Method and device for 3D tomographic reconstruction by X-rays

Abstract

The invention relates to a device and a method for 3D X-ray tomographic reconstruction of an object. The method comprises steps consisting in: - creating (210) a realigned volume mesh of an object; - constructing (212) from the realigned volume mesh a tree structure, said tree structure being constructed according to a hierarchy of bounding volumes and such that each node of the tree represents a geometric element of said mesh, each node is defined in a bounding volume, and each bounding volume groups together one or more nodes; - implementing (214) an iterative tomographic reconstruction algorithm on said tree structure until an end criterion is reached; and - defining (216) the tree structure obtained at the end of the iteration as being a 3D X-ray tomographic reconstruction of the object. Figure for abstract: Fig. 2

Description

Title of the invention: Method and device for 3D tomographic reconstruction by X-rays Field of the invention

[0001] The invention lies in the field of X-ray tomographic reconstruction, and relates in particular to a 3D reconstruction method and device. State of the Art

[0002] Tomography is a technique that consists of reconstructing the volume of an object (human body in the case of medical imaging, geological structure in the case of geophysics) from a series of measurements taken outside the object. These measurements can be carried out on the surface itself or at a certain distance. The result is a reconstruction of certain properties of the interior of the object, depending on the type of information provided by the sensors (capture of a particle, acoustic pressure, attenuation of a light beam, difference in speed or polarization of seismic waves).

[0003] X-ray absorption tomography is a non-destructive technique that allows the reconstruction of images of a three-dimensional object. Its principle is based on the multidirectional analysis of the interaction of an X-ray beam with matter, by recording with detectors the radiation transmitted after passing through an object.

[0004] The data acquired during the measurement (the duration of which varies from a fraction of a second to several hours depending on the installation) are collected according to multiple orientations (different angles by rotation of the object and according to several height positions) the number and pitch of which depend on the type of device and the resolution fineness.

[0005] Using this data, a digital image is calculated and mathematically reconstructed in gray or color levels, each of which translates point by point the local attenuation coefficient of the incident beam. This, after calibration and calibration, can be translated into a density scale.

[0006] X-ray tomography therefore allows access to the heart of the matter to assess variations in radiological absorption and differences in composition. It also makes it possible to locate very precisely any heterogeneity, singularity, void or inclusion present in an object, as well as to verify the assembly and positioning of complex mechanical assemblies.

[0007] Industrial tomography is a non-destructive testing technique that allows 3D visualization of the interior and exterior of large parts. Geometric complexity. The different views obtained make it possible to determine the absorption of each volume element, called "voxels," and thus to reconstruct an object in three dimensions. It is then possible to obtain several representations of the object's volume, including a visualization in the form of virtual sections. This representation is the most conventional and the most practical for determining porosity rates or measuring discontinuities.

[0008] In the automotive and aeronautics fields, tomography can be used to locate and quantify internal defects, but also to perform geometric control of prototype parts. In particular, geometrically very complex cored internal areas can be controlled without destructive testing. Many other high value-added industrial fields are interested in this type of non-destructive testing.

[0009] Indeed, the health analysis of the material consists of the search for defects, re-creases, porosities, cracks or other anomalies that may be present in manufactured parts and products. This type of material health analysis can highlight networks of porosity causing leaks or even cracks located in mechanically stressed areas.

[0010] The tomography data also allows dimensional checks and in particular the measurement of wall thickness, diameter, radius, anomaly size, distance between two points or walls.

[0011] Thus, from a mathematical point of view, tomography is divided into two major phases, which are a projection phase and a back-projection phase. A first phase consists of the development of a direct model of the object to be controlled, a model which must sufficiently faithfully describe the physical phenomena as they are measured. A second phase (known as the inverse problem) consists of a reconstruction of the object based on the direct model, in order to find the three-dimensional distribution.

[0012] In the context of X-ray tomography control, a major limitation lies in the high cost of 3D reconstruction algorithms in terms of computing time and memory space.

[0013] In particular, with current digital detectors reaching resolutions of up to 4096 by 4096 pixels, large reconstruction volumes (up to 40963 voxels, or volumes of more than 100 GB when encoded in 16 bits) are a challenge to overcome in terms of memory footprint.

