EP2561479A1

EP2561479A1 - Method of monitoring the appearance of the surface of a tyre

Info

Publication number: EP2561479A1
Application number: EP11707399A
Authority: EP
Inventors: Guillaume Noyel
Original assignee: Michelin Recherche et Technique SA Switzerland; Compagnie Generale des Etablissements Michelin SCA; Michelin Recherche et Technique SA France
Current assignee: Michelin Recherche et Technique SA Switzerland; Compagnie Generale des Etablissements Michelin SCA; Michelin Recherche et Technique SA France
Priority date: 2010-04-19
Filing date: 2011-03-04
Publication date: 2013-02-27
Also published as: US9002093B2; FR2959046B1; BR112012025402A2; FR2959046A1; CN102844791B; CN102844791A; US20130129182A1; JP2013532315A; WO2011131410A1; JP5779232B2

Abstract

Method of detecting an anomaly on the surface of a tyre comprising the following steps in the course of which: A - the image of a given anomaly present on the surface of at least one tyre is produced, B - a multivariate image of the said surface, in which each pixel is represented in the form of a pixel vector, is constructed, with the aid of a collection of filters, in a filter space, the components of each pixel vector having a value corresponding to the value of this pixel in the image transformed with the aid of each of the filters of said collection C - with the aid of a linear function, this multivariate image is transformed from the filter space into a spectral space of given dimension whose variables are the filters or combinations of filters of said collection, so as to form a spectral image, D - a classifier is constructed by determining, for this anomaly, those zones, representative of the spectral space, in which the points of the spectral image, of said anomaly transformed into said spectral space, lie in a statistically representative manner.

Description

METHOD OF CONTROLLING THE APPEARANCE OF THE SURFACE OF A

PNEUMATIC

[001] The invention relates to the field of tire manufacturing, and more particularly the control of the external or internal appearance of tires in progress or at the end of the manufacturing process, in order to determine their conformity. relative to control references established for the purpose of the use to be made of said tire. [002] The increase, at constant cost, computer computing power, now allows the development on an industrial scale of automatic control means intended in particular to assist the operators responsible for visual control. These means make extensive use of image processing techniques whose performance, in terms of speed of analysis and definition, largely depends on the computing power used. [003] The methods used to perform these treatments consist, as a rule, in comparing an image in two or preferably in three dimensions of the surface of the tire to be inspected with a reference image in two and preferably in three dimensions of the surface of said pneumatic. For this purpose, it is sought to match, the image or the surface of the tire to be inspected and the image or the reference surface, for example by superimposing them, and the manufacturing anomalies are determined by analyzing the differences between the two images or both surfaces.

[004] However, these methods do not allow the detection of surface defects that do not have a significant impact on the geometry of said surface.

[005] Also, the manufacturers are committed to developing image analysis methods, complementary to the methods mentioned above, able to bring out anomalies present on the surface of the envelope. These anomalies whose dimensions are reduced, are manifested by a particular coloration, an abnormal shape, or a particular and unusual spatial distribution, and are embedded in the overall image of the tire surface in which they can merge. In addition, their appearance is random on the surface of one tire or tire to another. This results in a scarcity of significant information for determining digital protocols. [006] Thus, the publication EP 2 034 268 uses the wavelet technique to detect repetitive structures such as exposed ply son on the inner surface of the tires.

[007] The publication EP 2,077,442 proposes a method for selecting filters able to digitally process the image of the surface of a tire and sensitive to a particular defect. This filter selection method uses known texture analysis methods, and proposes to select the filters by a so-called genetic selection method. This method consists in statistically varying a collection of previously chosen filters, and measuring using a cost function, the sensitivity of this modification on the detection of a previously identified defect, compared to the collection. initial filters.

[008] This method, which requires a long and expensive learning phase, however, has the disadvantage of not giving certainty on the convergence of these successive iterations on the one hand, and the elimination of local optimums of somewhere else.

The subject of the invention is a method of digital image processing of the surface of a tire by texture analysis, in which a combination of filters capable of identifying the signature of the image of a film is selected. anomaly present on the surface of the tire and which overcomes the disadvantages mentioned above.

[010] This method of detecting an anomaly on the surface of a tire comprises the following steps in which:

A - the image is taken of a given anomaly present on the surface of at least one tire,

B - using a collection of filters, one builds, in a space of the filters, a multivariate image of said surface, in which each pixel is represented in the form of a pixel vector, the components of each pixel vector having a value corresponding to the value of this pixel in the transformed image using each of the filters of said collection

C - using a linear function, this multivariate image is transformed from the filter space into a spectral space of given dimension whose variables are the filters or filter combinations of said collection, to form a spectral image, D - a classifier is constructed by determining, for this anomaly, the representative areas of the spectral space in which the points of the spectral image of said anomaly transformed in said spectral space are statistically representative. [011] This numerical analysis method makes it possible to statistically identify the zones of a space in which the image of a given anomaly transformed using a collection of filters are localized.

[012] The method of detecting an anomaly on the surface of any tire on the surface of which it is desired to detect the presence or absence of said anomaly then comprises the operations in which:

a digital image is made of all or part of said surface of said tire to be sorted,

the multivariate image of the tire to be sorted, of the image of the tire to be sorted using the filter collection, is determined in the space of the filters; the spectral image of the tire to be sorted is formed, by transforming, using the linear transformation, the multivariate image of the tire to be sorted, and,

the location of the points of the spectral image of the tire to be sorted in the spectral space is analyzed with respect to the zones of the spectral space representative of the anomaly identified with the aid of said classifier. [013] Preferably, during step D, the classifier is constructed using a method of linear discriminant analysis type, said representative areas being delimited by hypersurfaces of said factor space.

[014] According to a first variant embodiment of the invention, it is then entirely possible to implement the method according to the invention by considering that the space of the filters forms said spectral space and that the spectral image , corresponds to the multivariate image, obtained from an initial collection of filters.

