "road-watching is a delight, and the highway is -or at least might be -a work of art" [START_REF] Appleyard | The view from the road[END_REF]. Their notation is based on notation used by Lynch in [START_REF] Thiel | La notation de l'espace, du mouvement et de l'orientation[END_REF] and by Thiel.

Two components are considered: the space and the motion sensations on the one hand, the observer orientation on the other hand. For the first one, Appleyard, Lynch and Myer have classified the visual informations relative to the motion type they involve [START_REF] Appleyard | The view from the road[END_REF]. The motion sensation includes the apparent self-motion generated by the road (e.g. speed variation, direction variation, altitude variation, etc.) and the apparent motion of the visual field (e.g. deformations, rotations, translations, etc.) To this list, it should be appended spatial characteristics like light quality, space proportion, space transition, etc. An example of the notation corresponding to the motion and the space sensations is given in the left side of the Figure 6. The scheme represents an abstraction of a road which goes down to a turn with high lateral edges. At the end of the turn, the driver climbs and the view is opening [START_REF] Appleyard | The view from the road[END_REF]. On the road, a driver is orienting himself in the general environment. The orientation senses is certainly one of the most complex and conceptual aspect along the road. Appleyard, Lynch et al. define orientation sense as "the general image of the road and the landscape that develops in the mind, partly as a results of what is presently visible, partly as a result of the memory of past experience" [START_REF] Appleyard | The view from the road[END_REF]. In order to generate diagrams which represent an orientation sequence, they complete the notation of Lynch from [START_REF] Lynch | The image of the city[END_REF] and add to it a specific notation for goal approach. The result is illustrated by the right side of the Figure 6. While the left side of the scheme shows the road image and its events, the right side is the goal approach diagram.

'Envirotecture'

In [START_REF] Thiel | La notation de l'espace, du mouvement et de l'orientation[END_REF], Thiel provided another notation of space, motion and orientation in urban environments. His notation was inspired by the labanotation [START_REF] Hutchinson | Labanotation. New Directions[END_REF] which is used for choreography and describes the eye direction, movement speed and the body spatial position. Unlike the precedent notation, the notation of Thiel does not limit to the highway field. It extends itself to most general fields, which include urban planning and architecture, that Thiel groups under the term of envirotecture. The specificity of this method is to use a hemispherical projection where the vision axis is considered as a symmetrical axis for a hemisphere of 180° which includes a half part of the visual world. For Thiel the visual world is divided into three-dimensional objects, two-dimensional surfaces, screens which are intermediate elements between objects and surfaces, and relations between these elements also called SEEs (Space Establishing Elements).

Conclusion

An abstract notation to represent visual events allows to describe quickly and intuitively intentions in urban or architectural projects. However, a single abstract scheme could have several interpretations. For example, with the notation of Appleyard et al., the same symbol represents a river, a chain of mountains, or large wall. Hence, this notation should be completed by another type of document schemes of visual field or a text.

Regions of homogeneous aspect

The division of space into regions, where visual informations are homogeneous, allows to represent visual events which appear as transitions between two regions. We will present different kinds of methods which compute partition of two-dimensional or three-dimensional spaces.

Two-dimensional methods

The visual field is exposed to two kinds of change [Georgia Tech Research Corporation, 2001[START_REF] Panofsky | On the description of shape and spatial configuration inside buildings: convex patitions and their local properties[END_REF]. The first can be called continuous change and relates to our changing perspective views of the surfaces or partially visible surfaces. The second can be called discrete change and is associated with the appearance of clearly identifiable and finite elements of shape, namely discontinuities as defined below. Provided by Peponis et al., the epartition describes a structure of the changing visual field from the viewpoint of discrete changes in visual information.

In this section, what we call an environment is a wall configuration in a twodimensional plan. A wall is a real surface in Benedikt's terms [START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF], that is to say an opaque, material, visible surface (we disqualify the sky, glass, mirrors, mist, and perfectly black surfaces). These walls provide discontinuities like edges of freestanding walls and the corners formed at the intersection of two wall surfaces [START_REF] Panofsky | On the description of shape and spatial configuration inside buildings: convex patitions and their local properties[END_REF]. The walls are represented as lines without thickness.

Convex partitioning.

A space is said convex when any two of its points can be joined by a segment that lies entirely within the space. According to Hillier and Hanson, the convex spaces correspond to our intuition of two-dimensional spatial units which are completely available to our direct experience from any of their points. A first method uses circles in order to determine the convex partition [START_REF] Hillier | The social logic of space[END_REF]. A second one consists in extending wall surfaces, like with s-partition method (see below), and producing the largest overlapping convex spaces [START_REF] Hillier | Space is the Machine[END_REF]. A last method consists in partitioning the environment in order to provide the simplest representation of its spatial structure [START_REF] Panofsky | On the description of shape and spatial configuration inside buildings: convex patitions and their local properties[END_REF]. This method is known as the m-partition or minimal-partition because it produces the minimal number of the largest convex spaces which does not overlap. One of the drawbacks is that none of these methods take care of the visual events provided by an environment.

s-partition.

The e-partition is an extend of another method proposed by Hillier, called surface-partition or s-partition [START_REF] Hillier | Space is the Machine[END_REF]. The s-partition consists in extending walls inside the plan, on the same way as the scheme in Figure 7. Hence, we have an environment divided by s-lines into s-spaces. Each time an observer crosses an s-line, an entire surface either appears into the visual field or disappears outside it. Thus transitions from one s-space to another are associated with changes in the available visual information about shape. However, the reverse is not true. Surfaces and parts of surfaces may appear or disappear without crossing an s-line [START_REF] Panofsky | On the description of shape and spatial configuration inside buildings: convex patitions and their local properties[END_REF]. e-partition. The e-partition, or end-point partition, method does not extend only the walls but also diagonals. A diagonal is defined as a line that joins two discontinuities without crossing a wall, and some of them can be extended without going outside of the shape. Figure 8 shows examples of e-partioning obtained by extending both walls and diagonals. With this method, we obtain a new convex partition which has two singular properties: "first, every time we cross a demarcation line, a discontinuity either appears into or disappears from our field of vision. Second, the convex subshape defined by this partition are informationally stable" [START_REF] Panofsky | On the description of shape and spatial configuration inside buildings: convex patitions and their local properties[END_REF]. On the other hand, the e-partition can be used to calculate the integration of environment subspaces. The integration is defined in [START_REF] Hillier | The social logic of space[END_REF] as the way in which the parts of a system are linked into a whole. A space is said more integrated when all other spaces can be reached after traversing a small number of intervening spaces, and it is less integrated when the necessary number of intermediate spaces increases. Figure 9 shows the result of integration computation for an entire environment e-partitioned.

Three-dimensional methods

Aspect graph.

The 3D space can be divided into visually homogeneous regions. We say that a region is visually homogeneous if the topological structure of the scene image is the same for all the viewpoints in this region. This space subdivision is called VSP (Viewpoint Space Partition) [START_REF] Plantinga | Visibility, occlusion, and the aspect graph[END_REF]Dyer, 1990][Durand, 2000]. It can be generated by using a perspective or an orthographic projection (see Figure 10). The VSP allows to define a dual structure called aspect graph. An aspect graph records the topological structure of the visibility in each region. Each vertex represents a visually homogeneous region, and two vertices are connected by an edge whenever their viewpoint regions are themselves adjacent.

The boundaries between two adjacent aspects are determined by analysing the visual events. This visual events are transition regions where the image aspect is changed (i.e. a vertex or an edge of a polygon appears or disappears). Plantinga and Dyer define different kind of visual events:

• vertex-vertex: for a given viewpoint, the vertex of a polygon is in front of a vertex from another non-coplanar polygon; • vertex-edge: for a given viewpoint, the edge of a polygon is in front of a vertex from another non-coplanar polygon; • edge-edge: for a given viewpoint, the edge of a polygon intersects on the projection of an edge from another non-coplanar polygon; • edge-edge-edge: for a given viewpoint, three edges from different non-coplanar polygons intersect into a point on the projection. The aspect graphs and the study of visual events allow to compute the exact meshing of a scene, or discontinuity meshing [START_REF] Hedley | Discontinuity Meshing for Complex Environments[END_REF], in order to have a more realistic render of shading zone. One limitation of the aspect graphs method is that it only considers polyhedrons. Nevertheless, the method have been extended to compute aspect graphs of smooth and piecewise smooth objects [START_REF] Petitjean | The enumerative geometry of projective algebraic surfaces and the complexity of aspect graphs[END_REF]. Nowadays, the generation of visibility graph for curved objects is a research topic.

