FR2806194A1 - Data processing method for constructing multi-dimensional images from a point-diagram of known coordinates where the coordinate points are interpolated using a natural neighbor interpolation method and Delaunay triangulation - Google Patents

Abstract

Method involves definition, by natural interpolation, of the natural neighbors of current point on the diagram and evaluating its natural coordinates, each in correspondence with a natural neighbor. An implicit function is calculated representing a distance between a current point and a surface element comprising natural neighbors to the current element, to construct a whole surface built up from a multitude of points each used successively as a current point. The invention also relates to a device for use with the above natural neighbor interpolation method.

Description

<U> Data Processing for Advanced Construction </ U> <U> of Multidimensional Images </ U> The present invention relates to data processing for multi-dimensional image construction. Geometric modeling consists of developing a treatment of one or more three-dimensional objects measured by a telemeter sensor, such as a probe, a laser range finder, or three-dimensional imaging systems. The initial data is in the form of a set of points without a particular structure measured on the surface of the objects. Such a problem is encountered in particular in computer-aided design (CAD), computer graphics, medical imaging, molecular chemistry or geology. From the cloud of points which constitutes these initial data, one wants to be able to carry out all or part of the following operations, independently or in combination - to build a surface representative of this cloud, called the underlying surface, - to calculate information on the surface under superficial, such as normal or curvature at the surface, - calculate a polyhedral approximation (also called mesh) of the surface, - visualize this surface at different resolution levels, notably enlarge the image of a surface sample to observe ("zoom" some parts of the surface), - change the relative position of the measuring points relative to the underlying surface to smooth or deform the surface, - simplify the cloud of points by removing points from the cloud that do not do not satisfy a chosen condition. Geometric modeling, construction and / or surface reconstruction requires the prior development of a computer model. This model needs to be optimized to limit processing times to acceptable times. In terms of data flow management, it is also sought for a gradual transmission of the cloud of points. One wants to be able to visualize and update, in particular to refine, an approximation of the object as the data is transmitted. With the development of surface construction / reconstruction techniques, various processes have emerged. In particular, a known method, based on the consideration of the nearest neighbors (in selected numbers) of a current point, gave satisfactory results for the construction / reconstruction of surfaces. Details of the principle of this process are given in particular in [HDD + 92] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle. Surface reconstruction from oneorganized points. Comput. <I> Graphics, </ I> 26 (2 <B>) </ B>: 71-78. Proc. SIGGRAPH492. However, the application of this method assumes the prior checking of a condition the distribution of sampled points must be uniform on the surface. Such methods, although promising, have shown their limit, especially because of the unstructured nature that usually has a cloud of points, or because of the often prohibitive processing times they require. The present invention provides solutions to solve the problems posed by the implementation of all or part of the above operations. According to a different approach, the invention uses a spatial data interpolation, of the "natural interpolation" type, applied to geometric modeling. the principle of a natural interpolation is known in particular by [Sib81] R. Sibson. A brief description of natural neighbor interpolation. In Barnet, editor, Interpreting Multivariate Data, pages 21-36. John Wiley & Sons, Chichester, 1981. Without going into more detail, a natural interpolation generally consists in defining every point as the centroid of a subset of points in the cloud, these points then being defined as natural neighbors of this centroid. The weighting coefficients of the center of gravity, each associated with a natural neighbor, are called natural coordinates. The present invention proposes a method of data processing, in particular for the construction / reconstruction of multidimensional images. It can be both two-dimensional or three-dimensional images. As will be seen in detail below, this method applies to any dimension, greater than or equal to two.

