WO2015110762A1

WO2015110762A1 - Method for determining the trajectory of a point of a moving object

Info

Publication number: WO2015110762A1
Application number: PCT/FR2015/050161
Authority: WO
Inventors: Thomas CREVEAUX; Isabelle ROGOWSKI
Original assignee: Université Claude Bernard Lyon 1
Priority date: 2014-01-23
Filing date: 2015-01-23
Publication date: 2015-07-30
Also published as: FR3016721A1

Abstract

The invention concerns a method for determining the trajectory of a point of a moving object provided with markers, which comprises: acquiring (32) a scatter diagram, by means of a motion capture system, at a plurality of successive moments in time; selecting (56), from the acquired diagrams, points belonging to a trajectory of a given marker; and in which the selection of a subsequent point of the trajectory at a moment in time t+1 comprises: estimating the coordinates of the subsequent point, by means of an extrapolation function taking as argument the coordinates of a plurality of preceding points of the trajectory; identifying the point in the diagram acquired at the moment in time t+1 in which the measured coordinates are closest to the estimated coordinates, and adding the point identified in this way to the sequence of points of the trajectory.

Description

METHOD FOR DETERMINING THE PATH OF A POINT OF AN OBJECT

MOBILE

[Ooi] The invention relates to a method for determining the trajectory of a point of a moving object and a method of selecting points belonging to a trajectory. The invention also relates to an information recording medium and a computer for the implementation of this method.

[002] Motion capture systems are known, for example, used in the field of 3D imaging or biomechanics. Typically, in these systems, position markers are placed at points of a moving object (such as an actor) whose movement details are to be known. During the movement of the object, an optical measuring device measures at several successive times in time the positions occupied by each of these position markers. The result of this measurement is a set of point clouds. Known methods make it possible to determine the trajectory of these markers by selecting, within the point clouds, points which belong to the trajectory of the same position marker. In particular, the determination of the trajectory of these markers must take into account the fact that position markers may, at certain times, be masked during the movements of the moving object and therefore not be measured by the optical measuring device. . In addition, the system is also likely to record coordinates that do not match any of the markers. It is said that these are coordinates of a measurement artifact. This results in an error in the determination of the trajectory followed by the position markers.

[003] US Patent Application 2007/0146370 A1 (GORDON) discloses such a method. In this method, the selection is carried out, for a group of points, according to morphological criteria of the geometric form of the set including this group of points with respect to the shape including a group of points known as belonging to trajectories for previous moments of measurement. However, this method requires significant computing resources to be implemented and has insufficient reliability.

[004] From the state of the art is also known from the following documents:

L. Herda et al, "Using skeleton-based tracking to increase the reliability of motion capture," Human Movement Science, Vol. 20, p. 313-341, January 2001;

- Ch. Bailer et al, "A user-supported tracking framework for interactive video production," CVMP13, ACM, Nov. 2013.

[005] There is therefore a need for a method for determining the trajectory of a point of a moving object from point clouds measured by a motion capture system, this method having increased robustness. [006] The invention therefore relates to a method for determining the trajectory of a point of a moving object according to claim 1.

[007] By estimating the coordinates of the next point of each trajectory of a position marker from the points of the trajectory already known for all or part of the previous instants, we obtain an estimate of the position at which the point should be located. measured cloud acquired at the next instant that corresponds to this position marker. The selection is thus performed by identifying, if it exists, the point in the cloud acquired at the next instant whose coordinates are closest to those estimated. This results in a lower risk of affecting a measured point corresponding to a marker, to a trajectory of another marker. Thus, an increased precision is obtained in the determination of the respective trajectories of the position markers. Indeed, based on the criterion of proximity of the coordinates, the risk that a point is erroneously assigned to a trajectory is reduced.

According to another aspect, the invention relates to a method for selecting points belonging to a path for implementing the method for determining the trajectory of a point of a moving object according to the invention, in accordance with the invention. in claim 2.

Embodiments of the invention may have one or more of the features of claims 3 to 6.

[ooi o] These embodiments furthermore have the following advantages:

- the repetition of operations a] and b] on the remaining points from the initial moment until the final moment to build new trajectories makes it possible to take into account trajectories of position markers for which no coordinate has been measured at the initial moment.

the execution of the selection of the first and second times by temporally ordering the points of the trajectory in opposite directions, then the search for a common part makes it possible to detect whether two distinct trajectories correspond in fact to the same position marker and if necessary, group these two trajectories to form only one. This makes it possible to reconstruct the trajectory of a marker even when the coordinates of this marker have not been measured at least at a time t, for example because of the temporary occultation of this marker during the movement of the object.

the choice of the value of the predefined number W makes it possible to control the accuracy of the estimate during step a].

estimating first and second provisional coordinates by means of different extrapolation functions and then combining these first and second provisional coordinates makes it possible to improve the accuracy of the estimate made during step a]. In another aspect, the invention also relates to an information recording medium, comprising instructions for executing a method according to the invention when these instructions are executed by an electronic computer.

In another aspect, the invention also relates to an electronic computer for implementing the invention, the electronic computer being in accordance with claim 8.

