Patent Publication Number: US-11391648-B2

Title: Method for detecting a degradation of a wheel tire

Description:
The invention relates to the field of methods of detecting degradation of a wheel tire. 
     BACKGROUND OF THE INVENTION 
     The tires of airplane wheels are subjected to very high stresses, in particular during stages of takeoff and landing. On takeoff, the tires are subjected both to the weight of the airplane and to the speed of takeoff, and they heat up briefly, but considerably. On landing, at the moment when the wheels of the airplane touch the ground, the tires go from a speed of zero to a very high speed in a very short length of time. 
     These phenomena tend to subject tires to wear. Unfortunately, the deterioration of a tire can lead to excessive slip, to excessive friction, or even to said tire bursting. It is therefore fundamental, for safety reasons, to be able to estimate the wear of tires accurately and reliably in order to ensure that such wear remains at a level that is acceptable. 
     When the level of wear of a tire reaches a certain threshold, the tire is sent back to the factory for retreading. In general, it is tire manufacturers who act on behalf of airlines to supply and to maintain tires. The number of tires used by airlines is very large, so it is important for tire manufacturers that tires are removed at the right time, neither too soon, in order to avoid pointlessly taking usable tires out of service, nor too late, so that tire wear does not become excessive. 
     Thus, an accurate and reliable estimate of the level of tire wear is necessary for the safety of an airplane, and it is also advantageous from an economic point of view. 
     At present, two main methods are used by ground operatives in order to evaluate the wear of a tire. 
     A first method consists in visually estimating the level of wear and the degradation of the tire. 
     A second method consists in manually measuring the depth of the treads and the wear indicators of the tire. 
     Both of those methods give rise to a large number of errors. The estimates and measurements that are made are subjective, and they depend to a great extent on the ground operative concerned. Proposals have therefore been made to have the measurements taken by several ground operatives, however such a solution is expensive and time-consuming. 
     Furthermore, those methods serve only to detect when the level of wear means that the tire needs to be replaced, and they do not serve to anticipate replacement of said tire. 
     OBJECT OF THE INVENTION 
     One object of the invention is to detect degradation of a tire (such as excessive wear) in reliable manner, and another is to improve maintaining a large number of tires. 
     SUMMARY OF THE INVENTION 
     In order to achieve this object, there is provided a detection method for detecting degradation of a real tire of a wheel, the method comprising the steps of:
         acquiring at least one first three-dimensional object representative of the shape of the real tire by using an electronic appliance including at least one three-dimensional sensor, the first three-dimensional object being made up of a set of capture points;   determining the position of a center point for the real tire from the set of capture points;   registering the first three-dimensional object relative to a theoretical tire of known dimensions and orientation in order to obtain a second three-dimensional object forming a registered tire;   transforming the second three-dimensional object in order to obtain one or more two-dimensional objects; and   analyzing the two-dimensional object(s) in order to detect degradation of the real tire.       