The method of processing therefore comprises the following steps: a) firstly obtaining a cloud of known coordinate points, and b) defining, by a natural interpolation of this point cloud, the natural neighbors of a current point of the cloud and evaluate the natural coordinates of the current point, each in correspondence with a natural neighbor. According to a first important characteristic of the invention, the method further comprises the following steps: c) calculating, from the natural neighbors of a current point of its natural coordinates, an implicit function representative of a distance between this current point and a surface element substantially comprising the natural neighbors of the current element, repeating steps b) and c) with at least a portion of the points of the cloud taken successively as common points, and constructing a surface comprising a plurality of points taken from the step d) as common points and whose implicit function satisfies a selected condition, such as in one embodiment, the implicit function is zero. According to a second important characteristic of the invention, the method further comprises the following steps c11) estimating an orientation of a first selected surface element, preferably for the point of greatest abscissa as a current point, and c12) deducing the from each other and from the orientation of the first element, the respective orientations all the surface elements, which makes it possible to obtain the orientation of the unit vectors perpendicular to each one of a surface element.

According to a third important characteristic of the invention, step e) of the method comprises an operation of ignoring the points of the cloud whose distance to the surface to be constructed is less than a threshold value, with a view to simplifying of the point cloud, which makes it possible to construct a total surface from the cloud of points and / or to smooth this surface, preferably according to a chosen tolerance, and / or to locally deform this surface. According to another important characteristic of the invention, step b) of the method comprises the following preliminary operations applying a Delaunay triangulation to the cloud of points, b2) constructing Voronoi cells and deducing therefrom the centers of the cells, b3) adding to each cell two poles corresponding substantially to points furthest from the center of the cell, preferably located on either side of the surface, and whose associated natural coordinates are preferentially considered as zero, and b4 evaluating the natural coordinates in each cell thus increased. Thus, instead of calculating the natural coordinates on the Voronoi diagram of the initial point cloud, for each current point, these coordinates are calculated on the Voronoi diagram of the increased cloud of the poles. An interpolation thus executed has the following advantages - the results obtained by this interpolation are close to those obtained by a rigorous interpolation on any scatterplot, and the associated processing times are considerably reduced by at least a factor of ten. The method according to the invention can be implemented by a device comprising in particular - minus a memory for arranging the coordinates of each point of the cloud, - processor capable of cooperating with the memory to perform all or part of the operations of the method, - interface graphic arranged to cooperate with the processor, and - screen connected to the graphical interface to display at least the constructed surface. In this respect, the present invention also aims at such a device. Other features and advantages of the invention will become apparent from the following detailed description, and the accompanying drawings in which - Figure 1 schematically shows a device for implementing the method according to the invention. FIG. 2 illustrates the construction of a Voronoi cell in a two-dimensional space; FIG. 3 illustrates the principle of an insertion of a point x in a two-dimensional Delaunay triangulation; FIG. schematic of a surface with its normals, in a plane including the abscis axis its - figure 5 represents the poles S and S 'of a Voronoi cell whose point Ai is the center, and - figure 6 is a flowchart representing the steps of a process for the orientation of perpendicular unitary vectors (normal vectors). Annex I contains equations to which the description text hereinafter refers and Annex II retranscribes in the form of a pseudo-code a computer processing for the insertion of a point in a three-dimensional Delaunay triangulation. The drawings contain, for the most part, elements of a certain character. They can therefore not only serve to better understand the description, but also contribute to the definition of the invention, if any. Referring to Figure 1, the device is in the form of a computer comprising a central unit UC provided with a microprocessor uP which cooperates with a motherboard CM. This motherboard is connected to various equipment, such as a COM communication interface (Modem or other type), a ROM and a working memory RAM (RAM). The motherboard CM is further connected to a GUI GUI, which controls the display of data on an ECR screen that includes the device. I1 is further provided input means, such as keyboard CLA and / or input member called "mouse" SOU, connected to the central unit UC and allowing a user interactivity with the device. In the example shown in FIG. 1, a left part of the screen represents a cloud of points whose coordinates are known and previously recorded, for example in ROM of the device. On the right side of the screen is shown a reconstructed surface, for example in a three-dimensional space, by a treatment according to the method of the invention and performed by the microprocessor in cooperation with the various memories of the central unit. The input means CLA, SOU allow a user to enter for example a smoothing tolerance of the reconstructed surface, or to refine this surface. In another embodiment, the device can progressively receive points of the cloud in a chosen order, through its communication interface COM, then build a raw surface, while the ROM memory includes a module with which the microprocessor can cooperate to refine the surface by inserting selected points of coordinates, as will be seen later. The method according to the invention applies to the geometric modeling an interpolation of spatial data whose principle is described in [Sib81] and called "natural interpolation". Referring to FIG. 2, the natural interpolation allows, given a set of points A = @ A1, ... An} of a space E, to express any point X of E as the center of gravity of a sub. -A set of points of A called the natural neighbors of the point X. In equation 1 in the appendix the coefficients \ i are called the natural coordinates of X are each in correspondence with a natural neighbor Ai. To precisely define the coefficients ai, we must consider the Voronoi diagram of A or the Delaunay dual triangulation. In the example shown in FIG. 2, the polygon represented in dotted lines forms the Voronoi cell whose point X is the center. In three-dimensional space, this cell is delimited by a polyhedron. definitions and the properties of these geometric structures are described in books of algorithmic geometry, for example in BY98] Jean-Daniel Boissonnat and Mariette Yvinec. Algorithmic Geometry. Cambridge University Press, UK, 1998. Translated by Hervé Brdnnimann.

