EP0434720A1 - Method for reconstructing a three-dimensional arborescence by labelling - Google Patents

Abstract

To reconstruct an angiographic tree structure, two images are acquired in orientations substantially perpendicular to each other of a tree structure (IVA, CX) to be reconstructed. By a segment tracking operation, the coordinates of the segments of the tree structure are reconstructed. One raises the indeterminacies which result from the too small number of acquisitions carried out by emitting hypotheses (AV, IV) on forms deductible from the recorded acquisitions and by verifying these hypotheses against a model. The model has the particularity of being structural, that is to say being essentially descriptive. In this structural model, each segment of the tree is characterized by a number, by a direction (49-54), and by the numbers, direction, and number of the segments that precede or follow it. We show that by doing so we can reconstruct angiographic images more quickly and more simply.

Description

 METHOD FOR RECONSTRUCTING THREE-DIMENSIONAL TREE BY LABELING

The present invention relates to a three-dimensional (3D) tree reconstruction method by labeling. It is mainly intended for use in the medical field, where the trees studied are angiographic trees. The three-dimensional reconstruction makes it possible, by subsequent information processing on the reconstructed object, to present this object according to any modes: straight cuts, oblique cuts, or even 3D visualization. The 3D visualization of 3D objects is also known. The invention is essentially concerned with the acquisition of geometric information representative of a 3D tree structure, this information being subsequently used in visualization methods for visualizing this tree structure. The particularity of the method of the invention is that it allows the reconstruction of trees from two two-dimensional digital images in projection of the object to be reconstructed.

The field of application of the invention is in particular the study of the vascular network (arterial and venous) of any region of the human body having a tree structure (heart, brain, femoral artery, carotid, ...). The mode of acquisition of projected images is independent of the method. Although the invention is described in a radiology application, it can be transposed if the projection images are obtained by NMR, by ultrasonic insonification .... Digital radiology or analog X-ray (angiographic technique) currently allows obtaining images well suited to the implementation of the invention. The method of the invention is also applicable to any 3D wire structure other than medical.

The current angiographic reconstruction techniques are partly techniques derived from the computed tomography experiment called scanner. However, the corresponding acquisitions are complicated, on the one hand, by the desire to eliminate from the acquired images the contributions of all that does not represent the angiographic network, on the other hand by the fact that the flow of blood in the vessels is a variable phenomenon over time (it therefore requires synchronization), and finally that the acquisition must be a three-dimensional acquisition. For the elimination of the contributions to the images made by _: parts foreign to the angiographic network, injections of products increasing the contrast in the capillaries are used in a known manner. It should be noted, however, that these injections cannot be repeated as often as desired without trauma to the patient. The synchronization phenomenon can have the result of increasing the duration of the acquisitions while at the same time being a technique contrary to precautions aiming not to inject contrast product too often into the vessels of a patient. Finally, three-dimensional reconstruction requires, with scanner methods, the repetition of these experiments. One solution to this problem would be to use multirange ultra-detectors in scanners. However, this technique is essentially linked to the systematic use of so-called conical projections because the source X-ray remains punctual. The algorithms for reconstructing section images from conical projections do not then allow the desired precision to be achieved to allow the reconstructions. To overcome this drawback, a scanner has been designed capable of acquiring the images of four sections at the same time. The complexity of this machine is obviously multiplied by the number of simultaneous cuts that _; we want to acquire. Despite everything, the acquisition of a scanner has a drawback: it takes place over time and, in particular when one seeks to represent mobile organs such as the heart, it can ultimately only give blurred images of what one seeks to represent. . To avoid problems of synchronization (and of multiple injections of contrast products which would result therefrom), a device has been designed provided with fourteen x-ray generators each associated with a camera. Each of the 14 couples is then likely to give a projected image of the structure to be reconstructed. This system envelops a volume of the body from which a digital volume is produced. A digital volume is a collection of information, relating to a measured property, and virtually arranged in a volume at 3D addresses corresponding to the locations of the object from which the information originates. Interesting results have thus been obtained for the reconstruction of the coronaries. This system also makes it possible to view all of the structures exhibiting attenuation by X-rays. However, the drawbacks of this system are twofold. Firstly, they are technical: the cost of the material is incompatible with industrial distribution. On the other hand the definition of the images is not sufficient for the detection of fine structures. If a resolution adapted to these fine structures is desired, the number of data to be acquired and processed in a time compatible with medical exploitation requires a substantial increase in the power of the machines. In addition, the problem is theoretical: the X-ray beam used is a divergent beam. The "parallel section" approximation used for the reconstruction is therefore rough, the taking into account of the conical geometry in the reconstruction algorithms prohibits decomposing the problem into a superposition of two-dimensional reconstructions.