[0014] However, in the industrial field, many objects are partially composed of empty space, and therefore many voxels (or pixels) are not associated with matter.

[0015] For example, on a glass bottle which is seen as a hollow cylinder, the vacuum is predominant with respect to the material to be analyzed.

[0016] However, with known reconstruction algorithms producing a 3D representation of voxels, a very large number of ray tracings are required to perform the backprojection operation, the rays having to cross the entire object, and therefore cross the vast majority of empty space. This operation is very costly in terms of calculation time, and subsequently in terms of memory space to store an object, on which little material is ultimately usable.

[0017] Different approaches have been proposed to replace the representation of a volume of voxels, for example by replacing it with a tree representation of the “octree” type.

[0018] Those skilled in the art know the octree representation as a tree-like data structure in which each node can have up to eight children. Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants.

[0019] This is the case for the solution described in the article by Kim Seungki & al., “Efficient Iterative CT Reconstruction on Octree Guided by Geometry Errors” (iCT 2016), where the authors propose to use an octree for tomographic reconstruction.

[0020] However, the proposed methods have at least the following drawbacks: - they require large digital resources (for the projections of tetrahedra, and other shapes); - they do not fit the inspected object, for example a polygonal part or a curve; - they impose an identical resolution in the areas of interest and in the areas of non-interest (the void); - the structure of an octree depends on the positioning of the object in space; - octrees and all other methods of partitioning space also pave unnecessary areas (concavities, voids).

[0021] Also, there is a need for solutions for 3D tomographic reconstruction by X-rays which optimize the representation of a 3D volume.

[0022] The present invention meets this need. Summary of the invention

[0023] The present invention provides a method of 3D tomographic reconstruction by X-rays, which makes it possible to generate a 3D representation of an object to be inspected, which is adapted to the object to be inspected.

[0024] Advantageously, the method of the invention makes it possible to reduce the calculation cost and the memory cost associated with tomographic reconstruction.

[0025] Thanks to the method of the invention, it is possible to process larger reconstruction volumes, by reducing the number of variables and projections necessary for the reconstruction.

[0026] The general principle of the method of the invention is based on the creation of a tree structure of the "bounding volume hierarchy" type or (BVH) for "Bounding Volume Hierarchies" according to the established Anglicism, which is then used for the 3D reconstruction of an object.

[0027] The generally used uniform voxel grid is replaced by an accelerator tree structure, of the BVH type, which makes it possible to reduce the number of variables to be reconstructed.

[0028] There is no known use of BVH structures to represent a 3D volume to be reconstructed in X-ray tomography. Such structures have never been used to describe a space, because they are generally used to organize a set of elements, such as for the search for the nearest neighbor.

[0029] The use of a BVH provides a representation of a 3D volume which is adapted to the shape of the part to be reconstructed, which is much more efficient, in terms of number of cells, than a regular voxellic representation classically used for tomographic reconstruction.

[0030] An advantage of the present invention is that it is possible to use arbitrary primitives. BVHs make it possible to describe space with primitives of different shapes (i.e. cubes, curves), thus giving a more general and flexible character to the description of an object to be reconstructed.

[0031] By using a BVH type tree structure, the space is partitioned with a variable resolution depending on the interest of the area studied (area of ​​interest vs. empty area), which reduces the number of unknowns and the number of radiographs necessary to obtain a given image quality.

[0032] Advantageously, the method of the invention makes it possible to obtain the same image quality with less data.

[0033] Compared to known octree type representations, the BVH type tree representation according to the invention makes it possible to better adapt to the orientation of an object because it is not linked to the initial definition of the cubic volume defining the reconstruction zone.

[0034] In addition, it offers computing time benefits, among others for ray tracing which is an important elementary step of any reconstruction algorithm.

[0035] Advantageously, the reconstruction method according to the invention by the use of a BVH type tree structure makes it possible to avoid certain operations which consume resources and time, such as calculations occurring after a rotation or a translation of the object.

[0036] The aeronautical, railway or agri-food industry sectors which have increased needs for object control can derive considerable benefits from the use of the method of the invention.