The calculation of the Delaunay triangulation is possible in all dimensions. A particularly efficient algorithm in a space with two or three dimensions can be derived from the principle described in Dev98] Olivier Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. <I> Comput. </ I> Geom., Pp. 106-115, 1998.

In what follows, we call V (Ai) the cell of the Voronoi diagram of the set A and which is associated with the point. We denote by V (X) the cell of a point X in the Voronoi diagram. set A increased by the point X. Ai is a natural neighbor of X, then V (Ai) and V (X) a non-empty intersection V (Ai, X). The natural coordinate 1, i (X) is the ratio of the volume of V (Ai, X) to the volume of V (X). The calculation of natural coordinates in a two-dimensional space is described in particular in [Wat92] David F. Watson. Contouring <I>. </ I> A Guide to the <i> and </ i> Display <i> of Spatial </ i> Data. Pergamon, 1992. In a three-dimensional space, an evaluation of natural coordinates by the explicit calculation of the intersection between X's Voronoi cell and those of its neighbors is described in the thesis of S.J.Owen [Owe92] S.J. Owen. An implementation of natural neighbor interpolation in three dimensions. Master's thesis, Brigham Young University, 1992. However, this assessment, although satisfactory in principle, has shown some practical limitations, including the fact that the algorithm associated with this evaluation is not effective. is described below an effective evaluation method. The proposed treatment first relies on an X-point insertion algorithm in a three-dimensional Delaunay triangulation. As an indication, FIG. 3 illustrates in the two-dimensional space the principle of insertion of a point X in a Delaunay triangulation. All triangles whose circumcircle surrounds the point X must be deleted. These triangles are said to conflict with X. The hole thus created polygon pl to p6 in Figure 3) is then retriangulated by connecting X to the edges of the edge of the hole, as shown in dashed lines in Figure 3. Consider, in the example represented, a set of points p1 to p6. Each point is joined to its neighbor by the stop of a triangle. A point x is inserted if it is contained in all the discs delimited by circles in which the triangles are circumscribed, one by one. In three-dimensional space, the tetrahedra in conflict with the X-point are first identified. It is recalled that a "tetrahedron in conflict" is a tetrahedron whose circumscribed sphere contains the point X. The union of these tetrahedrons forms a polyhedron called "cavity" in what follows. The edges of the conflicting tetrahedra are located either on the boundary of this cavity, or in its interior. They are called respectively external edges and internal to the cavity. Then, the new filling cavity tetrahedra are created. They are based on the faces of the cavity and have a common vertex point X. The creation and updating adjacency relations between these tetrahedrons are preferably carried out by rotating around the outer edges of the cavity. The algorithm for calculating natural coordinates consists in describing a triangulation of the border of the regions subtilized by the point X to its neighbors. The volumes of V (Ai, X) are calculated from the triangulations, for example according to the principle described in [Ber87] M. Berger, Geometry <I> II, </ I> section 12.2, Springer, 1987. Natural coordinates Ai are then deduced from these volumes by normalization. Thus, conflicting tetrahedra are first found. Then, during the rotations around the inner and outer edges, the dual faces of these edges are reported. Each face of this type is common to two natural regions, and its vertices are the Voronoi centers of the traversed tetrahedra. The sequence of these vertices is then the triangulation used to calculate the volume. Reference may be made to the retranscribed processing in Appendix II and preferred here for point insertion in a three-dimensional Delaunay triangulation. According to the invention, an implicit function is calculated from local information on a surface to be reconstructed. This default function interpolates this information as follows. call A to a cloud of points A = {A1, ... An} 'a space E (E is in general the usual three-dimensional plane or space but the process applies in all dimensions measured on an orientable surface S. In At first, we consider at each point Ai, the normal vector <B> ni </ B> with a dot surface is known.