Another technique was used. This technique consists of an algorithmic approach by searching for homologous points. This method consists in determining, on projection images, homologous points. Homologous points are points of the images of each projection which are associated and which correspond to the same point in the 3D space of the tree structure to be reconstructed. The algorithmic method makes it possible to calculate the 3D coordinates of the point of the object knowing the acquired images and the geometry of the acquisition system. The methodology used in this case is as follows. We seek, with a first algorithm, on a first image in projection, a characteristic point. This characteristic point is located on the path of a particular X-ray. The path of this X-ray is called "straight 3D". The method consists in projecting this 3D line on the second image in projection using the second projection orientation. The homologous point of the chosen characteristic point must be sought in the second projected image: it must be on this 3D line projected so-called epipolar.

The most reliable characteristic points for vascular trees are the bifurcation points. Indeed the images in projection present drawings essentially of two types. In a first type, Y-shaped drawings represent a bifurcation: a main vessel is divided into two secondary vessels. In a second type, the drawings represent X crossings: in most cases these crossings do not correspond to any particular structure in the body. In fact, they are only the result of the projection, on a plane, of two independent segments, the only images of which intersect.

The automatic localization of the characteristic points requires an effective segmentation of the angiographies. The precision required in determining a homologous point in stereoscopic condition so that the estimation of the X, Y, Z coordinates of the corresponding points in the object is acceptable, is less than the pixel. This constraint can be relaxed if the angle between the shots can be increased, between the directions of projection. This can be obtained by using views whose projection orientations are deviated by an angle close to 90 ^e .

According to a particular version of the method, three projection images are acquired according to orientations included at an angle of 90 °. In this way, we solve the main difficulty of classical methods which is to reconcile two constraints

- opposites to obtain sufficient precision of the 3D precision of an element of the object. With orientation differences of the order of 90 ° between the projections, the accuracy of the calculation of the coordinates of the point of intersection of the lines corresponding to the homologous point. On the other hand, by choosing views with small projection angles between them, the problem of correspondences between images can be resolved. Ultimately the abandonment of scanner techniques can lead, for the reconstruction of the tree structure, to a simplification of the equipment. However, in the last mentioned method, presented elsewhere in a French patent application No. 87 16156 filed on November 23, 1987, it was still necessary to have three X-ray tube-camera equipment. With these three devices, the three images are acquired, the projection orientations of which form an angle between them of 90 ° and a few tens of degrees respectively. The object of the invention is to remedy the drawbacks cited by proposing a three-dimensional tree reconstruction method in which only two pieces of equipment can be used and where the absence of the third is compensated for by a priori knowledge of the tree to rebuild. The two X-ray tube-camera equipment, in a radiological application, are preferably oriented substantially at 90 ° from one another so as to improve the accuracy of the calculation of the point of intersection of the lines corresponding to the homologous points. Furthermore, in the invention, the model, in contrast to models already known for typical tree structures, is not a purely topographic model but it is an essentially structural model. By topographic model, we mean a model in which each part of the object is essentially determined by its coordinates as well as by its dimensions. By structural model, we essentially designate a set of information in which each segment of the tree structure is associated with a label representing the number of a bifurcation from which it originates, or of an upstream segment to which it is connected, as well as an orientation relative to a reference. In a way, the structural model is qualitative when the topographic model is quantitative.

We then realized that such a structural model made it possible, on the one hand, to easily remove the ambiguities of reconstruction which can result from the use of only two projections, and on the other hand, to be perfectly suited to the disparity appearance of the different objects or (individuals) studied. From this point of view, a topographic model requires very complex adjustments to go from a small individual to a large individual, even if the tree structure keeps the same appearance.

