Anatomical modeling using ball pivot algorithm

Abstract

A system includes a display and a processor. The processor is configured to obtain a point cloud comprising a plurality of points representing different respective locations in a body of a subject, the points being marked as respectively corresponding to respective anatomical structures to which the locations belong. The anatomical structure includes a first structure and a plurality of second structures. The processor is further configured to compute a grid comprising a plurality of triangles representing the anatomical structure by applying a ball pivot algorithm to the point cloud, wherein a constraint condition is that none of the triangles comprises two of the points marked as corresponding to different respective ones of the second structures. Other examples are also described.

Description

Technical Field

[0001] The present disclosure relates to the field of anatomical modeling. Background Art

[0002] A three-dimensional anatomical model typically includes a mesh of interpolated point clouds. Such a mesh can be constructed using a ball pivoting algorithm (BPA), which is described, for example, in "The ball-pivoting algorithm for surface reconstruction" by Bernardini, Fausto et al., IEEE transactions on visualization and computer graphics 5.4 (1999): 349-359, the disclosure of which is incorporated herein by reference. According to the BPA, when a ball of a user-specified radius touches three points and does not contain any other points, the three points form a triangle. Starting from a seed triangle, the ball pivots around an edge (i.e., it rotates around the edge while remaining in contact with the endpoints of the edge) until it touches another point, thereby forming another triangle (or other polygon forming a mesh). The process continues until all reachable edges have been tried, then starting with another sub-triangle until all points have been considered. The process can then be repeated with a ball of a larger radius to handle uneven sampling density.

[0003] Anatomical models (and in particular electroanatomical models) are often used by electrophysiologists to visualize the anatomy and electrical signals in cardiac tissue. These models can be constructed algorithmically using data collected by diagnostic catheters and / or ultrasound data, and such models typically include 3D triangulated meshes corresponding to the various anatomical structures of the heart. Triangular meshes are typical, but not required, as the meshes may also include quadrilaterals in some systems within the scope of some examples. A 3D model including more than one cardiac structure can be formed by stitching together the various 3D meshes generated. Example anatomical structures that can be modeled include, for example, the left atrium (LA) body and the left atrial appendage (LAA), the left inferior pulmonary vein (LIPV), the left superior pulmonary vein (LSPV), the right inferior pulmonary vein (RIPV), and the right superior pulmonary vein (RSPV). As an example, a 3D mesh representing the left atrium can be connected to other 3D meshes representing the pulmonary veins, pulmonary arteries, and / or other chambers. Image processing is usually required to connect the various 3D meshes so that the complete model can be displayed to the user. Color coding can be superimposed on the model to show the propagation of electrical signals across chambers or to show other EP properties of the heart. Users expect to see signals propagating in the atria and ventricles, but not in the pulmonary veins and arteries. The boundary lines (or anatomical structure boundaries) between atria / ventricles and veins / arteries must currently usually be defined manually by the user so that the signal propagation map does not cross veins and arteries. BRIEF DESCRIPTION OF THE DRAWINGS

[0004] The present disclosure will be more fully understood through the following detailed description of examples of the present disclosure in conjunction with the accompanying drawings, in which:

[0005] Figure 1 is a schematic diagram of an anatomical mapping system according to some examples of the present disclosure;

[0006] Figure 2 is a schematic diagram of an example calculation of a triangular mesh according to some examples of the present disclosure;

[0007] Figure 3 is a schematic diagram of a triangular mesh according to some examples of the present disclosure; and

[0008] Figure 4 is a flow chart of an example BPA algorithm according to some examples of the present disclosure. DETAILED DESCRIPTION

[0009] Overview

[0010] In many cases, using BPA to construct an anatomical model can be challenging. First, the model may erroneously join together two anatomical structures (such as two pulmonary veins) that are not actually joined to each other but are separated from each other by a distance less than the diameter of the BPA ball. Second, the model may not accurately mark the boundary between two joined anatomical structures (such as the main body of the left atrium and the pulmonary veins).