[015] However, the implementation of the method under these conditions may present some difficulties of implementation because of the large number of data to be handled, and also because of the absence of common metrics between the various directions of the spectral space leading to a sometimes difficult statistical interpretation during the construction of the classifi- cator. [016] Also, it is preferable to try to construct a metric adapted to statistical analysis in the spectral space, and to reduce the number of variables by judiciously selecting the axes of the spectral space and the filters of the initial collection. . [017] The determination of the adapted metric consists, after step B and before starting step C

- to search by means of a data analysis method a factorial space of dimension less than or equal to the size of the space of the filters, in which the transformed variables are decorrelated or independent, and

to determine the linear transformation making it possible to go from the space of the filters to said factor space,

[018] To improve the construction of the classifïcateur we can usefully, during step A, the image of a given anomaly present on the surface of a series of several different tires, allowing during the step B to determine the multivariate image of each of these images and, in step C, to construct a single multivariate image by assembling the multivariate images obtained from this series of images.

[019] Preferably, the data analysis is carried out according to a principal component analysis method, or according to a correspondence factor analysis method, or according to an independent component analysis method. [020] This series of operations greatly improves the construction of the classifier and it is also possible, according to a second embodiment of the invention, to implement the method, in which the factorial space forms said spectral space and in which the spectral image is obtained by the transformation in the factorial space, using the linear transformation, of the multivariate image, obtained from the initial collection of filters.

[021] When the number of filters in the initial collection remains too large it may be desirable to reduce the number of filters and reduce the size of the spectral space to lighten digital processing.

[022] Also, at the end of step C, using a first selection method, it is possible to usefully determine the most relevant factorial axes with respect to the multivariate image transformed in the factorial space. using the linear transformation. We then limit description of said multivariate image at the coordinates of said image, expressed on these axes alone, whose number is less than the number of axes of the factor space, so as to obtain a reduced factor space.

[023] Preferably, the first method of selecting the factorial axes consists in preserving the factorial axes whose sum of the inertias with respect to the point cloud of the multivariate image of the anomaly transformed in the factorial space, represents a given percentage of the inertia of all the axes relative to said cloud of points.

[024] Alternatively, the first method of selecting the factorial axes consists in preserving the factorial axes having the highest signal-to-noise ratio contained in the factors associated with the pixel vectors of the multivariate image transformed in the factorial space relative to to said axes considered.

[025] After determining the relevant factorial axes, this reduction and simplification step is continued by projecting the initial collection of filters into said reduced factor space. Then, using a second selection method, we determine the filters of the initial collection projected in the factorial space whose vectors are farthest from the origin of the factorial axes, so that the number of filters of the initial collection is reduced, and we recalculate the coordinates of the image in the reduced factor space.

[026] Preferably, the filters are selected whose quadratic sum of the distances at the origin represents a given percentage of the quadratic sum of the distances with respect to the origin of the set of filters of the initial collection projected in said reduced factor space, or whose square of the distance originally divided by the sum of the squares of the distances at the origin of all the filters of the initial collection projected in said reduced factor space is greater than the inverse of the number of filters (l / L).

[027] According to a third variant embodiment of the invention, the method in which the reduced factor space forms said spectral space and in which the spectral image is obtained by the transformation in the reduced factor space is then applied. , using the linear transformation, the multivariate image, obtained from the reduced filter collection.

[028] The invention also comprises a device for controlling and detecting an anomaly on the surface of a tire comprising: lighting and shooting means capable of producing the image of the surface or of a portion of the surface of a tire, and

- suitable calculation means

o storing for one or more given anomalies one or more collections of morphological filters, determined according to one of the implementation variants of the invention described above,

transforming an image of the surface of the tire to be sorted into a spectral image by means of a linear transformation (ζ) according to one of the implementation variants of the invention described above,

o to determine the presence or absence of anomaly on the surface of the tire to be sorted using a classifi- cator according to one of the implementation variants of the invention described above.

[029] The following description is intended to provide detailed guidance on the implementation of the method and is based on Figures 1 to 3, in which:

FIG. 1 represents a two-dimensional gray level image,

FIG. 2 represents a pixel vector in a multivariate image,

FIG. 3 represents a channel of a multivariate image,

FIG. 4 represents a multivariate image obtained by juxtaposing the responses of the filters,

FIG. 5 represents the multivariate image in the reduced factor space,

FIG. 6 represents an illustration of the mode of selection of the filters in the factorial space,

FIG. 7 represents a simplified diagram of the main steps of the method according to the invention.

[030] The detection method according to the invention comprises two distinct stages during which, successively, a factor space, a transformation function and a classifier are determined which are able to reveal the presence or the absence of the anomaly and that the it will be assimilated to a learning phase, and a detection step itself, detection of said anomaly on the surface of any tire to be sorted.

[031] The learning phase begins with the selection of at least one tire having a given anomaly visible on its surface. This type of anomaly may be, for example, a molding defect, a grease stain, a reinforcement gap or creep. erasers placed under the reinforcing plies, a foreign material, etc. A two-dimensional black-and-white image of said anomaly is then produced.

[032] As will be seen later, it is possible to make this learning phase more robust, by producing a series of two-dimensional images of said anomaly, present on the surface of several different tires.

[033] It would also be entirely possible to implement the invention, working from the color image of the tire surface. However, this possibility offers a fairly small scope due to the relatively monochrome nature of the tires, generally black. But it is not excluded to think that this situation can change, in which case it would be appropriate to adapt accordingly the nature of the filters of the initial collection, taking into account the color variations.

[034] As a general rule, the two-dimensional image of the surface of a tire is a gray-scale image, as represented in FIG. 1, in which, at any point or pixel x = (i, j) of the plane (E = [l, 2, ...] x [l, 2, ...], with ² ) represented as a point grid (that is, a 2D array), is associated with a value f {x) cz T with T c "for grayscale images Generally, T consists of integer values between 0 and 255 with:

The white corresponds to the value 255, and the black to the value 0. The other values (i.e. the intermediate gray levels) are between these two values. It would also be possible to make a color or multispectral image of the tire surface.