The invention therefore relates to a three-dimensional tree reconstruction method characterized in that: - at least a first image and a second two-dimensional image of a tree to be reconstructed are acquired, these images being obtained by projection of this tree structure in two different orientations, these images being made up of contiguous segments,

- a structural model is developed a priori of the tree structure to be represented, a first segment of the tree structure is reconstructed, - this first segment is assigned a label characteristic of a corresponding segment in the model,

- we verify the correctness of this allocation, and we repeat the operation for a segment next, and so on.

The invention will be better understood on reading the description which follows and on examining the figures which accompany it. These are given for information only and in no way limit the invention. Just as the method described in a radiological application can be transposed to applications in which the acquisitions are of different types, just as two images are necessary and sufficient, it is possible to implement the method of the invention with more than two images. The figures show:

- Figure 1: the mode of association of homologous points;

- Figure 2: the difficulties encountered in recreating a 3D structure with only two images;

- Figure 3: a radiology machine usable for implementing the method of the invention;

- Figures 4a and 4b: diagrams representative of the signals processed in the method of the invention; - Figure 5: the representation of the type of ambiguity encountered when implementing the method of the invention and the lifting of which is authorized by comparison with the model;

- ^• 6: a schematic representation of the known vasculature of the left ventricle of the heart, and

FIG. 7: the model which is drawn therefrom according to the teaching of the invention;

- Figures 8a and 8b: the general mode of reconstruction of the homologous points;

-. Figure 9: the complementary mode in case of failure to use the general mode.

FIG. 1 represents the general mode of association of two homologous points. An object to reconstruct 1 was subjected, in a radiological application, to two X-ray illuminations. In a first illumination the source was placed at a point 2 and the first projected image was formed on a plane 3 perpendicular to the central ray emitted by the source and placed on the other side of the object 1. Similarly in the second illumination the source was placed at 4 and the second image was projected on a plane 5. The structure 1 is shown in double lines. It presents in a simplified manner a foot 6 whose image is projected respectively at 7 and 8 on the planes 3 and 5. At the place of the plans 3 and 5 we have in fact placed a coupled luminance intensifier screen to a camera. The two images were taken simultaneously while a radiological contrast product was passing through the structure 1. In a known manner, to remove the structures which surround the structure 1, it is even possible to carry out an extraction of images. This means that according to each orientation we actually take two images, respectively with and without contrast product passing through the structure 1. By subtracting these two consecutive images from each other we can see appear, for each plane 3 and 5 , an image resulting from the projection of the tree 1 alone. In the rest of this presentation, we consider that we have the image of this tree alone.

The cameras associated with the luminance intensifying screens carry out a horizontal scan, oriented along ₃ and X5 in each of the two images. We can admit that, in the particular case of foot 6 of the tree structure, it will easily be determined that the counterpart of point 7 whose Y coordinate ₃ is zero will be a point such that its Y5 coordinate is zero. However this particular case is actually the least frequent, and we will often have to search for the counterpart of a particular point 9 which will be the image of a point 10 of the tree structure 1. To search for the counterpart of this point, we use the fact that the X-ray which ended at point 9 on screen 3 was carried by a line called 3D passing through this point 9 and by the origin 2 of the emission X. We then trace the projection in plane 5, from the source "4, from the 3D line found. This projection 11 is called the epipolar line of point 9. It is noted that this epipolar line is at an angle with respect to the axes X5 and Y5 of the plane 5. The epipolar line normally includes the point 12 homologous point 9. These two points 12 and 9 are representative, both of them, of point 10 of the tree structure 1. We know by computer processing to calculate the equation of the line 3D, and to deduce the equation, in the plane 5, from the epipolar line 11. It is then possible to search, among all the points representative of the image in projection of the tree structure on the plane 5, that of these points whose coordinates satisfy exactly (or as best as possible) the equation of the line 11. In principle, if the point 9 in the plane 3 is located on a segment, and if it is not at the intersection of two segments, there is only one candidate point in the plane 5 for which the equation is verified. Similarly if point 9 happens to be the image of a bifurcation such as for example the bifurcation 13 of the tree 1.