The invention will be better understood on reading the description which follows, given solely by way of nonlimiting example and with reference to the drawings in which:

Figure 1 is a schematic illustration of a motion capture system;

Fig. 2 is a flowchart of a method for determining the trajectory of a point of a moving object by means of the system of Fig. 1;

FIGS. 3A, 3B and 3C schematically illustrate an example of point clouds acquired during the process of FIG. 2 at different times t consecutive;

Figures 4 and 5 are flowcharts of point selection steps of the method of Figure 2.

In these figures, the same references are used to designate the same elements.

In the following description, the features and functions well known to those skilled in the art are not described in detail.

FIG. 1 represents a motion capture system 2 for measuring the movements of a mobile object 4,

The mobile object 4 is able to move over time. The object 4 comprises a plurality of position markers 6, fixed on the object 4, for example on the surface of this object 4. In known manner, the markers 6 are configured to be visible optically. For example, the markers 6 have identical dimensions and each comprise a reflective target for infra-red radiation. Object 4 is here an actor whose motions are to be measured for applications in biomechanics. To simplify FIG. 1, the markers 6 are represented by crosses arranged on the object 4.

The system 2 is capable of automatically acquiring a cloud of points of the object 4 at several successive instants in time, between an initial moment and a final instant. Each cloud of points acquired by the system 2 at a given instant t is denoted N _t and has p (t) points, called measured points. The quantity p (t) is an integer greater than or equal to zero. The quantity p (t) can vary from one measuring instant to another, in particular because markers 6 can be, at a given moment, temporarily hidden, making their measurement by the system 2 impossible, then that they are not hidden at another time. The quantity p (t) can also vary because the system 2 can also accidentally acquire one or more points that do not correspond to the position of a marker 6. This is called measuring artifacts. For example, for the same marker 6, two distinct points are mistakenly acquired during a single instant. Such measurement artefacts may be caused by adverse optical conditions, such as the presence of reflections or the presence of a source of stray radiation.

In what follows, to simplify the description, it is considered that each measured point corresponds to the position in the space occupied by one of the markers 6, at this moment t. In other words, in this example, there is no measurement artifact. Thus, each measured point comprises spatial coordinates, called measured coordinates, of the position occupied at this instant t by this marker 6. The measured coordinates are expressed in a reference R of the space. This reference R is here an orthonormal reference three-dimensional. The coordinates measured here are Cartesian coordinates. We denote x _t , k, y _t , k and z _t , _k the measured coordinates of the _kth point of the cloud N _t , where k is an integer belonging to the interval [1; p (t)]. Subsequently, the term "moment of measurement" will be used to designate such an instant t. The points of the same cloud differ from each other only by their respective coordinates. Typically, the system 2 is unable to identify, in addition to the coordinates measured by one point, other information that would make it possible to directly identify the marker corresponding to this position among the set of markers 6.

In this example, the object 4 moves in the space between the initial and final instants. Preferably, the initial moment is chosen to coincide with the start of the movement of the object 4. The point clouds are here acquired at regular intervals. The instants t are therefore separated two by two by a time step At identical. Subsequently, for simplicity, the moments will be expressed as multiples of this time step. Thus, we note t = 1 the initial moment and t = n the final moment where n is a natural integer strictly greater than 1. The moments of measurement will be continuously numbered chronologically between these initial and final moments. "Instant t" will be noted any moment of measurement chosen from all the measurement times between these initial and final instants. This instant can also be noted t = i, where i is an integer belonging to the interval [1; not]. Two moments of measurement t = i and t = i + 1 are consecutive. We also say that the instant t = i + 1 immediately follows the moment t = i.

The term "measurement instant" here refers in fact to a measurement period. However, in practice, the duration of acquisition of a cloud of points by the system 2 is so short compared to the duration between the initial and final instants as well as with respect to the time step At separating two consecutive measurements , that we consider that this duration is instantaneous. The system 2 comprises here:

an optical measuring device 8 able to measure the position of the markers 6, and

a calculation unit 10 for determining the trajectory of the markers of the object 4. The device 8 comprises here:

an infrared radiation source, configured to illuminate the object 4 by means of infra-red radiation, and

an infrared camera configured to measure the radiation reflected by the markers 6 of the object 4 when the object 4 is illuminated by the radiation source. In this example, the acquisition of a cloud of points consists of recording an image of the object 4 by means of the device 8. As the markers 6 reflect the infrared radiation but the object hardly reflects them. , then the acquired image contains only images of the markers 6.

The unit 10 is in particular programmed to select, automatically, among the point clouds acquired by the system 2, points belonging to a trajectory of the same marker. This makes it possible to have such a trajectory for each of the markers 6 between the instants t = 1 and t = n. Each trajectory here comprises a temporally ordered sequence from the initial moment and towards the final instant of measured points, each originating from a respective acquired cloud of points. In this description, the j-th trajectory TRj is denoted as follows: (Mj; Si, j; S ₂ , j, Sij, S _N j, j) where Mj is the number of measured points contained in this j -th trajectory. Mj is here a natural integer less than or equal to n. In other words, a trajectory TRj can not contain several points measured at the same time t. Sij here comprises the coordinates Xij, Yij and Z of the i-th point of the trajectory TRj and a variable T, j indicating the instant t at which this i-th point has been measured.