[035] The implementation of the invention can also be done from the color image of the tire surface with an adaptation not forming part of the present description, calculations explained below.

[036] We then select a collection of filters, more commonly referred to as morphological filters. A morphological filter, in the sense of the present description, is defined as a function that makes it possible to transform an image / grayscale image into another image F (f). The starting space of the filter is therefore the set of values of the image of E in T, A (E, T)

The response image of the filter can also be seen as a function which, at a pixel of E associates a gray level:

[037] Among the filters to be used, it is possible to select, by way of nonlimiting examples, morphological filters such as series of morphological openings and closures of increasing sizes, dilations or morphological erosions, or filters of the type wavelets that analyze the position and frequency of the objects composing the image, or curvelets that analyze the position, the frequency and which adapt to the discontinuity of the objects composing the image.

[038] A morphological filter is thus defined as a growing and idempotent transformation on a lattice. Here we mean by lattice a partially ordered set in which we can order some of its elements, and in which each pair of elements has an infimum (greater of the minor) and a supremum (smaller of the majors). A transformation ψ is increasing if it preserves the order relation between the images, or that the function ψ is increasing when:

V, g, f≤g => ψ (ί) ≤ψ ( _§ ).

[039] A transformation ψ is idempotent, if the application of this transformation twice in succession to an image is equivalent to applying it once: ψ is idempotent = ψ οψ = ψ

[040] A structuring element is a (small) set used to probe the studied image, it can be seen as a tool that would erode (ie remove material) or dilate (ie add material) to a picture. Thus, the expansion of the function / (ie the gray-scale image) by a structuring element B, denoted δ ₅ (), is the function that gives to every pixel xe E the maximum value of the image / in the observation window defined by B such that: δ _Β (f) (x) = sup {/ (x - y), y GB}.

[041] And in the same way, the erosion of the function / (ie the grayscale image) by the structuring element B, denoted δ ₅ (/), is the function that gives to every pixel xe E the minimum value of the image / in the observation window defined by B:

5 _B (f) (x) = M {f (x)

[042] A morphological opening by addition y _B is defined as the composition of an erosion ε _Β with a dilation δ _Β for a structuring element B such that:

Υ _Λ ω = δ _Λ ^ο ε _Λ ().

[043] Similarly, a morphological closure by adding φ ₅ is defined as the composition of an expansion δ _Β with erosion ε _Β for a structuring element B such that:

Φ, (/) = ε _Λ ο δ _Λ (/). [044] A wavelet is a summable square function on Euclidean space ", most often oscillating and of zero mean, chosen as a multi-scale analysis and reconstruction tool.

[045] It will be observed that the theoretical definitions of the different morphological filters commonly used in this type of analysis are not limiting. Moreover, the declination of the parameters of these transformation functions can generate collections of filters comprising several tens or even hundreds of different filters. A fortiori when the filters take into account the color variations. It may therefore be useful, as will be seen later, to simplify and select the most suitable filters to give relevant information in the presence of an image containing the anomaly that is to be revealed.

[046] The next step is to transform each of these images using the filters from the initial collection. We then obtain as many images as filters corresponding to the transformation of the initial image by each of the filters of the initial collection.

[047] By superimposing these images, we construct a multivariate image, in which each pixel contains several values, assimilated to a vector of values as schematically represented in FIG. 2. - E < ² , T c and T ^L = Τχ Τχ · · · χΤ, where L is the dimension of the image space T ^L , or space of the filters,

- x = x. \ z e {1, 2, · - ·,} is the spatial coordinate of the vector pixel f (x.), P is the number of pixels in E,

- /. \ j G {1, 2, · · ·, £} is a channel (L is also the number of channels), shown in gray in Figure 4,

- f _j i ^x i) ^is ^a pixel value vector f (x) on the channel /.. .

[048] The multivariate images are thus discrete functions, with typically several tens or hundreds of channels, or variables or spectral bands as shown in FIG. 3. Each pixel of a multivariate image is a vector whose values are associated with an index j corresponding to filter responses. The components of each pixel vector have a value corresponding to the value of this pixel in the image transformed using each of the filters of said collection. The arrival image expressed in the filter space is then composed of vectors (the pixel vectors) whose variables are the filters of the initial collection.

[049] In the case of the present invention, the multivariate image is obtained as being the juxtaposition of the responses to each of the filters forming the initial collection of filters. (F ₁ (f), F ₂ (f), ..., F _L (f)). Which gives in the form of an equation:

F '.., (x))

, ..., [F _L (f)] (x))

[050] The multivariate image, as illustrated in FIG. 4, is obtained by a series of filters applied to the grayscale image. Sometimes we speak of a stack of images which is the response series of each of the filters forming the initial collection.

[051] As indicated above, it is then possible, from this stage, to construct a classifier, according to a method which is explained in detail later in the present description, by considering the space of the filters as the space spectral, and by assimilating the multivariate image obtained with the help of the initial filter collection to the spectral image. The transformation ζ of step C is then reduced to a simple identity. However, the application of the method according to the invention to this stage of the data analysis process is reserved in the case where the number of filters of the initial collection is reduced and where it is not considered useful to proceed to simplification phases that have become unnecessary.

[052] And when the number of filters of the initial collection is important, it should be noted that in the absence of metric and in the absence of independence of the axes of representation of the image in the space of the filters considered as the spectral space, the statistical analysis implemented during the construction of the classifier can sometimes lead to erroneous interpretations.

[053] It is then recommended to continue the data processing by looking for a factorial space of dimension N less than or equal to the dimension L of the initial space according to the data analysis method used, and in which the variables, here combinations of filters, are the most independent possible between them. This is equivalent to finding the maximum variance between the variables associated with each filter.

[054] We then determine a linear transformation ζ making it possible to go from the initial space or space of the filters to the factorial space, and we apply this transformation to the multivariate image F ^f (x) = {F (x), F ( (X), ..., F [(X)) obtained previously to obtain a multivariate image of the anomaly c '(x) = (c' (x), c '{(x), ..., c '^ (x)) expressed in this new factor space.