     The detection method of the invention thus makes it possible to detect degradation of the real tire in a manner that is automatic, and thus objective and reliable. 
     The detection method also makes it possible to acquire and to conserve data about the state of a large number of real tires. Data is acquired both simply and quickly, since in order to perform detection, it suffices to bring the electronic appliance close to the real tire. 
     The detection method thus makes it possible to perform predictive maintenance operations on a very large number of real tires, and in particular it makes it possible to anticipate degradation and replacement of real tires. 
     There is also provided a detection method as described above, wherein determining the position of the center point of the real tire comprises the step of defining, for each capture point, a normal vector that is normal to a surface of the first three-dimensional object and that passes through said capture point, and the step of estimating a position for the center point of the real tire from the normal vectors. 
     There is also provided a detection method as described above, wherein the position of the center point is estimated by an iterative process during which, on each iteration, capture points that do not belong to the real tire are eliminated, capture points that belong to the real tire are conserved, and the estimate of the position of the center point is refined by using the normal vectors of the capture points belonging to the real tire. 
     There is also provided a detection method as described above, wherein the position of the center point of the real tire is determined by performing a data partitioning method to distinguish between first capture points belonging to the real tire and second capture points belonging to the ground. 
     There is also provided a detection method as described above, wherein registering makes use of a registration algorithm based on Euclidean transformations. 
     There is also provided a detection method as described above, wherein registering also uses an ICP algorithm. 
     There is also provided a detection method as described above, wherein transforming comprises the step of slicing the second three-dimensional object on planes perpendicular to the axis of rotation of the registered tire in order to obtain a plurality of three-dimensional slices of small thickness, and the step of approximating each three-dimensional slice by a two-dimensional slice of zero thickness, the two-dimensional object(s) comprising the two-dimensional slices. 
     There is also provided a detection method as described above, including the steps, for each two-dimensional slice, of calculating a radius r i (α) for the two-dimensional slice, which radius is a function of an angle α about the axis of rotation of the registered tire. 
     There is also provided a detection method as described above, wherein for each two-dimensional slice, a mean radius is calculated for the two-dimensional slice T 2   d   i , and wherein variation of the mean radius as a function of i is investigated (where i is the index of the slice T 2   d   i ). 
     There is also provided a detection method as described above, wherein variation of the mean radius is used to detect abnormal degradation of the tread of the real tire, as constituted by asymmetrical wear or by flattening or by bulging or by cupping or by the presence of a foreign body. 
     There is also provided a detection method as described above, wherein the positions of grooves in the tread are detected and depth is evaluated for each groove, the depths of the grooves being used to detect degradation that is excessive or abnormal, and the positions of the grooves are used to locate degradation that is excessive or abnormal. 
     There is also provided a detection method as described above, wherein the electronic appliance further includes a photographic sensor arranged to acquire color associated with each capture point, wherein transforming comprises two-dimensional projection applied to the second three-dimensional object, and wherein the two-dimensional object(s) comprise a two-dimensional image of the tread of the registered tire as obtained by said two-dimensional projection. 
     There is also provided a detection method as described above, wherein analyzing the two-dimensional image comprises the step of analyzing variation of a color gradient in the two-dimensional image. 
     There is also provided a detection method as described above, wherein the analyzed variation of the color gradient is used to detect abnormal degradation as constituted by excessive wear leading to a metal mesh of the real tire becoming apparent or as constituted by heat being given off or by contamination. 
     There is also provided a detection method as described above, wherein analyzing the two-dimensional image comprises the step of applying a Hough transform to the two-dimensional image. 
     There is also provided a detection method as described above, wherein the Hough transform serves to detect abnormal degradation as constituted by flattening or by bulging or by cupping or by the presence of a foreign body on the tread. 
     There is also provided a detection method as described above, wherein analyzing the two-dimensional image comprises the step of performing training based on convolutional neural networks applied to images of the real tire in good condition and also to images of the various looked-for degradations. 
     The invention can be better understood in the light of the following description of a particular, nonlimiting embodiment of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Reference is made to the accompanying drawings, in which: 
         FIG. 1  shows a first three-dimensional object that is representative of the shape of a real tire; 
         FIG. 2  shows, in a two-dimensional reference frame, a method that is used for estimating the position of a center point for the real tire; 
         FIG. 3  shows capture points and a first estimate of the position of the center point; 
         FIG. 4  is a histogram showing the distribution of distances between the capture points and the first estimate of the position of the center point; 
         FIG. 5  shows the capture points and a final estimate of the position of the center point; 
         FIG. 6  is a histogram showing the distribution of distances between the capture points and the final estimate of the position of the center point; 
         FIG. 7  shows the implementation of a data partitioning method; 
         FIG. 8  shows, the real tire and a theoretical tire prior to registration; 
         FIG. 9  shows, after registration, a second three-dimensional object as obtained by registering the first three-dimensional object and forming a registered tire; 
         FIG. 10  shows three-dimensional slices and two-dimensional slices of a registered tire; 
         FIG. 11  shows the tread of a real tire, showing normal wear; 
         FIG. 12  is a graph plotting a curve showing how the mean radius of the registered tire corresponding to the real tire of  FIG. 11  varies relative to the axis of rotation; 
         FIG. 13  shows the tread of a real tire that presents asymmetrical wear; 
         FIG. 14  is a graph plotting a curve showing how the mean radius of the registered tire corresponding to the real tire of  FIG. 13  varies relative to the axis of rotation; 
         FIG. 15  shows the tread of a real tire in which cupping has formed; 
         FIG. 16  is a graph plotting a curve showing how the mean radius of the registered tire corresponding to the real tire of  FIG. 15  varies relative to the axis of rotation; 
         FIG. 17  shows the tread of a real tire that presents flattening; 
         FIG. 18  is a graph plotting a curve showing how the mean radius of the registered tire corresponding to the real tire of  FIG. 17  varies relative to the axis of rotation; 
         FIG. 19  shows the tread of a real tire having a nail plunged therein; 
         FIG. 20  shows the tread of a real tire that once had a nail plunged therein, after the nail has been removed, leaving a hole; 
         FIG. 21  is a graph plotting a curve showing how the mean radius of the registered tire corresponding to the real tire of  FIG. 20  varies relative to the axis of rotation; 
         FIG. 22  shows the tread of a real tire, in which there can be seen two grooves and one hole; 
         FIG. 23  shows the application of a Hough transform to a two-dimensional image corresponding to  FIG. 22 ; 
         FIG. 24  shows the tread of a real tire, in which the metal mesh of the real tire has become apparent; 
         FIG. 25  shows the color gradients of  FIG. 24 ; 
         FIG. 26  shows the application of a Hough transform to a two-dimensional image of a real tire having flattening formed on its tread; 
         FIG. 27  shows the tread of a real tire that is contaminated; 
         FIG. 28  shows the variation of the color gradient in a two-dimensional image corresponding to a real tire that is not contaminated; 
         FIG. 29  shows the variation of the color gradient in a two-dimensional image corresponding to a real tire that is contaminated; 
         FIG. 30  shows the use of a contour-detection filter in HSV space, implemented on a two-dimensional image obtained from the tread of  FIG. 19 ; 
         FIG. 31  shows training steps based on neural networks and performed on two-dimensional images; and 
         FIG. 32  is a contour detection matrix. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The detection method of the invention is performed below for detecting degradation of a real tire of an airplane wheel. The term “real tire” is used to mean a genuine tire mounted on the wheel, as contrasted to a “virtual” tire such as the theoretical tire and the registered tire that are referred to below. 
     With reference to  FIG. 1 , the detection method starts with a step of acquiring at least a first three-dimensional object  1  that is representative of the shape of the real tire, by using an electronic appliance that includes both a three-dimensional sensor and a photographic sensor. 
     By way of example, the electronic appliance may be a smartphone that is brought up to the real tire by a ground operative. 
     By way of example, the three-dimensional sensor is a stereo camera adapted to perform a three-dimensional scan function. By way of example, the first three-dimensional object  1  is a three-dimensional image. 
     The first three-dimensional object  1  is formed by a set of capture points (also referred to as a “cloud” of capture points). 
     The smartphone acquires and stores the first three-dimensional object  1 . 
     It should be observed that it is possible to use any type of three-dimensional sensor that is capable of obtaining a three-dimensional object that is made up of points and that represents the shape of the real tire. It should also be observed that the electronic appliance could naturally be other than a smartphone. By way of example, a 3D camera connected to a computer could be used. 
     The photographic sensor serves to acquire color that is associated with each capture points. 
     Each capture point is made up of three-dimensional Cartesian coordinates (x, y, z). The capture points represent the scanned portion of the real tire. 
     The recording presents capture points at a density that is high enough for it to be possible to perform accurate calculations on the basis of the capture points. In this example, the density is 60 capture points per square centimeter on average. 
     Below, a fixed reference frame is used, specifically a cylindrical coordinate system, in which the axis of rotation of the real tire is caused to correspond to a straight line having the following coordinates:
 