[0011] Therefore, examples of the present disclosure modify BPA in order to address these challenges.The modified algorithm is applied to a point cloud where each point is labeled with an identifier of the anatomical structure to which the point belongs.

[0012] Specifically, when constructing a triangular mesh from the marked points, it is preferred that pairs of points from different corresponding unjoined structures are not allowed to belong to the same triangle. This constraint can reduce pseudo-joining of anatomical structures. In addition, any triangle edges that join pairs of points from different corresponding structures can be marked. After the mesh is constructed, the marked edges used to define one or more closed polylines can then be smoothed. The resulting closed curves are then overlaid on the model to indicate the boundaries between the joined anatomical structures.

[0013] System Description

[0014] First reference Figure 1 , which is a schematic diagram of an anatomical mapping system 20 according to some examples of the present disclosure.

[0015] The system 20 includes an intracorporeal probe 26 proximally connected to a console 32. The system 20 also includes a processor (PROC) 34 and a memory 38, which are typically housed in the console 32, and a display 36 that may be provided on the console 32. The memory 38 may include any suitable volatile memory, such as random access memory (RAM), and / or non-volatile memory, such as flash memory.

[0016] The processor 34 is configured to compute a triangular mesh 46 including a plurality of triangles 48 representing a plurality of anatomical structures. Figure 3 As shown, the grid 46 displayed to the user appears in the form of an anatomical model. The anatomical structure includes a first structure and a plurality of second structures. In some cases, the plurality of segment structures are in fluid communication with the first structure, but are not in fluid communication with each other.

[0017] For example, the first structure may include at least a portion of the body of a chamber of the heart 24 of the subject 22, and the second structure may include an appendage to the chamber and / or a blood vessel connected to the body of the chamber. As a specific example, the first structure may include at least a portion of the body of the left atrium of the heart 24, and the second structure may include the left atrial appendage and / or one or more pulmonary veins that deliver blood to the body of the left atrium. As another example, the first structure may include at least a portion of the chamber of the sinus, and the second structure may include an airway connected to the chamber.

[0018] To compute the mesh 46, the processor first obtains a point cloud 40 that includes a plurality of points 42 representing different corresponding locations in the body of the subject 22. The points 42 are labeled as corresponding to the corresponding anatomical structures to which these locations belong and to which the mesh is to represent. For example, a point 42 representing a location belonging to the main body of the left atrium of the heart 24 may be labeled as corresponding to the main body of the left atrium.

[0019] In some examples, the processor obtains the point cloud 40 without computing the point cloud; for example, the processor may receive the point cloud over a computer network or load the point cloud from an external storage drive.

[0020] In other examples, the processor calculates the point cloud by sampling a plurality of preliminary grids representing the anatomical structure, respectively. After calculating the point cloud, the processor may store the point cloud in the memory 38 and then read the point cloud from the memory when calculating the grid 46.

[0021] In such examples, a preliminary mesh is generated from the preliminary point cloud using any suitable surface reconstruction algorithm, such as the algorithm described in Lorensen, William E. and Harvey E. Cline, "Marching cubes: A high resolution 3D surface construction algorithm", ACM siggraph computer graphics 21.4 (1987): 163-169, the disclosure of which is incorporated herein by reference. To generate the preliminary point cloud, the processor 34 (or a different processor) tracks the position of the distal end of the probe 26 as the physician 30 moves along the surface of the anatomical structure. Such a point cloud can be acquired by ultrasound imaging of the heart chambers. Alternatively, the position of the data is reported by a position sensor on the catheter, as is known in the art. For example, a position sensor can be used 3System's Fast Anatomical Mapping (FAM) function is compatible with mapping catheters such as The data are collected in conjunction with a catheter, both of which are available from Biosense Webster, Inc., available from Biosense Webster, Inc., 3333 Diamond Canyon Road, Diamond Bar, Calif. 9176531A Technology Drive, Irvine, CA 92618. The processors found in the system can be programmed by one skilled in the art to perform the functions described below.