[055] The starting image contains very many channels (or axes), more or less relevant, so it is necessary to select those that are most relevant for the detection of anomalies. The advantage of such a transformation is to reduce the size of the image so as to reduce the calculation time, while retaining the information useful for further processing. Since, as a general rule, a single filter does not make it possible to discriminate an anomaly from the rest of the image, the object of the analysis is to determine the filter combinations that will have an answer with respect to the presence or the absence of said anomaly. [056] There are different methods of Data Analysis. As a non-limiting example, Principal Component Analysis (PCA), Correspondence Factor Analysis (CFA), Independent Component Analysis (ACI), which includes calculation algorithms better known under their names, can be cited as non-limiting examples. Anglo-Saxon acronyms such as the Fast ICA algorithm, the Joint Approximate Diagonalisation of Eigenmatrices (JADE) algorithm or the Independent Factor Analysis (IFA) algorithm, the use of which may also be considered . [057] All these methods, which are part of the general knowledge of the person skilled in the art, seek to make the variables, understood as the direction vectors of the factor space, the most independent possible between them. Independence is here understood in the statistical sense of the term.

[058] In the case of the Independent Component Analysis, the variables are actually independent, whereas in the other cases they are simply decorrelated according to the metric associated with the method used. This metric corresponds to the inverse metric of the variances for the Principal Component Analysis, or to the Chi-Square metric (χ ² ) for Factorial Correspondence Analysis.

[059] Here will be described in more detail the implementation of the Principal Component Analysis method. Indeed, one of the advantages of the Principal Component Analysis is that the high variance directions contain more information than the low variance ones, assuming that the noise is evenly distributed, which is tantamount to considering that the directions of high variance have a high signal-to-noise ratio. In addition, it is possible for practical metric reasons to center and reduce the variables of this Euclidean type space.

[060] To determine this factor space, we note F, the contingency matrix P L representation of the multivariate image F. F is composed of P lines representing the vector pixels (i.e. individuals) and L columns (i.e. the channels or variables) corresponding to the number of filters in the initial collection. We allow for matrix calculations to use the following notation:

^F j F

The vector-lines (ie vector-pixels or individuals) of F are the elements of T ^L and are assimilated to vectors of " ¹ where L represents the number of filters of the initial collection (^ (^ ₂ (... ( /)): F, = (F _n , ..., F _u , ..., F _iL )

with F _; = F (x _i ).

The column vectors (i.e. channels or variables) of F are elements of ^"F :

^ = (^., ..., ^, ..., ^)

In index notation, the contingency table associated with the image Î ^f can also be written:

^F = K; } j " ^■ ==! l ^■ -L

[061] It will be observed that, when the pixels F i (x _t ) of the multivariate image are stored in the contingency matrix, the spatial arrangements between pixels are lost. That is to say, we are only interested in the spectral response of each of the pixels.

[062] As a variant, when it is desired to increase the quality of the learning phase, it is possible, as we have seen above, to use the images of an anomaly of the same type, performed on a series s of different tires.

[063] During step B, the multivariate image of each of these images is constructed as before ¥ ^fcql (x) = (F ₁ ^fcql (x), F ₂ ^fcql (x), ..., F _L ^fcql (x)), x), ..., F ^cqs (x)) by stacking the filter responses of the initial collection of filters

(^ (^ ₂ (... (/)).

[064] Then we build the contingency table of each of these imag

U IL

-pfcql _ F ^fcQl F 'c ^f g ^c i ^Q J ^l . Fi ^ca \

[065] The construction of the contingency table F is then done by vertically concatenating the contingency tables of each of the images, simply storing the tables of contingencies one below the other. where the index P = s =, lί '

[066] It will be observed here that the contingency tables of the different images of the anomaly have the same number of columns because they are the product of the transformation of an image by the same initial collection of filters. However, these images may not have the same number of pixels, and consequently, the different contingency tables associated will not have the same number of lines.

[067] It will also be noted that the other methods of data analysis cited above, all of which are aimed at finding independent variables in a large space comprising scatter plots, originate from the same way and impose the determination of a contingency matrix. These methods are distinguished from each other, as has been mentioned, mainly by the metrics they use.

[068] The remainder of the processing of the contingency table is then the same, depending on whether one considers a single image of a given anomaly, or several concatenated images of said anomaly taken from a series of different tires. [069] The matrix of the transformed data C is then defined in the same way:

CC. ··· vs.

PI ^ Pj ^ 1

We then write X = F -F the matrix of the centered variables, i.e. replace the columns F. of F by F. - F. with F. the average of F..

[070] A linear application U is sought, which transforms the data X into a matrix C whose columns (variables) are decorrelated: C = XU

[071] The matrices X and C can be characterized by their moment of order 1, null expectations F [X] = X = 0, and F [C] = C = 0, as well as by their combined moments of order 2 in their covariance matrices, Σ _x , Σ _c .

[072] The covariance matrix of C, Σ _c can be decomposed as follows:

Σ _c = F [(C - C) (C - C) ^r ]

= F [(CC ^r ]

= U ^r F [XX ^r ] U

= u ^r Σ _x u

[073] Principal Component Analysis attempts to find a linear map U that maximizes U ^r Σ _x U. That is, if the components (columns) of C are decorrelated, the matrix Σ _x is a diagonal matrix. The linear application U is thus formed of the N eigenvectors of the covariance matrix of the centered _dataΣx .

[074] Therefore, applying a Principal Component Analysis on the data consists in finding the N eigenvalues and eigenvectors of _x : Σ _X U = μΙΙ

[075] The smaller dimension representation of the vector pixels F (x _i ) is obtained by projecting them on the linear basis generated by the columns of U: C = XU. The column vectors of C are called the main factors.

[076] It will be observed that, if each of the columns F. of F is centered and reduced with F - F

x = (ie with o _F the variance of F., instead of being centered, we then search for the eigenvalues of the correlation matrix cor _x , and no longer of the covariance matrix Σ _x . eigenvectors of the correlation matrix, also called the inertia matrix.