An approximation of the signed distance of a point X from E to the surface is estimated by the implicit function h (X) given by the formula corresponding to equation 2 in the appendix. Thus, the evaluation of the implicit function h (X) can be carried out by carrying out the following steps: determining, for each natural neighbor Ai of the current point X, a vector XAi between the current point and this natural neighbor, calculating the product scalar between the vector XAi and the unit vector <B> ni </ B> perpendicular to the surface element comprising this natural neighbor Ai, weighting the scalar product by the natural coordinate Ai (previously calculated) of the current point and associated with the neighbor natural Ai, and - estimate the sum of the scalar products thus weighted on all the natural neighbors of the current point X. The use of this implicit function has many advantages. Indeed, the function h is continuously differentiable. Moreover, the set SA of the points X for which the function h (X) is zero, is a surface which passes through the Ai and whose normal in Ai is the vector <B> ni. </ B> I1 is then proposed here an approximation of the surface S per surface SA.

The principle of calculating an implicit function from Ai and vectors <B> ni </ B> has been described in particular in [HDD + 92] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W Stuetzle. Surface reconstruction from oneorganized points. Comput. <I> Graphics, </ i> 26 (2): 71-78. Proc. SIGGRAPH492. However, in their works, the authors use the natural neighbors but the k nearest neighbors. Thus the method described in [HDD + 92] is unusable if the surface is not uniformly sampled. Besides the fact that it makes it possible to correctly treat cases of unevenly sampled surfaces, the use of the method according to the invention provides a smooth SA surface and gives good results even if the data are scarce, with few points in the cloud. The estimate of the normal vectors <B> ni </ B> is described below. In the following, we now call "natural neighbors" of a point Ai of a set A, the natural neighbors of Ai that we would obtain if we removed the point Ai from the set A. We can then calculate the neighbors and natural coordinates of Ai in the new set A \ @Ai}. To estimate the direction of the normal vector ni, a first approach consists of calculating the mean (least squares) plane passing through the natural neighbors of Ai weighted by the associated natural coordinates. Another approach, preferred here, is based on the insertion, among the natural neighbors Ai, of the poles of the Voronoi cell whose point Aj the center. These poles will be described in detail below The direction of the vector <B> ni </ B> being known, it remains to orient the vector ni, that is to say to choose an orientation among the two possible orientations. In particular, it is sought to carry out these orientations in a coherent manner for all the points Ai. Referring to Figure 6 for details of the steps of the normal vector orientation method <B> ni. </ B> After a start instruction 10, first (step 12) is selected, for the point of greater Ax abscissa, the orientation of the vector ni, such as this vector ni, forms an acute angle (FIG. 4) with the unit vector carried by the first coordinate axis (abscissa axis). A first point Garlic now has a normal vector ni ,. Consider then a general step of the method of assigning orientations, where a certain number of points of A already have a normal vector (but not all). A test (step 16) is first performed to determine whether or not a point Aj has a normal vector with j ranging from 1 to N where N is the total number of normal vectors to be orientated (step 14). For each point Aj which does not yet have a normal vector, its normal vector mj is estimated by the formula given by equation 3 in the appendix. In this equation 3, the vector <B> ni </ B> (Aj) is considered as zero if the point Aj does not have a normal vector yet. At each point Aj we associate (step 18) the value vj of the projection of the vector on the direction ô j. If the absolute value of vj is the largest of those calculated previously (test 20), then it is given the direction 6 j (steps 24 and <B> 25). </ B> Its orientation is determined according to the sign of vj (test 22). The values of the projections vk associated with the natural neighbors of. are updated (step 26) and then maintained the list of Aj sorted by decreasing values of the vj (step 28) These steps are repeated by recurrence (step 30) until the list is exhausted (test 32 and end instruction in) Thus, a normal vector ni is assigned to the first element of the list (the point Garl) and this list is progressively updated, for example using, in practice, data structure of the type "queue of priority". The method of orientation of the normals is particularly advantageous with respect to the other known methods, for example a method based on the principle described in [HDD + 92] and which assumes a uniform distribution of the points on the surface S. other determination normal vectors is based on a principle described in [ABK98] N. Amenta, M. Bern, and M. Kamvysselis A new voronoi-based surface reconstruction algorithm In Proc SIGGRAPH'98, Com However, only the direction of the normals is provided here, not their orientation. Particularly advantageous method for evaluating natural coordinates with reduced time processing time is described below. For each Voronoi V cell (Ai) we search for its farthest vertex S and the furthest vertex S 'in the direction of the vector SAi (FIG. 5). These points are called the poles. We denote by A + the set of points A and poles added. The evaluation of the natural coordinates is made by considering the Voronoï diagram of A 'but by posing that the natural coordinate associated with a point added is null. The number of volumes to be calculated is then proportional to the number of natural neighbors of the point which are neighboring sample points of X on the surface (and no longer in the whole space). This method makes it possible to divide the computation times by a factor of about 20. Hereinafter, a method for simplifying the initial point cloud is described below. Often the data are redundant and it is desirable to extract from the scatterplot A as small a subset as possible which represents to a tolerance e near the surface S. For this, we consider a small subset A 'of A and for all points of A \ A ', their distance to SA is evaluated using the implicit function described above. If the distance of a point Ai exceeds absolute value e, we add Ai to A 'We then re-evaluate the distances of the points of A \ A' whose point Ai has become a natural neighbor. The process is repeated until all the points of A \ A 'are at a smaller distance in absolute value than e of SA ,. This method differs from the usual methods which consist, for example, in constructing an initial mesh from the data points and then, in a second step, in simplifying this mesh. Thus, the simplification method described above is particularly advantageous in the case of very large data sets for which it is not conceivable to build a mesh. This situation is often encountered in modeling applications from measurements. This method also makes it possible to represent the surface at different resolution levels. Typically, if one sorts the points of the set A according to the insertion order described above, it is possible to vary the resolution of the reconstruction by retaining for example only a selected number of first points.

The proce 'finds a particularly advantageous application to the transmission of data by a link of the type using a COM communication interface (Figure 1). the points are transferred in the aforementioned order of insertion the reconstructed model can be progressively refined to and as the points are transmitted. An application to an online use ("internet" type) thus makes it possible to display progressively a complex three-dimensional object without having to wait for the complete data loading. Here is described a method for displaying on the screen ECR of built surface S. To visualize the surface S with the usual graphic cards (or graphical interfaces IG), it is necessary to mesh surface S, that is to say to build a polyhedron which approaches S to a certain tolerance <B> il </ B> predetermined. A known method consists in using a "marching cubes" type algorithm resulting from the principle described for example in reference [HDD + 92]. However, this method has several disadvantages, in particular the fact that the resolution depends on the size of the grid and not on the local properties of the surface and, on the other hand, the fact that the points Ai are not, in general, points of the mesh.

The process used here begins with a rough triangulation of the surface S, optionally followed by a plurality of steps consisting generally of refining this triangulation.