The unit 10 comprises here:

a programmable electronic calculator;

a communications interface 22, and

a support 24 for recording information.

The interface 22 is able to collect data measured by the device 8. The computer 20 executes instructions contained in the support 24. The support 24 comprises in particular instructions for the execution of the method of FIG. 0029] An example of use of the system 2 will now be described, with reference to the flowchart of FIG. 2 and FIGS. 1, 3 and 4.

In a step 30, the markers 6 are fixed without any degree of freedom on the object 4. Then, the object 4 is set in motion.

Then, during a step 32, a cloud of points is automatically acquired by the system 2 at several successive times in time between the instants t = 1 and t = n.

FIGS. 3A, 3B and 3C represent an example of acquired point clouds, respectively, at successive instants i-1, i and i + 1, where i is an integer belonging to the interval [1; not]. To facilitate the reading of these FIGS. 3A to 3C, the point clouds each comprise a reduced number of points and are displayed in a two-dimensional plane reference. In practice, a scatter plot can have at least ten or a hundred or a thousand points.

Then, points belonging to a trajectory of the same marker are automatically selected by the unit 10 by means of a method 50 for selecting points belonging to a trajectory.

For this purpose, during a step 52, these acquired point clouds are transmitted to the unit 10 by means of the interface 22. For example, these point clouds are transmitted to the unit 10 under the form of a computer file in which are recorded the coordinates of the points forming each of these clouds and the moments of measurement of these points.

Then, during a step 54, the trajectories are initialized from the points measured at the initial moment t = 1. In this example, it is considered that the points measured at the initial time each correspond to a position of one of the markers 6. The trajectories are thus initialized with the position of these measured points. Thus, for each of the p (1) measured points of the cloud Ni acquired at time t = 1, a corresponding trajectory TRj is constructed, whose first point is this measured point. At the end of this step 54, there is therefore a number p (1) of trajectories each containing a measured point of the cloud Ni.

Then, during a step 56, the trajectories are constructed point by point by selecting, for each moment of measurement, within the acquired point clouds, following points of the trajectory from points of this same trajectory. selected at previous times. To do this, for each of the instants t of measurement and for each TRj trajectory initialized:

the coordinates of the point of the trajectory at the instant t = i + 1, said next point, are estimated by means of an extrapolation function taking as arguments the coordinates of several points of the trajectory, prior to the moment t = i + 1;

the identification of the measured point of the cloud N _{i +} i which, among all the measured points of the cloud N _{i +} i, has measured coordinates closest to the coordinates of the estimated point. This point is then said to be identified and it is added to the trajectory TRj.

FIG. 4 shows in greater detail an example of implementation of step 56 for a given instant t = i + 1, after its implementation has made it possible to identify the points of the trajectories for the moments preceding the instant i + 1. For simplicity, step 56 is described here in detail only to select the next point S _{i +} ij TRj trajectory.

During an operation 70, the coordinates of the next point S _{i +} ij of each trajectory TRj are estimated. The symbol S _{i +} ij is used to differentiate this estimated point from point S _{i +} ij which is not yet identified at this time t = i + 1. The point S _{i +} ij does not is therefore not part of the trajectory TRj, because it does not correspond to the measured coordinates of one of the markers 6.

In this example, it is assumed that the point S _{i +} ij corresponds to the measurement instant t = i + 1, that is to say that the first i points of the trajectory TRj respectively correspond to measured points. at times 1 to i. The value of Mj is then equal to i. The coordinates of the points Sij to Sij are therefore known because they have been previously identified during an implementation of step 56 for earlier instants 1 to i.

Here, for each trajectory, we calculate coordinates estimated at _{i +} ij, βί + ij and Yi ₊ ij to predict the position of each of the coordinates, respectively X _{i + 1ij} , Y _{i + 1} j and Z _{i +} ij, which are not yet known. This calculation is made here from the coordinates of the last W points S _k j to Sij already known from this trajectory TRj, using a predefined extrapolation function f, where:

- W is a predefined parameter taking as value an integer belonging to the interval [1; Mj], and

k is a number equal to max (i - W, 1).

The choice of the value of W depends on the desired precision of the estimate, the number of points Mj forming the trajectory, the frequency of acquisition of the system, the movement studied, as well as the nature of the function. f. Here, we choose W = 5, that is to say that the five already known points preceding the time t = i + 1 are used for the estimation.

The function f is here a polynomial regression function taking for arguments the coordinates of the W points S _k j to Sij and of the time variable. In this example, the function f is a polynomial function of degree 1. The estimation of the coordinates thus involves a linear regression.

[0043] Thus, the estimated coordinates are calculated using the following formulas:

a _{i +} u = a _x ^* (i + 1) + b _x ;

β _{ί +} υ = a _y ^* (i + 1) + b _y ;

The coefficients a _x and b _x are computed by linear regression according to the coordinates X _k j to j and T _k j to T of the Mj-k points S _k j to Sij already known from this trajectory TRj. Thus, in a known manner, these coefficients are calculated by minimizing the following quantity: Σ _r = _k ... _Mj (X _r j - (a _x * T _rJ + b _x )) ² , which makes it possible to obtain known way, by least squares method:

and b _x = (1 / (Mj-k)) * Σ _{r = k} ... _Mj (X _rj ) - (a _x / (Mj-k)) * Σ _{r = k} ... _Mj (T _rj ) .