( r,Θ,z )=(0,0, z )
 
     The position of the center point of the real tire is determined from the set of capture points. The position of the center point of the real tire serves to enable the real tire to be extracted from the first three-dimensional object  1 , and thus serves to eliminate the surroundings of the real tire from the first three-dimensional object  1 . These surroundings include in particular the ground on which the real tire is standing. 
     In a first implementation, the position of the real tire is defined from an estimate of the position of the center point of the real tire. The center point of the real tire is a point that is situated “at the center” of the real tire. The center point is situated where the axis of rotation of the real tire intersects the plane of symmetry of the real tire that is perpendicular to the axis of rotation. 
     The position of the center point is estimated as follows. 
     The capture points of the recording are situated either on a surface of the real tire, or else on a surface of the ground. Each capture point thus forms a vertex positioned on a surface. The recording provided by the three-dimensional sensor produces the (x, y, z) coordinates of each vertex in a rectangular reference frame at life size. The center of this rectangular reference frame is determined by the three-dimensional sensor. 
     In order to simplify calculation, the capture points, or vertices, are normalized in [0, 1] in order to have a reference frame that is intrinsic to the data. This conserves a common scale for all of the capture points, and facilitates defining the normalizations performed in the subsequent calculations. 
     In order to produce the normalized vertices, the following calculation is performed:
 