Visibility skeleton.

The visibility skeleton is a data structure that records visual properties and visual relationships between objects in a three-dimensional scene [START_REF] Durand | The visibility skeleton: A powerful and efficient multi-purpose global visibility tool[END_REF]. It provides a global knowledge of the scene. In a lot of algorithms relating to aspect graph computations, and to antipenumbra or discontinuity meshing, visibility changes are characterized by relations between vertices and edges.

Durand et al. consider two basic relations. The extremal stabbing lines are lines incident to four edges. Thus, an extremal stabbing line can be a vertex-vertex line, a vertex-edge-edge line, a quadruple edge line, etc. (we consider a vertex as the intersection of two edges). Extremal stabbing lines can be associated to faces of polyhedral objects. As a result, this kind of lines have zero degree of freedom. On the other hand, Durand et al. define the line swaths. A swath is a surface swept by extremal stabbing lines when they moved after relaxing exactly one of the four edges defining the line. This particular lines are line swath. It has one degree of freedom. To put it more precisely, a visibility skeleton is a graph where vertices represent extremal stabbing lines and edges are line swaths.

On the left side of Figure 11, An extremal stabbing line (VE1E2) is defined by two swaths (VE1 and VE2). These two swaths are fixed on the vertex V, VE1 moves on the edge E1, and VE2 on the edge E2. Another swath appears on the left side of the scene (VE1') which divides the polygon which contains E2. The right side of Figure 11 represents the visibility skeleton of the scene: each extremal stabbing line is a vertex and each adjacent swath is an adjacent edge.

About space partitioning

There are some drawbacks to partition space into homogeneous regions. For e-partition method, Teller notices that the data amount, the computation time, and the pertinence depend tightly on the definition level required for the model [START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF]. Hence, discontinuity apparition, frequent in urban scenes, contributes to complicate the e-partition representation. What is more, the method is not appropriated for environments which contain curves.

On the other hand, the aspect graph is not really used in computer graphics because of "the difficulty of robust implementation of exact methods, huge size of data-structure and the lack of obvious and efficient indexing scheme" [Durand, 2000] 3 .

Some of these remarks are also valid for the visibility skeletons. So, we could ask about the quality of these methods in a view to represent visual events inside a large model of a city, for instance. However, they allow, more locally, to do good study of some environments or objects.

Conclusion

There are questions about the realism of a representation. Some methods consider what we really see and others what we expect to see. But the pertinence of a representation involves problems of time and of space in order to generate it. Nevertheless, the methods we survey provide a set of techniques which can be highlighted, like spherical projection or space partitioning. From another viewpoint, some of them provide good methods for local study of the visual perception with a good definition level. However, all of these methods are not sufficient to achieve analysis.

Space characterization

A representation is a passive way to provide a new interpretation for a set of objects. An active way is to provide also a set of measures to characterize this set, allowing to deduce the sensations produced.

The purpose of this section is to survey some methods which allow to deduce the sensations produce by a space and more specifically by an urban environment.

Isovist

To analyse the visible space, Benedikt introduced in 1979 the isovists. First used for landscape analysis, Tandy introduced isovist term in [START_REF] Tandy | The isovist method of landscape survey[END_REF], and presented it as a method of "taking away from the [architectural or landscape] site a permanent record of what would otherwise be dependent on either memory or upon an unwieldy number of annoted photographs." By using this approach and including the Gibson's perception theory [START_REF] Gibson | The Senses Considered as Perceptual Systems[END_REF][START_REF] Gibson | The Ecological Approach to Visual Perception[END_REF]], Benedikt proposed a set of analytic measures on isovist properties to be applied to achieve quantitative descriptions of spatial environments. Then, he provides another definition of isovist: "An isovist is the set of all points visible from a given vantage point in space and with respect to an environment." [START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF] To have a more formal notation, let P be an environment with a configuration of walls4 and x a vantage point in P . An isovist P x V , (or x V if P is understood) generate from x is the set of all points in P such as:

{ } xy P xy P y V P x = Ç Î = , That is, P x V
, consists of all points y in P with the property that y is visible from x . Figure 12 presents two isovists (in grey on the schemes) generated in a same environment from distinct vantage points, which are represented by small squares. On the one hand, we can notice that isovists (their shapes and their dimensions) entirely depend on their vantage point location. On the other hand, isovists are polygons and their boundaries can be divided into two parts: boundaries common with a wall or a part of a wall, and boundaries which cross P , called occluded boundaries of x V . To have a comparison, isovist is a method to structure space that could be compared to the ambient optic array proposed by Gibson [START_REF] Gibson | The Senses Considered as Perceptual Systems[END_REF][START_REF] Gibson | The Ecological Approach to Visual Perception[END_REF]. Gibson defined an optic array as a set of nested solid angles corresponding to surface elements in the environment. Moreover, Benedikt states that "the isovist is simply this optic array, with wavelength and intensity information omitted" [START_REF] Benedikt | Perceiving architectural space: From optic arrays to isovists[END_REF].

Diagram drawing

Benedikt and Davis propose an algorithm to compute isovists by using a triangulation of the isovist polygon around the vantage point [START_REF] Davis | Computational models of space: Isovists and isovist fields[END_REF]. Here, we show other methods to compute isovists.

One of them calculates the radial distances for a given subset of vision angles, between 0 and 360° [START_REF] Wise | The quantitative modelling of human spatial habitability[END_REF]. This method allows to considered curved wall and to directly draw graphs of radial distances (Figure 13). The centre of this graph represents the direction left to right from the vantage point. Moving to right on the graph means moving in the counter clockwise direction around the vantage point. We can notice some singularities in the graph like peaks, troughs or vertical breaks. These singularities correspond respectively to appearance of convex corner, concave corner and region hidden from the visual field. Figure 14 shows some correspondences between the discontinuities of the environment and the graph. Another way to represent isovists is to draw an isovist sequence, computed along a route, on a surface (Figure 15). This kind of representation shows the evolution of environment discontinuities along the route.

However, this kind of representation is not an easy way to interpret isovists and to deduce characteristic from an environment. Nevertheless, isovist can be considered as a polygon or as a distribution function. It allows to use geometrical and statistical measures.

Isovist measures

In order to give an interpretation of each isovist, Benedikt identified different geometric measures [START_REF] Davis | Computational models of space: Isovists and isovist fields[END_REF][START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF].

Area and perimeter.

The area and the perimeter measure how much space can be seen from a vantage point and how much environmental surface can be seen from this point [START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF]. In order to obtain the area of an isovist, we can consider isovist as a continuous set of radial distances. Hence, an isovist is a polar function. According to [Weisstein, 2001] and [START_REF] Batty | Exploring isovist fields: space and shape in architectural and urban morphology[END_REF], the area x A of a given isovist x is:

ò = p q q 2 0 2 ) ( d r A x x
Where x r is a function that calculates the radial distance in the isovist x for a given angle q . If we consider isovists as polygons determined by their vertices i v , the perimeter x B of an isovist is:

å + = i i i x v v B 1
Where MN is the Euclidean distance between the two points M and N .

Circularity.

From x A and x B , we can also calculate the circularity of an isovist. This measure compares a polygon to a circle from a formal viewpoint. For a circle with the area a and the perimeter p , we have the relation

a p p 4 2 = , then its circularity 2 4 p a p = Y
is 1. For any other geometrical figure, this ration is less than 1; but if Y is near from 1 the polygon is similar to a circle, and if Y is near from 0 the polygon is similar to a straight line.

The circularity x

Y for an isovist x is thus the ratio:

2 4 x x x B A p = Y
In his papers, Benedikt uses two other forms to calculate the circularity [START_REF] Davis | Computational models of space: Isovists and isovist fields[END_REF][START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF]. The first one is given by an inversion ( )

x x x x A B N p 4 1 2 = Y =
; the second one is called compactness and is given by

x x A B 2
. For Batty [START_REF] Batty | Exploring isovist fields: space and shape in architectural and urban morphology[END_REF], the compactness can be calculated by the ratio between the mean radial length and the maximal radial length for an isovist, or by the ratio ( ) ( ) [START_REF] Conroy | Spatial Navigation in Immersive Virtual Environments[END_REF] provides another circularity equation where the perimeter is replaced by mean radial distance of the isovist:

x x x B A Y = p p 2 . Finally, Conroy
( ) x x x A r 2 p = Y
. The circularity formula used here is equivalent to the circularity formula used by Teller for open spaces computation [START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF] (see section 3.3).