The coefficients a _y and b _y and the coefficients a _z and b _z are calculated in the same way except that the coordinates, respectively, Y _k j to Yij and Z _kJ to ¾ are taken into account in place of the coordinates. X _k j to Xij.

Thus, we obtain the estimated coordinates a _{i +} i, j, βί + ij and Y _{i +} ij for the point S ij. These calculations are repeated to estimate the coordinates of the points S _{i +} ij for each trajectory TR ,.

In the particular case where t = 2, then, for each trajectory TRj, the estimated coordinates <¾, β2 ,, and γ ₂ ,, of the point S ₂ , j are defined as being equal to the coordinates, respectively Xi, ,, Yij and Z'ij known from point Sij. In other words, it is assumed that the markers moved very little between the instants t = 1 and t = 2.

At the end of the operation 70, there is an estimated point for each of the p (1) trajectories TRj initialized.

Then, during an operation 72, the distances between, on the one hand, each of the following p (1) points S _{i +} i, j estimated during the operation 70 and, on the other hand, each of the p (i + 1) measured points of the cloud N _{i +} i are calculated.

We note here 5j, _k the distance between the estimated point S _{i +} i, j and the k-th measured point of the cloud N _{i +} i. This distance 5j, _k is here calculated using the following formula: 5j, _k = V [(a _{i +} ij - x _{i +} i, _k ) ² + ( _{i +} i, _j - y _{i +} i, _k ) ² + (Yi ₊ ij - z _{i +} i, _k ) ² ].

These distances 5j, _k are then stored in a data structure, such as a matrix. At the end of the operation 72, we thus have a set of p (1) * p (i + 1) distances 5j, _k for the different values of j and of k.

In an operation 74, the pairs of measured coordinates and estimated coordinates that are closest to each other are then selected. We choose here to take into account only the distances 5j, _k which are less than a maximum value Δ previously defined. This maximum value makes it possible not to take into account the measured coordinates which are located at a too high distance from estimated coordinates.

To this end, during a sub-operation 80, the distances 5j, _k calculated by increasing value are previously classified.

Then, during a sub-operation 82, it is determined whether there exists, in the set of distances, a distance which, among all the distances 5j, _k calculated, has the smallest value while being strictly less than the value Δ.

Note 5 _j0 , _k o this distance, which corresponds to the distance between, on the one hand, the coordinates X _{i +} ijo, Y + ijo and Z _{i +} i, _j0 of the point S _{i +} i, jo and, d on the other hand, of the coordinates Xi + i, _k o, yi + o and z _{i +} i, _k0 points of the ko-th point of the cloud N _{i +} i.

If this distance 5 _j0 , _k o exists, then, during a sub-operation 84, the point S _{i +} i, _j0 is said to be identified as belonging to the trajectory TR _j0 . The coordinates Xi + ij, Y _{i +} i, jo and Z _{i +} i, jo for T _{i +} i, _j0 = i + 1 are added to the trajectory TR _j0 to form the point If + i, jo. These coordinates Χ, -Η, Ρ, Yi + ijo and Z _{i +} i, _j0 are assigned the value of the coordinates, respectively, x _{i +} i, _k o, y _{i +} i, _k o and z _{i +} i, _k o. The value Mj is then incremented by one unit.

The distance δ, κο is then removed from the set of distances, so as not to be selected during subsequent iterations of the sub-operation 82. Moreover, here, the distances 5j, _k o and 5 _{j 0} , k are also removed from all distances, regardless of the values of j and k. Indeed, here, the same measured point of the cloud can not belong to more than one trajectory TRj. A trajectory TRj can not contain more than one measured point of a cloud acquired at a time t. To do this, the distance 5 _j0 , ko is here replaced in the set of distances by a numerical value strictly greater than the value Δ.

The sub-operation 82 is then reiterated, as long as there exists in the set of distances 5j, _k strictly less than the value Δ.

If there is no such distance 5 _j0 , _k o, then the operation 74 ends, because it means that there is no point of the acquired cloud that can be identified as belonging to one of the trajectories. TRj.

Thus, at the end of the operation 74, each measured point whose measured coordinates are closest to one of the estimated coordinates has been added to the trajectory corresponding to these estimated coordinates. At the end of this operation 74, there may however exist measured points, so-called remaining points, which have not been identified as belonging to one of the trajectories TRj. The treatment of these remaining points will be described in more detail later. Similarly, there may also exist TRj trajectories for which no point has been identified at this time. The case of these trajectories will also be described later.

To perform step 56 in its entirety, the operations 70 to 74 are repeated successively for each of the instants t following the initial time and until the final time.

For example, the operations are 70 to 74 are first applied for the moment t = 2. then for each of the following moments. When the value of t is equal to n, that is to say that the final instant is reached, then operations 70 to 74 have subsequently been applied for each of the p (1) trajectories at this instant n, then the initialized p (1) TRj trajectories are considered to be constructed. These p (1) TRj trajectories are then stored in a list of results. Step 56 is then considered complete.