To each triangle of the current triangulation, we associate a point on the surface, equidistant from the vertices of the triangle. This point is called the center of the triangle. This point is eventually added as the new vertex of the mesh. However, in the case of point data, we do not know any initial mesh. Nevertheless, the Voronoi diagram and the Delaunay triangulation of the set A have been calculated to evaluate the natural coordinates, and are therefore available. The facets of an "initial" mesh are determined as follows. In a first step, we search for edges called "bipolar" and which correspond to edges of Voronoi whose function distance (evaluated according to the equation 2 of the appendix) is positive at one of their ends and negative to the other (in other words, these edges cut S). The facets of the initial mesh are then the Delaunay triangulation facets whose dual edge is bipolar. This mesh can then be refined by inserting the centers of the facets of the mesh and by progressively updating the set of faces of the mesh. Thus, center is inserted if its distance to the corresponding triangle is greater than a predetermined threshold. For more details on the mathematical principle of which this method advantageously adapted, one can refer to [Che97] Chew. Guaranteed quality Delaunay meshing in 3d. Proc. 13th Annu. ACM Sympos. Comput. Geom., Pages 391-393, 1997. The mesh obtained has as vertices the points Ai and centers added. Smooth surfaces can thus be obtained even with very few data points. This method therefore finds a particularly interesting application for the transmission of data (for example online) and the compression of geometric models. It is sufficient to transmit the points Ai and, on reception, to use the mesh method described above.

Another interesting application is in the interactive creation of objects from points. From a small sample, it is then possible to build a first surface that can then be modified. Such modifications can be made by deforming the constructed surface. The method that can be used consists in choosing for a current point a set of parameters ai to be added or subtracted each to one of the scalar products of equation 3, in order to deform the constructed surface at this current point. Thus, by replacing, for a set of selected parameters ai, equation 3 by equation 4 in Appendix I, or by modifying one or more normal vectors <B> ni, </ B> can in a simple manner locally deform the SA surface. It is then possible to edit for example a model from points, as described above. Of course, the invention is not limited to the embodiment described above by way of example; it can be extended to other variants nevertheless defined in the context of the claims below. ANNEX <B><U> I </ U></B>

<B><U>ANNEXE II</U></B>

<B><U> ANNEX II </ U></B>

void <SEP> delaunay :: create (tetrahedron <SEP> * n, <SEP> Index <SEP> i)
<tb> {tetrahedron <SEP> * son, <SEP> * nn;
<tb> // create <SEP> the <SEP> tetrahedron <SEP> leaning <SEP> on <SEP> the <SEP> i-th <SEP> side <SEP> of <SEP> n
<tb> // and <SEP> update <SEP> adjacencies
<tb> (1) <SEP> its <SEP>n-> its [i] <SEP> = <SEP> new <SEP> tetrahedron (insertedPoint, <SEP> n, <SEP>i);
<tb> (2) <SEP>son-> Neighbor [0] <SEP> = <SEP>n-> Neighbor [i] <SEP>;
<tb> (3) <SEP>n-> Neighbor [i] ->
<tb> Neighbor [n-> Neighbor [i] ->n-> findNeighborIndex (n)] <SEP>sound;
<tb> // recursively <SEP> create <SEP> the <SEP> sounds <SEP> neighbors
<tb> (4) <SEP> for (j <SEP> = <SEP> 1 <SEP>;<SEP> j <SEP><<SEP> 4 <SEP>;<SEP> j ++ <SEP>)
<tb> (5) <SEP> rotate <SEP> around <SEP> the <SEP> edge <SEP> opposite <SEP> to <SEP> [i, j]
<tb> until <SEP> the <SEP> next <SEP> cavity <SEP> face. <SEP> let <SEP> nn <SEP> be <SEP> the <SEP> corresponding <SEP> tetra
<tb> and <SEP> k <SEP> be <SEP> this <SEP> face
<tb> // create <SEP> the <SEP> tones <SEP> neighbor <SEP> and <SEP> link <SEP> it
<tb> (6) <SEP> if <SEP>(<SEP>!<SEP>nn-> sound [k] <SEP>) <SEP> create (nn, k);
<tb> (7) <SEP>son-> Neighbor [j] <SEP> = <SEP>nn-> sound [k] <SEP>;