[0022] In some such examples, to facilitate tracking of the probe, one or more electromagnetic sensors 28 are coupled to the distal end of the probe and a magnetic field is generated near the subject 22. The magnetic field induces a position-related signal in the sensor 28. Based on the signal, the processor determines the position of the distal end of the probe. Such magnetic-based tracking is disclosed, for example, in U.S. Patents 5,391,199, 5,443,489, and 6,788,967 to Ben-Ham, U.S. Patent 6,690,963 to Ben-Ham et al., U.S. Patent 5,558,091 to Acker et al., and U.S. Patent 6,177,792 to Govari, the corresponding disclosures of which are incorporated herein by reference.

[0023] Alternatively or in addition, one or more electrodes coupled to the distal end of the probe may deliver current to a plurality of electrode patches coupled to the subject's body at different respective locations. Based on the current and the body impedance measurements derived therefrom, the processor may determine the position of the distal end of the probe, as taught, for example, in U.S. Pat. No. 7,756,576 and U.S. Pat. No. 7,536,218, which are incorporated herein by reference. Hybrid techniques combining such impedance-based tracking with magnetic-based tracking are described in U.S. Pat. No. 8,456,182 to Bar-Tal et al., the disclosure of which is incorporated herein by reference.

[0024] After obtaining the point cloud 40, the processor applies any suitable version of the ball pivot algorithm (BPA) to the point cloud 40, as described below with reference to Figure 2 As further described, a grid 46 is thereby calculated. After calculating the grid 46, the processor 34 displays the grid on the display 36.

[0025] Generally speaking, the processor 34 may be embodied as a single processor, or as a group of collaborative networked or clustered processors. In some examples, as described herein, the functions of the processor 34 may be implemented only in hardware, for example, using one or more application-specific integrated circuits (ASICs) or field programmable gate arrays (FPGAs). In other examples, the functions of the processor 34 are implemented at least in part in software. For example, in some examples, the processor 34 is embodied as a programmed digital computing device comprising at least a central processing unit (CPU) and a random access memory (RAM). The program code (including software programs and / or data) is loaded into the RAM for execution and processing by the CPU. For example, the program code and / or data may be downloaded to the processor in electronic form via a network. Alternatively or in addition thereto, the program code and / or data may be provided and / or stored on a non-transient tangible medium, such as a magnetic, optical or electronic memory. Such program code and / or data, when provided to the processor, generates a machine or a special-purpose computer configured to perform the tasks described herein.

[0026] Computational Grid

[0027] Reference now Figure 2 , which is a schematic diagram of example calculations of a grid 46 according to some examples of the present disclosure.

[0028] Processor 34 ( Figure 1 ) can use a mapping module to initially connect the locations of the point cloud (e.g., data) to define a grid of line segments. The grid 46 is typically a triangular grid, but this is not required. In one embodiment, the processor uses a ball pivoting algorithm (BPA) to generate the grid 46. Typically, where BPA is used, the size of the ball is set to correspond to the size of the voxels of the subject's anatomical model. Alternatively, the grid can be generated as a Delaunay triangulation, which includes a plurality of triangles having vertices. The triangles of the triangulation can be based on a Voronoi diagram formed around the locations of the grid. However, the processor can use any convenient method known in the art for forming a grid. In this example, the processor 34 ( Figure 1 ) is configured to apply BPA to the point cloud 40, wherein the constraint is that none of the polygons (here the triangles 48) includes two points 42 that are marked as corresponding to different respective ones of the second structures.

[0029] By way of example, Figure 2 FIG. 4 shows a scene in which a triangle 48a is formed during the application of BPA to a point cloud. The triangle 48a includes three points 42: the first point Second point And the third point First point And the second point The first structure is labeled as corresponding to the first structure (as indicated by the superscript "f"), which may include, for example, at least a portion of a chamber of the heart or at least a portion of a sinus. Labeled as corresponding to a second structure s1 (as indicated by the superscript "s1"), the second structure may include, for example, a blood vessel or an airway.