On the other hand, if the point 9 is placed in the plane 3 at a crossing of two segments, one will normally find two candidate points in the plane 5 which will satisfy the equation of the epipolar line 11. There is therefore ambiguity. Figure 2 also shows another type of ambiguity resulting from the angle important (close if possible to 90 °) which separates the two views. Indeed, suppose for example that in the plane Y3 = Y5 = O we recognize three points 14, 15, and 16. The images of these points in the planes 3 and 5 are respectively 17 to 19 and 20 to 22. We note that the image 22 of point 16 is placed in an intermediate position between the images of points 14 and 15 in the plane 5, while it was located on their right (in 19) in the image on the plane 3. This another type of ambiguity results from the wide angle presented by the projections 3 and 5 relative to each other. In the cited patent application, this ambiguity was resolved by using another projection, for example on a plane 23 making a relatively small angle with one of the two projections. Note that the projections of points 14 to 16 on plane 23 are arranged in the same order as they had on plane 3. Ultimately, a small angle of disorientation of the projections makes it possible to keep the concept of arrangement between the points. However, we note that a slight error 24 in assessing the coordinates of the image of a point on a projection sounds like a large error 25 in the position of the point to be reconstructed. We will show in the rest of this description how the use of a structural model makes it possible to resolve these ambiguities.

FIG. 3 represents a radiology machine usable for implementing the method of the invention. A patient 26 is subjected to X-ray radiation emitted by a generator 27 in the direction of a luminance amplifier 28 placed on the other side of this patient relative to the generator 27. A device 29 for injecting a contrast product is shown schematically to show that the device is intended to acquire angiography images. There are two ways to do this. Or, as shown, the patient is subjected to two successive, synchronized irradiations, having meanwhile moved in correspondence the X-ray tube 27 and the screen 28 on a hoop 30 by means of a motor 31 so as to acquire images whose projection orientation is significantly different. Preferably chooses orientation differences of the order of 90 °. However, if one does not want to synchronize, and if one does not want to have to inject the contrast product twice into the patient, one can choose to install on the arch 30 two pairs of equipment 27-28 making between them a large angle, preferably a right angle. A computer 32 makes it possible to manage the acquisition of the images, the synchronization, the injection of the contrast product, as well as a segmentation processing aimed at skeletonizing, in each acquired image, the tree structure.

Note on the luminance intensifier screen 28 the X orientation of the scanning of the associated camera. Figures 4a and 4b show in the video-line signal of this camera, the shape of the corresponding gray level signal NG. The subtraction operation aims to eliminate the continuous component 33 representative of the bottom, so as to leave only signals such as 34 representative of the vessels alone. The projected image is then, in the memory of the computer 32, a collection of addresses X3 and Y _{3 with} which gray levels are associated (Y3 marks the scanned line) corresponding to the peaks 34 of the detected signals.

In a skeletonization phase, rather than being interested in detected points in each image, we are interested in straight segments to which belong these different points. We can identify each segment, in a known manner, by applying mathematical morphology techniques, or peak tracking. You can also determine the outline of the segments. In the skeletonization phase, each segment is given an attribute. This multidimensional attribute indicates the segment number, the coordinates of its extreme points, the average gray level of the segment, the direction of this segment, and the numbers, numbers, directions, and gray levels of the predecessor and successor segments of this segment. This skeletonization operation is known, it has been described in previously published works. In particular it is described in the thesis of Mrs. CHRISTINE TOUMOULIN, defended on November 24, 1987, UNIVERSITE DE RENNES.

In the aforementioned patent application, with a mathematical morphology technique, the main interest was to follow the coordinates of the peaks 35 of the detected signals. Then we evaluated the width of the segments in question. This width could preferably be determined by deriving the detected video signal. In this way, the edges of the vessels studied appear through ridges, such as ridges 36 and 37 shown in FIG. 4b.