[077] On the other hand, when using reduced centered variables, the metric between the individuals (i.e. the vector pixels) underlying the Principal Component Analysis is the inverse metric of the variances.

[078] The image space of arrival of the transformation ζ is called factorial space. This factorial space is composed of directional vectors carried by the factorial axes A _l , A ₂ , .... A _k , ... A _N ; and whose components, or coordinates of the pixel vectors in the factor space, c, c ' ₂ , ..., c, ..., c' _N, which are linear combinations of the filter vectors of the starting space, are the factors associated with the pixel vectors. The cloud of variables (the filters) and individuals (the pixels) is thus arranged so as to have the maximum of dispersion according to the factorial axes.

[079] At the end of this analysis step we also obtain another representation space of the data of dimension N, equal to or smaller than the dimension L of the space of the initial filters, L representing the number of filters from the initial collection. We also obtain, using the linear transformation ζ, a new multivariate image c \ x) = (c '{(x), c' (x), ..., c ' _f (x)) of dimension N, in which the variables c, c, ..., c, ..., c ' _N are linear combinations of filters of the initial collection (F ₁ (f), F ₂ (f), ..., F _L (f)).

[080] In the same way, the filter vectors of the initial filter collection have an image in this new factor space of {, d ', d', ... d '{.

[081] It is also possible at this stage to go straight to the classifier construction stage, which consists of determining the areas of the factor space in which are statistically significant the pixels considered to form the image of the anomaly. We then consider that the factor space forms the spectral space in which the spectral image c '(χ) = (c' {(x), c '{(x), ..., c' ^f _N (x)) is obtained by the linear transformation z of the multivariate image F ^f {x) = ( ₁ (x), ₂ (x), ..., (x)) obtained using the initial filter collection (F _l (f), F ₂ (f), .. .F _L (f)).

[082] As mentioned above, it is often desirable to make further simplifications by reducing the dimensions and variables of the factor space in order to simplify the calculations and improve the identification of the zones. representative of the anomaly in the factor space. Indeed, we observe that when the factorial spaces have a large number of dimensions, they are often filled with empty space, or in other words, areas that are not very dense in useful information. [083] It is then recommended to reduce again the dimensions of the factor space, so as to reduce the number of factorial axes and to restrict the number of filters to those responding positively to the anomaly.

[084] To do this, the factorial axes Δ are selected; the most significant ones to describe the coordinates c, c ' ₂ , ..., c, ..., c' _N of the multivariate image as represented in the factorial space after transformation by the function ζ.

[085] The simplest method is to classify the factorial axes Δ; according to their decreasing inertia compared to the cloud of points formed by the multivariate image in the factorial space. Only the factorial axes whose sum of the inertias represents for example 80% of the total inertia are retained. [086] Another method consists in selecting the axes according to the signal-to-noise ratio measured by the computation of the variance on the channels of C. The variance of the noise corresponds to the height of the peak at the origin, and the variance signal corresponds to the amplitude of the original variance after suppression of the noise peak.

[087] This consists of calculating the Signal to Noise Ratio (SNR) on pixel factor images and retaining only those with an SNR greater than a given threshold.

RSB - ^{yar si} S ^na

yar (noise)

To determine the SNR, the spatial covariance centered on the images of the pixel factors is calculated. The variance of the noise corresponds to the amplitude of the peak at the origin. This peak is suppressed by a morphological opening with a square structuring element of small, such size than a square of 3x3 pixels. The variance of the signal is the amplitude of the covariance at the origin after morphological opening. The spatial covariance is defined by the following equation:

^~ g _k {h) = EW _k {xy _k {x + h) \. with c (x), the centered channel k of the image of the factors c '. The centered channel is obtained by subtracting its average: c (x) = c (x) - E [c (x)], where E is the mathematical expectation of a random variable, that is to say its average.

[088] These selection methods make it possible to keep only the axes, and therefore the only c components that are the most relevant. We thus obtain a space of representation of the data of smaller dimension, described by the factors c \ x) = (c {x), c {x), ..., c {x)) with (K <N), which are the coordinates of this image on the only axes A _l , A ₂ , .... A _k , ... A _K retained during this selection.

[089] The last stage of reduction of the space consists in selecting the filters of the initial collection corresponding to the anomaly, and whose coordinates in the reduced factor space are the factors associated with the filters represented in the form of vectors of " ^K , of {, d (, d, ..., d in the reduced factor space The interest is to reduce the number of filters to calculate by obtaining a good approximation of the To do this, we measure the distance between the factorial axes A _k of the new space and the variables (the filters) represented as points in the factor space, as shown in a simplified manner in FIG. the factor space has been reduced to a two-dimensional space, and the most distant filters from the origin of the factorial axes are retained (d ', d' {, d ', d', d ', { ₀ ), and the closest filters to the origin

(d ', d', d ', d', _g 'd') are eliminated.

[090] As previously, we retain only the filters whose distance to the origin is greater than a given threshold or the filters whose quadratic sum of the distances at the origin represents, for example 80% of the quadratic sum of distances from the origin of all the filters of the initial collection projected in the reduced factor space (d ', d',, d ', d'). initial reduced filters F _l (f), F ₂ (f), ..., F _n (f), - - -, F _M (f) with M lower or even much lower than L.

[091] Alternatively, one can also transform the initial collection of filters (F _l (f), F ₂ (f), ..., F _L (f)) in the reduced factor space (d ', d ₂ , d', ... d '[) and, in this space, we select the filters of the initial collection (F _l (f), F ₂ (f), ..., F _n (f), ..., F _M (f)) whose square of the The distance to the origin divided by the sum of the squares of the distances at the origin of all the filters of the initial collection projected in said reduced factor space is greater than the inverse of the number of filters (l / L).

[092] The values of the components of the reduced multivariate image are then recalculated in the reduced factor space c ₁ , c ₂ ,..., C _k ,..., C _K (see FIG. 5), while not taking only the filters of the reduced initial collection just determined.