[0030] After forming the triangle 48a, the BPA ball 51 pivots at different corresponding times about the two sides of the triangle 48a: the first side 50a, which places the second point Join to the third point and a second side 50b, which separates the first point Join to the third point When the ball 51 pivots about the first side 50a, the ball contacts the fourth point marked as corresponding to the second structure s1 As the ball pivots about the second edge 50b, the ball contacts a fifth point labeled as corresponding to another second structure s2 (which may include, for example, another blood vessel or airway). Therefore, if Figure 2 The BPA algorithm may add a fourth point to the triangle mesh, as indicated by the dashed edge. and / or the fifth point

[0031] Assume that the second point is included Third Point And the fourth point The resulting triangle 48b does not violate the constraint condition, so the fourth point is added However, the fifth point are not added to the mesh, since such addition would result in a third point being labeled as corresponding to a different corresponding second structure And the fifth point belong to the same triangle.

[0032] segmentation

[0033] In some examples, for each of the second structures, the processor identifies a plurality of edges of triangle 48, each of the plurality of edges passing between any first point in the points marked as corresponding to the first structure and any second point in the points marked as corresponding to the second structure. Figure 2 As indicated by the bold line in FIG. 1 , for the second structure s1, the processor may identify the first side 50a, the second side 50b, and the second point Connect to the fourth point The third side 50c.

[0034] Typically, these "boundary edges" are identified when applying BPA to the cloud of points 42. For example, in response to adding each new point to the grid, the processor may check whether the newly added point is joined to a point corresponding to a different structure. If so, the edge or edges joining the newly added point may be identified as a boundary edge. For example, in response to the fourth point With the addition of , the third edge 50c can be identified as a boundary edge.

[0035] Reference now Figure 3 , which is a schematic diagram of a mesh 46 according to some examples of the present disclosure. The mesh 46 includes a first mesh portion 46a representing the surface of the left atrium body and a second mesh portion 46b representing the surface of the pulmonary vein.

[0036] Based on the identified boundary edges, the processor displays a boundary 54 between each of the first and second structures on the grid. Figure 3 In the illustrated case, the processor displays the boundary 54 between the main body of the left atrium and the pulmonary veins.

[0037] Typically, the identified boundary edges form a closed polyline 52. Thus, the processor may display the polyline 52 as the boundary. However, typically, the processor smoothes the polyline and then displays the smoothed polyline 56 as the boundary. To smooth the polyline, the processor may use spline interpolation or any other suitable technique.

[0038] In some cases, one or more identified boundary edges diverge from the polyline 52. The processor is configured to trim these diverging edges from the polyline before displaying or smoothing the polyline. It should also be understood that numerous other suitable means may be used to indicate the boundaries between structures, including but not limited to as raised features, depressions, assigning different colors to the surfaces of each of the structures, adding one or more icons at or near the boundary, and / or superimposing arrows pointing to the boundary, etc.

[0039] Example BPA Algorithm

[0040] Reference now Figure 4 , which is a flow chart of an example BPA algorithm 58 that represents a novel improvement over conventional BPA algorithms that allows accurate, automatic identification of boundaries between different anatomical structures. The algorithm may be implemented by a processor 34 ( Figure 1 )implement.

[0041] The algorithm 58 begins at an initialization step 60 where the grid 46 ( Figure 1) is initialized with at least one triangle. As described above, other examples within the scope of the claims may operate on meshes formed by polygons other than triangles or polygons other than triangles. After the initialization step 60, the processor selects a seed triangle at a seed selection step 62. Then, at a pivoting step 64, the processor pivots the ball 51 ( Figure 1 ). The processor then checks whether the ball touches another point at a check step 66. If not, the processor proceeds to another check step 78 described below. Otherwise, at a tag identification step 68, the processor identifies the tag of the point that was touched.