FIG. 5 shows, in terms of segments, the ambiguities resulting from the use of projections forming between them a large angle and not allowing the certain determination of two homologous points in these two projection planes. It was shown, at a bifurcation 38, the birth of two segments 39 and 40 of the object to be reconstructed. The segments 39 and 40 project respectively into 41 and 42 and 43 and 44 on the previous planes 3 and 5. If we draw both dihedrons passing through the sources 2 and 4 of projection and through the segments 39 and 40, one realizes that these dihedrons intersect at the location of the object to be reconstructed according to two other fictitious other segments 45 and 46. Obviously, the segments 45 and 46 are also "solution" for the projection into image segments 41 and 42 and 43 and 44. The intervention of the model of the invention makes it possible to remove this ambiguity. It is therefore qualitative. It consists in principle in noting that the segments 39 and 40 do not have the same spatial orientations at all as the segments 45 and 46. In the invention it is noted that the segments 39 and 40, taking into account their numbers, from the number of their predecessor, are believed to represent two typical segments of a normal anatomical model.

The normal anatomical model is therefore compared to the couple of segments 39 and 40 on the one hand, and to the couple of segments 45 and 46 on the other. Qualitatively it becomes possible to eliminate from these couples the candidate couple who does not meet the model. In practice, couples are each assigned a label in turn, and it is checked that the label assigned corresponds to their actual appearance.

FIG. 6 represents, in the case of the left ventricle, in perspective, the representation of the inter-ventricular-anterior arteries IVA and circumflex CX connected in a common trunk to the artery aorta AA by a bifurcation point 47. According to topographic models known the IVA artery and the CX artery are supposed to be on the surface of an elipsoid 48. This topographic representation is unfortunately not well adapted to the disparities presented by the different individuals and makes impossible the elaboration of simple criteria allowing an automatic reconstruction of the 3D tree. Reconstruction techniques using such a topographic model necessarily require that reconstruction to a large extent be manual. In the invention, on the contrary, everything can be automatic.

FIG. 7 shows in comparison, for the same structure, the contribution of the invention. In this one, on the one hand, it has been demonstrated that the IVA artery was generally situated in an interventricular IV plane while the circumflex artery was located in an AV atrioventricular plane. We then use the benchmark constituted by the IV and AV planes to structurally qualify each of the secondary arteries connected to the IVA and the CX. We therefore abandon in this structural modeling the knowledge that the IVA and CX arteries are located on the surface of an elipsoid 48. -Compared with the IV-AV coordinate system, we then determine directions 49 to 54 said respectively year forward, back, up, down, right, and left. These directions make it possible, for example, to qualify the septal arteries S as generally oriented downward from the IVA artery. Likewise, diametric arteries D will be said down and forward from the artery IVA. On the other hand, the lateral arteries L connected to the CX will be said behind.

It can therefore be seen, with reference to FIG. 5, that it is possible to assign to each segment to be reconstructed a label representative of a segment of an artery in the model. This label will include at least for one of its moments, the qualifiers forward, backward, above, ... retained for the artery concerned. It then becomes possible to check which of the segments 39, 40, 45 or 46 satisfy by their orientation to the label thus proposed. We note in passing that the common trunk, in the case of the heart, is appreciably included in the plane IV of the artery IVA. We will now indicate with the aid of FIGS. 8 to 9 how the reconstruction process according to the invention is initialized. The 3-dimensional starting point as well as the direction of travel at the origin can be set manually. They can also be searched automatically by implementing a procedure based on the properties of the images. In fact, the AA aorta artery has a much higher gray level, due to its size, than all of the other vessels. It is therefore possible to be automatically placed on a segment belonging in each image in projection to this aortic artery. For this purpose, the segment for which the gray level is the highest is chosen from all the segments.

Figure 8a shows the uelettized images obtained respectively in the previous plans 3 and 5. Let Pι, I P2, j be the projections in planes 3 and 5 of the most contrasting starting point in each of the images. It is assumed that these two points are homologous to each other and represents a point Pn of the structure to be reconstructed. The point Pι, j belongs to a first element of line Dι _f j going from P _l , j to Pι, j + ι of the root segment of the tree. It is the same for? 2, j ^{and D} 2, j- Normally, we look for the homolog of the point Pι, j + _l , belonging to the image in the plane 3, this homolog being located in the image in the plan 5. Let P ^! 2, j + 1 ^this point. If P'2, j + 1 belongs to D2, j (between P ₂ , j and P2, j + _l ) we can reconstruct a first 3D vector from points Pi, j-Pi, j + 1 and P2, j - P'2, j + 1 * Figure 8b shows what vector V reconstructed. On the other hand if P * 2, j + i is not between P2, j and P2, j + l we choose to search for the counterpart of P2, j + _l (image in the plane 5) on the segment Dι j ( image in the plan 3). This being admitted, we place ourselves in the case where P ^! 2, j + 1 ^has been validated: we have found this point. We introduce a new line element P'2, j + 1 " ^p 2, j + l <rP- we seek to match the line element Pi, j + ι ~ Pι, j + 2 d The image in plane 3. The procedure described above is repeated until an end of segment is detected in one of the views.