Variance and skewness.

Benedikt proposes two other measures. The first one is called the variance and calculates the dispersion of the perimeter relative to the vantage point x . The second one is the skewness and calculates the asymmetry of the dispersion of the perimeter to x .

In order to calculate these two measures, Benedikt uses the second and the third radial moment M , for an isovist x is given by: ò

- = q q q p d r r M p x x x p ) ).( ( 2 1 , Where ò = q q q d r r x x
). ( is the mean value of function x r . The second radial moment allows to calculate the standard deviation coefficient which is given by

x x M , 2 = s
and could be compared to the equivalent method of Teller (see section 3.3).

Drift.

Another measure is provided by Conroy, called drift, which calculates distance between the location from which the isovist is generated and its centre of gravity [START_REF] Conroy | Spatial Navigation in Immersive Virtual Environments[END_REF]. Drift tends to be minimal at the centre of spaces and along centre-line of roads.

Applications of isovists

Isovists can be helpful to solve some problems where the visibility is a predominating factor. One of them consists to preserve the privacy. The problem is to find "[...] an optimum balance [...] between the 'information' which comes to a person and that which he puts out" [START_REF] Canter | The spatial environment[END_REF]. Isovist size measures, such as x A and x B , approximate the amount of this kind of information [START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF]. Other problems consist in seeing much without being overly exposed or reduce the security by minimizing the occlusivity fields (spaces leaved unseen from a point), for example. This kind of problems can be treated using isovist theory.

In his report [START_REF] Wise | The quantitative modelling of human spatial habitability[END_REF], Wise used isovist in order to improve the design of spatial cabins. For him, there are three main concepts: the visual aspects, the kinaesthetic aspects and the social logic (with the same meaning as [START_REF] Hillier | The social logic of space[END_REF]). For the visual aspect, Wise was interested in the perceived size of an environment, its apparent orientation and its affective connotation. The isovist analysis allowed him to have a direct method to measure visual qualities.

Finally, an isovist variation, called viewshed, is used in landscape analysis [START_REF] Burrough | Principles of Geographical Information Systems for Land Resources Assessment[END_REF][START_REF] Fisher | An exploration of probable viewsheds in landscape planning[END_REF]. The originality of this method is that it takes into account the level informations of all portion of the ground. Hence, the viewscheds allow to locate the hidden dips from a viewpoint and also the ground area visible from this point.

Visibility graphs from Space Syntax

Instead of representing the visibility area as isovist do, Turner et al. provides a data structure, called visibility graph, representing the intervisibility relationships between points of an environment [Tuner and Penn, 1999][Turner et al., 2001[START_REF] Turner | Depthmap: A program to perform visibility graph analysis[END_REF].

The visibility graphs are topological graphs where each vertex is associated to a vantage point on a map. The presence of an edge between two vertices involves that one "can see" and "can be seen from" the other. Each vertex is disposed regularly on a virtual grid. In mathematical terms, let ( )

E V G , =
be a visibility graph, where

{ } n v v v V , , , 2 1 K = is a set of vertices and { } n j i e E ij , , 1 , K Î Í
a set of edges. Each vertex vi is associated to a location ). Figure 16 shows the beginning of a visibility graph construction. We can notice that the white vertex neighbourhood is included in the isovist generated by these vertices (in grey on the scheme). When the visibility graph construction is completed, this property allows us to measure visibility informations on each vertex without generating corresponding isovist.

Visibility graph measures

Like isovist analysis, the visibility graphs were mainly applied to house planning. However, in [START_REF] Batty | Exploring isovist fields: space and shape in architectural and urban morphology[END_REF], Batty extended visibility graph applications to urban analysis.

In this paper, we will introduce the possible measures in urban scene by illustrating them with an actual case in Nantes. We present an analysis, with our implementation of visibility graph, of place du Martray and a part of rue Sarrazin in Nantes. This two urban locations are relatively enclosed locations and easy to model5 . With a 12 906 vertices division on a 205 m´265 m map, each vertex covers a surface of 1.4 m 2 . The Figure 17 shows the model and the studied part. Considering an outlying zone, enables to have more realistic measures for the studied zone.

Neighbourhood size.

One of the first measure proposed by Turner et al. is the neighbourhood size i N which calculates the adjacent vertices number for each vertex. As each vertex covers small map surface, the neighbourhood size of vertex vi is proportional to the isovist area Ai for the vantage point it represents.

{ }

. . E e v N A ij j i i Î = » d d
Where d is a coefficient corresponding to the part of surface covered by each vertex. On the upper left of Figure 18, we represent the neighbourhood size for each vertex on the map. The darker is a point, the larger is its visibility area.

Clustering coefficient.

Another measure, provided by Turner et al., is the clustering coefficient i g . It compares the number of adjacent edges in the neighbourhood of a vertex with its theoretical maximum:

{ } ( ) 1 . , - Î Î = i i i k j jk i N N N v v E e g
The clustering coefficient gives a measure of the apparent space convexity from a location. If i g is near from 1, the most part of the vertices in the neighbourhood are visible between them. This implies that the generated isovist would be convex. If i g is near from 0, then the space looks like a star. Another way to interpret i g is about the visibility information preservation. By moving inside a region where i g is near from 1, the changes of information would be less important than moving inside a region where the i g is near from 0.

Mean shortest path length.

The shortest path between two vertices i v and j v in a graph is the least number of edges ij d between them. The mean shortest path length i L for a vertex i v is simply the average of the shortest path lengths from that vertex to every other vertices in the graph.

V d L V v ij i j å Î =
The mean shortest path length provides a measure about visual accessibility of a location with respect to observer movement. That is to say it allows to estimate the average number of movements necessary before a location can be seen. As it is a global measure, it depends on the model size.

Visual distances.

In [START_REF] Batty | Exploring isovist fields: space and shape in architectural and urban morphology[END_REF], Batty provides measures about the distance between one vertex and vertices in its neighbourhood. He defines the maximum distance max { }

max j v max j i N i v v d i Î = { } min j v min j i N i v v d i Î = i V v j i i N v v d j å Î = Where j i v v
is the Euclidean distance between locations represented by i v and j v .

To these measures we can add the distance standard deviation i s for each vertex. As it indicates the range of radial distances for any single isovist, the standard deviation gives us an idea of the environment shape regularity.

( )

V d v v V v i j i i j å Î - = 2 s
Other measures.

In [START_REF] Turner | Depthmap: A program to perform visibility graph analysis[END_REF], Turner proposes other measures for analysing visibility graphs. The first one is taken from the theory of Hillier and Hanson [START_REF] Hillier | The social logic of space[END_REF] and allows to calculate a control value i c for a location. According to [START_REF] Hillier | The social logic of space[END_REF], the control gives a local measure which value varies around 1. If the value for a location is above 1 then the control is strong, however the control is considered as weak.

å Î = i j N v j i N c 1
Another measure gives an idea of the frequency distribution of the shortest path length (or depth). This measure i s is called point depth entropy and is calculated using the Shannon's formula. Where max d is the maximum length from the current vertex and pd is the frequency of the length d from the current vertex. According to Turner, the "point depth entropy can give an insight into how ordered the system is from a location" [START_REF] Turner | Depthmap: A program to perform visibility graph analysis[END_REF].

Comments on results

At first sight, it is not easy to distinguish the six pictures in Figure 18. For Place du Martray, a division appears with the clustering coefficient, the maximum distance, and the distance standard deviation due to dead end in the north of Rue Sarrazin. With the other measures, the brightness from all locations of the place is relatively the same and seems to delimit it. For Rue Sarrazin, the measures have interesting value in the east end, and near Place du Martray. Inside the street, they do not seem to vary a lot. Near Place du Martray and in the east side of the street, the space shape is not convex and provides more visibility area; this implies a local darkening of the coefficients.

Actually, the cathedral appears in the visual field when we walk in the east side of rue Sarrazin. It is cathédrale Saint-Pierre located 700 m far from the studied area. It is not shown in figure 16 and would not be correctly studied by the visibility graph even if it were drawn on the map. This is done because of walls which stand between the viewpoint and the cathedral. But as they are in a dip, they are taken into account by two-dimensional methods6 , though they do not appear in the visual field. This particularity shows a mistake linked to the map transformation of the urban environment.