 P norm:=( P −min( P ))/|max( P )|
 
where:
         Pnorm is the set of normalized vertices having the coordinates (xpnorm, ypnorm, zpnorm), which are normalized in [0, 1]   P is the set of non-normalized vertices, having the coordinates (xp, yp, zp);   min(P) is the minimum value of xp, yp, and zp; and   max(P) is the maximum value of xp, yp, and zp.       

     The three-dimensional sensor also serves, for each vertex, to determine the vectors that are normal to the surface (of the real tire or of the ground). Each normal vector has a norm equal to 1. 
     The normalized vertices and the normal vectors are used to evaluate the position of the center point. 
     With reference to  FIG. 2 , the circle  2  is an approximation to a view of the tread of the real tire as seen in section on a plane perpendicular to the axis of rotation of the real tire. The circle  2  thus defines the surface of the real tire at its tread. The circle  2  has a center  3 . 
     Likewise, lines  4  define the surface of the ground. 
     By definition, each normal vector ni that is normal to the surface of the real tire and that passes through a capture point Pi situated on the circle 2 points away from the center  3  of said circle  2 . The vector −ni that is opposite to the normal vector thus points towards the center  3  of the circle  2 , which is an estimate of the position of the center point. 
     In contrast, the normal vectors that are normal to the surface of the ground and that pass through capture points Pi situated on the lines  4  point in other directions. 
     The position Pi−ni/2 is thus calculated for each capture point Pi. 
     For the great majority of capture points Pi, which are situated on the tread (i.e. on the circle  2  of  FIG. 2 ), these positions lie within a first zone  5  that is close to the center point  3 . 
     For the “interfering” capture points Pi, which belong to the ground on which the real tire stands, these positions lie within a second zone  6  that is remote from the center point  3 . 
     The estimated center point  3  is the geometrical mean of the points situated in the first zone  5  and in the second zone  6 , with this applying on each iteration. 
     The position of the center point is estimated by using an iterative process during which, on each iteration, capture points that do not belong to the real tire (and that thus comprise the capture points belonging to the ground) are eliminated, while capture points that belong to the real tire are conserved, and the estimate of the position of the center point is refined by using the normal vectors of the capture points belonging to the real tire. 
     With reference to  FIG. 3 , a first estimate Pc 1  for the position of the center point is obtained from the normal vectors:
 
 Pc   i =(Σ Pi−Pi−Σ{right arrow over (ni)}/ 2)/ N   points  
 
=(Σ Pi−−{right arrow over (ni)}/ 2))/ N   points .
 
where N points  is the number of capture points under consideration.
 
     The distance between each capture point and the first estimate Pc 1  for the position of the center point is then calculated. 
     Assuming that the ground operative uses the smartphone to acquire mainly the real tire, and assuming that the real tire is spherical in shape, the capture points are concentrated on a given radius. 
     This can be seen clearly in  FIG. 4 . The peak of histogram portion  7  corresponds to the tread of the real tire, while histogram portion  8  corresponds to the surroundings of the real tire, and in particular to the capture points that are situated on the ground. 
     The capture points that do not belong to the peak of histogram portion  7  are then eliminated and the position of the center point is calculated once more. This serves to limit the set of capture points to a zone covering the radius that appears the most frequently. 
     A second estimate PC 2  is thus obtained for the position of the center point. 
     This process is repeated until the following relationship is obtained between the current estimate Pc n  for the position of the center point and the estimate Pc n-1  that was obtained at the preceding iteration:
 
∥ Pc   n   −Pc   n-1 ∥&lt;ε
 
where ε is a predetermined stop threshold, e.g. equal to 0.001 meters.
 