Unfortunately the structural calibration of the apparatus, in particular the exact knowledge of the different projection angles, as well as measurement errors, can lead to uncertainties on the belonging of the homologous points to the lines ^D l, j or ^D 2, j. In this case, there is a failure to search for homologous points: P * 2, j + 1 ^is outside D2, j and P'ι, j + ι is outside Di _^ j. Figure 9 shows an additional procedure to be implemented. We are in the case where P'2, j + 1 as well as P'ι, j + ι do not exist. It follows that Pι, j + ι and P2, j + ι have no identified counterparts. We then seek to reconstruct a 3D vector from the two elements of the lines Di, j and D ₂ , j- We notice that Di j is contained in a plane JΓT. defined by on the one hand and source 2 on the other. Similarly D2, j is contained in a plane π2 defined by D2, j ^and l ^at source 4. The support of the vector 55 sought is the line of intersection of the two planes τ. χ and 7T ₂ . We know ^"the origin of the vector since it corresponds to projected Pι, j j and P2 which we already know they are homologous. It is decided that the end of the reconstructed segment 55 corresponds by approximation due to the errors, either to Pi j + i or to P2, j + 1 * ^ choice can be made on a length criterion of the 3D vector. Preferably we take the shortest.

In the case of the heart, the two main branches CX and IVA, coming from the common trunk AA, characterize the planes. The CX forms an arc defining a plane substantially orthogonal to the plane containing the IVA. The two starting segments in each plane correspond one to the CX the other to the IVA. They are broken down into elements on the right. We are interested in the first element on the right of each of the segments. The procedure for calculating the 3D vectors corresponding to each is in principle identical to that described above in the case of a single 3D vector. The new problem is, according to FIG. 5, that there is ambiguity as to the ownership of the segments. We then build the 4 3D vectors of which only two are solutions.

The criterion for choosing the acceptable solution is based on the assumptions linked to the model. According to these hypotheses, one of the branches, the IVA in this case, has good continuity with the common core. In contrast, the tree structure of the vascular network means that the second branch, the CX in this case, is distant from a direction parallel to that of the common trunk. It is therefore possible to eliminate the couple of reconstructed 3D vector which would not additionally have a label behind it (for 1 * IVA), and on the other hand (for the CX).

At the end of this stage, there are therefore two 3D vectors allowing a first estimate of the AV and IV planes. If one moves along the common trunk towards the first bifurcation (point 47), the invariants of the anatomical model allow the following elements to be considered as established. The core curriculum gives birth to two branches which are CX and IVA. The IVA is a continuation of the core curriculum. The CX is almost orthogonal to the IVA at the bifurcation point. The previously calculated 3D vector verifying the continuity property will receive an IVA label. The other will receive a CX label provided that he checks the property of orthogonality. If this last property is not checked, the reverse assignment is attempted. If these two solutions fail, we can choose to consider another model.

After initialization, we choose to fully follow one of the branches: for example the CX branch. The monitoring of the first segment of the CX is identical to the monitoring carried out for the common core. The CX plan is re-estimated at each end of the CX segment. A re-estimation of this plan can be made after detection of a first connection point on the CX. This branching point can be the bifurcation corresponding to the first lateral branch or to a crossing with a vessel. The condition for launching the plan reestimation calculation is that the curvature observed on all the points of the CX exceeds a certain threshold. To re-estimate the plane, we look for a plane that approximates at best (in the least squares sense) the set of 3D points of .la CX. The calculation of the normal to this plan is also resumed. This reestimation calculation can also be performed after each connection point.