[0042] After identifying the label, at another check step 70, the processor checks whether the aforementioned constraints allow the contacted point to be added to the grid based on the label. Specifically, the processor checks whether any of the edge endpoints corresponds to one of the second structures, and if so, checks whether the contacted point corresponds to the same second structure. If the contacted point does not correspond to any second structure, or if the contacted point corresponds to the same second structure as one or both of the endpoints, the processor concludes that the contacted point can be added.

[0043] If the contacted point is constrained so that it cannot be added to the mesh, the processor proceeds to a check step 78. Otherwise, at the point adding step 72, the processor adds the contacted point to the mesh. Subsequently, at another check step 74, the processor checks whether one or both of the edges joining the new point to the mesh are boundary edges. If so, the processor marks the boundary edges at a marking step 76. Subsequently, or if no boundary edges are marked, the processor performs a check step 78.

[0044] At a check step 78, the processor checks if there are any edges left for pivoting. If so, the processor returns to the pivot step 64, where the processor pivots the BPA ball around the next edge. Otherwise, at another check step 80, the processor checks if there are any seed triangles left. If so, the processor returns to the seed selection step 62, where the processor selects the next seed triangle. Otherwise, the algorithm 58 ends.

[0045] After executing algorithm 58, the processor displays the grid. Figure 3 As described, the processor may overlay one or more borders 54 on the grid, which may be defined based on the marked boundary edges. For example, each boundary may be a closed curve that smoothly interpolates the closed polylines defined by the marked boundary edges.

[0046] Example

[0047] The following examples relate to various non-exhaustive ways in which the teachings herein may be combined or applied. It should be understood that the following examples are not intended to limit the coverage of any claims that may be provided at any time in this patent application or in the subsequent submissions of this patent application. It is not intended to make a disclaimer. The following examples are provided only for illustrative purposes. It is envisioned that the various teachings herein may be arranged and applied in a variety of other ways. It is also envisioned that some variations may omit certain features mentioned in the following examples. Therefore, any of the aspects or features mentioned below should not be considered decisive unless otherwise explicitly indicated by the inventor or the successor with an interest in the inventor at a later date. If any claim proposed in this patent application or in the subsequent submissions related to this patent application includes additional features other than those mentioned below, these additional features should not be assumed to be added for any reason related to patentability.

[0048] 1. A system (20) comprising a display (36) and a processor (34). The processor is configured to obtain a point cloud (40) comprising a plurality of points (42) representing different corresponding locations in a body of a subject (22), the points being labeled as corresponding to corresponding anatomical structures to which the locations belong, respectively. The anatomical structures include a first structure and a plurality of second structures. The processor is further configured to form a mesh (46) comprising a plurality of triangles (48) representing the anatomical structures by applying a ball pivoting algorithm to the point cloud, wherein a constraint is that none of the triangles includes two of the points labeled as corresponding to different corresponding second structures in the second structures. The processor is further configured to display the mesh on the display.

[0049] 2. The system (20) of Example 1, wherein the first structure comprises at least a portion of a chamber of the heart (24).

[0050] 3. The system (20) of embodiment 1, wherein the first structure comprises at least a portion of a sinus.

[0051] 4. The system (20) of any one of embodiments 1 to 3, wherein the processor (34) is further configured to:

[0052] For each of the second structures in the second structure:

[0053] identifying a plurality of sides of the triangle (48), each of the plurality of sides passing between any first point of the points (42) marked as corresponding to the first structure and any second point of the points marked as corresponding to the second structure, and

[0054] Based on the identified edges, a boundary (54) between the first structure and the second structure is displayed on the grid (46).

[0055] 5. The system (20) of claim 4, wherein the identified edges form a closed polyline (52), and wherein the processor (34) is configured to display the boundary (54) by:

[0056] smoothing the polyline, and

[0057] The smoothed polyline (56) is displayed.

[0058] 6. A system (20) according to any one of embodiments 4 to 5, wherein the processor (34) is configured to identify the edges of each of the second structures when applying the ball pivot algorithm to the point cloud (40).