[093] The number of axes and the number of filters having been reduced, the linear function ζ determined during the Principal Component Analysis is again applied to the initial image considered as the multivariate image of the anomaly. obtained by transformation using the only reduced collection of filters F _l (f), F ₂ (f), ..., F _n (f), ..., F _M (f), so as to obtain a multivariate image c {x) = ({x), c ₂ {x), ..., c _K {x)) in the reduced-dimensional factor space whose variables c ₁ , c ₂ , ..., c _k , ..., c _K are combinations of filters of the reduced initial collection placed in the reduced factor space composed of the factorial axes A _l , A ₂ , .... A _k , ... A _K previously selected .

[094] It will be observed here that the result obtained, namely a linear transformation ζ, a space comprising a limited number of axis A _l , A ₂ , .... A _k , ... A _K and a number of filters F _x {f), F ₂ {f), ..., F _n {f), ..., F _M {f) reduced, can be achieved in the same way with a single image of the anomaly or with a set of images of said anomaly taken from several different tires. Only the initial calculations are affected during the determination of the contingency table. In return, this additional step of calculation starting from step C makes it possible to make the analysis of the anomalies more reliable.

[095] At this stage the implementation of the method according to the invention can be done by considering that the reduced factor space forms said spectral space. The spectral image is the result of the transformation in the reduced factor space, using the linear transformation (ζ), of the multivariate image {F ^f {x) = {F {x), F ₂ ^f {x), ..., F ^ {x)) obtained from the reduced filter collection (F ₁ (f), F ₂ (f), ..., F _n (f), ..., F _M ()).

[096] The method then provides for the construction of a classifier that will make it possible to detect the presence (or absence), as well as the position of the anomaly. The classifier allows to isolate certain areas of the spectral space formed by the space of the filters, by the factorial space or preferably by the reduced factor space, in which are located in a significant way the clouds of points corresponding to the spectral image of said anomaly obtained by the projection of the multivariate image by means of the linear transformation ζ.

[097] In the present case, significant is understood to mean the results of a statistical analysis making it possible to identify the zones of the spectral space in which said point clouds are located. One is indeed able to distinguish the pixels or group of pixels located on the anomaly and those which are placed on an area of the image free of anomaly. The statistical analysis will consist in looking for the areas of the spectral space in which these two classes of pixels are preferentially located.

[098] The most appropriate method is to apply a method of analysis based on a linear discriminant analysis, better known by its acronym LDA, and which will be briefly recalled below. This method of analysis is intended to separate classes of points by hypersurfaces, assuming that the distribution of points in a class is Gaussian. This works well in many cases, even if the points of the classes do not quite have a Gaussian distribution. The LDA can of course be used in multidimensional spaces.

[099] To classify is to determine the joint probabilities, Pr (G | X), of the classes G = k knowing the data X = x. Suppose that f _k (x) is the conditional distribution of the data X in the class G = k and let _k be the _prior probability of the Bayes theorem gives:

In terms of classification, to know Pr (G = k \ X = x) is to know f _k (x). Suppose we model the distribution of each class as a Gaussian with the mean

[0101] It is also assumed that all the classes have the same covariance matrix Σ ^ ¹ = Σ \ / k. Comparing two classes and using the logarithm of the ratio, we obtain a linear equation in x:

. Pr (G = k \ X = x). f _k (x). _k

log- ^! = log ^{J ky} + log-

Pr (G = / | = x) f _t ix) π,

= log ^ - 1 (μ, + μ, f Σ ^"1 (μ, - μ,) + χ ^ Σ ^{" 1} (μ, - μ,)

π _ί 2

This equation is that of the boundary between classes k and /. This is the equation of a hyperplane in dimension p. The classes of points will thus be separated by hyperplanes.

From the above equation, we deduce the linear discriminant functions that are equivalent to the decision rule, with G (x) = argmax ^ _k : δ, ( ^χ ) = x ^r Σ ^" i - ^ μ [Σ ^_1 μ * + iog¾

As in practice we do not know the parameters of the Gaussian distributions, we estimate them by considering the location of the pixels or group of pixels considered, as representative of the anomaly and the location of the pixels considered as belonging to a healthy part of the surface:

- iz _k = N _k IN, where N _k is the number of individuals in class k;

- μ = _ _k x _l IN _k , where g _l is the class of an individual;

- ± = Σl _l Σ _gr _{k k} (x _i - _i _k ) (x _i - _i _k ) ^r / (N - K).

When the covariance matrices are not of equal dimensions, the discriminant functions δ _i (x) are of quadratic form and the method of analysis is then evoked.

Discriminant Quadratic, the zones are then separated by quadratic hypersurfaces and no longer by hyperplanes. Once these parameters have been determined statistically, we are then able to identify the areas of the spectral space in which the pixels of the spectral image representing a given anomaly will be statistically representative. In case of statistically representative presence of pixels in these areas it will be possible in return to conclude the probability of the presence of an anomaly and to determine the location on the image.

The construction of the classifier can also be done at three distinct stages of the implementation of the invention, the steps of which have been described above.

According to a first variant, this step can be achieved by considering that the space spectral is formed by the space of the filters whose directional vectors are those of the canonical base ² associated with the initial collection of filters {F _x {f), F ₂ {f), ..., F _L (f)) , and that the spectral image corresponds to the multivariate image, obtained using the initial filter collection F ^f (x) = (F (x), F ₂ ^f (x), ..., F [ (X)).

According to a second variant, it is also possible to construct the classifier just after determining the factor space and the transformation function ζ. In this case, the factor space forms the spectral space and we search for the representative zones of this space in which are located, in a statistically representative way, the points of the spectral image c '(x) = (c \ (x ), c ' ₂ (x), ..., c' _7V (x)) of said anomaly obtained with the aid of the initial filter collection (F ₁ (f), F ₂ (f), ... , F _L (f)) and transformed in the factor space using the linear transformation ζ.