Visibility graph criticism

With visibility graph, Turner et al. provide a regular data structure that helps to analyse visibility in 2D environments [START_REF] Turner | Making isovists syntactic: isovist integration analysis[END_REF]][Turner et al., 2001[START_REF] Turner | Depthmap: A program to perform visibility graph analysis[END_REF] 7 . Its main advantage is to structure environment and to record visibility informations which is considered as a first-order relation. In fact, visibility graph analysis can be considered as an extend or an alternative to isovist field analysis (see section 3.1).

However, we can highlight two weaknesses for the visibility graph method. Above, we have seen the results of this method could be altered by the two-dimensional transformation of the urban environment. In an other viewpoint, the computation time of the visibility graph increases rapidly with its resolution. For example, let's suppose an empty square environment which is 5 km length for each edge. For a definition of 1 m 2 per vantage point, it is necessary to generate one million points, producing a matrix of 6.25´10 14 elements for the graph representation. As some algorithms are

) ( 2 n O
in the worst case (like the algorithm for graph construction or the measure for the mean shortest path length) 8 , the processing time would theoretically be around one billion (10 12 ) years with an 1 GHz computer. But, a solution to solve this problem would perhaps be to optimise these algorithms.

Thus, the visibility graph method seems to be adapted to analyse parts of a plane city, or larger models with a lower but sufficient resolution.

Open space indicators

Unlike isovist or visibility graph analysis methods, Dupagne and Teller consider the third dimension and analyse the urban scene through the spherical projection. Dupagne and Teller reuse the "urban boxes" concept from Camillo Sitte, and analyse shapes formed by buildings [START_REF] Dupagne | A multidisciplinary survey of visibility[END_REF][START_REF] Teller | Townscope II -A computer system to support solar access decisionmaking[END_REF][START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF].

Sky opening

Sky opening is defined as the ratio between the sky area in isoaire projection and the area of the circle in which image is projected. This coefficient is relative to the enclosure sensation in a scene: it is valuated to 0 in a closed volume and to 1 on a plane without any object.

In a urban scene, the sky opening coefficient changes with the observer location. Near a wall, the scene seems to be more closed than in the middle of a street or of a place. It is possible then to draw the sky opening coefficient variation on a map. Figure 19 shows the sky opening coefficient variation map for la Grand'Place d'Arras [START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF]. We can notice the coefficient values in the streets, near the wall in places and in the middle of places. First International Workshop on Architectural and Urban Ambient Environment;Nantes February 6-8, 2002 3.3.2. View depth One of the drawbacks of sky opening measure (with spherical projection) is to let the same visual weight for a high and far volume than for a smaller but closer volume. To correct or to complete the sky opening coefficient, Teller analyses the view distances with two methods [START_REF] Teller | La régulation morphologique dans le cadre du projet urbain : Spécification d'instruments informatiques destinés à supporter les modes de régulation performantiels[END_REF].

The first one calculates mean view length m L , for a given vantage point, of distances i l between the vantage point and visible faces i f weighted by their area i s in isoaire projection:

å å = i i i i i m s l s L .
This measure is independent from the sky opening. Thus, a mean length of faces 50 m far from the observer which occlude 80 % of sky surface is equivalent to a face configuration which occludes 20 % of sky surface with the same distance from the observer. In order to differentiate this two cases, Teller proposes to take into account the occluded sky surface:

å = i i i i c s S L L .
r S is the visible sky surface and the result c L is called the typical length. This measure varies between the mean length and the infinity depending on whether the faces covers 100 % or 0 % of the sky surface.

Sky regularity

The statistical tools can provide different kinds of indicators relative to the sky shape and its regularity. To realize these measures, Teller proposes to use the equidistant spherical projection which allows to hold the visible height proportions with respect to a vantage point. Thus, we can calculate the maximal and the minimal height, the mean height or the height standard variance. We can add the sky surface compacity 2 4 P A C p = , as we saw above in the isovist section (section 3.1).

All the results obtained by these measures could be compared to those obtained by isovist analysis. Actually, it would be interesting to compare 3D analysis methods with 2D ones for similar measures.

Spreading and eccentricity

A measure like compacity is extremely sensitive to noise. The increase of the object definition causes apparitions of peaks which increase the perimeter without modifying the area a lot. In this case, the change generates an important modification in the compacity value. To have a less sensitive measure, Teller proposes to use the moment of inertia of sky shape. The ) ( j i + -th moment of inertia ij M of an homogeneous shape is computed by the formula:

òò = dxdy y x M j i ij
In this section, we focus on the second moment of inertia providing M is the 0-th moment of inertia which corresponds to the area. The spreading S calculates the mass dispersion of a figure and is similar to the compacity. Nevertheless, the spreading does not depend on the perimeter; thus it is less sensitive to the shape noise. The lower limit of S is 2 p , which is the spreading of a circle. The eccentricity E is a ratio which gives an idea of the symmetry of a shape with respect to its gravity centre. If the shape is symmetrical, E is 1; if it is not, E is greater than 1.

Visual accessibility of an object

In the previous sections, we have seen methods to analyse visual field of an observer in an urban environment. The purpose of this section is to show methods to analyse an object as seen by a set of observers.

Visual accessibility in an urban environment

To measure the visual accessibility of an object, Nivet uses the term of intermittence [START_REF] Nivet | De Visu : un logiciel pour la prise en compte de l'accessibilité visuelle dans le projet architectural[END_REF][START_REF] Nivet | Simulation inverse de l'accessibilité visuelle en mileu urbain[END_REF]]. The intermittence is a relation which qualify the visibility between an observer and an object in a scene. In fact, Nivet proposes two measures of intermittence: the space intermittence and the object intermittence. Those two measures allow to represent the visual accessibility.

The space intermittence e I measures the proportion of points in a space from which a given object is totally or partly visible.

( ) (

)

space total A space sub A I e _ _ = The object intermittence ) ( p I o
measures ratio between the visible surface of an object from the point p and its visible surface from the same point if it were alone in the scene.

( ) ( ) ( ) ( ) ( ) area total A area hide A area total A area visible A p I o _ _ 1 _ _ - = = Nivet uses the couple ( ) o e I I ,
in a view to qualify the visual intentions in the architectural projects. For example, the intention ( ) 1 , 1 means "see completely" or "from all point of the considered space, see the whole of the object", and the intention ( ) 0 , 0 means "see nothing" or "do not see anything of the object from all point of the considered space".

Another proposition was made by Morin in order to study the visual accessibility of la Tour de Bretagne in Nantes [START_REF] Morin | Lecture de la Tour de Bretagne -développement d'un outil de lecture de la ville (simulation de l'accessibilité visuelle)[END_REF]. This work consists in using Solene [START_REF] Groleau | Solene : un outil de simulation des éclairements solaires et lumineux dans les projets architecturaux et urbains[END_REF], a software dedicated to sun lighting simulation in urban environment, to determine the surfaces of the object seen or leave unseen. [START_REF] Koglin | Multiobjective optimization with evolutiionary algorithms for the synthesis of optimal overhead lines[END_REF] propose a method for generating an optimal solution in order to build overhead lines. Their method is based on cost criterion, on optical impact criterion, and on "approval ability" criterion. To solve the optical impact criterion of overhead lines, they use a method developed at Saarland University [START_REF] Koglin | A valuation system for the visibility of overhead lines[END_REF] that takes into account the virtual size of the pylon looked at and the colour difference between pylon and background.

Object visibility and landscape protection

In their paper [Koglin andZewe, 1995, 1996], Koglin and Zewe provide different measures mainly based on method of Groß [START_REF] Groß | The analysis of visibility -environmental interactions between computer graphics, physics, and physiology[END_REF]. The psychophysical factors relate to the observer density or the observer attention. The physical factors are given below.

• The solid angle W is a measure of the apparent size of an object. It is calculated as the ratio between the object visible surface and the square of the visual distance from the observer (

2 d S = W
).

• The colour difference E D between the object and the background. The difference is calculated as the geometric distance between the colour values using the CIE Yxy colour space (where Y is the luminance, and x and y the colour location in the chart). Moreover, colours in the landscape depend on the atmospheric attenuation.

As a basis, these factors help to draw up a method for calculating the visibility of an object. One of the first measure is called the location-specific visibility S ¢ ¢ . It calculates the optical impact of an object at a particular observer location. We suppose that each observer occupies an area A D of size 1 m 2 .