[0059] 7. A system (20) according to any one of embodiments 1 to 6, wherein the processor (34) is configured to calculate the point cloud (40) by respectively sampling a plurality of preliminary grids representing the anatomical structure.

[0060] 8. A method, comprising obtaining a point cloud (40) comprising a plurality of points (42) representing different corresponding locations in a body of a subject (22), the points being labeled as corresponding to corresponding anatomical structures to which the locations belong, respectively. The anatomical structures include a first structure and a plurality of second structures. The method further comprises calculating a mesh (46) comprising a plurality of triangles (48) representing the anatomical structures by applying a ball pivoting algorithm to the point cloud, wherein a constraint is that none of the triangles includes two of the points labeled as corresponding to different corresponding second structures in the second structures. The method further comprises displaying the mesh.

[0061] 9. The method of embodiment 8, wherein the first structure comprises at least a portion of a chamber of the heart (24).

[0062] 10. The method of Example 8, wherein the first structure comprises at least a portion of a sinus.

[0063] 11. The method of any one of embodiments 8 to 10, further comprising:

[0064] For each of the second structures in the second structure:

[0065] identifying a plurality of sides of the triangle (48), each of the plurality of sides passing between any first point of the points (42) marked as corresponding to the first structure and any second point of the points marked as corresponding to the second structure, and

[0066] Based on the identified edges, a boundary (54) between the first structure and the second structure is displayed on the grid (46).

[0067] 12. The method of embodiment 11, wherein the identified edges form a closed polyline (52), and wherein displaying the boundary (54) comprises:

[0068] smoothing the broken line; and

[0069] The smoothed polyline (56) is displayed.

[0070] 13. The method of any one of embodiments 11 to 12, wherein identifying the edges of each of the second structures comprises identifying the edges when applying the ball pivoting algorithm to the point cloud (40).

[0071] 14. A method according to any one of embodiments 8 to 13, wherein obtaining the point cloud (40) includes calculating the point cloud by sampling a plurality of preliminary grids representing the anatomical structure, respectively.

[0072] 15. A computer software product comprising a tangible, non-transitory computer-readable medium having program instructions stored therein. The instructions are executed by a processor (34)

[0073] When read, the processor is caused to obtain a point cloud (40) including a plurality of points (42) representing different corresponding locations in the body of the subject (22), the points being labeled as corresponding to the corresponding anatomical structures to which the locations belong, respectively. The anatomical structures include a first structure and a plurality of second structures. The instructions further cause the processor to calculate a mesh (46) including a plurality of triangles (48) representing the anatomical structures by applying a ball pivoting algorithm to the point cloud, wherein a constraint is that none of the triangles includes two of the points labeled as corresponding to different corresponding second structures in the second structures. The instructions further cause the processor to display the mesh or a smoothed model created from the mesh.

[0074] It should be understood by those skilled in the art that the present disclosure is not limited to the contents specifically shown and described above. On the contrary, the scope of the present disclosure includes the combinations and sub-combinations of the various features described above, as well as variations and modifications that are not within the scope of the prior art that may occur to those skilled in the art when reading the above description. The documents incorporated by reference into this patent application are considered an integral part of this application, unless any term defined in these incorporated documents conflicts with the definition explicitly or implicitly given in this specification, then only the definition in this specification shall be considered.

Claims

1. A system, comprising: monitor; and A processor, the processor being configured to: obtaining a point cloud comprising a plurality of points, the plurality of points representing different corresponding locations in the body of the subject, the points being labeled as corresponding to corresponding anatomical structures to which the locations belong, respectively; The anatomical structure includes a first structure and a plurality of second structures, and A mesh comprising a plurality of triangles representing the anatomical structures is calculated by applying a ball pivoting algorithm to the point cloud, wherein a constraint is that none of the triangles comprises two of the points marked as corresponding to different respective ones of the second structures.