     The final estimate Pc f  for the position of the center point is thus obtained, as can be seen in  FIG. 5 . 
     On the basis of the distances between the capture points and the final estimate Pc f  for the position of the center point,  FIG. 6  shows clearly a histogram portion  9  that corresponds to the real tire and a histogram portion  10  that corresponds to the ground. 
     The capture points belonging to the real tire are then isolated from the capture points belonging to the surroundings of the real tire (and in particular on the ground), with only the capture points belonging to the real tire being conserved. 
     It is possible to define the position of the tread from the spherical shape of the real tire and from the final estimate Pc f  for the position of the center point. This is based on the principle that all of the capture points of the tread are situated at a constant distance R from the center point. 
     The position of the real tire is thus obtained. 
     In a second implementation, and with reference to  FIG. 7 , the position of the real tire is determined by performing a data partitioning method to distinguish between first capture points  11  belonging to the real tire and second capture points  12  belonging to the ground. 
     Data partitioning (also known as data “clustering”) is an analysis method that serves to subdivide a dataset into a plurality of sub-sets that share common characteristics. 
     When detecting the position and the orientation of the real tire in the set of capture points, it is postulated that the portion of the real tire that is in contact with the ground cannot be captured. This implies some form of “cut-off” between the first capture points  11  and the second capture points  12 . 
     In this example, the data is partitioned by using a DBSCAN algorithm (for “density-based spatial clustering of applications with noise”). 
     As can be seen in  FIG. 7 , the first capture points  11  belonging to the real tire are clearly distinguished from the second capture points  12  belonging to the ground: this enables the position of the real tire to be determined effectively. 
     With reference to  FIGS. 8 and 9 , once the position of the real tire  13  has been estimated, the first three-dimensional object  13  is registered relative to a theoretical tire  14  in order to obtain a second three-dimensional object  15  that forms a “registered” tire. The second three-dimensional object  15  is made up of a set of registered points. 
     To do this, the number of capture points is initially reduced by sampling. 
     Thereafter, on the basis solely of a portion of the tread and of a portion of the sidewalls of the real tire, a registration algorithm is applied for registering relative to a cloud of theoretical points that correspond to the theoretical tire  14 . 
     Registration serves to determine the axis of rotation of the real tire. The theoretical tire  14  is created specifically for registering purposes. In particular, the theoretical tire  14  presents dimensions and an orientation that are known. Use is made in particular of input data including the axis of rotation and the center point of the theoretical tire  14 . 
     Registration makes use of a registration algorithm based on Euclidean transformations. 
     Euclidean transformations (rotation, translation) are performed towards a known reference frame, which do not transform the object. Euclidean transformations are defined by:
 
 T ( v )= R v+t,  
 
where:
         v is a vector of the object;   R is an orthogonal transformation; and   t is a translation vector.       