About methods for space characterization

The methods described here give an original approach to characterize space, and usually provide a set of measures which allow to draw different kinds of visual variation map for a given environment. However, some of these methods (e.g. isovist, visibility graph, and methods for landscape analysis) are not adapted to large urban environment. Others methods, like the Nivet's method, intend to take up any other applications.

Conclusion

The visual interpretation of an urban environment needs a way to model it, with the aim to highlight some visible elements (e.g. shape, colour, visual events, etc.), and to analyse it in order to provide a characterization of the environment. In this paper, we saw different kinds of methods that allow to interpret the visual events.

In the section 2, we have presented several representation methods of visual field and of visual events. They provide a set of concepts which can be highlighted. For example, the spherical projection gives a mean to represent the whole visual world; the notations provided by Thiel or Lynch et al. use an abstraction of the visual world to represent what we see; the convex partition methods structure the environment into visually homogeneous regions.

However, these methods do not allow to achieve analysis. In section 3, we have seen three complete methods -isovist, visibility graph and sky opening indicators -that allow to analyse the visual perception of architectural and urban scene by using tools that come from statistics, graph theory, physics, and social logic of space. Other methods attend to only considered the visual perception of one object in a scene. They qualify the quantity seen of this object or the contrast it produces with the background (in order to analyse the efficiency of the camouflage for this object).

Most of these methods fail to model or analyse entire cities with a high level of resolution. All of them are reasonably good if the model is reduced to a district or a neighbourhood. Nevertheless, the methods we saw are mainly based on human visual system, in order to have a more intuitive representation of urban environment and to analyse it as human do. However, these elements are often limited to shape perception. With the aim to analyse visual events, it would be interesting to take into account the motion perception. Most of these methods are able to study it by generating space variation maps. But, they do not integrate the motion perception. Thus, it is difficult to interpret what a person can observe actually.

Similar questions raise about other attributes analysed by human visual system and about the visual events during a motion. For example, attributes like colour (study by the method saw in the section 3.4.2), texture or lighting are directly analysed by human visual system but leaved unexploited.

Figure 2 :

 2 Figure 2: Spherical projection for the same object at different distances.

Figure 3 :

 3 Figure 3: Three transformations to flatten a sphere [Teller, 2001]: (a) stereographic projection, (b) orthogonal projection, (c) isoaire projection.

Figure 4 :

 4 Figure 4: Stereographic projection in Liège (right: place Xavier-Neujean [Teller, 2001], left: Cité administrative [Dupagne et al., 1997]).

Figure 5 :

 5 Figure 5: Examples of picturesque elements [Panerai et al., 1999]: symmetry (1a), opening (3a), convexity (4a).

Figure 6 :

 6 Figure 6: On the left, the scheme shows a use of the space and motion notation for a road portion. On the right, the scheme shows the orientation notation for another road portion [Appleyard et al., 1964].

Figure 7

 7 Figure 7: s-partitions of two plans.

Figure 8

 8 Figure 8: e-partitions of three plans.

Figure 9 :

 9 Figure 9: The integration pattern of Farnsworth House [Peponis et al., 1997].

Figure 10 :

 10 Figure 10: Aspect graph of a cube in perspective projection [Durand, 2000].

Figure 11 :

 11 Figure 11: Visibility skeleton construction.

Figure 12 :

 12 Figure 12: Two 2D isovist polygons generated in the same environment from distinct vantage points.

Figure 13 :

 13 Figure 13: Two 2D isovist diagrams generated in two environments.

Figure 14 :

 14 Figure 14: Examples of isovist behaviour. A convex angle is represented by a peak on the graph (a) and concave angle by a trough (b). If a part of the environment is unseen from the vantage point, it generates a vertical break in the graph (c).

Figure 15 :

 15 Figure 15: 3D diagram representation of an isovist sequence (following the arrow).

  p-th centred radial moment x p

Figure 16 :

 16 Figure 16: A step in the visibility graph construction.

Figure 17 :

 17 Figure 17: The study area corresponds approximately to the grey zone. It corresponds to the place du Martray (a) and a part of the rue Sarrazin (b) in Nantes.

Figure 18 :

 18 Figure 18: Six measures on a 12 906 vertices graph (from upper left to lower right): visibility area, clustering coefficient, integration ratio, maximum distance, average distance, distance standard deviation.

Figure 19 :

 19 Figure 19: Sky opening map for la Grand'Place d'Arras [Teller, 2001].

  sensitive to location and orientation. The reference axis orientation is given by the eigenvalues 1 I and 2 I of the matrix of inertia I M :The two last measures is used by Teller to calculate the spreading S and the eccentricity E of the space shape:

  of entire visual impression caused by an object in the landscape. On the other hand, the efficiency of camouflage calculates the location-specific visibility for the same object from the same observer point but in front of a clear sky and without any obstacle leads to the maximum location-specific visibility max S

"The loxodrome is the path taken when a compass is kept pointing in a constant direction"[START_REF] Weisstein | Concise Encyclopedia of Mathematics CD-ROM[END_REF].

Panerai uses the french term enchaînement that could to be translated into the term 'linkage' used for cinema.

A good discussion of the pros and the cons is given in[START_REF] Faugeras | Why aspect graphs are not (yet) practical for computer vision[END_REF].

We call a wall, an opaque, material, visible surface, humanly perceivable[START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF].

There is another reason why we choose these locations that we will explain later.

The same problem appears with the isovist method.


François Sarradin

Daniel Siret

Jacques Teller

Visual urban space assessment from sky shape analysis

Introduction

Urban ambient environments are defined as the singular combination of factors that confers its perceptive distinctiveness to a space. These factors typically include noise and climate, amount of light or visual enclosure [START_REF] Lynch | The image of the city[END_REF]. Different computer-based methods have recently been proposed to characterize the shape of urban open spaces. Field-oriented approaches have been defined by Teller as those computer methods which tend to assimilate ambient environments to a continuous field, whose characteristics vary throughout the open space. It is hereby proposed to adopt this ontology, in the view of characterizing the perception of observers in motion.

It is actually well known that movement and speed deeply influence our perception of the environment. Several techniques have already been proposed to study the visual perception of the urban environment along a route or a path [START_REF] Cullen | The concise townscape[END_REF][START_REF] Appleyard | The view from the road[END_REF][START_REF] Thiel | La notation de l'espace, du mouvement et de l'orientation[END_REF][START_REF] Bosselman | Representation of places: reality and realism in city design[END_REF]. Some of them are based on Gibson's concept of motion perspective [START_REF] Gibson | The Perception of the Visual World[END_REF]. Motion perspective refers to the gradual change in the rate of displacement of contour lines in the visual field. Initially developed in the field of aviation psychology, this effect proved to be of paramount importance in the perception of any observer in displacement. In this paper, we propose to develop a computer method to analyze this motion perspective. Our method is based on Teller's spherical metric [START_REF] Teller | A spherical metric for the field-oriented analysis of complex urban open spaces[END_REF]. It takes advantage of skeletonization-a technique heavily used in image analysis.

Section 2 briefly reviews existing computermethods to analyze the visual perception of urban environments. We then propose in section 3 a description of our method, based on a combination of Teller's spherical projections and the skeletonization technique in order to analyze the motion perspective. Some measures, derived from our method, are described in section 4. An interpretation of preliminary results is then proposed. It is especially discussed how these measures can help to determine sequences in the observer route. Section 5 is a brief conclusion about the presented measures and their applications.

Background

Different field-oriented methods have been proposed to relate the visual attraction of an urban environment, the way we see it, and its morphology [START_REF] Sarradin | Visual analysis of urban environment[END_REF]. Following Gibson's perception theory [START_REF] Gibson | The Perception of the Visual World[END_REF], Benedikt developed isovists which compute the shape on a plane of our visual field and study its geometrical surface [START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF]. Space syntax theory, developed by Hillier and Hanson proposes graph analysis of visibility relationships within buildings and urban configurations [START_REF] Hillier | The social logic of space[END_REF]. Turner's visibility graphs build upon this kind of analysis combined with isovists [START_REF] Turner | From isovists to visibility graphs: a methodology for the analysis of architectural space[END_REF]. It links the potential locations of an observer between them if they are visible one from the other. Peponis' e-partitions divide the space into visually homogeneous regions, which enable to study the visual events in urban spaces [START_REF] Peponis | On the description of shape and spatial configuration inside buildings: convex partitions and their local properties[END_REF].