2. The system according to claim 1, wherein: The first structure includes at least a portion of a chamber of the heart.

3. The system according to claim 1, wherein: The first structure includes at least a portion of a sinus.

4. The system according to claim 1, wherein: The processor is further configured to: For each of the second structures in the second structure: identifying a plurality of sides of the triangle, each of the plurality of sides passing between any first point of the points marked as corresponding to the first structure and any second point of the points marked as corresponding to the second structure, and Based on the identified edge, a boundary between the first structure and the second structure is displayed on the grid.

5. The system according to claim 4, wherein: The identified edges form a closed polyline, and wherein the processor is configured to display the boundary by: smoothing the polyline, and Displays the smoothed polyline.

6. The system according to claim 4, wherein: The processor is configured to identify the edge of each of the second structures when applying the ball pivot algorithm to the point cloud.

7. The system according to claim 1, wherein: The processor is configured to compute the point cloud by respectively sampling a plurality of preliminary meshes representing the anatomical structure.

8. A method comprising: obtaining a point cloud comprising a plurality of points, the plurality of points representing different corresponding locations in the body of the subject, the points being labeled as corresponding to corresponding anatomical structures to which the locations belong, respectively; The anatomical structure includes a first structure and a plurality of second structures; as well as A mesh comprising a plurality of triangles representing the anatomical structures is calculated by applying a ball pivoting algorithm to the point cloud, wherein a constraint is that none of the triangles comprises two of the points marked as corresponding to different respective ones of the second structures.

9. The method according to claim 8, wherein: The first structure includes at least a portion of a chamber of the heart.

10. The method according to claim 8, wherein: The first structure includes at least a portion of a sinus.

11. The method according to claim 8, further comprising: For each of the second structures in the second structure: identifying a plurality of sides of the triangle, each of the plurality of sides passing between any first point of the points marked as corresponding to the first structure and any second point of the points marked as corresponding to the second structure, and Based on the identified edge, a boundary between the first structure and the second structure is displayed on the grid.

12. The method according to claim 11, wherein: The identified edges form a closed polyline, and wherein displaying the boundary comprises: smoothing the broken line; and Displays the smoothed polyline.

13. The method according to claim 11, wherein: Identifying the edges of each of the second structures includes identifying the edges while applying the ball pivoting algorithm to the point cloud.

14. The method according to claim 8, wherein: Obtaining the point cloud includes calculating the point cloud by respectively sampling a plurality of preliminary grids representing the anatomical structure.

15. A computer software product comprising a tangible, non-transitory computer-readable medium having program instructions stored therein, the program instructions, when read by a processor, causing the processor to: obtaining a point cloud comprising a plurality of points, the plurality of points representing different corresponding locations in the body of the subject, the points being labeled as corresponding to corresponding anatomical structures to which the locations belong, respectively; The anatomical structure includes a first structure and a plurality of second structures in fluid communication with the first structure but not with each other, and A mesh including a plurality of triangles representing the anatomical structure is calculated by applying a spherical pivoting algorithm to the point cloud, wherein: The constraint is that none of the triangles includes two of the points that are marked as corresponding to different respective ones of the second structures.

16. The computer software product of claim 15, wherein: The first structure includes at least a portion of a chamber of the heart.

17. The computer software product of claim 15, wherein: The first structure includes at least a portion of a sinus.

18. The computer software product of claim 15, wherein: The instructions further cause the processor to: For each of the second structures in the second structure: identifying a plurality of sides of the triangle, each of the plurality of sides passing between any first point of the points marked as corresponding to the first structure and any second point of the points marked as corresponding to the second structure, and Based on the identified edge, a boundary between the first structure and the second structure is displayed on the grid.

19. The computer software product according to claim 18, wherein: The identified edges form a closed polyline, and wherein the instructions cause the processor to display the boundary by: smoothing the polyline, and Displays the smoothed polyline.

20. The computer software product of claim 18, wherein: The instructions cause the processor to identify the edge of each of the second structures when applying the ball pivot algorithm to the point cloud.

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