Comparison of feature vectors of data using similarity function
View Patent ↗The invention concerns a method to compare two data obtained from a sensor or interface, carried out by processing means of a processing unit, the method comprising the computing of a similarity function between two feature vectors of the data to be compared, characterized in that each feature vector of a datum is modelled as the summation of Gaussian variables, said variables comprising: a mean of a class to which the vector belongs, an intrinsic deviation, and an observation noise of the vector, each feature vector being associated with a quality vector comprising information on the observation noise of the feature vector, and in that the similarity function is computed from the feature vectors and associated quality vectors.
1. A method to compare two data obtained from a sensor or interface, implemented by a processor, the method comprising steps of:
extracting features from the two obtained data, resulting in feature vectors x,y, and in quality vectors qx,qy associated with the feature vectors x,y respectively,
applying a learning algorithm to determine the covariance matrices of the means of the classes to which the vectors belong and of the deviations of the vectors from the class means,
computing a similarity function between the two features x,y of the two obtained data, wherein each feature vector of a datum is modified as the summation of three independent Gaussian variables μ+ω+ε, where said variables are:
a mean μ of a class to which the vector belongs,
an intrinsic deviation ω, and
an observation noise ε of the vector, quality vectors qx,qy comprising information on the observation noise of the feature vectors x,y respectively, the components of the quality vectors qx,qy being generated as a function of type of datum and type of features forming the feature vectors x,y respectively, and wherein the similarity function is computed from the feature vectors x,y and the associated quality vectors qx,qy as a function of the covariance matrices of the components of the feature vectors x,y, and the observation noise covariance matrices of the features vectors x,y are obtained as a function of the associated quality vectors qx,qy respectively; and
comparing the result of the computed similarity function with a threshold to determine whether the two data belong to a common class.
2. The comparison method according to claim 1 , wherein the covariance matrixes of the components of the feature vectors comprise the covariance matrices that are respectively the covariance matrix of the means of the classes to which the vectors belong is called inter-class covariance matrix, and the covariance matrix of vector deviations from the class means is called intra-class covariance matrix.
3. The comparison method according to claim 1 , wherein the similarity function is the logarithm of the ratio between a probability density the feature vectors with the feature vectors belonging to one same class, and a probability density of the feature vectors with the feature vectors belonging to two different classes.
4. The comparison method according to claim 1 , wherein the learning algorithm is an algorithm of expectation-maximization type.
5. The comparison method according to claim 1 , wherein the similarity function is given by the formula:
LR ( x,y|S ε x ,S 107 y )= x T ( A −( S μ +S 107 +S ε x ) −1 ) x+y T ( C− ( S μ +S 107 +S ε y ) −1 ) y+ 2 x T By− log| S μ +S 107 +S 249 x |−log| A |+constant
where:
A =(S μ +S ω +S ε x −S μ (S μ +S 107 +S 249 y ) −1
B =−AS μ (S μ +S ω +S ε y) −1
C =(S μ +S ω +S ε y ) −1 (I+S μ AS μ (S μ +S ω +S ε y) −1 )
and where S μ is the covariance matrix of the means of the classes, S 107 is the covariance matrix of the deviations from a mean, and S εx and S εy are the covariance matrices of the observation noises of vectors x and y respectively.
6. The comparison method according to claim 1 , wherein the computer data derived from sensors or interfaces are data representing physical objects or physical magnitudes.
7. The comparison method according to claim 6 , wherein the computer data derived from sensors or interfaces are images, and the feature vectors are obtained by applying at least one filter to the images.
8. A computer program product comprising a non-transitory computer-readable medium comprising code instructions that, when executed by a processor, carry out a method comprising steps of:
extracting features from two obtained data, resulting in feature vectors x,y, and in quality vectors qx,qy associated with the feature vectors x,y respectively,
applying a learning algorithm to determine the covariance matrices of the means of the classes to which the vectors belong and of the deviations of the vectors from the class means,
computing a similarity function between the two features x,y of the two obtained data, wherein each feature vector of a datum is modified as the summation of three independent Gaussian variables μ+ω+ε, where said variables are:
a mean μ of a class to which the vector belongs,
an intrinsic deviation ω, and
an observation noise ε of the vector,
quality vectors qx,qy comprising information on the observation noise of the feature vectors x,y respectively, the components of the quality vectors qx,qy being generated as a function of type of datum and type of features forming the feature vectors x,y respectively, and wherein the similarity function is computed from the feature vectors x,y and the associated quality vectors qx,qy as a function of the covariance matrices of the components of the feature vectors x,y, and the observation noise covariance matrices of the features vectors x,y are obtained as a function of the associated quality vectors qx,qy respectively; and
comparing the result of the computed similarity function with a threshold to determine whether the two data belong to a common class.
9. A system comprising:
a database comprising a plurality of labelled data;
a data acquisition unit; and
a processing unit comprising a processor which compares two obtained data by implementing a method comprising steps of:
extracting features from the two obtained data, resulting in feature vectors x,y, and in quality vectors qx,qy associated with the feature vectors x,y respectively,
applying a learning algorithm to determine the covariance matrices of the means of the classes to which the vectors belong and of the deviations of the vectors from the class means,
computing a similarity function between the two features x,y of the two obtained data, wherein each feature vector of a datum is modified as the summation of three independent Gaussian variables μ+ω+ε, where said variables are:
a mean μof a class to which the vector belongs,
an intrinsic deviation ω, and
an observation noise ε of the vector,
quality vectors qx,qy comprising information on the observation noise of the feature vectors x,y respectively, the components of the quality vectors qx,qy being generated as a function of type of datum and type of features forming the feature vectors x,y respectively, and wherein the similarity function is computed from the feature vectors x,y and the associated quality vectors qx,qy as a function of the covariance matrices of the components of the feature vectors x,y, and the observation noise covariance matrices of the features vectors x,y are obtained as a function of the associated quality vectors qx,qy respectively; and comparing the result of the computed similarity function with a threshold to determine whether the two data belong to a common class.