The analysis of the first bifurcation is identical to the case of initialization. We are looking for matching and labeling in relation to the known model. We will use the criteria evaluated on the standard anatomical model according to which the first bifurcation encountered on the CX corresponds to the birth of a branch lateral and in pursuit of the CX. The starting segment of the CX is in continuity with the finishing segment of this same CX and the starting segment of the lateral branch is behind the segments of the CX. We automatically determine which segment belongs to the CX and which segment belongs to the lateral artery.

Knowing the plane of the CX, we can know the normal vector j at this plane. Similarly, we can know the normal vector N ^ v in the AV plane of the IVA artery. We can simply check which segment belongs to the CX and which segment belongs to the lateral artery by performing the scalar product of the two vectors of the successor segments by the vector N ^ v- The largest scalar product is in principle that of the CX.

Then we continue the study of the segments supposed to belong to the CX. The information concerning the lateral branch is memorized for a later resumption as soon as one arrives at the end of the CX. The end of the CX is detected by identification of a point without successor in at least one of the planes of the image. The IVA branch is reconstructed in the same way (with possible reestimation of the IVA plan at each stage). Then the branches left waiting are also reconstructed, for example the lateral branch detected during the course of the CX.

The implementation of the method of the invention requires the acquisition, if possible, of two images simultaneously. Different sources of errors exist such as. the calibration of the radiology system or the sampling of the images and the uncertainties of the segmentation drawn from the skeletonization. The fact of working from images of angles of view very different gives access to greater reconstruction accuracy. The speed of the procedure is due to the very structured description of the data and the strong participation of the symbolic model. The method is applicable to any other arboreal vascular structure, as soon as the corresponding anatomical 3D model is acquired and is integrated into the system.

In cardiac application, this rapid method can allow the study of the vascular network in movement from images acquired in two incidences and at different phases of cardiac movement. In practice, the reconstruction of the tree structure of the image takes the same order of time as the skeletonization: it is of the order of 3 seconds. For the models other than the left ventricle of the heart, one uses to develop them, on the one hand the typical anatomical knowledge, and on the other hand, preferably, an interactive generator of wire reconstruction. This type of generator is available as software. An example is the INTERACTIVE GENERATOR OF 3D VASCULAR STRUCTURES software available at the University of RENNES, Laboratory of Signals and Images in Medicine, Faculty of Sciences, Campus de Beaulieu, 35042 RENNES CEDEX. For the characterization of the models, we first try to find the main planes, orthogonal or not. Then we describe, using the interactive generator, the different segments encountered with qualifiers previously mentioned, continuity, front, back, top, bottom, right to left ... If the anatomical study of individuals invites we can, for a given tree structure, develop several models. In the case of the left ventricle, three models were thus developed, one usable in 80% of the cases and corresponding to a balanced vascularization, and two others, each usable in 10% of cases and corresponding to preponderant left or right vascularizations.

Furthermore, taking into account the IV and AV planes, the importance of which is thus highlighted, it is preferable to acquire the images in projection according to directions contained in bisecting planes of the main planes of the model, taking into account the patient's position in the machine. The structural model can of course be supplemented, insofar as the criterion is sufficiently solid, with topographic (quantitative) information. Thus to a segment of number N belonging to the IVA (or to the CX), connected to a segment Nl, oriented in front, we can add an additional label in the form: expected length between a and b, level medium gray (equivalent to the diameter) between c and d. Verification of the correctness of the label can also consist of the additional verification that the reconstructed segment has an adequate length and gray level. These topographic checks can be optional and only become critical if structural recognition fails.

Claims

1 - Method of computer construction (32) of a three-dimensional image of a three-dimensional physical tree structure (1), this physical tree structure consisting of segments of the same material, characterized in that:

- We acquire (26-32) by a physical process (27,28) at least ^" a first image (3) and a second two-dimensional image (5) of the tree structure to be constructed, these two-dimensional images being obtained by projection of this tree structure in two different orientations (2,4,4), these two-dimensional images being made up of contiguous segments (41,42),

- we develop a structural model (32, IV, AV, 49-54) a priori of the three-dimensional tree structure to be represented, this structural model consisting of image segments accompanied by a label, this label being constituted by a signal coded,

- a first segment (55) of the image of the tree structure is constructed,

a label is assigned to this first segment, this label being characteristic of a segment assumed to correspond in the model,

- we verify the correctness of this allocation, by comparing the coded signal of the label with the coordinates

(Dι_ j, D ₂₁ j) of the constructed segment,

- and the operation is repeated for a following segment and so on.

