# US 11,113,881 B2 · Systems and methods for generating a three-dimensional surface from a segmented volume > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 11,113,881 B2 - Document ID: US11113881B2 - Status: Granted - Kind: B2 - Application number: 16/991,134 - Filed: 2020-08-12 - Published: 2021-03-11 - Granted: 2021-09-07 - Earliest claimed: 2019-09-06 - Assignees: St. Jude Medical, Cardiology Division, Inc. - Applicants: St. Jude Medical, Cardiology Division, Inc. - Inventors: Frank Miller - Web page: https://patentgrep.com/patent/US11113881B2 ## CPC - G06T 17/20: Finite element generation, e.g. wire-frame surface description, {tesselation} - G06T 17/205: {Re-meshing} - G06T 1/20: Processor architectures; Processor configuration, e.g. pipelining - G06T 15/503: {Blending, e.g. for anti-aliasing} - G06T 19/20: Editing of three-dimensional [3D] images, e.g. changing shapes or colours, aligning objects or positioning parts - G06T 2219/2004: Aligning objects, relative positioning of parts - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL ## Abstract Systems and methods for generating a three-dimensional surface from a segmented volume including a plurality of voxels are provided. The method includes executing a first pass over a plurality of cells to generate a list of active cells, and executing a second pass over the plurality of active cells to generate a quadrilateral mesh, the quadrilateral mesh including a plurality of points that define a plurality of quadrilaterals. The method further includes executing at least one additional pass over the quadrilateral mesh to generate a smoothed mesh, wherein executing the at least one additional pass includes computing, for at least one point, a balanced curvature for the at least one point based on curvatures at points that neighbor the at least one point and moving the at least one point to a new location based on the computed balanced curvature. The method further includes displaying the smoothed mesh. ## Claims ### Claim 1 A computer-implemented method for generating a three-dimensional surface from a segmented volume including a plurality of voxels, the segmented volume divided into a plurality of overlapping cells that each include a plurality of neighboring voxels, the method comprising: executing, using a computing device, a first pass over the plurality of cells to generate a list of active cells; executing, using the computing device, a second pass over the plurality of active cells to generate a quadrilateral mesh, the quadrilateral mesh including a plurality of points that define a plurality of quadrilaterals, each of the plurality of points located within a corresponding active cell; executing, using the computing device, at least one additional pass over the quadrilateral mesh to generate a smoothed mesh, wherein executing the at least one additional pass comprises: computing, for at least one point of the plurality of points, a balanced curvature for the at least one point based on curvatures at points that neighbor the at least one point; and moving the at least one point to a new location based on the computed balanced curvature; and displaying, using the computing device, the smoothed mesh. ### Claim 2 (depends on 1) The method of claim 1, wherein computing a balanced curvature comprises computing the balanced curvature by averaging the curvature at the at least one point with negative curvatures at the neighboring points. ### Claim 3 (depends on 1) The method of claim 1, wherein executing a second pass comprises determining a location of each of the plurality of points within the corresponding active cell using a point displacement lookup table. ### Claim 4 (depends on 1) The method of claim 1, wherein the computing device includes a graphics processing unit (GPU). ### Claim 5 (depends on 1) The method of claim 1, wherein executing at least one additional pass comprises executing a plurality of additional passes. ### Claim 6 (depends on 1) The method of claim 1, wherein executing at least one additional pass further comprises: identifying at least one non-manifold point of the plurality of points; and adjusting a position of the at least one non-manifold point using elastic relaxation. ### Claim 7 (depends on 1) The method of claim 1, wherein moving the at least one point to a new location based on the computed balanced curvature comprises increasing a curvature of the at least one point while decreasing the curvatures at the neighboring points. ### Claim 8 A computing device for generating a three-dimensional surface from a segmented volume including a plurality of voxels, the segmented volume divided into a plurality of overlapping cells that each include a plurality of neighboring voxels, the computing device comprising: a memory device; and a processor communicatively coupled to the memory device, the processor configured to: execute a first pass over the plurality of cells to generate a list of active cells; execute a second pass over the plurality of active cells to generate a quadrilateral mesh, the quadrilateral mesh including a plurality of points that define a plurality of quadrilaterals, each of the plurality of points located within a corresponding active cell; execute at least one additional pass over the quadrilateral mesh to generate a smoothed mesh, wherein executing the at least one additional pass includes: computing, for at least one point of the plurality of points, a balanced curvature for the at least one point based on curvatures at points that neighbor the at least one point; and moving the at least one point to a new location based on the computed balanced curvature; and display, on the computing device, the smoothed mesh. ### Claim 9 (depends on 8) The computing device of claim 8, wherein to compute a balanced curvature, the processor is configured to compute the balanced curvature by averaging the curvature at the at least one point with negative curvatures at the neighboring points. ### Claim 10 (depends on 8) The computing device of claim 8, wherein to execute a second pass, the processor is configured to determine a location of each of the plurality of points within the corresponding active cell using a point displacement lookup table. ### Claim 11 (depends on 8) The computing device of claim 8, wherein the processor comprises a graphics processing unit (GPU). ### Claim 12 (depends on 8) The computing device of claim 8, wherein to execute at least one additional pass, the processor is configured to execute a plurality of additional passes. ### Claim 13 (depends on 8) The computing device of claim 8, wherein to execute at least one additional pass, the processor is further configured to: identify at least one non-manifold point of the plurality of points; and adjust a position of the at least one non-manifold point using elastic relaxation. ### Claim 14 (depends on 8) The computing device of claim 8, wherein to move the at least one point to a new location based on the computed balanced curvature, the processor is configured to increase a curvature of the at least one point while decreasing the curvatures at the neighboring points. ### Claim 15 Non-transitory computer-readable media having computer-executable instructions thereon, wherein when executed by a processor of a computing device, cause the processor of the computing device to: execute a first pass over a plurality of overlapping cells in a segmented volume to generate a list of active cells, each cell including a plurality of neighboring voxels; execute a second pass over the plurality of active cells to generate a quadrilateral mesh, the quadrilateral mesh including a plurality of points that define a plurality of quadrilaterals, each of the plurality of points located within a corresponding active cell; execute at least one additional pass over the quadrilateral mesh to generate a smoothed mesh, wherein executing the at least one additional pass includes: computing, for at least one point of the plurality of points, a balanced curvature for the at least one point based on curvatures at points that neighbor the at least one point; and moving the at least one point to a new location based on the computed balanced curvature; and display, on the computing device, the smoothed mesh. ### Claim 16 (depends on 15) The non-transitory computer-readable media of claim 15, wherein to compute a balanced curvature, the processor is configured to compute the balanced curvature by averaging the curvature at the at least one point with negative curvatures at the neighboring points. ### Claim 17 (depends on 15) The non-transitory computer-readable media of claim 15, wherein to execute a second pass, the processor is configured to determine a location of each of the plurality of points within the corresponding active cell using a point displacement lookup table. ### Claim 18 (depends on 15) The non-transitory computer-readable media of claim 15, wherein to execute at least one additional pass, the processor is configured to execute a plurality of additional passes. ### Claim 19 (depends on 15) The non-transitory computer-readable media of claim 15, wherein to execute at least one additional pass, the processor is further configured to: identify at least one non-manifold point of the plurality of points; and adjust a position of the at least one non-manifold point using elastic relaxation. ### Claim 20 (depends on 15) The non-transitory computer-readable media of claim 15, wherein to move the at least one point to a new location based on the computed balanced curvature, the processor is configured to increase a curvature of the at least one point while decreasing the curvatures at the neighboring points.