By estimating the coordinates of the next point of each trajectory of a position marker from the points of the trajectory already known for the previous instants, we obtain an estimate of the position at which the measured point of the cloud should be situated. acquired which corresponds to this position marker. The selection is thus performed by identifying, if it exists, the point whose coordinates are closest to those estimated. This results in a lower risk of affecting a point measured corresponding to a marker at a trajectory of another marker. By constructing the trajectories on the basis of such a selection method, increased accuracy is obtained in determining the respective trajectories of the position markers.

Advantageously, during a step 100, trajectories TR'j are determined automatically from the remaining points which have not been identified as belonging to a trajectory during step 56.

We denote p '(t) designating the number of remaining points of the cloud N _t acquired, that is to say the measured points of this cloud which have not been considered as belonging to a trajectory TR _j . The number p '(t) is an integer less than or equal to p (t).

This step 100 comprises for example:

determining the smallest time t ₀ between t = 1 and t = n from which there is a remaining point of the cloud of points acquired at this instant, and then

the application of a step identical to step 56, except that it:

• is carried out for the following instants of the instant t = t ₀ , that is to say considering the instant t = t ₀ as initial moment instead of t = 1;

• applies only to the remaining points.

Thus, the constituent operations 70 to 74 of step 56 are first applied for the moment t = t ₀ , to initialize a number p '(t ₀ ) of new paths. Then, these operations 70 to 74 are applied successively, for each of the instants t = t ₀ +1 to t = n, to gradually build the p '(t ₀ ) new trajectories. These new trajectories, once constructed, are then added to the results table.

Advantageously, step 100 is repeated as long as there are remaining points among the n clouds acquired.

Thus, the trajectories of position markers whose coordinates have not been measured at the initial time are taken into account.

Advantageously, during a step 120, secondary trajectories are constructed from the acquired point clouds temporally ordered from the final instant to the initial instant. These secondary trajectories are compared with previously defined trajectories, in particular to complete incomplete trajectories. Incomplete trajectory is a path TRj which has a number of points less than the number of times of measurement. A trajectory may, for example, be incomplete because the marker 6 corresponding to this trajectory has undergone a significant displacement between two consecutive instants of measurement, so that the point acquired after this important displacement has not been added to this trajectory because the estimate for this moment could not anticipate this displacement so that the acquired point is then too far from the estimated point.

FIG. 5 shows in greater detail an example of this step 120. During an operation 122, the step 56 is applied successively to all the clouds acquired, from the final instant to the initial instant, to form a plurality of points sequences, called inverse sequences. The points of each inverted sequence are oriented temporally in the order from the final moment to the initial moment. Thus, for each instant t = i + 1 to which these steps are applied, it is named, with reference to the step 56 thus applied, "previous points" of each sequence, points which will in fact have been measured after the instant t +1. Advantageously, a step 124, identical to step 100, is also applied to construct other inverted suites from points remaining at the end of step 122.

Then, during an operation 126, the sequences thus formed are compared with the trajectories formed during steps 56 and 100, which are incomplete, that is to say which have a number of points less than the number of points. moments of measurements.

For this purpose, this operation 126 includes a pairing between the formed sequences and these incomplete trajectories, in order to identify whether the points composing the sequences formed are likely to be part of the incomplete trajectories. This pairing includes here in particular the search for points in common between the sequences formed and the incomplete trajectories so as to present a common part.

It is considered that two sequences have a common part if there exist distinct instants t ₁ and t ₂ between which the two sequences have the same points, that is to say that there exists:

in the first sequence, from a first stopping point to an instant ti where the first sequence stops, and

in the second sequence, from a second stopping point to an instant t ₂ where the second sequence stops,

the instant t ₂ being separated from the instant ti by at least one intermediate instant for which a cloud of points has been acquired, the points forming the first and second sequences being the same between the instants t ₁ and t ₂ . Two points are here said to be the same if their coordinates are equal to 5% or close to 2% or 1%.

The operation 126 thus comprises here, for each pair formed of a sequence formed of an inverted continuation and of an incomplete trajectory, the search for the existence of a common part between this inverted continuation and the incomplete trajectory. These pairs are here classified according to the number of points in common that they present with each other in this common part. As long as there remain pairs, say remaining pairs, having a common part of at least a predetermined nonzero number Y of points, then a path is created, by pairing, from the meeting of the points of the inverted sequence and of the incomplete trajectory forming the pair which, among these remaining pairs, presents the greatest number of points in common in their common part. The number Y is for example greater than or equal to two or ten. The trajectory TR, thus completed is formed of the points of the incomplete trajectory and points of the inverted continuation. This completed trajectory is then added to the result list. The incomplete path is then removed from the results list.

Thus, trajectories that have a discontinuity can be identified and reconstructed with increased accuracy. The system 2 can thus acquire the movements of the object 4 with greater resilience in the event of temporary masking of one or more of the markers 6.

Finally, during a step 140, the trajectories determined and contained in the result file are automatically transmitted for example by means of an output interface of the unit 10.

[0080] Many other embodiments are possible.

Measurement artefacts may be recorded by the system 2. In this case, the quantity p (t) at a given instant may be greater than the number of markers 6 actually present on the object 4.