2 - Method according to claim 1 characterized in that: - the two images are acquired by, each time, two exposures of the tree to X-rays,

- the exposures being differentiated in that the tree structure is subjected (29) to a radiological contrast product during one of these exposures.

3 - Method according to claim 1 or claim 2 characterized in that to acquire,

- the images are skeletonized-seg by tracking method, each segment being characterized by

- a number assigned to it,

- the coordinates of each of its ends,

- a medium gray level,

- the direction of this segment, - and the numbers, numbers, directions, gray level of its predecessors and successors,

4 - Method according to claim 3 characterized in that the monitoring method comprises

a phase of locating the central axes of the segments in each image, following the peaks (35) of the detected signals,

- a measurement phase (36, 37) of the contours of the segments.

5 - Method according to any one of claims 1 to 4 characterized in that

- the attributions, verifications, reiterations, are carried out by computer processing (32).

6 - Method according to any one of claims 1 to 5 characterized in that - the structural model is developed a priori of the tree structure by assigning to each segment of a typical tree structure a label representative of a bifurcation (47) of which it comes from, and from an orientation (49-54) in relation to a reference (AV-IV). 7 - Method according to any one of claims 1 to 5 characterized in that

- The a priori structural model of the tree structure is developed by assigning to each segment of a typical tree a label representative of an upstream segment (AA) to which the segment is connected, and of an orientation relative to a reference.

8 - Process according to claim 6 or claim 7 characterized in that the structural model is supplemented by a topographic model, the label comprising information relating to the diameter of the segments and to their size.

9 - Method according to any one of claims 6 to 8 characterized in that one chooses a reference consisting of a Cartesian coordinate system including two first main planes (IV, AV) are associated with particular branches of the tree.

10 - Method according to claim 9, characterized in that the label comprises a moment said forward, backward, up, down, right, or left, according 1'orientation of the segment relative to one of the planes principal of the Cartesian coordinate system.

11 - Method according to any one of claims 1 to 10 characterized in that to reconstruct. a first segment

- a pair (Pi j / P2, j) ^of homologous points representative of a starting point (PQ) at the first end of this first segment is determined in the two images, - an epipolar line (11) is projected in the second image from the other end of this segment in (9) the first image,

- it is verified that this epipolar line intersects the image (D2, j) of this segment in the second image, - and we retain as another end of this segment the point which corresponds (P'2, j + l) ^to this intersection.

12 - The method of claim 11 characterized in that to reconstruct a following segment, it repeats the previous operations by choosing the end of the first segment as the starting point of the next segment.

13 - Method according to any one of claims 1 to 12, characterized in that - to assign a label to a neighboring segment, it is assigned a label corresponding to a supposed position (IVA) of this segment, this supposed position being deduced in a hypothesis of the structure of the model,

- to verify we verify the correctness of this hypothesis,

- if the verification fails, we start again by assigning another label.

14 - Method according to any one of claims 1 to 13 characterized in that

- we develop several models,

- we choose one of these models,

- and if the reconstruction fails, we choose another model. 15 - Method according to any one of claims 1 to 14 characterized in that by checking, one assesses the resemblance of a reconstructed segment with a segment of the model.

16 - Method according to any one of claims 11 to 12 characterized in that

- if the verification that the epipolar line cuts the image of this segment in the second image fails, - the directing vectors of the line of intersection of the two planes (π ₁ , 112) respectively containing the origin of the projections and the projected images of the segment are calculated. 17 - Method according to any one of claims 1 to 16 characterized in that the development of the model is carried out by an interactive generator of wire reconstruction from an anatomical model. 18 - Method according to any one of claims l to 17 characterized in that the two images are obtained by projection according to bisecting orientations of the angles delimited by the two main planes, that is to say for the heart by the planes IV and AV.

19 - Method according to any one of claims 6 to 9 characterized in that the reference changes from one segment to another. •

20 - Method of reconstruction of the arterial tree of the left ventricle of the heart in which one seeks substantially orthogonal planes supposed to belong to the IVA, and to the CX.