     Registration consist in finding the transformation that serves to minimize the difference between the cloud of capture points and the cloud of theoretical points. In this example, use is made of an algorithm of the iterative corresponding point (ICP) type. 
     There follows a description of the processing performed on the second three-dimensional object  15  forming the registered tire. 
     This processing consists in transforming the second three-dimensional object  15  forming the registered tire so as to obtain one or more two-dimensional objects, and then in analyzing the two-dimensional object(s) in order to detect degradation of the real tire. 
     With reference to  FIG. 10 , in a first implementation, the transformation consists initially in slicing the second three-dimensional object  15  on planes perpendicular to the axis of rotation Z of the registered tire in order to obtain a number n of thin three-dimensional slices T 3   d   1  . . . T 3   d   i  . . . T 3   d   n . The thickness e of each three-dimensional slice T 3   d   i  is of millimeter order. 
     A number n of the three-dimensional slices T 3   d   i  is obtained that make up the registered tire when they are stacked together along the axis of rotation Z of the registered tire. 
     The sum of the thicknesses of all of the three-dimensional slices T 3   d   i  is thus equal to the width of the tread of the registered tire. 
     The thickness of each three-dimensional slice T 3   d   i  is very small compared with the radius of the registered tire. 
     Each three-dimensional slice T 3   d   i  is thus approximated by a two-dimensional slice T 2   d   i , of zero thickness. The two-dimensional objects that result from the transformation thus comprise the two-dimensional slices T 2   d   i . 
     Each two-dimensional slice T 2   d   i  is thus generally in the shape of a circle if the smartphone acquires the entire circumference of the real tire, or in the shape of an angular portion of a circle if the smartphone acquires only an angular portion of the circumference of the real tire. 
     A radius r i (α) is then calculated for each two-dimensional slice T 2   d   i . The radius r i (α) is a function of an angle α about the axis of rotation z. The radius r i (α) is not necessarily constant as a function of the angle α, since the wear of the real tire is not necessarily uniform around the entire circumference of the two-dimensional slice T 2   d   i . 
     Variation in the radius r i (α) is then investigated by varying i in order to detect any difference in radius of the registered tire along the axis of rotation Z (i.e. across the width of the tread), and thus to detect any degradation of the real tire. 
     The differences between the radii r i (α) for varying i should then present variations that are regular, representative of the presence of structures of the real tire, and the depths of the structures can then be quantified. 
     The presence of grooves in the tread of the real tire should thus be perceptible, which grooves are presently used for visually evaluating the wear of the real tire. 
     Naturally, this analysis may be performed at constant α, or else by causing the angle α to vary over a defined angular interval. 
     It is also possible to calculate the mean the radius r i  of each two-dimensional slice T 2   d   i . Variation in the mean radius r i  is then investigated as a function of i, i.e. along the axis of rotation z. 
     Variation in the radius r i (α) with varying angle α is also investigated in order to detect angular variations in the radius of the registered tire, and thus in order to detect degradation of the real tire. 
     For a given two-dimensional slice T 2   d   i , the radius r i (α) should normally present very little variation as a function of the angle α, which implies wear that is regular. 
     If this is not so, then the coordinates (r, Θ, z) of the capture points serve to provide information about the presence, the shape, and the depth of an anomaly. 
     One or more parameters are then analyzed from among the variation of the radius r i (α) as a function of i, the variation of the radius r i (α) as a function of α, and the variation of the mean radius r i  as a function of i. By studying these radius variations, it is possible to determine an unexpected change, such as a localized or continuous reduction of this radius. 
       FIG. 11  shows the tread  20  of a real tire  21  that presents normal wear. It can be seen that the four grooves  22  are worn symmetrically and regularly around the axis of rotation of the real tire  21 . 
     The curve  23  in  FIG. 12  is a plot as a function of the value of i showing variation in the mean radius r i  of the registered tire that corresponds to the real tire  21  of  FIG. 11 . 
     From the curve  23 , there can be seen four curved portions  24 , each corresponding to a small mean radius r i  and to a respective one of the four grooves  22  present in the tread  20  of the real tire  21  (on the graph, the grooves  22  are represented by bold lines showing the positions of said grooves  22  across the width of the tread  20 ). 
     It is thus possible to detect the positions of the grooves  22  on the tread  20  and to evaluate the depth of each groove  22 . 
     Evaluating the depth of each groove  22  can make it possible to detect the presence of degradation of the tread  20 . 
     Detecting the positions of the grooves  22  serves to position the degradation on the tread  20 . 
     In this example, the tread  20  does not present any abnormal degradation. The wear of the real tire  21  is normal and symmetrical, and each of the grooves  22  has a depth that is more or less constant. 
       FIG. 13  shows the tread  26  of a real tire  27 , which tread presents wear that is abnormal, asymmetrical, and poorly distributed across the tread  26 . 
     The curve  28  of the graph in  FIG. 14  shows that the grooves  29  and  30  present depths that are very small compared with the other grooves. The mean radius of the registered tire varies very little in these grooves, which is representative of wear that is excessive and not symmetrical, since the wear relates to two grooves both situated on the same side of the tread  26 . 
       FIG. 15  shows that cupping  32  has formed in the tread  33  of a real tire  34 , between the groove  35  and the groove  36 . 
     The curve  38  in  FIG. 16  shows that the mean radius decreases in the curved portion  37  that lies between the two grooves  35  and  36 , which is representative of the presence of cupping. 
     Clear or repeated variations in the mean radius may specifically be indicative of a surface presenting anomalies of the following types: cupping, bulging, abnormal excrescences, tearing, zig-zags, cracking, etc. 
       FIG. 17  shows the presence of flattening (i.e. a flat spot)  40  present on the tread  41  of a real tire  42 . This flat spot  40  is a result of braking without the real tire  42  rotating. 
     The flat spot  40  can be seen in the curve  45  of the graph of  FIG. 18 . Over a zone that is relatively flat, curve portion  46  presents a succession of small-amplitude peaks and troughs that are representative of the presence of the flat spot. 
     A curve portion of reduced mean radius cannot be seen: the grooves  47  are not detected because of the flat spot  40 . 
     With reference to  FIG. 19 , it is also possible to detect the presence of a foreign body in the outer layer of the tread  50  of a real tire  51 . By way of example, the foreign body is a nail  52  plunged into the tread  50 . The presence of the nail  52  is detected by identifying a localized change in the mean radius of the registered tire within a given interval:
 
[( r,Θ,z ),( r+δ 1,Θ+δ2, z+δ 3)]
 
where [|δ1|, |δ2|, |δ3|] represent the dimensions of the emergent portion of the nail  52 .
 