The unit 10 can be dissociated from the system 2. In this case, the unit 10 is able to automatically access a plurality of point clouds measured by a system 2.

The marker 6 can be made differently. For example, the marker 6 has a predetermined optical pattern. The device 8, for example an optical camera, is then able to optically recognize this optical pattern among other elements by means of a pattern recognition method. In a variant, the markers 6 do not all have the same dimensions.

The device 8 can be made differently and depends in particular on the nature of the markers 6 used. Alternatively, the radiation source of the device 8 is integrated with the camera. The device 8 may comprise several cameras. In this case, each camera may have its own source of radiation. The measurement of the position of the markers is then carried out more precisely.

In a variant, the device 8 also makes it possible to obtain a value of the measurement error of the position of the markers 6. This error can advantageously be taken into account in the method for constructing the trajectory TRj.

The method 50 may be performed differently. Alternatively, to improve the accuracy, the time step At can be reduced, so that the markers move little from one moment to another. The determination of the trajectory is thus more precise. When the acquired point clouds have a large number of points (for example because a high number of markers 6 are fixed on the object 4), all the acquired data can be divided into several subsets. This reduces the amount of data to be processed by the computer 20. Each subset then contains the clouds acquired between times t, and t _{i +} i. The intervals delimited by the instants t, and t _{i +} i are all included within the interval delimited by the initial and final instants. In this case, the steps of the method 50 are separately applied to each of these intervals to obtain partial trajectories between these instants t, and t _{i +} i. The partial trajectories obtained from each of these subsets are then recombined to obtain the trajectories between the initial and final instants. The recombination is for example carried out analogously to the operation 126.

The estimation carried out during the operation 70 may use non-linear regression functions, such as a polynomial regression of any degree greater than or equal to two or three, provided that there is a sufficient number W of previous points. For example, W is greater than or equal to two or three or ten. For example, f is a quadratic function of the time variable. The estimated coordinates are thus calculated as follows:

a _{i +} i, j = a _x ^* (i + 1) ² + b _x ^* (i + 1) + c _x ;

β _{ί +} υ = a _y ^* (i + 1) ² + b _y ^* (i + 1) + c _y ;

Yi ₊ u = a _z ^* (i + 1) ² + b _z ^* (i + 1) + c _z .

[0088] The coefficients a _x, b _x c and _x are then calculated by minimizing the following quantity: Σ _r = i ... i (X _r j - (a _x ² ^* T _r, j + b ^* T + _x c _x )) ² . This amount can be minimized according to the well-known least squares method. Also, we will not describe here the result, for lack of space. The same applies to the coefficients a _y , b _y and c _y and the coefficients a _z , b _z and c _z .

[0089] Alternatively, f is a polynomial function of degree three. The estimated coordinates are then calculated as follows:

a _{i +} i, j = a _x ^* (i + 1) ³ + b _x ^* (i + 1) ² + c _x ^* (i + 1) + d _x ;

β _{ί +} υ = a _y ^* (i + 1) ³ + b _y ^* (i + 1) ² + c _y ^* (i + 1) + d _y ;

Y i + u = a _z ^* (i + 1) ³ + b _z ^* (i + 1 f + c _z ^* (i + 1) + d _z .

The coefficients a _x , b _x , c _x and d _x are then calculated by polynomial regression by solving the following matrix equation, for example by means of the Cholesky factorization method:

The same applies to the coefficients a _y , b _y , c _y and d _y and the coefficients a _z , b _z , c _z , and d _z .

The use of polynomial functions of degree greater than or equal to two makes it possible to improve the accuracy of the estimation, in particular for a degree equal to two or three or four.

The estimation of the coordinates can comprise the use of several different extrapolation functions. For example, estimating the coordinates of a next point involves estimating two sets of provisional coordinates of the same next point by, respectively, two distinct extrapolation steps that differ from each other in particular by the nature of the extrapolation function f used and / or the number W of points used by this function f to perform the extrapolation. These two sets of provisional coordinates are then combined to define the estimated coordinates of the point.

The value of W may be different. In particular, the value of W may be equal to that of Mj.

The coordinates may be different. For example, coordinates are expressed in a two-dimensional space only.

The distance δ ,, κ can be calculated differently. For example, in the case where the space has only two dimensions, then the distance δ ,, κ is calculated by means of the formula δ ,, κ = V [(a _{i +} i, j - χ, ₊ ι, κ ² + (βί ₊ ι, ί - y +) ² ] - Other distance measurements can also be used such as, for example, Minkowski distance or Chebyshev distance (maximum coordinate difference). This makes it possible to improve the reliability of the determination of the trajectories, by privileging certain directions of the space. Indeed, when the illumination of markers 6 has anisotropy, measurement errors can occur with a higher probability in certain directions of space.

Step 56 can be performed differently. In particular, the stop condition of the operation 74 may be chosen differently than the absence of distance less than the value Δ. For example, for each instant t, if the number of initialized trajectories is greater than p (t), then operation 74 continues as long as there remain measured coordinates that have not been assigned to one of the initialized trajectories. In another example, if p (t) is greater than the number of initialized trajectories, then the operation 74 continues as long as there remain initialized trajectories for which no point measured for this instant t has been affected.

