Method for automatically segmenting teeth

Abstract

A method for segmenting a digital tooth model 4 comprising a three-dimensional triangular mesh 41, the method comprising the steps of: - classifying, within the mesh 41, at least one triangle into the concave category and / or at least one triangle into the convex category; and - identifying, within the mesh 41, at least one tooth region containing triangles, so that each triangle of the region has at least one neighboring triangle within the region, and all triangles of the region do not belong to either the convex or concave category. A method for carrying out the above.

Description

Technical Field

[0001] The present invention relates to medical imaging in the field of dental prostheses. Specifically, the present invention relates to the segmentation of digital models of teeth including three-dimensional triangular meshes.

Background Art

[0002] An optical scanner is used to measure the dimensions of the dental arch inside a patient's mouth. This device, associated with three-dimensional vision software, is used to obtain and display a very accurate triangular mesh of the dental arch. This technology is useful for dental technicians to create the shape of dental prostheses and is utilized to transmit and store information related to the dimensions of a patient's dental arch.

[0003] However, this type of scanner cannot be used to accurately measure information regarding the color tone and translucency of a patient's teeth. As a result, the majority of dentists continue to use traditional color tabs held by hand to manually compare the patient's teeth with color tabs in order to select a color tone that, when looking at the manufactured prosthesis with the naked eye, appears to best match the color tone of the patient's teeth. However, this type of comparison is very approximate, and the manufactured prosthesis does not fit well enough with the color of the patient's teeth. This means that the prosthesis does not look good in the mouth.

[0004] In order to obtain accurate information on color tone and translucency, other technologies also exist, such as a spectrophotometer (such as the "Rayplicker" in the name of the applicant) that can be used to accurately identify the color and shade of the color and translucency of a tooth in a given tooth and align the color and shade of the color and translucency with respect to the tooth in a file representing the tooth in two dimensions.

[0005] However, these three-dimensional dental arch measurement technologies and two-dimensional tooth color determination technologies are not compatible. In other words, a spectrophotometric system cannot be integrated into a dental arch digital measurement system. This is due to the nature of these two technologies. The permanent movement of the optical scanner used to digitize the patient's entire dental arch in three dimensions does not meet the stability requirements over a period of about one second or more required to perform a spectrophotometric analysis of a single tooth.

[0006] To solve this problem, it is necessary to digitally associate a single tooth related to the local color tone and translucency values obtained using a spectrophotometer with the corresponding tooth represented by a triangular mesh obtained using an optical scanner. However, here two different digital representations are being described. One is a two-dimensional representation of the tooth, and the other is a three-dimensional representation of the tooth that is not specified.

[0007] Therefore, first, it must be possible to identify which tooth in the three-dimensional triangular mesh is involved. Further, in order to find the corresponding tooth, a reference tooth with known color tone and translucency values must be compared with each of the teeth identified within the mesh.

[0008] The prior art (specifically, the document "A Fast Segmentation Method for STL Teeth Model" (Zhanli Li)) has already described a method for segmenting a digital model of teeth including a three-dimensional triangular mesh that utilizes a conventional "region growing" algorithm to identify a tooth region including this seed triangle using the seed triangle as an input value.

[0009] However, the tooth region identified using this algorithm is not accurate enough and may extend over multiple teeth, although these multiple teeth are separated. Therefore, it becomes difficult to find the tooth corresponding to the reference tooth within the mesh.

[0010] In addition, in order to start segmentation by the method described, seed triangles located on each tooth must be supplied. Therefore, this method cannot perform automatic tooth segmentation that starts only from a triangular mesh without using any other information.

Prior Art Documents

Non-Patent Documents

[0011]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0012] Specifically, the aim of the present invention is to improve the segmentation of a tooth digital model including a three-dimensional triangular mesh.

[0013] Another object of the present invention is to enable automatic segmentation of the model from the mesh.

[0014] Another object of the present invention is to simplify the identification of teeth corresponding to a reference tooth in a two-dimensional display within the triangular mesh.

Means for Solving the Problems

[0015] Accordingly, the present invention relates to a method for segmenting a digital model of a tooth including a three-dimensional triangular mesh, characterized in that this method automatically performs the following steps referred to as initial steps: - A step of classifying at least one triangle in the mesh into a concave category and / or at least one triangle into a convex category, and - A step of identifying at least one tooth region including triangles within a mesh such that each triangle in the region has at least one adjacent triangle within the region, and such that all triangles of the region do not belong to either a convex category or a concave category.

[0016] Teeth are actually separated from their adjacent teeth and tooth roots by deep concave regions. In addition, the apex of the tooth, which functions as an intermediate portion between the outer side of the model and the surface of the tooth exposed inside the dental arch, corresponds to a very distinct convex region. By classifying the triangles of the mesh into a convex category or a concave category, the boundaries of the teeth are identified. Triangles that are not classified into either the concave category or the convex category are unclassified, and in other words, are intended to be part of the tooth region to be identified.

[0017] Therefore, by identifying the tooth region, it becomes possible to identify the triangles forming the tooth, which are delimited by its boundary composed of a concave category or a convex category that is not part of the tooth. Therefore, a tooth region extending across one tooth is identified. Therefore, as a natural result, tooth regions extending across each digitized tooth of the dental arch can be identified within the mesh.

[0018] In addition, by using this method, it becomes easier later to compare the teeth within the mesh with a two-dimensional reference tooth. The teeth of the mesh or each tooth are identified in a form starting only from one tooth and at least most of the outer surface of the said tooth corresponding to the tooth region. Therefore, it becomes easier to identify the contours and compare these contours with the contours of the reference tooth.

[0019] Advantageously, in order to perform the step of classifying the triangles into a concave category or a convex category, the present automatic means performs the following sub-steps: - In at least one triangle of the mesh's triangles, determining an angular value between the triangle and each adjacent triangle of each triangle neighbour with respect to the triangle, and - Classifying the triangle into a concave category or a convex category according to the determined angular value.

[0020] Thus, this means classifies the triangle in consideration according to its "second neighbour", where the "second neighbour" is the neighbour of the neighbour of this triangle. Thus, a region larger than the region of the direct neighbours can be considered.

[0021] Preferably, this automatic means determines the angular value using the normal of the triangle and the normals of each triangle adjacent to each triangle neighbour with respect to this triangle.

[0022] Thus, the angle is determined quickly because these normals are known from the digital model.

[0023] Advantageously, in at least one triangle within the concave category, this automatic means performs the following steps: - Determining the number of triangle neighbours with respect to the triangle within the concave category, and - Removing the triangle from the concave category if this number is less than a predetermined value.

[0024] Thus, this additional pass reduces the noise generally present within the concave region, in other words, removes triangles that are classified into the concave category but are clearly isolated and do not belong to the concave region of the mesh.

[0025] Preferably, to perform the step of identifying the tooth region, this automatic means performs the following sub-steps: - Determining a seed triangle within the mesh that belongs to neither the concave category nor the convex category, - Selecting triangle adjacents to a seed triangle, each having a normal with a value within a predetermined interval and belonging to neither a concave category nor a convex category, and - Treating each of the selected triangles as a seed triangle for the purpose of identifying a tooth region that includes the selected triangle, and repeating the previous step at each seed triangle until there are no unclassified triangles left to be selected.

[0026] Accordingly, a "region growing" algorithm is implemented to determine a region that includes triangles located on one tooth and their adjacents to each other. Accordingly, triangles belonging to various teeth are identified. By extracting "convex" triangles or "concave" triangles, it is possible to establish regions that stop at the intersection between teeth (concave regions) or the intersection with other elements (convex regions at the top, concave regions at the tooth root), and thus avoid the region extending across multiple separate teeth.