     It should be observed that it is also possible to make use of color data in order to determine a localized difference exceeding a certain threshold, providing the foreign body presents a color or a brightness that is significantly different from the rubber of the real tire. 
     It is also possible to envisage using a specific sensor, e.g. an ultrasound sensor, in order to detect a change of material that is representative of the presence of a foreign body or indeed of the metal mesh of the tire becoming apparent. 
     It is also possible to detect an anomaly by analyzing a temperature gradient by using a suitable thermal camera, possibly incorporated in the smartphone. 
       FIG. 20  shows the tread  54  of a real tire  55  that has had a nail plunge therein, thereby forming a hole  56 , with the nail subsequently becoming extracted from the tread  54 . 
     It can be seen from the curve  57  of the graph in  FIG. 21  that the mean radius of the registered tire decreases considerably in the curve portion  58  between the two grooves  59 , with this being representative of the presence of the hole formed by the nail. 
     As described above, in the first implementation, the transformation of the second three-dimensional object of the registered tire produces two-dimensional objects that are two-dimensional slices T 2   d   i  of the registered tire. In a second implementation, the transformation is a two-dimensional projection of the three-dimensional object  15 . The two-dimensional objects include a two-dimensional image of the tread of the registered tire as obtained by performing said two-dimensional projection. 
     The two-dimensional objects also include respective two-dimensional images of the right sidewall and of the left sidewall of the registered tire. In order to obtain the images of the sidewalls, the shape of the sidewalls means that no two-dimensional projection is needed. 
     In order to perform a two-dimensional projection, use is made of cylindrical coordinates together with the following formulae:
 
 x=R ·(λ−λ0)
 
 y=R ˜(tan(ϕ))
 
λ corresponds to a current point of the projection, and λ0 corresponds to a point set as the origin of the reference frame.
 