In a variant, the operation 74 is carried out by means of an optimization method, for example by means of the Hungarian algorithm (known as Kuhn-Munkres) or the Jonker-Volgenant algorithm (R. Jonker et al., Computing, Vol 38, pp. 325-340, 1987). For example, the trajectories are constructed by assigning, for each instant t, the acquired points so that the sum of the distances δ ,, κ defined for acquired points is minimal. This improves the reliability of trajectory determination without the need to evaluate all combinations. According to another variant, during step 56, at a time t, it is possible to decide not to add points to a trajectory TRj from this instant t if no acquired point has been added. to this trajectory TRj during the previous X instants, where X is a predefined non-zero integer. For example, X is greater than or equal to five or ten. In other words, we stop adding acquired points to a trajectory when we consider that the estimate for this trajectory has a too important error. This makes it possible to improve the precision of the determination of the trajectories.

Measured coordinates of the same point of an acquired cloud can be assigned to more than one trajectory TRj. This makes it possible to take into account a case where markers 6 are superimposed during a measurement instant. Such a situation may occur, for example, when the object 4 is an actor and markers 6 are placed near joints of this actor. In this case, during the sub-operation 82, the distances 5j, _k o are not removed from the set of distances.

[00101] The value of Δ is not necessarily constant during the execution of the process. For example, the value of Δ is updated at each instant t as a function of the points identified at the previous instants. Similarly, at a given moment, the value of Δ is not necessarily the same for all the points. It may indeed be advantageous to define particular values of Δ specific to one or more trajectories, because some markers 6 may be subject more frequently than other markers 6 to occultations or to measurement artefacts, for example due to their position on the object 4. The value of Δ depends in particular on the minimum distance between the markers 6 on the object 4 and the accuracy of the estimates made. In particular, for each of the trajectories, it is possible to determine a confidence interval for each of the estimates made.

Alternatively, the Δ value is omitted.

[00103] Step 100 can be omitted. The same is true for step 120 and for step 124. Step 140 can also be omitted or performed differently.

Step 120 may also apply to the case where a trajectory has several discontinuities. Several inverse sequences and incomplete trajectories can then be combined to form a trajectory TRj.

[00105] The operation 126 can be performed differently. For example, alternatively, the pairs can be classified according to the average distance between the points of the respective trajectories in the part of these trajectories that is common to the two trajectories. In another variant, instead of looking for sequences that have points in common, we look for sequences of points that have discontinuities. It is considered that there exists a discontinuity between two series of points if there are instants ίΊ and t ' ₂ such that neither of the two sequences has a point between the instants t'i and t' ₂ .

This operation therefore comprises, for each pair formed of an inverted continuation and of an incomplete trajectory, the search for the existence:

in the incomplete trajectory, from a first stopping point to an instant t 'i, the incomplete trajectory no longer having any point after this instant t'i, and

in the inverted sequence, from a second stopping point to an instant t ' ₂ , the inverted sequence no longer having any point after this instant t' ₂ .

If a discontinuity is found, then a trajectory is created comprising the meeting of the incomplete trajectory and the inverted continuation. In addition, points corresponding to the discontinuity are interpolated from the points of the incomplete trajectory and the inverted sequence.

The operation 126 may also include the search for a discontinuity which has just been described, in addition to the search for common points, for example if, after examining whether the points sequences have common points, it remainder of points which do not present any point in common.

In a variant, in step 126, two points are said to be the same if the distance separating them is less than or equal to a previously predetermined threshold.

Claims

1. A method of determining the trajectory of a point of a moving object, comprising:

- Fixing (30) a plurality of position markers on a moving object, said markers being fixed at different locations on this moving object;

the automatic acquisition (32) of a cloud of points, by a motion capture system, at several successive instants in time between an initial instant and a final instant, each cloud acquired at a given instant t with p ( t) points, said measured points, each measured point having measured coordinates, in a reference, of the position occupied at this instant t by a respective marker, the points of the same cloud differing from each other only by their respective coordinates ;

the selection (56), within the acquired point clouds, of points belonging to a trajectory of the same marker, so as to obtain an ordered temporal sequence of measured points, each of the measured points of this sequence coming from a acquired cloud respective points;

this method being characterized in that the selection of a next point of the trajectory at a time t + 1 from previously selected points of the same trajectory comprises:

a] the estimation (70) of the coordinates of the next point of the trajectory at the instant t + 1, the coordinates being estimated by means of an extrapolation function taking for argument the coordinates of several previous points of the trajectory already contained within the sequence of points of this trajectory, the extrapolation function being a polynomial regression function of degree greater than or equal to two taking as arguments the coordinates of a predefined number W of preceding points of the trajectory and a time variable;

b) the identification (74) of the point of the cloud acquired at time t + 1 whose measured coordinates are closest to the estimated coordinates and the addition of the point thus identified following points of the trajectory.