[0037] In particular, thin-walled hollow cylinder type objects require fine resolution to detect possible small defects in the wall. An example of such a thin-walled hollow cylindrical object is illustrated in [Fig.l] where there is a crack F whose size is much smaller than the outer diameter D of the cylinder. Thus, for such an object of about 2 meters in diameter which is essentially composed of voids, the reconstruction of the wall with sufficient resolution represents an insurmountable challenge for conventional reconstruction algorithms.

[0038] It is also recognized in the aeronautical field, a strong demand for the control of tank-type objects with an overall diameter of the order of a meter, for which it is desired to inspect a thin wall with a resolution of the order of ten microns.

[0039] More generally, the present invention is also of interest for all other applications of industrial control by X-ray tomography.

[0040] To achieve the desired results, a computer-implemented method of X-ray tomographic 3D reconstruction of an object is provided, the computer comprising at least one processor coupled to a memory storing non-transitory code instructions which, when executed, cause the processor to perform steps consisting of: - create a recalibrated volume mesh of an object; - constructing from the recalibrated volume mesh a tree structure, said tree structure being constructed according to a hierarchy of enclosing volumes and such that each node of the tree represents a geometric element of said mesh, each node is defined in an enclosing volume, and each enclosing volume groups together one or more nodes; - implementing an iterative tomographic reconstruction algorithm on said tree structure until an end criterion is reached; and - define the tree structure obtained at the end of the iteration as a 3D X-ray tomographic reconstruction of the object.

[0041] The method may operate according to alternative or combined embodiments.

[0042] In one embodiment, the step of implementing an iterative tomographic reconstruction algorithm comprises steps consisting of: - determine during ray tracing, the lengths crossed by the X-rays in each node of the tree; - update the values ​​of the meshes in the tree so as to be consistent with the experimental values ​​of the projections; and - iterate the previous ray tracing and structure update steps until an end criterion is reached.

[0043] In an alternative embodiment, the step of implementing an iterative tomographic reconstruction algorithm comprises steps consisting of identifying homogeneous zones and merging said homogeneous zones.

[0044] In an alternative embodiment, the step of implementing an iterative tomographic reconstruction algorithm comprises steps consisting of identifying discontinuous zones and dividing said discontinuous zones.

[0045] In an alternative embodiment, the tomographic reconstruction algorithm further takes as input data, measurements of the real object or experimental projections obtained by the acquisition of a plurality of images of the real object on X-ray launches according to multiple orientations, for different angles and several positions.

[0046] In an alternative embodiment, the step of implementing a tomographic reconstruction algorithm consists of implementing a SART type reconstruction algorithm (“Simultaneous Algebraic Reconstruction Technique” in English).

[0047] In an alternative embodiment, the step of creating a recalibrated volume mesh of an object comprises steps consisting of receiving or creating a 3D CAD surface model; generating registration parameters from the surface model; and creating from the surface model a volume mesh of a CAD model.

[0048] In an alternative embodiment, the method further comprises a step consisting of storing the 3D X-ray tomographic reconstruction of the object.

[0049] In an alternative embodiment, the step of implementing an iterative tomographic reconstruction algorithm comprises a step of determining whether a maximum number of iterations is reached or whether the tree structure contains a number of cells of maximum size.

[0050] The invention also relates to a tomographic reconstruction device, the device comprising means for implementing the steps of the method of the invention.

[0051] The invention also relates to a computer program product which comprises code instructions making it possible to carry out the steps of the 3D tomographic reconstruction method by X-rays of the invention, when the program is executed on a computer. Description of the figures

[0052] The [Fig.l] already described, schematically illustrates a hollow cylinder with a thin wall containing a crack to illustrate the problem linked to control by X-ray tomography.

[0053] Other characteristics and advantages of the invention will appear with the aid of the following description and the figures of the attached drawings.

[0054] [Fig.2] is a flowchart illustrating a tomographic reconstruction method according to one embodiment of the invention.

[0055] [Fig.3a] illustrates in a simplified example the grouping of geometric objects to create a BVH according to an embodiment of the invention.