[0027] Advantageously, the present automatic means determines a plurality of separate seed triangles within the mesh that belong to neither a concave category nor a convex category for the purpose of identifying a plurality of separate tooth regions.

[0028] Accordingly, a plurality of tooth regions are established within the mesh.

[0029] Preferably, the present automatic means performs the following steps: - Determining the number of adjacent triangles located within the tooth region adjacent to the tooth region, in the tooth region or in at least one of a plurality of tooth regions; - When the number of adjacent triangles exceeds a predetermined value, combining the tooth region with an adjacent tooth region so that one tooth region is formed by two regions as a result.

[0030] Thus, at the end of the previous step, although multiple regions may correspond to one tooth, here the adjacent tooth regions are combined, and as a result, one tooth region comes to correspond to one tooth.

[0031] Advantageously, the present automatic means performs the following steps: - Determining the number of triangles in the region and the average curvature value of the region in the tooth region or in at least one of the plurality of tooth regions; - Marking the tooth region so as not to further identify the triangles of the tooth region as part of the tooth region if the number of triangles exceeds a predetermined maximum value, the number of triangles is less than a predetermined minimum value, and / or the average curvature value is less than a predetermined threshold value.

[0032] Thus, at the end of the previous step, tooth regions corresponding to other elements of the mesh may be maintained, but here these possible regions are removed, and as a result, each remaining region comes to correspond to one tooth. The elements to be removed are extremely flat (such as any digitized dental pedestal), extremely large (such as the tooth root), or extremely small to correspond to a tooth. This avoids maintaining elements that will have the shape of a tooth when two-dimensionally projected but do not correspond to a tooth in three dimensions. This is essential for later searching for teeth within the surface, which is known in two dimensions, within the three-dimensional mesh.

[0033] Preferably, before the initial step, the present automatic means performs the following steps: - Determining the orientation of the normal of the triangle in at least one of the triangles of the mesh; and - Marking the triangle so as not to identify it as part of the tooth region if the normal is directed towards the inside of the mesh.

[0034] This step is carried out to mark the triangles of the mesh that will correspond to the internal area of the dental arch, such as the inner surface of the teeth. This can be carried out before all other steps. In practice, there is only an interest in the outer surface of the teeth. The reason is that on the outer surface of one of these teeth, the values of the shade and / or translucency are measured, and these outer tooth surfaces must be compared to a reference tooth having these values that are known in order to find the corresponding tooth within the mesh.

[0035] Advantageously, after the initial step, the automatic means carries out the following steps: - Determining the base triangle of the tooth area in the tooth area or in at least one of a plurality of tooth areas; - Determining the contour of the tooth including the base triangle from the base triangle.

[0036] Accordingly, in the tooth area, starting from one triangle of the area, an "area expansion" algorithm is carried out to obtain the exact contour of the tooth. When the contour of the tooth area is compared to the exact contour of a reference tooth represented two-dimensionally, the contour of the tooth area may not actually be accurate enough.

[0037] Preferably, since the base triangle is the central triangle located at the center of the tooth area, the automatic means carries out the following steps for its determination: - Using the coordinates of the center of each triangle of the tooth area to determine the coordinates of the center of the tooth area within the mesh, and - Determining the central triangle of the tooth area by comparing the coordinates of each triangle of the tooth area with the coordinates of the determined center of the area and identifying the triangle closest to the center of the tooth area as the central triangle.

[0038] Accordingly, the central triangle of each region is identified as the base triangle of each region. The base triangle is the most suitable triangle for later obtaining the tooth profile. The reason is that once the tooth region is established, it is known that the base triangle is at the center of the tooth and thus this "region expansion" algorithm is optimal.

[0039] Advantageously, to determine the tooth profile, the automatic means performs the following steps: - In each tooth region, identifying each base triangle of the tooth region as a part of the tooth surface corresponding to the tooth region; - In each tooth region, determining the angular value between each triangle of the region and the adjacent object of the triangle; - According to the determined angular value, determining an average angular value for each triangle of the region; - If the average angular value is less than a predetermined value, identifying the triangle as a part of the tooth surface corresponding to the tooth region; - In each triangle adjacent to the base triangle, when the adjacent triangle belongs to the tooth region of the base triangle, identifying the adjacent triangle as a part of the tooth surface corresponding to the tooth region; - Considering each selected adjacent triangle as the base triangle, and repeating the previous steps for each base triangle until there are no triangles in the region to be identified as part of the surface; - On each tooth surface, expanding the surface by increasing the surface triangles that are adjacent to the triangles of the present surface and belong to the same tooth region as the triangles of the present surface; - On each tooth surface, eroding the surface by removing the surface triangles that have adjacent objects belonging to the same tooth region but are not identified as part of the present surface; - Determining the profile of the tooth surface by calculating one or more Bézier curves.

[0040] This "area expansion" algorithm is used to obtain the exact contour of the tooth. Although the already identified tooth area is used, for the purpose of obtaining the exact contour of the tooth, the method used to obtain the triangles located at the boundary of the tooth is improved by the various steps mentioned.

[0041] Advantageously, - the number of triangles on the surface is less than the number of triangles in the tooth area, or - if the number of triangles added after expansion is less than a predetermined number, the surface is newly expanded.

[0042] Therefore, the number of expansions is determined by the efficiency of each new expansion pass and the size of the tooth surface formed after each pass. Therefore, this number is optimized to determine the outermost contour while considering the shape of the tooth.

[0043] Preferably, in order to determine the correspondence between the reference tooth in the two-dimensional display and the tooth in the tooth digital model including the three-dimensional triangular mesh, this automatic means performs the following steps: - the step of segmenting the triangular mesh according to one of the previous methods to identify the contour of at least one tooth of the mesh, - the step of obtaining a two-dimensional display of the surface of the reference tooth, - the step of obtaining a two-dimensional display of the surface of the tooth of the mesh delimited by the contour, - the step of determining a first ratio between the height and width of the surface of the reference tooth and a second ratio between the height and width of the surface of the tooth of the mesh, - the step of identifying the tooth of the mesh that does not correspond to the reference tooth if the difference between the first ratio and the second ratio is greater than a predetermined value, Otherwise, - the step of transforming the two-dimensional display of the reference tooth according to the Levenberg-Marquardt algorithm for the purpose of performing a comparison by overlapping the surface of the reference tooth and the surface of the tooth of the mesh, - the step of determining the overlapping value between the surface of the reference tooth and the surface of the tooth of the mesh, - When the duplicate value is within a predetermined interval, a step of identifying the teeth of the mesh corresponding to the reference tooth.

[0044] Therefore, after obtaining the surface of the teeth of the mesh, for each tooth of the mesh, the two-dimensional surface of the teeth of the mesh is compared with the surface of the reference tooth in order to determine whether they correspond.

[0045] Advantageously, instead of directly using the duplicate value to identify the corresponding teeth, the automatic means performs the following steps: - A step of cutting the surface of the reference tooth to identify a plurality of parts of the surface, - A step of cutting the surface of the teeth of the mesh in a corresponding manner, - A step of determining the values associated with each part of the determined surface, - A step of determining a comparison value between the value determined for each part of the surface of the reference tooth and the respective value for each corresponding part of the surface of the teeth of the mesh, - A step of determining a specific value between the surface of the reference tooth and the surface of the teeth of the mesh according to the comparison value and the duplicate value, - When the specific value is within a predetermined interval, a step of identifying the teeth of the mesh corresponding to the reference tooth.