Teller's spherical metric proposes to consider the shape of the sky perceived from given locations within the open space [START_REF] Teller | A spherical metric for the field-oriented analysis of complex urban open spaces[END_REF]. The variation of some parameters of this sky shape, as for instance its opening, is used to highlight the underlying structure of urban open spaces-limits, central area, main axes. The main advantage of this technique, when compared to the previous ones, is to consider the third dimension of urban open spaces while allowing to cope with its non-bounded character (the sky is assumed to be at an infinite distance from the ground). Several indicators of urban open spaces can be defined, which estimate the opening of sky shape, its eccentricity or its spreading.

All of these methods are based on a field-oriented approach of the urban open space. They are intended to highlight variations within the open space, which is no longer considered as static. They hence constituted an important step towards a better consideration of the dynamics of perception. Still none of these methods have been designed to characterize the dynamic variation of the visual environment, its progressive expansion, as it is perceived by an observer in motion. This effect, defined as the motion perspective by Gibson, would typically require to trace the deformation of visible shapes and apparition of new ones during movement. In this paper, we present a new method which consists in following these dynamic variations.

Analysis of sky shape

The method we propose is based on spherical analysis of open spaces. In spherical views, all the urban environment visible from a given point can be represented within a single view and the sky is central to the figure. Projections are computed from urban 3D models and produce discrete images whose properties can be analyzed.

Our method consists in applying a morphological transformation to spherical projections. It extracts the shape of the sky from the picture and generates a simplified representation of this shape, defined as the skeleton or medial axis transform (MAT). According to the Blum's definition of the MAT [START_REF] Blum | A transformation for extracting new descriptors of shape[END_REF][START_REF] Choi | One-sided stability of medial axis transform[END_REF], let S ⊂ R 2 be a shape,

MAT(S) = {(p, r) ∈ R 2 × [0, ∞) | B r (p): maximal inscribed circle in S}, ( 1
)
where p is a skeletal point and r the radius it is associated with. More explicitly, MAT(S) is the set of all pairs of the centers of the maximal inscribed circles in S and their radius. MAT keeps the geometrical and topological information of the original shapes. It means that the shape can be reconstructed from information contained in the skeleton. It is heavily used to decompose shapes in image analysis, but it has not yet been used to analyze the urban environment. Figure 1 represents the first three steps of our method: the route selection in a virtual urban environment, spherical projections from successive points of the route, and the skeletonization of the projection centered on each point. The next step of our method consists in analyzing the deformation of those skeletons from one view to another one. Several skeletonization algorithms have already been proposed in the literature [START_REF] Loncaric | A survey of shape analysis techniques[END_REF][START_REF] Fol-Leymarie | Three-dimensional shape representation via shock flows[END_REF]. We decided to use the skeletonization method developed by Pavel and Siddiqi, which is called Hamilton-Jacobi skeletonization [START_REF] Dimitrov | Robust and efficient skeletal graphs[END_REF][START_REF] Siddiqi | Hamilton-jacobi skeletons[END_REF]. According to the Teller's spherical projection and the Blum's definition (equation 1), it provides the most accurate skeletons and the less sensitive one to the noise of the boundary.

The sky shape boundaries are actually characterized by some noise, essentially due to the discretization process and lack of consistency of most urban 3D models. Effects of noise upon the results have to be strictly controlled even if spherical views tend to naturally reduce it (they give a greater importance to what is near the observer, which appears in detail, and compress what is far from the observer).

Measures and interpretation

Several measures can be performed with skeletons along a route in an urban environment. Here, we describe the greatest maximal disk (GMD) measure. The GMD is the skeletal point with the higher minimal distance from the boundary. Let S ⊂ R 2 be a shape, GMD(S) is a pair of skeletal point and radius (p, r) ∈ MAT(S) such as ∀ (p', r') ∈ MAT(S), r ≥ r'. As it is not located near the end points of MAT, GMD is weakly influenced by the noise of the boundary.

We will consider here two measures from the GMD: the GMD radius and the rear-front GMD location. In order to study it, we will test them along a route in a model of rue Xavier-Neujean in Liège, represented in figure 2. This route has four interesting sections: S1 is a church, S2 is a place, S3 is an open parking lot, and S4 is crossroads behind a theater. A projection of the sky is calculated every 5 meters on a route of 245 meters. We now describe these two measures (GMD radius and GMD location) and present a way to combine them in order to characterize visual sequences of an urban route.

Greatest maximal disk radius

The radius of the GMD provides results comparable to Teller's open space indicators [START_REF] Teller | A spherical metric for the field-oriented analysis of complex urban open spaces[END_REF]. This kind of indicator estimates the sense of openness that an observer may feel in an urban space. Figure 3 represents the variation of the GMD radius measure along the route in figure 2. The x-axis represents the image number (position in the path) while the y-axis gives the percentage of GMD radius divided by the radius of the projection circle (maximal value of GMD).

It can be seen from the graph that the variation of GMD radius along the route is characterized by four peaks: position 11, around position 28, position 37, and at the end of the route. Except for the first peak, the others correspond to the sudden appearance of S2, S3, and S4 openings. The first peak in the graph corresponds to the visual opening characterizing points located between the start of the route and the bell tower of the church (S1). Minimums of the curve are also important. The first one is a transition between the space before the church and the place (S2). The next one is due to a narrow part between the place and the parking lot (S3). The last one is a long narrow crossing between S3 and S4. The GMD radius measure is not tied with the direction of the observer movement. But it detects local openings in the visual environment of the observer. Its variations highlight spaces with a high openness and transitions between these spaces.

4.2

Relative GMD location Along a route, the location of the GMD varies around the center of the spherical projection: the GMD can be located in the front or in the back of the observer, with respect to his direction. By this way, it is possible to determine at which time an observer perceives the most important local opening.

Figure 4 shows the rear-front location measure of the GMD, in the environment represented in figure 2. It is computed according to the center of the projection and the observer orientation in the route. When the value is superior to 0, the observer sees the GMD, otherwise it is in his back. From the graph of figure 4, we can notice the four series of peaks. These are due to the appearance of the four openings described in the preceding section. For example, between positions 19 and 26, the observer can see an opening on his front before his entrance in place (S2). The entrance starts at the image 22. After image 26, the observer is still in the place but his visual field contains the narrow part between the place and the parking lot. This narrow part is a transition.

The rear-front GMD location provides a mean to situate the local opening from a given location. In the route context, it highlights interesting visual events which are the appearance and disappearance of openings in the stream of urban shape variation. Hence, this measure is relative to the observer direction and it benefits of the same stability than the GMD radius measure. Moreover, it highlights openings in front of the observer.

Combination between the GMD radius and the GMD location

The GMD location describes a partition of the route into parts where GMD is in front of the observer and transition parts. The GMD radius provides information about the importance of the GMD. The combination of these two measures brings a rich interpretation of the selected route.

Figure 5 represents the route partition according to the graph in figure 4. It highlights the part of the route (with lines in bold), where the GMD is in the visual field of the observer. The part of the route which is highlighted in the place (S2) is one of the most important. According to figure 3, it is characterized by a wide opening that the observer sees on his right during a long time. This place appears suddenly. Just before, for approximately the same time, the observer perceives a narrowing between the church (S1) on his left and the building on his right. After in the place, the observer begins to see another narrowing before to arrive near the parking lot (S3). The effect between S2 and S3 is interesting. Indeed there is a kind of competition between these two openings. Finally, according to the graphs 3 and 4, the opening in S4 is seen directly in the visual field of the observer and grows gradually till the end of the route.

With the help of the GMD radius, the GMD rearfront location measure enables to partition a given route into sequences, with respect to the potential interest of the observer.

Conclusion

A new method to analyze urban open spaces has been introduced and discussed in this paper. It is based on the study of the sky shape variations in the visual field of the observer along a route. This method uses spherical projections and skeletonization, which brings a new approach to analyze the motionperspective.

The measures associated with this method are based on the extraction of the GMD, which is the skeletal point with the higher distance from the boundary. The GMD radius is relevant to the visual environment of the observer. Whereas, the GMD rear-front location is relevant to the observer direction along a route. The combination of these two measures allows to partition urban routes into sequences, with respect to the potential interest of the observer.

The method presented here is dedicated to the characterization of dense urban spaces. It gives a dynamic assessment of urban visual quality, and can help to enhance existing tools which analyze the urban environment location by location. Nevertheless, tests and improvements of the measures will certainly be required in order to have a better precision and interpretation of the method.