[0056] [Fig.3b] illustrates for the simplified example of [Fig.3a], a hierarchical structure in the form of a tree.

[0057] [Fig.4a] illustrates on an example of Stanford Bunny, a hierarchical structure of BVH with volume mesh to be reconstructed.

[0058] [Fig.4b] illustrates for the example of [Fig.4a] a section of the mesh which contains the information of the leaves of the tree.

[0059] [Fig.5] is a flowchart illustrating steps of tomographic reconstruction according to one embodiment of the invention. Detailed description of the invention

[0060] [Fig.2] is a flowchart illustrating a tomographic 3D reconstruction method according to one embodiment of the invention.

[0061] The method 200 begins with a step 202 of receiving or creating a 3D CAD surface model (also referred to as a mesh), representing an object.

[0062] The CAD model of the object is on the one hand submitted in step 204 to a 3D / 2D registration module, which makes it possible to generate registration parameters, in order to bring the CAD model and the real object into the same reference system, and this from a set of measurements made on the real object.

[0063] The measurements of the real object also designated by experimental projections 208 are obtained by the acquisition of a plurality of images of the real object on X-ray projections according to multiple orientations, for different angles and several positions.

[0064] The CAD surface model of the object is furthermore submitted in step 206 to a volume mesh creation module, a module also referred to as a mesh generator. This step 206 can be carried out by any type of mesh generator which makes it possible to generate a volume mesh of a CAD model.

[0065] In this step 206, depending on the type of cells desired (i.e. polyhedron-type primitives, or curves), the surface model undergoes processing to create a volume mesh.

[0066] According to embodiments of the processing, cells may be added to the surface of the object in order to expand the mesh and include the surface of the object with some margin.

[0067] In one embodiment, step 206 of creating a volume mesh uses a tetrahedral meshing algorithm, such as for example the known meshing algorithm “HXT”. Other meshing algorithms can be used.

[0068] In a following step 210, the method makes it possible to recalibrate the volume mesh by taking into account the recalibration parameters calculated in step 204.

[0069] Step 210 thus makes it possible to generate a volume mesh recalibrated from the initial CAD model.

[0070] Each cell of the recalibrated volume mesh defines a value which physically represents the absorption of X-ray energy. This value is an unknown that the tomographic reconstruction must resolve.

[0071] Advantageously, in a following step 212, the method makes it possible, from the recalibrated volume mesh model, to create a tree having a hierarchy of encompassing volumes.

[0072] A bounding volume hierarchy (BVH) is a tree structure over a set of geometric elements. All geometric elements, which form the leaf nodes of the tree, are wrapped in bounding volumes.

[0073] The nodes are then grouped into small sets and enclosed within larger bounded volumes. These are in turn grouped and enclosed within other larger bounded volumes recursively, resulting in a tree structure with a single bounded volume at the top of the tree.

[0074] [Fig.3a] illustrates in a simplified example the grouping of geometric elements to create a BVH. The geometric elements that fill the scene are grouped into bounding boxes in a hierarchical manner.

[0075] Thus, in the example which includes 6 geometric shapes or elements, a first box C groups two shapes. This box C is itself included in a bounding box B which also groups two other geometric shapes. Another box D groups two other geometric shapes. The distinct boxes B and D are themselves grouped in a box A which then forms the complete bounding volume.

[0076] [Fig.3b] illustrates the encompassing structure of [Fig.3a] in the form of a BVH hierarchical tree.

[0077] The BVH tree is initialized from the recalibrated 3D CAD volume model of the object. For each of the nodes of the tree, a bounding box is associated.

[0078] In the example of [Fig.3b], the tree has four nodes (A, B, C, D) representative of the bounding boxes (A, B, C, D) of [Fig.3a]. Each node has branches to which are attached either another node or one or more leaves representative of the geometric shapes grouped in the respective bounding box.

[0079] In the context of the invention, the BVH tree is thus representative of the recalibrated volume mesh of the CAD object.

[0080] Advantageously, only the geometric shapes considered are defined in the tree that is created. The areas of non-interest are thus not defined.

[0081] In one embodiment, even if in the tree itself two bounding boxes overlap, the fact of going through a volume mesh ensures the non-overlapping of two values ​​for the same area of ​​space.