[0046] Therefore, by using the values obtained in relation to a part of each tooth, the shape characteristics of each tooth are considered, and as a result, the identification of the corresponding teeth becomes more accurate.

[0047] Preferably, after determining the duplicate value or the specific value for a plurality of teeth of the mesh compared with the reference tooth, the automatic means identifies the teeth of the mesh having the most appropriate duplicate value or specific value as corresponding to the reference tooth.

[0048] Therefore, a comparison is made between the reference tooth and each tooth of the mesh, and the tooth of the mesh that best corresponds to the reference tooth is selected as the corresponding one.

[0049] Alternatively, if any tooth does not have one or more values within the interval mentioned, it becomes impossible to select any tooth of the mesh as corresponding.

[0050] Advantageously, when the corresponding tooth of the mesh is identified, the automatic means identifies one or more color tone values related to the portion of the reference tooth at some portions of the corresponding tooth of the mesh within the mesh, where the portion of the reference tooth and the portion of the corresponding tooth of the mesh correspond to each other.

[0051] Accordingly, the corresponding tooth, as well as its color tone value and / or translucency value, can be directly seen in three dimensions within the mesh.

[0052] The present invention further provides a computer program including code instructions capable of controlling the execution of the steps of the method described above.

[0053] The present invention further provides a method for obtaining such a program for downloading the program over a communication network.

[0054] Finally, the present invention further provides a computer-readable medium for storing the above computer program.

[0055] The present invention is better understood by reading the following description given by way of example only with reference to the accompanying drawings.

Brief Description of the Drawings

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DETAILED DESCRIPTION OF THE INVENTION

[0057] I. Outline of the Method According to the Present Invention As shown in FIG. 1, first, the dental arch of patient 1 is digitized using an optical scanner 3, and then one of the teeth of the same patient 1 is subjected to spectrophotometric analysis using a spectrophotometer 5, such as "Rayplicker" commercially available by the applicant, for example, to estimate the tooth color tone and translucency values from the measurement values of the spectrophotometer 5. In the remainder of this document, the spectrophotometer 5, or a device such as Rayplicker that processes the measurement values obtained using the spectrophotometer 5, will be described without distinction.

[0058] The optical scanner 3 is used to obtain a digital model 4 of the teeth including a three-dimensional triangular mesh 41, in other words, a three-dimensional digital representation of the dental arch of patient 1 digitized by the optical scanner 3. In this case, this representation is encoded in a file of the "stl" type, but this representation may correspond to any type of 3D file such as "obj" or "ply". In this model, the surface The surface is represented by triangles, and each of these triangles has a normal vector oriented in the direction in which the triangle faces. Each normal vector is a normalized vector and thus has a length of 1. The normal vectors are used to specify the orientation of the triangles and to create the boundary between what is inside and outside a certain volume of the dental Bow-shaped arch, and the normal vectors are oriented outward from the triangles towards the outside of the dental arch. The coordinates of each vertex of the triangle can be determined, and furthermore, the coordinates of any point on the triangle can be determined. Thus, the dental Of the bow dimensions become clear. However, these triangles may represent a part of a tooth in some cases, a part of the tooth root in some cases, or other elements of the dental arch, and these triangles are not specified as part of any particular region. Similarly, the color tone and translucency values of the dental arch are not associated with these triangles. Of the bow ​

[0059] The spectrophotometer 5 can be used to obtain a two-dimensional display 8 of one tooth 2, and the values of the tooth color tone and translucency are associated with this two-dimensional display 8. These values are associated with the corresponding tooth portions of these values. For example, the portion 7 of the tooth 2 has a value of the color tone and a value of translucency determined using the spectrophotometer 5. These values may be different from the values associated with another portion of the tooth 2.

[0060] The aim of the present invention is specifically to find the tooth 2 obtained using the spectrophotometer 5 within the mesh 41, where the entire dental arch of the patient 1 is digitized.

[0061] Therefore, automatic means, such as one or more data processing devices 6, which are, for example, one or more computers, implement a method aimed at achieving the above-mentioned purpose. In the remainder of this document, "means" or "automatic means" refers to any type of automatic means such as the above-mentioned automatic means used to automatically and digitally implement the steps of the method by utilizing the computing capabilities provided by any processor and further possibly by an electrical communication network. These means have or use a database service for storing or obtaining any type of data required to implement the described steps, such as computed values, coordinates, or two-dimensional or three-dimensional images. Therefore, the steps described in the remainder of this document can be written as one or more computer programs that can be automatically executed when required by the user of the present invention.

[0062] The user of the present invention specifically refers to a dentist or other expert in the dental field such as a dental technician. In order to interact with the present invention, the user can have an interface, where the user can start to execute all or only some of the steps to be described as required. The user can further display the results of the present invention on this interface and interact with the file or the displayed image.

[0063] As shown in Figure 2, the first phase 100 aims to segment the mesh 41 to identify and distinguish the teeth within the mesh. Therefore, this aim is to identify, possibly for each tooth of the mesh, all the triangles belonging to a given tooth. In the second phase 200, the automatic means 6 determines which tooth of the mesh 41 corresponds to the tooth 2 obtained using the spectrophotometer 5. Finally, the means 6 applies the values of the color tone and translucency of the tooth 2 to the corresponding tooth 2 within the mesh 41. Therefore, the tooth 2 and its color within the mesh 41 can be displayed in three dimensions.

[0064] Therefore, as a result of the second phase 200, the user can view on the screen the tooth within the tooth mesh 41 that corresponds to the tooth 2 obtained using the spectrophotometer 5, where the color tone and translucency are directly applied within the mesh 41 to the corresponding tooth.

[0065] Next, each of these steps will be described.

[0066] II. Segmentation within the triangular mesh II.a: Identification of tooth regions and their central triangles

[0067] The method corresponding to phase 100 is shown in Figure 3, which refers to 20 from Figure 4. Its aim is to identify the teeth within the triangular mesh 41.

[0068] The digital model 4, which includes the triangular mesh 41 shown in FIG. 4, has an origin O and three axes X, Y, and Z. The digitized dental Of the bow Each of the triangles forming the surface has a normal in the form of a vector. All triangles have vertices, and the coordinates of these vertices can be automatically determined on each axis with respect to the origin 0.

[0069] The first step 11 is intended to exclude the triangles oriented towards the inside of the mesh 41 for the purpose of maintaining only the triangles that reproduce the surface of the exposed dental arch. The reason is that the values of color tone and translucency are obtained on the surface of the teeth exposed on the outside. In this way, the dental Of the bow All triangles are inspected. In each triangle, the automatic means 6 determines a vector extending from the center of the triangle to the end of the normal of the triangle. Then, as shown in FIG. 5, two distances (the distance 111 between the vector and the origin O of the model 4, and the distance 112 between the origin O and the center of the triangle having coordinates calculated using the coordinates of the vertices of the triangle) are calculated. If the first distance 111 is greater than the second distance 112, this means that the normal of the triangle is oriented towards the outside of the model. Therefore, the triangle is maintained. Otherwise, the triangle is deleted. The reason is that it is considered to be oriented towards the inside. Therefore, it is not inspected in the next step. Obviously, other ways of proceeding to exclude the triangles oriented towards the inside of the model are also possible. It can also be expressed as "marking" instead of "deleting". In all cases, although clearly the triangle is still part of the digital model, the triangle should not be specified as "to be processed" in the next step. Refer to the figure shown in FIG. 6. Here, the marked triangle 113 is considered to be oriented towards the inside.