A method of selecting points belonging to a path for carrying out the method of claim 1, comprising:

automatic access to a plurality of point clouds acquired at successive moments of measurement, each cloud acquired at a given instant t having p (t) points, said measured points, each measured point comprising measured coordinates, in a reference frame , from a position of space occupied at this moment t by a respective position marker, the points of the same cloud differing from each other only by their respective coordinates;

the selection (56), within the acquired point clouds, of points belonging to a trajectory of a same marker, so as to obtain a temporally ordered sequence of measured points, each of the measured points of this sequence coming from a acquired cloud respective points;

a] the estimation (70) of the coordinates of the next point of the trajectory at the instant t + 1, the coordinates being estimated by means of an extrapolation function taking for argument the coordinates of several previous points of the trajectory already contained within the sequence of points of this trajectory; b) the determination (74) of the point of the cloud acquired at time t + 1 whose measured coordinates are closest to the estimated coordinates and the addition of the point thus determined following points of the trajectory.

3. Method according to claim 1 or 2, wherein step a] is first performed for several trajectories of several markers so as to obtain the estimated coordinates of the next point at time t + 1 for each of these trajectories. , then, in step b]:

b1] for each next point whose coordinates have been estimated in step a], the method comprises calculating (72) the distance between the estimated coordinates of this next point and the measured coordinates of each point of the cloud acquired at the moment t + 1, then,

b2] the method comprises:

The identification of the point belonging to the cloud acquired at time t + 1 for which the distance calculated during the operation b1] between the measured coordinates of this point and the estimated coordinates of a next point is the smallest among the set of calculated distances, and

• adding the point (82) thus identified following points of the trajectory used to estimate the estimated coordinates whose measured coordinates of this identified point are closest;

b3] the method comprises the repetition of the operation b2] but without taking into account:

• the distances calculated from the points belonging to the cloud acquired at time t + 1 which have already been added to a sequence of points during a previous iteration of the operation b2] ni, • the distances calculated from the estimated coordinates of the points obtained from sequences of points at which a point belonging to the cloud acquired at time t + 1 has already been added during a previous iteration of the operation b2].

4. Method according to claim 3, wherein the operations b2] and b3] are repeated for each moment as long as there is at least one distance to be taken into account which has a value lower than a predetermined threshold and, if at as a result of these reiterations, there exists within the clouds of points a number M 'of points, called remaining points, which have not been added to a series of points, then the steps a] and b] are repeated ( 100) for these M 'remaining points, for each cloud of points containing these remaining points, so as to define M' new trajectories.

5. Method according to any one of the preceding claims, in which: the selection, within the cloud acquired at time t + 1, of the points belonging to the trajectory, is executed:

• a first time, by temporally ordering the points of the trajectory in the order from the initial moment to the final instant so that the points preceding the next point are the points measured before the moment t + 1, this first execution of the selection to obtain a first sequence of points;

A second time (122, 124), by temporally ordering the points of the trajectory in the order from the final instant to the initial instant so that the points preceding the next point are the points measured after the instant t + 1, this second execution of the selection making it possible to obtain a second sequence of points;

the method further comprising searching (126) for a common portion between the first and second series of points, i.e., the existence:

In the first sequence of a first stopping point at a time t i where the first sequence stops, and

In the second sequence, from a second stop point to an instant t ₂ where the second sequence stops,

the instant t ₂ being separated from the instant ti by at least one intermediate instant for which a cloud of points has been acquired, the points forming the first and second sequences being the same between the instants t ₁ and t ₂ , and

if a common part is found, then the method further comprises a step of cross-checking the data in which the first and second series of points are replaced by a third series of points consisting of the meeting of the first and second series of points.

The method according to claim 3, wherein, during the operation b1], the calculated distance is the algebraic distance δ = Λ / [(α-χ) ² + (β-γ) ² + (γ-ζ) ² ] where α, β and γ are the estimated Cartesian coordinates and x, y and z are the measured coordinates of the point of the cloud acquired at time t + 1, expressed in this same frame.

7. Support (24) for recording information, characterized in that it comprises instructions for the execution of a method according to any one of claims 1 to 6 when these instructions are executed by an electronic calculator .

8. Electronic calculator (20) for the implementation of any one of claims 1 to 6, the electronic calculator being programmed for:

automatically obtaining a file containing a plurality of clouds of points acquired at successive moments of measurement, each cloud acquired at a given instant t having p (t) points, said measured points, each measured point comprising measured coordinates, in a reference frame , a position of the space occupied at this instant t by a respective marker of position, the points of the same cloud differing from each other only by their respective coordinates;

selecting, within the acquired point clouds, points belonging to a trajectory of the same marker, so as to obtain a temporally ordered sequence of measured points, each of the measured points of this sequence coming from a respective acquired cloud of points;

characterized in that selecting a next point of the trajectory at a time t + 1 from previously selected points of the same trajectory comprises:

a] the estimation of the coordinates of the next point of the trajectory at the instant t + 1, the coordinates being estimated by means of an extrapolation function taking for argument the coordinates of several previous points of the trajectory already contained in the within the sequence of points of this trajectory, the extrapolation function being a polynomial regression function of degree greater than or equal to two taking as arguments the coordinates of a predefined number W of preceding points of the trajectory and a variable time;

b] the identification of the point of the cloud acquired at time t + 1 whose measured coordinates are closest to the estimated coordinates and the addition of the point thus identified following points of the trajectory.