Claims (13)

<U> Claims </ U> A data processing method for multi-dimensional image construction, comprising the steps of a) obtaining a scatter of points (E) of known coordinates; b) defining, by natural interpolation of this point cloud, the natural neighbors (A \ (Ai)) of a current point (Ai) of the cloud (E) and evaluate the natural coordinates (Xj) of the current point (Ai), each in correspondence with a natural neighbor (Aj), characterized in that it further comprises the steps of c) calculating, from the natural neighbors of a current point (Ai) and the natural coordinates, an implicit function representative of a distance (h (Ai)) between this current point and a surface element (SAi) substantially comprising the natural neighbors (Aj) of the current element (Ai), d) repeating steps b) and c) with at least a portion of the points of the cloud successively taken as current points, and e ) construct a surface (SA) comprising a plurality e of points taken in step d) as common points and whose implicit function satisfies a chosen condition. 2. Method according to claim 1, characterized in that step e) comprises the following operations el) determine the current points whose implicit function is zero, and e2) insert these current points in the surface to be built. 3. Method according to one of claims 1 and 2, characterized in that step c) comprises the following operations cl) determine, for each natural neighbor (Ai) of the current point (X), a vector (XAi) between the current point and this natural neighbor, c2) calculating a dot product between the vector (RAi) determined in step c1) and a unit vector <B> (ni) </ b> perpendicular to the surface element comprising this natural neighbor, c3) weight the scalar product by the natural coordinate of the current point (ki) which is in correspondence with natural neighbor), and c4) estimate the sum of scalar products thus weighted on all the natural neighbors of the current point. 4. Method according to one of the preceding claims, characterized in that it further comprises steps c11) estimate an orientation (ni,) of a first selected surface element, and c12) deduce from each other and to from the orientation of the first element, the respective orientations (# of all the surface elements, which makes it possible to obtain the orientation of the unit vectors perpendicular to each one of a surface element. 5. Method according to claim 4, characterized in that the orientation (ni,) of the first surface element is estimated for the point of greatest abscissa (Ail) as the current point. 6. Method according to one of the preceding claims, characterized in that step e) comprises an operation of ignoring the points of the cloud whose distance to the surface to be constructed is less than a threshold value (s), in order to perform a simplification of the point cloud. 7. Process according to claim 6, characterized in that the threshold value () is chosen according to a smoothing tolerance of the surface to be built. 8. Method according to one of claims 3 to 7, characterized in that it comprises an operation of choosing a set of parameters (ai) to be added or subtracted from each of the scalar products, in order to deform the surface built at this point. 9. Method according to one of claims 4 to 8, characterized in that it comprises an operation of changing the coordinates of at least one vector <B> (ni) </ B> normal to a surface element, in to deform the constructed surface into a surface element. 10. Method according to one of the preceding claims characterized in that step b) comprises the following preliminary operations b1) apply a Delaunay triangulation cloud points, b2) build Voronoï cells and deduce centers (X) of cells, b3) add to each cell two poles (S, S ') substantially corresponding to points furthest from the center of the cell, and b4 evaluate said natural coordinates in each cell thus increased. Method according to claim 10, characterized in that in step b4), the natural coordinates associated with the added poles (S, S ') are considered as zero. Method according to one of claims 10 and 11, characterized in that it further comprises the following steps hl) determining, from the Delaunay triangulation in step b1), at least one facet, as well as a center of this facet, h2 estimate, by calculating the implicit function of the center of the facet, the distance between the facet and its center, and h3 insert this center into the constructed surface if the estimated distance is greater than a predetermined threshold ( it), which makes it possible to refine the constructed surface. 13 Device for implementing the method according to one of the preceding claims, characterized in that it comprises - at least one memory (ROM) to store the coordinates of each point of the cloud, - a processor (pP) able to cooperate with the memory for performing all or part of the operations of the method, - a graphical interface (GU) arranged to cooperate with the processor, and - a screen (ECR) connected to the graphical interface for displaying at least the constructed surface.