[0070] In the next step, only the "retained" triangles representing the surface of the dental arch that are oriented towards the outside are considered. Thus, this step can be used to eliminate a number of triangles that are not useful for the purposes of the present invention and to perform the next step with only the remaining triangles.

[0071] In step 12 shown in FIG. 7 of that sub - method, the aim is to classify the triangles into a concave category or a convex category. Triangles that do not belong to either the concave region or the convex region are left as "unclassified". The purpose of this step is to determine the boundaries of the teeth within the mesh 41. Teeth are actually separated from each other by deep concave regions. Similarly, the regions separating the teeth from the tooth roots are concave. Finally, the boundary between the surface of the tooth oriented towards the outside of the model 4 and the surface of the tooth oriented towards the inside of the model 4, that is, the region located at the top of the tooth, is clearly convex.

[0072] In order to determine these boundaries, the curvature between the triangles must be examined. In this case, the automatic means 6 examines each triangle of the mesh maintained in the previous step. In each of these triangles, the means determines the adjacent triangles in sub-step 121, or in other words, determines the triangles that share an edge segment or a vertex with the triangle under consideration. Then, in sub-step 122, the means determines the triangular neighbors of this triangle, which can be called "second neighbors". Figure 7 shows a triangle 71, an adjacent triangle 72, and thus a second neighbor 73 which is the triangular neighbor of the adjacent triangle 72 (the triangle 72 itself being a neighbor of the triangle 71). Then, in sub-step 123, the means determines the angle between the triangle and each second neighbor. In other words, the means calculates the angle between the triangle and the triangular neighbor of the triangular neighbor with respect to this triangle. To do this, the means uses the normal of each triangle. By calculating the angle between the normal of one triangle and the normal of its second neighbor, the curvature angle between these two triangles is obtained. Furthermore, by calculating the scalar product between the normals, it is possible to determine whether the angle is convex or concave. If the scalar product is negative, the means automatically adds 180 degrees to this angle, and this angle can no longer be considered concave.

[0073] If the angle between the triangle being inspected and a second neighbor of one of its second neighbors is within the range of 30° to 150°, the triangle being inspected is considered to potentially be located within a concave or convex region. The reason is that this region of the triangle is clearly curved. The choice between concave and convex is determined by the direction of the normal of the triangle with respect to each other, and thus by the scalar product between the two normals. Thus, if the scalar product is negative and 180° needs to be added to this angle, this angle is considered "convex". Conversely, if the angle is originally positive, it is considered "concave". Therefore, the counter associated with the triangle being inspected immediately locates the angle between the triangle being inspected and a second neighbor of one of its second neighbors within a predetermined range, and also potentially after adding 180°, and increments it by one unit to add one unit to the "convex angle" category or the "concave angle" category. Thereby, in each triangle being inspected, the number of second neighbors that are significantly inclined as convex or concave with respect to the triangle being inspected is calculated.

[0074] In sub-step 124, after all angles with second neighbors have been calculated in the triangle being inspected, the means determines whether the inspected triangle 71 must be left unclassified, classified into the "concave" category, or classified into the "convex" category. To do this, the means uses a concave angle counter or a convex angle counter. These counters are specific to one triangle being inspected. If one of these counters has a value greater than the number of neighbors of the triangle divided by 4, the triangle is considered to be located within a "concave" region or a "convex" region respectively, and is thus separated into these categories by the means. Thus, when all these steps are completed, all triangles of the mesh are considered to be "concave", "convex", or "unclassified". If a triangle is a neighbor, the triangle forms a region of multiple concave or convex triangles.

[0075] In step 125, the aim is to eliminate the noise within the concave regions of the mesh. In reality, some triangles may be classified into the concave category, but these triangles are either separated or form only small regions. However, this objective is to determine the large regions of the multiple concave triangles that form the intersections between teeth and the intersections between teeth and tooth roots. These will inevitably form large groups of triangles. Therefore, this means performs an additional check for each inspected triangle classified into the "concave" category. As a result, this means checks, for each "concave" triangle, whether each of its adjacent triangles is also classified into the concave category. If this is not the case, the triangle under consideration is classified as "unclassified". By declassifying the triangles previously classified as the concave category that have adjacent triangles not classified into the concave category, a reduction step is performed. Then, a second check is performed for each triangle remaining in the "concave" category. In this second check, only the triangles that do not have adjacent "concave" triangles are declassified. As a result, the separated triangles will be declassified.

[0076] Next, refer to FIGS. 8 and 9. FIG. 8 shows the marked triangle 81 classified into the concave category. FIG. 9 shows the marked triangle 82 classified into the convex category. Note that these correspond to the boundary regions of the teeth. Other triangles maintained within the mesh that are neither convex nor concave become "unclassified".

[0077] At this point, the triangles that are not important in later steps have been eliminated, and the regions of the concave triangles and the regions of the triangles located in the convex portions that form the tooth boundaries have been identified. The objective of step 13 is to identify the tooth regions located within the scope of these boundaries. Referring to the sub-steps of step 13 shown in FIG. 10, means 6 first determines the seed triangles and, from these seed triangles, identifies the regions of the triangle adjacencies to each other that form the tooth regions. Next, these steps will be described in detail with reference to FIGS. 10 to 16.

[0078] First, at step 131, a seed triangle is selected on the surface of the triangular mesh. To do this, the automatic means 6 uses a first plane A with a fixed Y coordinate and a second plane B with a fixed X coordinate. When the X-axis defined by the intersection of these planes cuts the triangles of the mesh as shown in FIG. 11, this triangle is regarded as a seed triangle and saved as a seed triangle. Then, the Y coordinate is modified according to a predetermined step, and the newly cut seed triangles are saved. The same principle is applied to the X abscissa, and as a result, finally, the seed triangles distributed over the entire dental arch are determined at regular intervals on the mesh. Then, when the Y coordinate is modified according to a predetermined step, new seed triangles distributed over the entire dental arch are determined at regular intervals on the mesh. However, the automatic means only maintains unclassified triangles as seed triangles, and as a result, these seed triangles do not become a part of the boundary region between teeth and are necessarily located within the teeth. Refer to the image shown in FIG. 12. Here, the marked triangles 91 are the determined "seed" triangles. Each of these seed triangles is indexed as a part of the tooth region specific to the seed triangle. Thus, at the end of this step 131, there will be as many tooth regions as there are seed triangles, and each tooth region is composed only of its seed triangle.

[0079] At step 132, the means examines each seed triangle 91. An adjacent of a seed triangle is regarded as a part of the same tooth region as the seed triangle when it is neither concave nor convex and the projection of its normal with respect to the Z-axis does not exceed a predetermined value of 0.75. This value means that the triangle is located within the "occlusal region" at the top of the tooth, and the occlusal region is a flat region but a region that does not correspond to the tooth surface. FIG. 13 shows various normals, including one normal marked S located on the top. In the case of this normal, the adjacent of the seed triangle is neither convex nor concave, but the corresponding triangle is not selected as a part of the tooth region of the seed triangle.

[0080] Step 133 consists of considering, in each tooth region, the triangles that are successively selected as seed triangles. Then, step 132 is repeated for each of these new seed triangles, thereby extending each region to adjacent triangles that are neither concave nor convex, are not located further within the occlusal region, and are not assigned to another region. When there are no more triangles to be added, this step 133 ends. In this way, each region expands as shown in FIG. 14, where each tooth has one or a series of tooth region adjacencies with respect to each other. Each tooth region has a unique index. Thus, all the triangles of a given region have the same index. By excluding concave and convex triangles as well as the occlusal region, and by ensuring that each triangle is assigned to only one region, each tooth region extends over only one tooth rather than multiple teeth.