[0082] Indeed, geometric primitives can overlap in a BVH structure. However, in the context of the invention, the primitives represent space, it is important that they do not overlap, otherwise a point in space could potentially have several values. Also, the step of creating the volume mesh according to the method of the invention makes it possible to avoid this drawback.

[0083] [Fig.4a] illustrates on the Stanford Bunny, the hierarchical structure of the BVH which contains the volume mesh whose values ​​we wish to reconstruct.

[0084] [Fig.4b] illustrates a sectional view of the mesh (here tetrahedral) which contains the information of the leaves of the tree.

[0085] Returning to [Fig.2], once the initial BVH structure has been created, the method in a following step 214 makes it possible to implement an iterative tomographic reconstruction algorithm, which takes into account the experimental projections 208, in order to reconstruct the object in 3D.

[0086] Tomographic reconstruction step 214 makes it possible to browse the BVH tree to test which boxes are touched during each ray cast, and thus generate a reconstructed 3D object.

[0087] In a following step 216, the 3D object can be stored in memory in the form of the BVH tree structure in its final version.

[0088] [Fig.5] is a flowchart illustrating steps of a tomographic reconstruction according to one embodiment of the invention.

[0089] In one embodiment, the tomographic reconstruction algorithm is a weighted backprojection algorithm.

[0090] In an alternative embodiment, the backprojection algorithm is a (SART) algorithm (Simultaneous Algebraic Reconstruction Technique) which is based on the (ART) algorithm (Algebraic Reconstruction Technique), an algebraic tomographic reconstruction technique with simultaneous updates.

[0091] The general principle of the ART algorithm (and of the SART or SIRT algorithm) consists of iteratively updating the values ​​of the volume being reconstructed by adding the weighted backprojection of the residue between the experimental projections and those of the direct model.

[0092] Returning to [Fig.5], the steps 500 of an implementation of a tomographic reconstruction algorithm applied to a BVH tree structure are detailed.

[0093] Once an initial BVH structure X(0) has been created (step 502), the method allows entering an iterative phase until an end criterion is reached (step 518), which allows a version of the BVH to be retained as the final optimized version X(end) of the structure.

[0094] Step 506 of tomographic reconstruction consists of carrying out tests of intersection of X-ray throws with the bounding volumes. This step makes it possible to traverse the B VH tree, to determine, during ray throws, whether or not an X-ray intersects a bounding volume of a given node of the tree. For volumes which are not affected, the method makes it possible to no longer consider, in the initial tree, the subtree adjoining this node (i.e. all dependent nodes). The structure of the tree is then updated in an intermediate version X® (step 516).

[0095] Thus, in one embodiment, step 506 consists, during ray tracing, in determining the lengths traversed by the X-rays in each node of the tree, and step 516 consists in updating the values ​​of the meshes in the tree so as to be consistent with the experimental values ​​of the projections. ; and

[0096] During the iterations which continue until a stopping criterion is reached (No branch of step 518), the method also makes it possible to carry out fusions or divisions of cells (i.e. meshes, boxes, volumes).

[0097] The method makes it possible on the one hand to identify (step 508) homogeneous zones (neighborhood zones), i.e. to identify neighboring cells which have similar values, then to merge (step 512) the similar cells to reduce the number of variables. Advantageously, the merging step makes it possible to reduce the memory space for storing the reconstruction of the object.

[0098] The method also makes it possible to identify (step 510) areas with strong discontinuities, i.e. such as the edges of the object or changes in the environment, then to split (step 514) the corresponding boxes to increase the resolution and thus better describe a variation in the material.

[0099] In one embodiment, if the difference in values ​​between a cell and the neighboring cells is significant, the method allows this cell to be divided with a known '1-4' flip or '2-3' flip mechanism. Conversely, if an area is homogeneous, i.e. the values ​​between several neighboring cells are close, the method allows the cells to be merged with inverse flip operations, i.e. '4-1' flip and '3-2' flip.