Figure 1 :

 1 Figure 1: Computation of urban skeletons.

Figure 2 :

 2 Figure 2: The route in rue Xavier-Neujean in Liège.

Figure 3 :

 3 Figure 3: GMD radius variation along the route in figure 2.

Figure 4 :

 4 Figure 4: GMD rear-front location graphics for the route in figure 2.

Figure 5 :

 5 Figure 5: The route partition in rue Xavier-Neujean with respect to the figure 4.


Huan Jia

Yann Nguyen

Baptiste Hochet

Mustapha Smail

Isabelle Mosnier

Hao Wu

Olivier Sterkers

Michel Kalamarides

Daniele Bernardeschi

NF2-Related Intravestibular Schwannomas: Long-Term Outcomes of Cochlear Implantation

Keywords: tumor resection and hearing rehabilitation tumor evolution, surgical outcome, cochlear implant outcome neurofibromatosis type 2, vestibular schwannoma, intra-labyrinthine tumor, intravestibular tumor, cochlear implant

Objective: Intravestibular schwannomas (IVSs) are uncommon tumors in Neurofibromatosis type 2 (NF2) and are mainly associated with multiple internal auditory meatus (IAM) and cerebellopontine angle (CPA) tumors. They usually induce profound hearing loss which can be rehabilitated by cochlear implantation (CI). The aim of this study was to analyze the longterm outcomes of CI during the unpredictable evolution of NF2 disease. Study Design: Retrospective case review. Setting: Tertiary referral center. Patients: Three adults with neurofibromatosis type 2 and intravestibular schwannomas, and who were cochlear implant recipients. Interventions: Periodic radiologic follow-up

INTRODUCTION

Neurofibromatosis type 2 (NF2) is a genetically determined disorder whose main manifestation is the development of benign nerve sheath tumors along the cranial nerves with 90-95% of patients developing bilateral vestibular schwannomas (VS). This tumorigenesis can be found anywhere along the vestibular nerve from the cerebellopontine angle (CPA) to the inner ear. When these tumors arise primarily in the inner ear, they are called intralabyrinthine vestibular schwannomas (ILS) [START_REF] Wolf | Imaging quiz case 2: Intralabyrinthine schwannoma[END_REF][START_REF] Tieleman | Imaging of intravestibular schwannomas: a retrospective study of 52 cases with emphasis on lesion growth[END_REF]. These intralabyrinthine lesions can be classified into several subtypes, including intravestibular schwannoma (IVS), intracochlear schwannoma, etc. [START_REF] Kennedy | Intralabyrinthine schwannomas: diagnosis, management, and a new classification system[END_REF][START_REF] Abel | Primary inner ear schwannomas: a case series and systematic review of the literature[END_REF][START_REF] Choudhury | Intralabyrinthine Schwannomas: Disease Presentation, Tumor Management, and Hearing Rehabilitation[END_REF].

NF2-related ILS have rarely been reported despite their high prevalence in temporal bone on NF2 cadavers [START_REF] Nam | Temporal bone histopathology in neurofibromatosis type 2[END_REF]. The impossibility of surgical preservation of residual hearing while removing intralabyrinthine tumors makes surgical timing and procedure different from NF2-"classic" VS without intralabyrinthine involvement, and consequently hearing rehabilitation by cochlear implant (CI) should be counseled when hearing is lost [START_REF] Jia | Intravestibular schwannomas: symptoms and managements[END_REF][START_REF] Aschendorff | Treatment and auditory rehabilitation of intravestibular schwannoma by means of cochlear implants[END_REF][START_REF] Plontke | Cochlear implantation after partial or subtotal cochleoectomy for intracochlear schwannoma removal -A technical report[END_REF]. In this study, we present three cases of NF2 with IVS which were followed up for more than 12 years. After IVS excision, CI achieved high performance on long-term especially as intracanalicular associated-VS had also been removed through a translabyrinthine (TL) approach.

PATIENTS AND METHODS

Following institutional review board approval, the authors carried out a retrospective review of NF2 patients and the cochlear implant register in a French tertiary medical center for the period between 2000 and 2017 in order to identify patient with IVS and in whom a cochlear implantation had been performed. The age at diagnosis, sex, hearing status and evolution (AAO-HNS classification [START_REF] Monsell | Committee on Hearing and Equilibrium guidelines for the evaluation of hearing preservation in acoustic neuroma (vestibular schwannoma)[END_REF]), tumor size and evolution, pre-operative management, surgical records, rehabilitated hearing outcome, and imaging data were collected.

The surgical indications for these patients were discussed by a multidisciplinary team composed of the otologists, neurosurgeon, audiologist, speech therapist, neuro-radiologist and psychologist. The surgery was performed with collaboration between the senior otologists and the neurosurgeon. The intraoperative auditory tests were performed by the senior audiologist.

Pure tone and speech audiometry in a quiet environment were performed in a soundproof room. CI performance was evaluated using open-set word (WRS) and sentence (SRS) recognition scores in quiet and noise (Fournier bisyllabic words and sentences lists). VS size was measured on enhanced-gadolinium magnetic resonance images (MRI) by the senior neuro-otologists, and included both the maximal CPA diameter classified in four stages (1: intracanalicular; 2: <15 mm; 3: <30 mm; 4: ≥30 mm) and its internal auditory meatal (IAM) invasion [START_REF] Zhang | Surgical treatment of sporadic vestibular schwannoma in a series of 1006 patients[END_REF]. Postoperative MRI controls were performed when necessary by 1.5 T MRI under bandaging protocol if cochlear implantation had been carried out.

RESULTS

Two male (cases 1 and 2) and one female patient (case 3) with unilateral NF2-related IVS were identified in the study period. The intralabyrinthine lesions were strictly restricted to the vestibule (Fig 1A ,2A,3A), and these lesions were identified several years after that contralateral large VS had been excised first in cases 1 and 2. The mean age at diagnosis of IVS was 26.3 years (range: 24 -30 years). IVS were associated with ipsilateral intracanalicular VS in 2 cases (Fig 1C and2B) which were recognized later on, or small CPA meningioma in the last one (Fig 3A). No other NF2-related tumor was observed in these patients. Family history with a gene mutation identification was found in case 3. Observation with serial MRI and audiometric tests were initially undertaken for them, and hearing on the IVS side was lost after 4±1.5 years without local tumor growth. All the 3 cases were implanted with cochlear implant concomitantly to IVS removal through TL. One year after cochlear implantation, WRS achieved 87±9.4% (n=3) however the evolution of NF2-related tumors differed between cases during their follow-up of 10±5.1 years.

In case 1 (male, 30 years-old), large right VS was excised in another department through RS but hearing could not be preserved. Left . The tumor could be dissected from the auditory nerve and was completely removed by enlargement of the previous TL approach to expose the IAM and CPA while the CI was left in place (2013). Immediately after surgery, recovery of CI performance was noticed and the patient felt that his hearing had improved sound quality. This good performance has remained stable for the last 5 years (WRS: 90%; SRS: 100%, 87%, 73% in quiet, noise+10 dB SNR, and noise+5 dB SNR, respectively) and was even better than after the initial IVS removal and cochlear implantation 15 years earlier (Cochlear CI24, 20 active electrodes). In the meantime, a symptomatic C6 ependymoma was excised (2015). In 2018, the patient is tumor-free (Fig 1F) and is working as a data processing consultant and can use phone.

DISCUSSION

Although the largest NF2 cadaver study to date reported the presence of ILS in 88% of ears [START_REF] Nam | Temporal bone histopathology in neurofibromatosis type 2[END_REF], at the present time, clinical prevalence is lower at about 15% and 8% of ears in NF2 and sporadic VS [START_REF] Kennedy | Intralabyrinthine schwannomas: diagnosis, management, and a new classification system[END_REF][START_REF] Asthagiri | Mechanisms of hearing loss in neurofibromatosis type 2[END_REF], respectively. In fact, cadaver studies were mainly performed on the individuals with more aggressive NF2 disease compared with the living NF2 patients. Furthermore, intracochlear schwannomas (50-51%) occurred more frequently than intravestibular ones (19-29%) in a systematic review [START_REF] Abel | Primary inner ear schwannomas: a case series and systematic review of the literature[END_REF][START_REF] Choudhury | Intralabyrinthine Schwannomas: Disease Presentation, Tumor Management, and Hearing Rehabilitation[END_REF], as well as in the cadaver study [START_REF] Nam | Temporal bone histopathology in neurofibromatosis type 2[END_REF].