[0081] Furthermore, step 134 consists of integrating the regions included in a tooth so that, for each tooth, one tooth corresponds to one region as a result.

[0082] Thus, means 6 identifies the boundary between two regions at a time, which is composed of the triangles within a given region adjacency of the triangles of only one other region.

[0083] When all the boundaries are determined, if the number of boundary triangles exceeds a predetermined threshold, these two regions are integrated to form one region. In this case, this threshold is obtained from the following calculation: (Number of triangles of the digital model / 50000) + 1 Therefore, this threshold value is determined by means 6 based on the number of triangles of the model. This threshold value is set empirically and may be different. Generally, this threshold value is determined by the resolution of the mesh, and thus by the type of intraoral scanner used to digitize the patient's dental arch, and means 6 can automatically adapt the threshold value according to the scanner used. Integrating two regions means that means 6 assigns the same index to the triangles of the two regions. Since this assignment is carried out simultaneously at all boundaries, three or more regions can be integrated simultaneously. Therefore, if region A contains a large number of triangular neighbors of region B (where region B itself has a large number of triangular neighbors of region C), regions A, B, and C will be integrated into one region simultaneously, where all triangles will have the same index.

[0084] With this step 134, refer to the figure in FIG. 15. Here, each tooth has one tooth region. In other words, in a given tooth, all the triangles of the tooth have the same index, and this index is different from the index of the triangles forming another tooth.

[0085] However, at the end of step 134, in addition to the tooth regions that actually correspond to the teeth, the mesh includes regions corresponding to other elements such as tooth roots. However, in order to compare these teeth of the mesh with the two-dimensional teeth obtained using a spectrophotometer, when projected into two dimensions, they will have the shape or even the dimensions of the teeth, but it is important to eliminate the regions that are clearly not teeth within the mesh.

[0086] This is the reason why the aim of step 135 is specifically to eliminate these regions. These regions can be distinguished from the tooth regions due to the fact that the number of triangles within these regions is very large, or very small, or due to the fact that these regions are extremely flat. Apart from the tooth roots, the dental arch can be digitized using a base in some cases. In this case, this step can be used to eliminate the regions corresponding to the base.

[0087] Therefore, means 6 determines the average curvature of each region. Therefore, this means uses the normal of the triangle and adds 180° to the angle with a negative scalar product to determine the curvature between each triangle and its adjacent triangle. In this way, this means estimates the average curvature within the region. If this average curvature exceeds 170°, in other words, if this average curvature is close to 180°, this region becomes extremely flat corresponding to the tooth and is thus eliminated. Again, "elimination" means "marking". Therefore, these triangles will not be considered and processed later. This means that the triangles of the region have no indicators, or in any case, there is no further indicator corresponding to the tooth region. In other words, these triangles cannot be identified as part of the tooth. Means 6 further determines the number of triangles in each region. If this number is less than the first threshold or exceeds the second threshold, the region is eliminated in a similar way. The reason is that these numbers are too few or too many to correspond to the tooth. In this case, the first threshold is set as 100 triangles. Even if it is a different value, if it is less than this value, the number is considered too small for the region to correspond to the tooth. The second threshold coincides with the result of the following calculation: (the number of triangles in the model / the number of regions in the model). Therefore, this threshold calculated by means 6 is determined by the resolution of the model. Very intentionally, the accidental elimination of the region corresponding to the tooth is avoided.

[0088] Therefore, at the end of step 13, the triangular mesh is segmented. Refer to the figure in Fig. 16. The tooth region corresponding to the tooth is shown, and other regions are not shown. Therefore, starting from the received mesh 41, the method performing step 13 automatically realizes the segmentation of the model to identify the triangles belonging to each tooth of the mesh 41. No information other than the mesh is provided to means 6. Specifically, it is not necessary to manually identify one or more triangles. Therefore, no work by the user is required to perform the segmentation automatically.

[0089] However, although this method realizes the segmentation of teeth, the contours of a plurality of teeth or the contours of some of the plurality of teeth may remain inaccurate. By excluding the triangles located in the concave and convex regions, and by excluding the triangles directed inward and the triangles located within the occlusion region, triangles that should actually be part of the teeth may be excluded. Therefore, the boundaries of the teeth may deviate slightly from the actual boundary shape and dimensions. However, in order to compare the two-dimensional teeth 2 obtained using the spectrophotometer 5 with the mesh 41 for finding the teeth, the tooth contours of the mesh 41 must be accurate in order to avoid identifying inappropriate teeth within the mesh as corresponding to the teeth 2 or failing to identify the corresponding teeth.

[0090] II.b: Identification of the contour of each tooth Therefore, the method of phase 14 shown in FIG. 17 continues step 14 with the aim of determining the accurate contour of the teeth.

[0091] For this purpose, the aim of step 141 is to determine the center of the tooth region segmented in step 13. Therefore, means 6 determines the coordinates of the center of each triangle in the region using the coordinates of the vertices of the triangles in the digital model in each region. Then, means 6 determines the coordinates of the center of the region using the calculated coordinates of the center of each triangle.

[0092] With the coordinates of the center of the region known, mesh 6 determines which triangle in this region is closest to this center. To do this, means 6 compares the distance between the center of each triangle and the center of the region and assigns the role of the center triangle of the region to the triangle with the closest center. When this is done in each region, in each tooth of the mesh, the center triangle, which is labeled with reference sign C for example for only one tooth, is identified (see the figure in FIG. 18).

[0093] In step 142, in each region, means 6 operates as follows: In each triangle of the region, means 6 determines the average angle between this triangle and its adjacent triangles by calculating all the angle values between this triangle and its adjacent objects. If the average angle value is less than -0.05 radians, the triangle is regarded as part of the tooth surface. This threshold is determined to select triangles belonging to flat teeth such as molars or incisors, but is also determined to select triangles belonging to curved teeth such as canines. This threshold can be modified to be adjusted according to the resolution of the digital model.

[0094] Next, in step 143, means 6 starts the "region expansion" algorithm, aiming to identify all the triangles forming the tooth surface from the center of each region identified in step 141 to the end of the tooth. Therefore, means 6 identifies all the triangle adjacents of the central triangle of the same region, even if they are not identified as above in the previous step 142 and are also part of the surface. Then, in each of these triangles identified as part of the surface, the means identifies those adjacent triangles that are within the same region as part of the tooth surface. By doing so, the tooth surface will first include all the triangles of the tooth having an average curvature value less than -2.864 degrees, but will further include all the triangles connected by the path of triangle adjacents up to the central triangle, which is also part of the same tooth region. When there are no more triangles to be added, this continuous addition of adjacent triangles is completed. The reason is that the adjacent triangles are part of another region or not part of any region. At the end of this step 142, the tooth surface including all the triangles identified as part of the tooth surface generally corresponds to the tooth. Specifically, the surface usually has no holes at all, that is, it has no triangles surrounded by triangles that are not identified as part of the tooth surface but are part of the tooth surface. Only its contour can be re-specified for the next step.

[0095] Next, in step 144, an enlargement step is performed. If this means does not add the adjacent triangles even in any triangle on the surface that was not selected in step 142, the surface is further enlarged in this way.