     As mentioned above, colors are also available in association with the capture points in the set of acquired capture points stored by the smartphone. 
     The two-dimensional images is analyzed by analyzing variation in a color gradient of the two-dimensional image and/or by applying a Hough transform to the two-dimensional image. 
     Analyzing color gradient variation serves to detect abnormal degradation that results in abnormal variation of the colors of the tread, while the Hough transform serves to detect contours, and thus to detect abnormal degradation that results in abnormal portions in relief on the tread. 
       FIG. 22  shows the tread  60  of a real tire  61  on which there can be seen two grooves  62  and a hole  63 . Two-dimensional projection is applied to the second three-dimensional object in order to obtain a two-dimensional image of the tread. The Hough transform is then applied to the image in order to obtain the image of  FIG. 23 . 
     It is considered that each groove is defined by two lines in a two-dimensional plane, each line corresponding to a respective edge of said groove. The Hough transform thus makes it possible to detect the grooves  62 , each of which is defined by two lines  64 , and also to detect the hole  63 . 
       FIG. 24  shows the tread  66  of a real tire  67 , with the metal mesh  68  of the real tire  67  being visible. The metal mesh  68  is visible because of excessive wear of the real tire  67 . By way of example, the excessive wear may be due to an excessive amount of heat being given off over a portion of the real tire  67  as a result of a braking problem, a runway that is wet or frozen, etc. 
       FIG. 25  shows variation in the color gradient in the two-dimensional image. 
     A zone  69  can be identified in which abnormal color differences are to be observed, which in this example are representative of the metal mesh  68  becoming apparent. 
     With reference to  FIG. 26 , a tread may include a flat spot. The flat spot is characterized by a circular shape on the tread. 
     The two-dimensional image of the tread is produced, the two-dimensional image is then processed in order to remove noise that might impede a detection, and then the Hough transform is applied to the two-dimensional image. More specifically, in this example, a circle Hough transform (CHT) type algorithm is applied. 
     The Hough transform serves to obtain a shape  70  that is representative of a flat spot. 
     With reference to  FIG. 27 , the tread  71  of a real tire  72  may also be degraded by wear associated with heat being given off or with contamination by a corrosive liquid (oil, brake fluid, etc.). 
     In the event of damage of this type, variation of the color gradient is used to identify zones that present granularity that is abnormal. Since the real tire  72  is made out of a single material, it can be assumed that if the real tire  72  is in a normal state, then any observed color gradient will be simple, and associated solely with external factors such as exposure to the sun. In contrast, the presence of discontinuity in the linearity of the color gradient, or indeed the presence of zones that present colors that differ from the colors of the remainder of the real tire and that are not associated with exposure to external light, are signs of degradation of the rubber layer of the tread  71 . 
       FIG. 28  shows how the color gradient varies when the real tire is not contaminated.  FIG. 29  shows how the color gradient varies when the real tire is contaminated. 
     The differences between these two figures showed clearly that color gradient variation is a parameter that is relevant for detecting contamination of a real tire. 
     With reference to  FIG. 30 , by using a filter for detecting contours in hue-saturation-value (HSV) space, it is possible to detect a foreign body in the real tire, and also a groove of the real tire. 
     The shape  75  corresponds to the nail  52  in  FIG. 19 , while the shape  76  corresponds to the groove situated immediately to the left of the nail  52  in  FIG. 19 . 
     The two-dimensional images obtained by two-dimensional projection of the second three-dimensional object  15  of the registered tire can also be analyzed by training neural networks on the basis of images of the real tire in good condition and of images of various kinds of degradation that are to be found. 
     Use is made of a database having a very large amount of data constituted by similar two-dimensional images acquired from a very large number of real tires. 
     Since the two-dimensional projections are performed in a standardized manner, the two-dimensional images can be compared effectively, while eliminating the differences that are due to the ways in which the data is acquired (and thus differences that are not relevant for analysis). 
     During a preliminary stage, the data needs to be classified manually into a plurality of distinct categories. 
     Convolutional neural networks (CNN or CovNets) are used to provide the prediction algorithm. 
     With reference to  FIG. 31 , for a given two-dimensional image, training comprises an initial step of convoluting the two-dimensional image with a predefined matrix (step E 1 ). In this example, the contour detection matrix of  FIG. 32  is used. 
     Thereafter, a correction function is applied. 
     By way of example, the function used is of the rectified linear unit (ReLu) type.
 
 f ( x )=max(0, x );
 
or else a hyperbolic tangent function:
 
 f ( x )=tan  h ( x );
 
or else a saturating hyperbolic tangent function:
 
 f ( x )=|tan  h ( x )|
 
or else a sigmoid function:
 
 f ( x )=(1+ e   −x ) −1 .
 
     Thereafter, a pooling (or, commoning) operation is performed to reduce the size of the two-dimensional image (step E 2 ). 
     It is then possible to process each of the zones of the two-dimensional image in individual manner via an artificial neural network (step E 3 ). 
     The last step (step E 4 ) consists in applying the Softmax formula: 
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     The input layers of the neural network are thus converted into a distribution probability. It is then possible to classify the two-dimensional image data and to detect abnormal degradation in the two-dimensional images. 
     It is also possible to implement neural network training directly on the second three-dimensional objects of the registered tire. 
     In a first step, once again, the data needs to be classified manually into a plurality of distinct categories. 
     In order to prepare the prediction algorithm, use is made likewise of convolutional neural networks (CNN or CovNets). 
     It should be observed at this point that, when degradation of a real tire is detected, a warning message is generated. The warning message may be issued by the smartphone for the attention of the ground operative, or else it may be transferred from the smartphone to a server that centralizes warning messages coming from a large number of real tires (e.g. all of the real tires used by an airline). 
     The warning message contains means for identifying the tire in question (e.g. a reference of the tire or its position on the airplane), optionally together with the type of the degradation and its position on the tire. 
     The set of capture points together with the results of the analyses performed are stored, and they can be used for the purposes of verification and data analysis on a large scale. Such analysis may reveal correlations between excessive deterioration of tires and particular runways, particular takeoff, landing, or taxiing situations, particular weather, the way certain pilots pilot airplanes, etc. 
     Naturally, the invention is not limited to the implementations described, but covers any variant coming within the ambit of the invention as defined by the claims.