Schwannomas strictly restricted to the vestibule are rare conditions even in NF2 as only three cases were found in our database of more than 250 NF2 patients. Progressive or fluctuating hearing loss was the main symptom although there was no extension into the cochlea.

Hearing was lost in a short period of observation (4 years) without clear tumor growth, at variance with the much slower hearing decline with NF2 [START_REF] Evans | Neurofibromatosis type 2 (NF2): a clinical and molecular review[END_REF][START_REF] Peyre | Natural history of vestibular schwannomas and hearing loss in NF2 patients[END_REF] or with sporadic VS [START_REF] Hunter | Hearing outcomes in conservatively managed vestibular schwannoma patients with serviceable hearing[END_REF][START_REF] Sughrue | The natural history of untreated sporadic vestibular schwannomas: a comprehensive review of hearing outcomes[END_REF]. This may be accounted for by direct damage to the organ of Corti by local abnormal metabolites, such as elevated intralabyrinthine protein, or interruption of potassium cycling [START_REF] Asthagiri | Mechanisms of hearing loss in neurofibromatosis type 2[END_REF][START_REF] Frisch | Intralabyrinthine schwannomas[END_REF].

Surgical resection of intralabyrinthine tumors with hearing preservation has been considered

to be impossible [START_REF] Abel | Primary inner ear schwannomas: a case series and systematic review of the literature[END_REF][START_REF] Jia | Intravestibular schwannomas: symptoms and managements[END_REF][START_REF] Bouchetemblé | Intralabyrinthine schwannomas: A case series with discussion of the diagnosis and management[END_REF]. Thus it has been proposed to remove these tumors when hearing was lost and to perform cochlear implantation in a single surgical procedure through a TL approach to avoid the occurrence of intracochlear fibrosis and/or ossification which might preclude a subsequent electrode array insertion. In such cases, CI provided a good outcome whether the ILS was excised from the cochlea or not [START_REF] Aschendorff | Treatment and auditory rehabilitation of intravestibular schwannoma by means of cochlear implants[END_REF][START_REF] Bento | Minimally invasive surgery for intracochlear schwannoma removal and simultaneous cochlear implantation[END_REF][START_REF] Slattery | Middle fossa decompression for hearing preservation, a review of institutional results and indications[END_REF]. However, long-term CI performance might be altered by either ILS recurrence or tumor development within the ipsilateral IAM. This occurred in the present study more than 5 years after cochlear implantation by either VS growth in cases 1 and 2, or meningioma recurrence in the IAM and CPA in case 3. Indeed, the decreased CI performance may be accounted for by compression of both auditory nerve and cochlear blood supply as evidenced by the transient benefit observed after IAM decompression [START_REF] Slattery | Middle fossa decompression for hearing preservation, a review of institutional results and indications[END_REF][START_REF] Bernardeschi | Internal auditory canal decompression for hearing maintenance in neurofibromatosis type 2 patients[END_REF] and the improved CI performance with subsequent VS removal (case 1). Accordingly, in case 2, IAM decompression had no effect on fluctuating hearing loss which was induced by tumor development within the vestibule. However, long-term CI benefit was achieved by resection of both IVS and intracanalicular VS. On the other hand, IAM invasion by meningioma precluded preservation of the auditory nerve so the CI had to be explanted (case 3). At present time chemotherapy (bevacizumad) could be advocated to preserve CI benefit [START_REF] Plotkin | Hearing improvement after bevacizumab in patients with neurofibromatosis type 2[END_REF] and IAM restricted to CI performance decline in case of growing intracanalicular VS. Further NF2 tumorigenesis should be monitored in these young patients although the presence of the magnetic artifact in case 3 made MRI follow-up difficult. This might be overcome by an experienced neuro-radiological team or an improved positioning of the receiver/stimulator [START_REF] Tod | MRI artifacts and cochlear implant positioning at 3T in vivo[END_REF][START_REF] Walton | MRI without magnet removal in Neurofibromatosis type2 patients with cochlear and auditory brainstem implants[END_REF][START_REF] Shew | Magnetic resonance imaging in a neurofibromatosis type 2 patient with a novel MRI-compatible auditory brainstem implant[END_REF], as in case 2.

In conclusion, these three IVS cases were initially treated in the early 2000s by surgical removal which might not be at the present time the first-line treatment for NF2 apart from cases with life-threatening large VS [START_REF] Jia | Neurofibromatosis type 2: Hearing preservation and rehabilitation[END_REF][START_REF] Tan | Impact of cochlear implantation on the management strategy of patients with neurofibromatosis type 2[END_REF]. However, this study demonstrates that removal of IVS with concomitant CI implantation provides a long-term benefit from CI, although it could be altered by the occurrence of other intracanalicular and/or CPA NF2-related tumors, the treatment of which might restore the initial CI benefit.

  IVS which was already visible at diagnosis in 2000 (Fig 1A) was recognized 3 years later as hearing deteriorated rapidly on the only hearing ear. IVS was removed and a cochlear implant (Cochlear CI 24) positioned concomitantly (Fig 1B). CI performance progressively declined over time and a 6mm-intracanicular VS was disclosed 8 years after implantation (Fig 1C) and appeared to grow quite rapidly after 6 months (Fig 1D). IAM decompression through MF was performed (2011) with an immediate recovery of CI performance. However, CI performance declined again 2 years later because of a fast growing VS which extended slightly into the CPA (overall length of VS, 11 mm) (Fig 1E)

For case 2 (

 2 male, 24 years-old), excision of a large VS was performed through TL in another department in 2005. Because of a left progressive and fluctuating hearing loss in the only hearing ear, MRI was performed and revealed both IVS and small nodular intracanalicular VS in 2009 (Fig 2A). The patient was referred to us in 2011 as hearing had declined such that he had no benefit of hearing aid. IAM decompression by MF did not achieve any benefit (2012) and consequently excision of both IVS and intracanalicular VS and cochlear implantation (Med-EL Concerto, 31mm) were performed through TL during the same surgical procedure (2013). Five years later, the patient presented bilateral small (3 mm) and stable enhancement of the fundus of the IAM (Fig 2D), and was at work and a phone user. CI performance (11 active electrodes) in 2018 was: WRS 76% and SRS 100%, 80%, 80%, 33% in quiet and in noise, +10, +5, and 0 dB SNR, respectively. In case 3 (female, 25 years-old), a right sudden hearing loss had recovered partially under steroid therapy in 2000 and NF2-related tumors were evidenced with IVS and CPA meningioma on the right side and intracanalicular VS on the left one (Fig 3A) ; Because left VS was growing rapidly with a normal hearing (Fig 3B), and on the right side hearing was non-serviceable, both right IVS and CPA meningioma were removed through TL and CI implanted (Cochlear CI24) concomitantly in 2002. Then left stage 2 VS was excised through RS 6 months later (2003). Hearing was preserved in the left ear with a slight decrease of 15 dB (PTA) and the patient was CI user to restore binaural cues. During the first postimplantation 3 years CI performance remained high but slightly deteriorated (90% WRS and 100% SRS at 1 year vs 60% WRS and SRS at 3 years). The patient was lost of followed-up for several years and another MRI was performed 10 years after CI implantation when CI did not achieve any benefit and had been abandoned. Meningioma recurrence on the right side was observed (Fig 3C) and removed. CI was explanted as cochlear nerve was not preserved during the surgical procedure although post-operative facial nerve function remained normal (2014). Binaural hearing was rehabilitated by CROS hearing aids. Two years later, hearing declined slightly on the left only hearing ear and another right menigioma and a possible left de novo or recurrent intracanalicular VS were found (Fig 3D). Then treatment with Bevacizumad was started recently as hearing still declined and NF2-related tumors grew.

Figure legends : Figure 1 .

 :1 Figure legends:

Figure 2 .

 2 Figure 2. Case 2. MRI from 2009 to 2018 showing the undiscovered IVS at diagnosis (A)and ipsilateral slow growing VS (B-C). On the last follow-up, bilateral small enhancement were observed without any evidence of recurrence (D).

Figure 3 .

 3 Figure 3. Case 3. MRI from 2000 to 2018 showing IVS (A) associated with other NF2related tumors (ipsilateral CPA meningioma and contralateral intracanalicular VS), contralateral growing VS after 1 year (B) and ipsilateral meningioma recurrence 14 years later (C). Final imaging disclosing another CPA meningioma which may have been hidden by the magnet artifact on previous MRI and non-visible left lesion on this view (D).