[0096] This enlargement step can be repeated a specific number of times. If the number of triangles on the surface is less than the number of triangles in the tooth region and at least 20 triangles can be added to the surface during the previous enlargement step, a new enlargement step is performed and repeated as long as the conditions for additional enlargement are met. Obviously, the triangles added to the tooth surface must be part of the same tooth region.

[0097] In step 145, a reduction step is performed by means 6. Its aim is to eliminate triangles such that not all of their adjacent objects are part of the same surface. In other words, if a triangle has adjacent triangles that are not part of its surface, this triangle is deselected or a specific state is removed. This triangle ceases to be part of the surface.

[0098] At the end of step 145, all teeth have a surface composed of triangles, and in a given tooth, the boundary of the surface corresponds more to the boundary of the tooth than to the boundary of the tooth region. Next, refer to the figure in Fig. 19. Thus, the contour of each of these surfaces can be determined.

[0099] Optionally, the aim of the additional step 145 (second time) is to deselect some of the triangles of the surface such that their orientation is significantly different from that of the remainder of the tooth. Thus, means 6 uses the normal of each triangle of the surface to determine the average normal of the surface. Then, for each triangle of the surface, the angle between the average normal and the normal of the triangle is calculated. If this value is greater than 50° or less than -50°, the triangle is deselected and this triangle ceases to be part of the surface. The aim of this optional step is to adjust the shape that the tooth will have when projected two-dimensionally and compared with the 2D contour of the tooth 2 obtained using the spectrophotometer 5. This is optional. The reason is that its aim is to fit the teeth of the mesh 4 to the teeth obtained using the spectrophotometer 5. The image obtained using the Rayplicker with a wide-angle lens may actually be distorted compared with the image of the teeth obtained from the mesh. However, this distortion depends on the color determination device (in this case, the Rayplicker). This is why this step is optional. Thus, this is not necessary for all comparisons. This may be, for example, a reference tooth for which the image is obtained using another device such that it is not distorted. Additionally, if obtained using a spectrophotometer such as the spectrophotometer 5 of the "Rayplicker" that slightly distorts the shape of the tooth, instead, similar steps may be applied to the 2D contour of the reference tooth 2 for the purpose of distorting the contour of the tooth 2.

[0100] In step 146, the principle of Bézier curves is applied to each tooth surface, thereby establishing a curve that accurately specifies the contour of each surface.

[0101] Thus, on each tooth surface, means 6 determines the triangles forming the surface contour by selecting triangles having adjacent triangles not specified as part of the surface. Means 6 determines the number of "check points" defined by the Bezier curve algorithm according to the number of triangles forming the surface contour. Alternatively, this number of check points may be determined by the number of triangles forming the entire surface. Finally, by inspecting each triangle on this contour, check points are determined in intervals of regular triangles. These check points can be used to determine a Bezier curve. The Bezier curve represents the contour of the tooth surface as shown in FIG. 20.

[0102] At the end of step 14, the segmentation method is completed. Thus, starting from mesh 41, means 6 automatically and accurately determines the contour of each tooth of the mesh, where no other information is provided by the user. Thus, phase 100, including steps 11 to 14, which aims to obtain the tooth contour, is completed. At this point, the tooth contour can be used for various purposes. Next, method 200 will use these contours to find which tooth in mesh 41 in the 3D mesh corresponds to the 2D tooth 2 obtained using spectrometer 5. The aim is to be able to associate the color tone and translucency of this tooth 2 with the corresponding tooth in mesh 41 in model 4.

[0103] III. Correspondence between 2D Teeth and 3D Mesh Next, method 200 shown in FIG. 21 will be described. The aim is to compare the display of tooth 2 obtained using spectrometer 5 with the segmented mesh 41 in order to find the corresponding tooth within the segmented mesh 41.

[0104] In step 201 of method 200, means 6 obtains a two-dimensional representation of the contour of each segmented tooth. These contours are the contours determined at the end of method 100, but this method 200 is also applicable to the tooth contours determined using yet another method. Thus, the contour of each tooth is projected onto a surface substantially parallel to the tooth. Thus, in any tooth 421 of the mesh shown three-dimensionally in FIG. 22, a corresponding image 422 representing the contour two-dimensionally is obtained. The surface is filled with white pixels, and the area outside the surface is filled with black pixels. Thus, image 422 is binary. Thus, this means determines the surface of each tooth of the mesh two-dimensionally. Further, this means determines an image of the surface of tooth 2 that is already represented two-dimensionally. A later step consists of comparing this image of the surface of tooth 2 with each of the images of the surface of the mesh that is two-dimensional. In the remainder of this document, reference is made to a tooth having a measurement value considered to be a "reference tooth" by spectrophotometry. Among the teeth within the mesh, a search is carried out to find the "corresponding tooth" to the reference tooth.

[0105] At each surface (the surface of the teeth of the mesh and further the surface of the reference tooth) the following steps are carried out. Each pixel of the surface has an abscissa on the horizontal X-axis and an ordinate on the vertical Y-axis.

[0106] In step 202, first, an axis perpendicular to the surface is determined to divide the surface into two parts in order to divide the surface into two equal parts using an affine function of the form a×x + b. To do this, means 6 first determines the center material ymid of the surface using the coordinates ymin of the pixel at the lowest point of the surface and the coordinates ymax of the pixel at the highest point of the surface. Then, this means determines two points: the first point has the average X and Y coordinates of all the pixels of the surface located within this interval [ymin+(ymid - ymin) / 4; ymid-(ymid - ymin) / 4], and the second point has the average X and Y coordinates of all the pixels of the surface located within this interval [ymid+(ymax - ymid) / 4; ymax-(ymax - ymid) / 4]. Finally, means 6 determines the axis that cuts these two points using the corresponding affine function of the form a×x + b. In this case, the tooth surface is divided into two parts, one on the left side of the determined axis and the other on the right side.

[0107] In step 203, means 6 determines 19 axes that are substantially horizontal and equidistant from each other to divide the tooth surface into 20 adjacent parts from the top to the bottom. To do this, this means reproduces calculations similar to those in step 202, but here, instead of dividing into two parts along a vertical axis, the aim is to separate the surface into 20 parts along a horizontal axis. These 20 parts are cut as follows: 19 points are determined from the axis determined during step 202, and at each of these points, an affine function orthogonal to the function determined in step 202 is determined. Here, it can be said that the image is "cut". Then, referring to FIG. 23. Here, in two parts, the surface is cut into 40 parts.

[0108] In step 204, means 6 will determine 40 values associated with the exact points of the surface, as a result of which this surface can be compared with other surfaces.

[0109] Therefore, on 40 horizontal axes (each of the 20 horizontal axes being separated by the vertical axis), this means determines the length of the axis, or rather, the distance (as the number of pixels) between the points on the surface that are located on the horizontal axis and farthest from the vertical axis, and further determines the length of this horizontal axis. This distance is saved and associated with the horizontal axis.

[0110] In step 205, this means makes a comparison between each tooth surface obtained from the mesh and the surface of the reference tooth. The distances calculated in step 204 are compared in a 2×2 form for these corresponding axes. Therefore, in each comparison between the surface of the reference tooth and the surface of the tooth of the mesh, this means determines the average difference between, on the one hand, each distance calculated in step 204 on the surface of the reference tooth and, on the other hand, the corresponding distance on the surface of the tooth being compared. The smaller the average difference, the more likely the tooth of the mesh being compared corresponds to the reference tooth. This average difference is saved and used later when determining the corresponding tooth.

