# US 9,436,888 B2 · Method and system for determining a boundary surface network > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 9,436,888 B2 - Document ID: US9436888B2 - Status: Granted - Kind: B2 - Application number: 13/776,987 - Filed: 2013-02-26 - Published: 2013-08-29 - Granted: 2016-09-06 - Earliest claimed: 2012-02-29 - Assignees: Siemens Aktiengesellschaft - Applicants: Siemens Aktiengesellschaft - Inventors: Thomas Beck; Dominik Bernhardt; Jan Kretschmer - Web page: https://patentgrep.com/patent/US9436888B2 ## CPC - G06T 7/13: Edge detection - G06V 10/44: Local feature extraction by analysis of parts of the pattern, e.g. by detecting edges, contours, loops, corners, strokes or intersections; Connectivity analysis, e.g. of connected components - G06V 20/64: Three-dimensional [3D] objects - G06T 2207/10081: Computed x-ray tomography [CT] - G06T 2207/10088: Magnetic resonance imaging [MRI] - G06T 2207/30028: Colon; Small intestine - G06T 2207/30061: Lung - G06T 2207/30101: Blood vessel; Artery; Vein; Vascular - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL - G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING ## Abstract A method is disclosed for determining a boundary surface network of a tubular object. An ordered series of contours is first supplied on the basis of image data in a source space. A transformation function is created for at least two consecutive contours in the series, and a unit space segment object is created in the unit space on the basis of the consecutive contours. A local signed distance function is determined in the unit space. In addition, a relative positional information of a query point is determined in the source space from a surface of a segment object in the source space, the segment object being based on the consecutive contours, on the basis of the local signed distance function in the unit space and using the transformation function. Finally, the boundary surface network is created on the basis of the relative positional information that has been determined. ## Claims ### Claim 1 A method for determining a boundary surface network of a tubular object, comprising: providing an ordered series of contours on the basis of image data in a source space; specifying a transformation function for at least two consecutive contours in the ordered series, from the source space into a unit space, the unit space being a three-dimensional Euclidean space having a normalized length, width and height, and which is different from the source space; creating a unit space segment object in the unit space on the basis of the at least two consecutive contours; determining a local signed distance function in the unit space for the unit space segment object; determining relative positional information of a query point in the source space from a surface of a segment object in the source space, the segment object being based on the consecutive contours, on the basis of the local signed distance function in the unit space and using the transformation function; and creating the boundary surface network on the basis of the determined relative positional information; wherein the contours are freeform contours. ### Claim 2 (depends on 1) The method of claim 1, wherein each unit space segment object is assigned a dedicated transformation function for transformation into the unit space. ### Claim 3 (depends on 1) The method of claim 1, wherein the contours in each case are transformed into a circular boundary edge which lies in a plane in the unit space in each case, and wherein the space segment object comprises the boundary edges of the contours. ### Claim 4 (depends on 3) The method of claim 3, wherein the unit space segment object is bounded at least sectionally by a circumferential surface that is formed by the shortest connections between two boundary edges of the contours. ### Claim 5 (depends on 4) The method of claim 4, wherein the planes of the boundary edges in the unit space are so disposed as to be tilted by an angle relative to each other. ### Claim 6 (depends on 4) The method of claim 4, wherein the boundary edges of two different contours include one or more shared points in the unit space. ### Claim 7 (depends on 3) The method of claim 3, wherein the planes of the boundary edges in the unit space are so disposed as to be tilted by an angle relative to each other. ### Claim 8 (depends on 3) The method of claim 3, wherein the boundary edges of two different contours include one or more shared points in the unit space. ### Claim 9 (depends on 1) The method of claim 1, wherein values of the signed distance function represent separations in the unit space from the surface of the unit space segment object. ### Claim 10 (depends on 1) The method of claim 1, wherein a global position indicator function is determined for a plurality of unit space segment objects on the basis of the signed distance functions of the unit space segment objects. ### Claim 11 (depends on 1) The method of claim 1, further comprising: providing a representation of the tubular object on the basis of the image data, wherein the representation includes the ordered series of contours; providing local measurement information for points of the representation; creating a breakdown structure depiction of the tubular object by way of breakdown cells including different spatial extents, based on the local measurement information; and deriving a boundary surface network on the basis of the created breakdown structure depiction. ### Claim 12 (depends on 1) A computer program product, including a non-transitory computer-readable storage medium storing sections of program code that, when executed, cause at least one processor at a boundary surface network determination system to perform the method of claim 1. ### Claim 13 (depends on 1) The method of claim 1, wherein the tubular object is a hollow organ. ### Claim 14 (depends on 1) A non-transitory computer readable medium including program segments for, when executed on at least one processor at a boundary surface network determination system, causing the boundary surface network determination system to implement the method of claim 1. ### Claim 15 (depends on 1) The method of claim 1, wherein the source space is based on a measurement space of an imaging system used to obtain the image data. ### Claim 16 A boundary surface network determination system for determining a boundary surface network of a tubular object, comprising an input interface, configured to supply an ordered series of contours on the basis of image data; a segment object determination unit including a computer system configured to execute computer-readable instructions to specify a transformation function for respectively transforming consecutive contours in the ordered series of contours from a source space into a unit space, the unit space being a three-dimensional Euclidean space having a normalized length, width and height, and which is different from the source space, and create a unit space segment object in the unit space on the basis of the consecutive contours; a distance determination unit, configured to determine a separation from a unit space segment object on the basis of a signed distance function established for each segment object in the unit space; a position determination unit, configured to determine relative positional information of a query point in the source space from a surface of a segment object in the source space, said segment object being based on the consecutive contours, on the basis of the local signed distance function; and an output interface, configured to supply a boundary surface network on the basis of a multiplicity of relative positional information determined via the position determination unit; wherein the contours are freeform contours. ### Claim 17 (depends on 16) The boundary surface network determination system of claim 16, wherein the tubular object is a hollow organ.