[0100] The general principle of tomographic reconstruction consists of assigning gray level values ​​(which correspond to an attenuation coefficient of the matter) to each voxel of the volume considered. With the BVH structures according to the invention, there are no longer voxels but cells. However, the method allows the notion of values ​​to be retained. Thus, areas with high discontinuity are cells with different values ​​(i.e. different gray levels) and homogeneous areas are cells which have a close value.

[0101] Returning to [Fig.5], the iterative process ends when the stop or end criterion is reached (yes branch of step 518), and the last update X(end) of the BVH tree structure which represents an optimized reconstruction of the object, can be stored (step 520).

[0102] The stopping criterion can for example be chosen as being a maximum number of iterations, or as being a number of cells of maximum size.

[0103] The inventors compared the tomographic reconstruction by BVH according to the invention to a tomographic reconstruction on voxels according to the prior art, for an example taking the Stanford rabbit. For this object, the volume mesh comprised 3923 nodes, the geometric shapes were 6526 triangles and 12659 tetrahedra. A reconstruction made on voxels whose volume is equivalent to the average volume of the tetrahedra would require 335,217 voxels, or 26.48 times more than the approach proposed by the present invention.

[0104] More advantageously, the approach by tree structure with hierarchy of bounding volumes, would make it possible to reconstruct a bounding box and not just an area which contains the object which only represents 37% of this box. The number of unknowns to be resolved is then greatly reduced.

Claims

Claims

1. A computer-implemented method (200) of X-ray tomographic 3D reconstruction of an object, the computer comprising at least one processor coupled to a memory storing non-transitory code instructions which, when executed, cause the processor to perform steps consisting of: - creating (210) a registered volume mesh of an object; - constructing (212) from the registered volume mesh a tree structure, said tree structure being constructed according to a hierarchy of bounding volumes and such that, each node of the tree represents a geometric element of said mesh, each node is defined in a bounding volume, and each bounding volume groups together one or more nodes; - implementing (214) an iterative tomographic reconstruction algorithm on said tree structure until an end criterion is reached;and - define (216) the tree structure obtained at the end of the iteration as being a 3D X-ray tomographic reconstruction of the object.;

2. The method according to claim 1 wherein the step of implementing an iterative tomographic reconstruction algorithm comprises steps consisting of: - determining (506) during ray casting, the lengths traversed by the X-rays in each node of the tree; - updating (516) the values ​​of the meshes in the tree so as to be consistent with the experimental values ​​of the projections; and - iterating (518) the previous steps of ray casting and updating the structure until an end criterion is reached.

3. The method according to claim 1 or 2 wherein the step of implementing an iterative tomographic reconstruction algorithm comprises steps of identifying (508) homogeneous areas and merging (step 512) said homogeneous areas.

4. The method according to any one of claims 1 to 3 wherein the step of implementing an iterative reconstruction algorithm to- mographic comprises steps of identifying (510) discontinuous areas and dividing (step 514) said discontinuous areas.

5. The method according to any one of claims 1 to 4 wherein the tomographic reconstruction algorithm further takes as input data, measurements of the real object or experimental projections (208) obtained by acquiring a plurality of images of the real object on X-ray scans according to multiple orientations, for different angles and several positions.

6. The method according to any one of claims 1 to 5 wherein the step of implementing a tomographic reconstruction algorithm consists of implementing a SART type reconstruction algorithm.

7. The method according to any one of claims 1 to 6 wherein the step (210) of creating a registered volume mesh of an object comprises steps consisting of receiving or creating (202) a 3D CAD surface model; generating (204) from the surface model registration parameters; creating (206) from the surface model a volume mesh of a CAD model.

8. The method of any one of claims 1 to 7 further comprising a step of storing (520) the 3D X-ray tomographic reconstruction of the object.

9. The method of any one of claims 1 to 8 wherein the step of implementing an iterative tomographic reconstruction algorithm comprises a step of determining whether a maximum number of iterations is reached or whether the tree structure contains a maximum size number of cells.

10. A computer program product, said computer program comprising code instructions for performing the steps of the X-ray tomographic 3D reconstruction method according to any one of claims 1 to 9, when said program is executed on a computer.

11. A 3D X-ray tomographic reconstruction device, the device comprising means for implementing the method steps of any one of claims 1 to 9.

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