[0111] In step 206, means 6 determines the height / width ratio at each surface, or rather, determines the ratio between the height of the tooth (the maximum distance along the Y-axis between two points on the surface of the tooth) and the width of the tooth (the maximum distance along the X-axis between two points on the surface). Each ratio of the tooth of the mesh is compared with the ratio of the surface of the reference tooth. If the difference between the ratio of the reference tooth and the ratio of the tooth of the mesh is less than 0.4, the tooth to be compared in the next step is selected. Otherwise, the tooth to be compared in the next step is not selected.

[0112] In step 207, the Levenberg - Marquardt algorithm is used to transform the surface of the reference tooth. The aim is to correct its position in the two-dimensional display, but further potentially to rotate the surface of the reference tooth or modify its size so as to enable the surface of the reference tooth to be superimposed on the surface of the tooth of the mesh as a result, and also to calculate the associated overlap coefficient.

[0113] As an alternative to using the Levenberg-Marquardt algorithm, the contour of the reference tooth may be rotated in order to orient the two contours (the contour of the reference tooth and the contour of the tooth of the mesh) in the same way. Thus, the value of the rotation angle is calculated from the vertical axis determined in step 203. Subsequently, the corresponding rotation from this angle is performed on the contour of the reference tooth. This method is considered to provide better results than the Levenberg-Marquardt algorithm while making this step 207 faster.

[0114] In step 208, means 6 determines, for each surface selected in step 206, its overlap coefficient based on the surface of the reference tooth transformed in step 207. This overlap coefficient is determined by placing the surface of the reference tooth under the surfaces of the teeth being compared. Refer to the image in Figure 24. Thus, the number of pixels belonging to these two surfaces is determined and compared to the total number of pixels of the two surfaces. One way to calculate this overlap coefficient is to determine the number of pixels of the overlapping image 24 that do not belong to either the contour of the surface or the contour of the reference tooth.

[0115] In step 209, the means calculates the final difference between the surface of the reference tooth and each surface selected in step 206. This calculation takes into account the average distance (in pixels) calculated in step 205 and the overlap coefficient of step 208. The formula is as follows: (2 × average distance + overlap coefficient) / 3. When the value becomes very small, the tooth used for comparison is considered to correspond to the reference tooth.

[0116] Thus, means 6 automatically determines the tooth of the mesh 41 corresponding to the reference tooth 2, the display of which can be obtained using the spectrophotometer 5.

[0117] In the final step 210, means 6 applies the values of the color tone and translucency calculated by the spectrophotometer 5 for tooth 2 to the corresponding tooth within the mesh. This can be seen on the triangular mesh of the dental arch, where the texture corresponding to the reference tooth is applied to the corresponding tooth, so that the values of the color tone and translucency can be directly viewed in the 3D file on the corresponding tooth. To do this, a texture that is two-dimensional and has values obtained using a spectrophotometer can be stretched to cover the 3D surface of the triangular mesh. Thus, at the end of this method, means 6 exports a folder having the "stl" file of mesh 4, a file containing the values of the color tone and translucency, and a file containing all the information of segmentation and specification determined using the described method, whereby the mesh can be associated with the values of the color tone and translucency. This folder will be used to display the dental arch using its associated color tone via software such as "Rayplicker" in the name of the applicant. The dental technician can decompress the stl file containing the mesh to process the prosthesis. Obviously, the software used to display the dental arch using its color tone is preferably the same as the software used to implement the method of the present invention. Alternatively, other visual software may be used to view the dental arch and its color tone. Thus, the teeth of the triangular mesh shown in FIG. 25 can be obtained, where a plurality of parts of the teeth correspond to specific values of the color tone and / or translucency and are displayed within mesh 41 in the digital model 4.

[0118] The present invention is not limited only to the described embodiments, and other embodiments will be apparent to those skilled in the art.

[0119] Accordingly, as an alternative to step 210 of selecting the tooth of the mesh that best corresponds to the reference tooth, functionality can also be provided for manually selecting another tooth as the corresponding tooth among the segmented teeth. This means can further sort the segmented teeth to provide a sorted list of teeth corresponding to the reference tooth, such that if the first tooth on the list is not the appropriate tooth, the next tooth is presented to the user.

[0120] Situations can also be envisioned where the corresponding tooth is not determined in step 210. This can apply when no tooth is selected in step 206, or when the smallest final difference is not less than a predetermined value. Other methods of not specifying the tooth of the mesh as the corresponding tooth are also conceivable.

[0121] The spectrophotometer 5 integrated into the applicant's Rayplicker is a special measuring instrument used to obtain values of color tone and translucency by transmission or reflection at various wavelengths. This can also be called a spectrophotometer. However, within the scope of the present invention, any type of device or instrument that can be used to obtain values of the color tone and / or translucency of teeth may also be acceptable. The present invention is not actually influenced by the method for obtaining the surface of the reference tooth in two dimensions and for use when associating values of color tone and / or translucency. The present invention uses this surface to find the tooth of this surface within the mesh, and thus the method for obtaining the tooth of this surface is not important.

[0122] Similarly, the type of intraoral scanner used to obtain the mesh 4 is not important.

[0123] Furthermore, instead of fully digitizing the dental arch, the segmentation method can also be involved with a partial dental arch. In either case, if the dental arch contains teeth, the method can be used to identify the teeth.

[0124] It is also possible to change all of the shown threshold values and interval values, provided that the selected values can produce the required technical effects. In addition, the formulas and methods used to calculate the shown values or intervals can also be modified in order to produce the required technical effects.

[0125] Furthermore, one of the methods described can be stopped at any step. Specifically, the tooth regions determined in step 13 may be sufficient in some operations. Similarly, the tooth surfaces determined in step 144 or their contours determined in step 145 may later be compared to the teeth by a method different from the method of method 200. As a natural result, method 200 can use the segmented tooth contours by a method different from the method of method 100. For example, the user can draw or design the tooth contours himself on the interface. However, method 100 is particularly adapted to provide tooth contours that optimize the comparison of method 200, and the prioritization of the two methods can be automated without using the user's work.

Claims

1. A method (100, 200) for segmenting a digital model (4) of a tooth including a three-dimensional triangular mesh (41), the automatic means (6) performing the following steps, referred to as the initial steps: - Classifying at least one triangle (81) into a concave category and at least one triangle (82) into a convex category within the mesh (41), and - Identifying at least one separate tooth region within the mesh that includes triangles, wherein each triangle of the tooth region has at least one adjacent triangle within the tooth region, and all triangles of the tooth region do not belong to either the convex category or the concave category, identifying at least one separate tooth region (13) characterized by performing the method (100, 200).

2. To perform the step (12), the automatic means (6) performs the following sub-steps: - Determining, for at least one triangle among the triangles (71) of the mesh, an angular value between the triangle (71) and each adjacent triangle (73) of each adjacent triangle (72) of the triangle (71) (123), and - Classifying the triangle into a concave category or a convex category according to the determined angular value (124) The method (100, 200) according to claim 1, wherein the method is performed.

3. The method (100, 200) according to claim 2, wherein the automatic means (6) determines the angular value using the normal of the triangle and the normal of each adjacent triangle (73) of each adjacent triangle (72) of the triangle (71).

4. In at least one triangle within the concave category, the automatic means (6) further performs a step (125) of checking whether each triangle adjacent to a triangle classified into the concave category is also classified into the concave category. The method (100, 200) according to claim 2 or 3.