According to the third variant, the construction of the classifier is done after reducing the number of filters in the initial collection and the dimensions of the factor space. The reduced factor space then forms said spectral space and the spectral image of the anomaly c (x) = (c _l (x), c ₂ (x), ..., c _k (x), ... , c _K (x)), is obtained by the transformation in the reduced factor space, using the linear transformation (ζ), of the multivariate image F ^f (x) = (F (x), F ₂ ^f (x), ..., F _j f (x)), obtained from the collection of small filters (^ () ^ ₂ (), ..., ^ (), ..., ^ ()).

The detection of an anomaly on the surface of a tire to sort any then becomes possible using the calculation tools and the method as described above.

In a first step, the gray level digital image is produced of the surface of the tire that is to be sorted.

It may be practical to cut the surface of the tire to be sorted into smaller surface elements, and whose size may correspond substantially to the size of the images of the anomaly used to build the analysis tools.

[0112] The multivariate image is then determined.

^ (χ) = (^ (χ), ^ (χ), .. ^^ of the surface or of the surface element of said tire to be sorted, using, depending on the case, the filters of the initial collection, (F _l (f), F ₂ (f), ..., F _L (f) or the filters of the reduced collection selected, F ₁ (/), F ₂ (/), ..., F _n (/), ..., F _M (/), on the elements of the image of the tire to be sorted.

This multivariate image is projected using the application ζ in the spectral space that can be formed, according to the variant embodiments of the invention, by the space of the filters, by the factorial space or by the reduced factor space, and in which the classifi- cator has been constructed. The spectral image of the tire to be sorted is then expressed by the factors pixels respectively, F ^ft (x) = (F ₁ ^ft (x), F ₂ ^ft (x), ..., F / '(x)), c "(x) = (c '[(x), c" ₂ (x), ..., c " _k (x), ..., c" _N (x)), c' (x) = {vs[

The position of the cloud of points of the spectral image of the surface or of the surface element of said tire to be sorted in the spectral space is then observed, and it is questioned, using the classifikator, to know if the pixels are distributed statistically representative in the areas of the spectral space delimited by the classifier, and if there is potentially (or not) an area of the image of the tire to be sorted which could correspond to said anomaly.

The detection method of an anomaly just described is adapted to highlight a given anomaly present on the surface of a tire.

It is therefore obvious that it is necessary to apply said method as many times as distinct anomaly to identify.

In practice, this amounts to determining as many sets of filters, of spectral space and of transformation function ζ as of distinct anomalies to be identified on the surface of the tire, then, in the detection phase, to successively apply these operators, according to the sequence of operations described in a simplified manner in Figure 7, each surface element to detect the presence or absence of one of these anomalies.

It is also possible to consider grouping the images of all the anomalies in the contingency table as described above, and to use a classifier comprising as many classes as there are anomalies or a classifier with two classes indicating only the presence any anomaly or lack of anomaly.

The method described above is intended to apply preferably to search for anomalies present on the surface of a tire. It is also particularly useful when seeking to examine the interior surface of a tire on which known patterns such as streaks or streaks formed by the patterns present on the baking membrane in order to promote the flow of occluded gases. These patterns, which are generally more or less randomly located from one tire to another because of the elastic nature of the baking membrane, are not strictly speaking anomalies. As such, it is appropriate to determine the series of filters relevant for the identification of these streaks by applying the teachings of the method according to the invention, then to identify these streaks so as not to assimilate them with anomalies.

Claims

1) Method for detecting an anomaly on the surface of a tire by digital image processing of the surface of a tire, in which a combination of filters capable of identifying the signature of the image of a tire is selected an anomaly present on the surface of the tire comprising the steps in which:

B - using a collection formed of a plurality of filters ((f (f), F ₂ (f), ..., F _L (f)), ( _j (f), F ₂ ( ), ..., F _M ())), we construct, in a space of the filters, a multivariate image

(F ^f (x) = ( ₁ (x), (x), ..., (x)), F ^f (x) = (F (x), F ₂ ^f (x), ..., F ((x))) of said surface, wherein each pixel is represented as a pixel vector (F ^f (x)), the components of each pixel vector having a value corresponding to the value of that pixel in the pixel. image transformed using each of the filters of said collection

C - using a linear function (ζ) this multivariate image is transformed from the filter space into a spectral space of given dimension (L, M) whose variables are the filters or filter combinations of said collection, to form a spectral image (F ^f (x) = ( ₁ (x), ₂ (x), ..., (x)), c '(x) = (c (x), c (x)) , ..., c (x)), c (x) = ((x), c ₂ (x), ..., c _K (x))),

D - a classifier is constructed by determining, for this anomaly, the representative areas of the spectral space in which are statistically representative points of the spectral image of said anomaly transformed in said spectral space (F ^f (x) = (F (x), F ₂ ^f (x), ..., F [(X)), c '(x) = (c (x), c (x), ..., c (x) ) c (x) = ((x), c ₂ (x), ..., c _K (x))).

2) Detection method according to claim 1, wherein, to detect an anomaly on the surface of a tire to be sorted,

a digital image is made of all or part of said surface of said tire to be sorted, in the space of the filters, the multivariate image of the tire to be sorted is determined (F ^ft (x) = ('(X), (X), ..., (X)), F ^ft (x) = of said image of the tire to be sorted by means of the filter collection (( ₁ (AF ₂ (A) ()) (AF ₂ {), ..., F _M ())),

the spectral image of the tire to be sorted ('(x) = ( ₁ ' (x), (x), ..., (x)), c '{x) =

c '(x) = (c ₁ ' (x), c ₂ '(x), ..., c _K ' (x))) by transforming, using the linear transformation (ζ), the multivariate image (F ^ft (x) = ('(X), (X), ..., (X)), F ^ft (x) = {F' (x), F * (x), ... , F (X))) of the tire to be sorted and,

the location of the points of the spectral image of the tire to be sorted (F ^ft (x) = (F ₁ ^ft (x), F ₂ ^ft (x), ..., F _L ) is analyzed in the spectral space; ^ft (x)), c * (x) = (c (x), c " ₂ (x), ..., c" _K (x)), c '(x) = (ci (x), c ₂ '(x), ..., c _K ' (x))) with respect to areas of the spectral space representative of the anomaly identified by said classifiers.