5. To perform the step (13) of identifying the tooth region, the automatic means (6) performs the following sub-steps: - Determining a seed triangle (91) within the mesh that does not belong to either the concave category or the convex category (131), - A step (132, 133) of selecting a triangular neighbor for the seed triangle (91) that belongs to neither the concave category nor the convex category and has a value whose projection of the normal line with respect to the Z-axis is within a predetermined interval. configured to perform The method (100, 200) according to any one of claims 1 to 4, wherein for the purpose of identifying a tooth region including the selected triangle, each of the selected triangles is regarded as a seed triangle, and the selection step (132, 133) is repeated until there are no unclassified triangles to be selected, and the selection of triangular neighbors for each of the triangles is performed. **Claim 6** The method (100, 200) according to claim 5, wherein the automatic means (6) determines a plurality of separated seed triangles (91) within the mesh (41) that belong to neither the concave category nor the convex category for the purpose of identifying a plurality of separated tooth regions. **Claim 7** The automatic means (6) performs the following steps: - A step of determining the number of adjacent triangles of a boundary triangle that constitutes a triangle of a predetermined tooth region adjacent to a triangle of another tooth region. - When the number of adjacent triangles of the boundary exceeds a predetermined value, a step (134) of integrating the different tooth regions of the boundary. The method (100, 200) according to any one of claims 1 to 6, wherein the method is performed. **Claim 8** The automatic means (6) performs the following steps: - A step of determining the number of triangles in the tooth region and the average curvature value of the tooth region. - When the number of triangles exceeds a predetermined maximum value, the number of triangles is less than a predetermined minimum value, and / or the average curvature value exceeds a predetermined threshold value, a step (135) of distinguishing the tooth region so as not to further identify the triangles of the tooth region as a part of the tooth region. The method (100, 200) according to any one of claims 1 to 7, wherein the method is performed. **Claim 9** Before the initial step, the automatic means (6) performs the following steps: - A step (11) of determining the direction of the normal line of the triangle in at least one triangle of the triangles of the mesh (41), and - When the normal line is directed towards the inside of the mesh (41), a step (113) of marking the triangle so as not to identify it as a part of the tooth region is performed, the method (100, 200) according to any one of claims 1 to 8.

10. After the initial step, the automatic means (6) performs the following steps: - In the tooth region, or in at least one of a plurality of the tooth regions, a step (141) of determining the base triangle (C) of the tooth region, - From the base triangle (C), a step (14) of determining the contour of the tooth including the base triangle (C) is performed, the method (100, 200) according to any one of claims 1 to 9.

11. In order to determine that the base triangle (C) is the central triangle located at the center of the tooth region, the automatic means (6) performs the following steps: - Using the coordinates of the center of each triangle in the tooth region, determining the coordinates of the center of the tooth region within the mesh (41), and - By comparing the coordinates of each triangle in the tooth region with the determined coordinates of the center of the tooth region, and by identifying the triangle closest to the center of the tooth region as the central triangle, determining the central triangle of the tooth region is performed, the method (100, 200) according to claim 10.

12. In order to determine the contour of the tooth (14), the automatic means performs the following steps: - In each tooth region, a step of identifying each base triangle (C) of the tooth region as a part of the tooth surface corresponding to the tooth region, - In each tooth region, a step (142) of determining the angular value between each triangle in the tooth region and the adjacent of the triangle, - According to the determined angular value, a step (142) of determining an average angular value for each triangle in the tooth region, - When the average angular value is less than a predetermined value, a step of identifying the triangle as a part of the tooth surface corresponding to the tooth region, - In each triangle adjacent to the base triangle, when the adjacent triangle belongs to the tooth region of the base triangle, a step (143) of identifying the adjacent triangle as a part of the tooth surface corresponding to the tooth region - Repeating the step (143) in each base triangle until there are no more triangles in the tooth region to be specified as part of the surface, with each selected adjacent triangle as the base triangle; - Expanding the surface (144) by increasing the surface triangles that are adjacent to the triangles of the surface and belong to the same tooth region as the triangles of the surface on each tooth surface; - Diminishing the surface (145) by removing the surface triangles that have adjacent objects belonging to the same tooth region but are not specified as part of the surface on each tooth surface; - Determining the contour of the tooth surface (146) by calculating one or more Bézier curves. The method (100, 200) according to claim 10 or 11, wherein the steps are carried out.

13. - When the number of triangles of the surface is less than the number of triangles of the tooth region, and - When the number of triangles added after expansion is less than a predetermined number, The surface is newly expanded (144). The method (100, 200) according to claim 12.

14. For determining the correspondence between the teeth of the digital model (4) of the tooth including the three-dimensional triangular mesh (41) and the reference tooth (2) in two-dimensional display, the automatic means (6) performs the following steps: - Segmenting the triangular mesh according to any one of claims 10 to 13 to identify the contour of at least one tooth of the mesh (100); - Obtaining a two-dimensional display of the surface of the reference tooth (201); - Obtaining a two-dimensional display of the surface of the tooth of the mesh delimited by the contour (201); - Determining a first ratio between the height and width of the surface of the reference tooth and a second ratio between the height and width of the surface of the tooth of the mesh (206); - Identifying the tooth of the mesh that does not correspond to the reference tooth (2) when the difference between the first ratio and the second ratio is greater than a predetermined value; Otherwise, - Converting the two-dimensional display of the reference tooth (2) according to the Levenberg - Marquardt algorithm for the purpose of comparison by overlapping the surface of the reference tooth and the surface of the tooth of the mesh (207). - a step (208) of determining an overlap value between the surface of the reference tooth (2) and the surface of the tooth of the mesh; - a step (210) of identifying the tooth of the mesh corresponding to the reference tooth when the overlap value is within a predetermined interval The method (100, 200) according to any one of claims 10 to 13, wherein the steps are performed. **Claim 15** A method according to claim 14 for performing all steps according to claim 14 except step (210), wherein the automatic means further comprises the following steps: - steps (202, 203) of cutting the surface of the reference tooth to identify a plurality of portions of the surface; - steps (202, 203) of cutting the surface of the tooth of the mesh in a corresponding manner; - a step (204) of determining a value associated with each determined portion of the surface; - a step (205) of determining a comparison value between the value determined for each portion of the surface of the reference tooth and each respective value for the corresponding portion of the surface of the tooth of the mesh; - a step (209) of determining a specific value between the surface of the reference tooth and the surface of the tooth of the mesh according to the comparison value and the overlap value; - a step (210) of identifying the tooth of the mesh corresponding to the reference tooth when the specific value is within a predetermined interval The method (100, 200) according to claim 14, wherein the steps are performed. **Claim 16** After determining an overlap value or a specific value for a plurality of teeth of the mesh compared to the reference tooth, the automatic means (6) identifies the tooth of the mesh having the most appropriate overlap value or specific value as corresponding to the reference tooth. The method (100, 200) according to claim 14 or 15. **Claim 17** When the corresponding tooth of the mesh is identified, the automatic means (6) identifies a value of one or more color tones associated with a portion of the reference tooth (2) in some portions of the corresponding tooth of the mesh within the mesh (41), where the portion of the reference tooth and the portion of the corresponding tooth of the mesh correspond to each other. The method (100, 200) according to any one of claims 14 to 16. **Claim 18** A computer program comprising code instructions that can control the execution of steps of the method (100, 200) according to at least one of claims 1 to 17 when executed on a computer. **Claim 19** A method for obtaining the program according to claim 18 for downloading the program on a communication network. **Claim 20** A computer-readable medium for storing the computer program according to claim 18.

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