3) Detection method according to one of claims 1 or 2, wherein, during step D, the classifier is constructed using a method of linear discriminant analysis type, said representative zones being delimited by hypersurfaces of said factorial space .

4) Detection method according to one of claims 1 to 3, wherein the space of the filters forms said spectral space and wherein the spectral image ((x) = ( ₁ (x), (x), .. ., (x)), ('(x) = ( ₁ ' (x), (x), ..., (x))), corresponds to the multivariate image obtained from an initial collection of filters ((^ (), ^ ₂ (), ..., ^ ()).

5) Detection method according to one of claims 1 to 3, wherein at the end of step B and before starting step C,

- using a data analysis method (ACP, AFC, ACI) we search a factorial space of dimension less than or equal to (N) the dimension of the space of the filters (L), in which the transformed variables (c, c ' ₂ , ..., c, ..., c' _N ) are decorrelated or independent, and the linear transformation (ζ) for passing from the space of the filters to said factor space is determined,

6) Detection method according to claim 5, wherein

during step A, the image is taken of a given anomaly present on the surface of a series of several different tires,

during step B, the multivariate image of each of these images is determined, and

during step C, the multivariate images are assembled to form a single multivariate image.

7) detection method according to one of claims 5 or 6, wherein the data analysis is done using a method of the principal component analysis type, or according to a method of correspondence analysis type analysis, or according to a method of type independent component analysis.

8) detection method according to one of claims 5 to 7, wherein the factor space forms said spectral space and wherein the spectral image (c '(x) = (c (x), c' ₂ (x ), ..., c ' _N (x)), c "(x) = (c" ₁ (x), c " ₂ (x), ..., c" _N (x))) is obtained by the transformation in the factorial space, using the linear transformation (ζ), of the multivariate image (F ^f (x) = ( ₁ (x), (x), ..., (x)) , F ^f x) = ('(X), (X), ..., (X))) obtained from the initial filter collection (F ^f (x) = ( ₁ (x), ₂ (x ), ..., (x))).

9) Detection method according to one of claims 5 to 7, wherein at the end of step C, using a first selection method, the factorial axes (A ₁ , A _{2) are determined.} , .... A _k , ... A _K ) the most relevant with respect to the multivariate image transformed in the factorial space by means of the linear transformation (ζ), and the description of said image is limited multivariate at the coordinates of said image (c (x), c ' ₂ (x), ..., c (x), ..., c' _K (x)), expressed on these axes alone, the number of which ( K) is smaller than the number of axes (N) of the factor space, so as to obtain a reduced factor space. 10) Detection method according to claim 9, in which the first method of selecting the factorial axes consists in preserving the factorial axes (A ₁ , A ₂ , ... A _k , ... A _K ) whose sum of inertias with respect to the point cloud of the multivariate image of the anomaly transformed into the factor space (c '(x) = (c \ (x), c' ₂ (x), ..., c ' _N (x))), represents a given percentage of the inertia of all the axes with respect to said scatterplot.

11) Detection method according to claim 9, wherein the first method of selecting the factorial axes (A ₁ , A ₂ , ... A _k , ... A _K ) consists in preserving the factorial axes with the highest ratio. signal on noise contained in the factors associated with the pixel vectors of the multivariate image transformed in the factorial space with respect to said considered axes.

12) Detection method according to one of claims 9 to 11, wherein, after determining the relevant factorial axes, projecting the initial collection of filters (F _l (f), F ₂ (/), ..., F _L (f)) in said reduced factor space and, using a second selection method, the filters of the initial collection projected in the factor space (d ', d', d {, ... d ') whose vectors are the farthest from the origin of the factorial axes (A _l , A ₂ , ... A _k , ... A _K ), so that the number (M) of filters (F ^ f), F ₂ (f), ..., F _n (f), ..., F _M (f)) of the initial collection is reduced, and the coordinates of the image are recalculated (c (x) = (c _l (x), c ₂ (x), ..., c _k (x), ..., c _K (x))) in the reduced factor space.

13) Method for detection according to claim 12 wherein is projected filters the initial collection (F _l (f), F ₂ (/), ..., F _L (f)) in the factor space reduced

(of {, d ',, {, ... d') and, in this space, we select the filters

{F _x {f), F ₂ {f), ..., F _n {f), ..., F _M {f)) whose quadratic sum of the distances at the origin represents a given percentage of the sum quadratic distances from the origin of all the filters of the initial collection projected in said reduced factor space, or whose square of the distance to the origin divided by the sum of the squares of the distances at the origin of all the filters of the initial collection projected in said reduced factor space is greater than the inverse of the number of filters (l / L). 14) A method of detection according to one of claims 12 or 13, wherein the reduced factor space forms said spectral space, and wherein the spectral image (c (x) = (c _l (x), c ₂ ( x), ..., c _k (x), ..., v _K (x)), c ^t {x) = {c _l ^t {x), c ₂ ^t {x), ..., c _K '{x))) is obtained by the transformation in the reduced factor space, using the linear transformation (ζ), of the image (F ^f (x) = (F (x), F ₂ ^f (x), ..., F ^ (x)), F ^ft (x) = {F * {x), F ₂ ^ft {x), ..., F * (*))) obtained multivariate from the collapsed filter collection (^ (), ^ ₂ (), ..., ^ (), ..., ^ ()).

15) device for controlling and detecting an anomaly on the surface of a tire to be sorted comprising

lighting and shooting means capable of producing the image of the surface or of a portion of the surface of a tire, and

- suitable calculation means

o storing for one or more given anomalies one or more morphological filter collections, determined according to one of claims 3, 5 or 14,

transforming an image of the surface of the tire to be sorted into a spectral image by means of a linear transformation (ζ) according to one of claims 3, 5 or 14,

o determining the presence or absence of abnormality on the surface of the tire to be sorted using a classifier according to one of claims 3, 5 or 14.