Method and device for image inspection

Abstract

An optical-inspection system for inspecting a sample includes a microscope that receives light that has interacted with the sample to form an image, a camera that receives the image, an image database comprising images collected by the camera, and an image processor. The image processor includes a splitter that builds a training subset and a testing subset from the image database, first and second condensers for constructing corresponding first and second condensed-databases from the training and testing subsets, respectively, and a validated model that has been developed by training a latent model using a machine-learning process and the first and second condensed-databases.

Description

[0001]METHOD AND DEVICE FOR IMAGE INSPECTION CROSS REFERENCE TO RELATED APPLICATIONS This application claims the benefit of the filing date of US Application No. 63 / 614,055, filed December 22, 2023, the contents of which is hereby incorporated by reference in their entirety. STATEMENT OF GOVERNMENT RIGHTS This invention was made with government support under grant 2224708 awarded by the National Science Foundation. The government has certain rights in the invention. FIELD OF INVENTION The invention relates to machines used for the inspection of articles of biological or non-biological origin. BACKGROUND In the field of quality control, it is often useful to inspect articles for defects. In some cases, the article to be inspected is of non-biological origin. An example is an article designated for implant in a human. In such cases, it is useful to carefully inspect the material from which the article is made to spot any manufacturing defects. In other cases, the article is of biological origin. For instance, cancer cells and healthy cells often have slightly different properties that are ascertainable by close inspection thereof. One way to inspect an article is visual inspection, i.e., to simply look at it. However, this method has limits. In some cases, the features that are to be inspected are difficult to discern. An alternative way to carefully inspect an article is to drag one’s finger across it. The sensitivity of human touch enables one to detect rough spots or cracks on a surface that are difficult to see. Indeed, this technique is commonly applied by those who wash dishes by hand to confirm that all food particles have, in fact, been removed from the surface of a dish. For structures of smaller scale, there exist machines that carry out this type of tactile inspection. These machines operate by dragging a cantilevered probe across a surface. The deflections of this probe as it moves along the sample’s surface provides information on the nature of the article’s surface. One can observe these deflections by illuminating a mirror on the probe with a laser and observing the movement of the reflected beam as the probe is dragged across the surface. This approach has several drawbacks. First, the process of actually moving the probe across the article’s entire surface is time consuming. The equipment required for this task also sufficiently specialized so that it is not commonly found. In addition, an inspection method along the lines of the foregoing requires actual contact between the probe and the sample. This can be problematic for the probe making contact. For instance, the same human who uses his finger as a probe to confirm that a dish has been washed clean would not want to use this technique on a hot frying pan. Accordingly, there exists a need for a superior method for quality inspections of various articles of biological and non-biological origin. SUMMARY An objective of the invention is that of overcoming the foregoing disadvantages by using an optical-inspection system to acquire information about properties of the sample using only the interaction of light with that sample. Based on the patterns of interaction between light and a sample, it is possible to obtain information about the physical properties of the sample itself without having to actually make mechanical contact with the sample. In one aspect, the invention features an optical-inspection system for inspecting a sample. Such an optical-inspection system includes a microscope that receives light that has interacted with the sample to form an image, a camera that receives the image, an image database comprising images collected by the camera, and an image processor. The image processor includes a splitter that builds a training subset and a testing subset from the image database, first and second condensers for constructing corresponding first and second condensed-databases from the training and testing subsets, respectively, and a validated model that has been developed by training a latent model using a machine- learning process and the first and second condensed-databases. Embodiments include those in which the microscope is a confocal microscope. These include embodiments in which the microscope is a scanning-laser confocal microscope and those in which the microscope is a Raman confocal microscope. Still other embodiments include those in which the microscope is configured to capture images resulting from phase imaging, Nomarski imaging, dark-field imaging, fluorescence imaging, reflection, cross-polarized, fluorescence polarized, fluorescence cross-polarized, and transmission imaging, and through various spectroscopic imaging techniques, like Raman, Brillouin microscopy, and infrared microscopy, including near infrared, mid-infrared, and far infrared, in which the microscope is configured to form images based on illumination of the sample with electromagnetic radiation of different wavelength and intensity. In other embodiments, the image processor controls illumination of the sample by the microscope based on information in an image provided by the microscope. Among the embodiments are those that include calibration circuitry in communication with the image processor and the microscope for controlling illumination by the microscope to promote visibility of features in the sample. Embodiments include those in which the first condenser is configured to construct the first condensed-database by projecting the training data into a subspace of dimensionality lower than that of the training-data database. This results in the first condensed-database having a lower dimensionality than that of the training-data database. Still other embodiments include those in which the first condenser is configured to construct the first condensed-database by carrying out tensor addition to generate tensor sums that combine information from the training-subset database along one or more slices corresponding to one or more indices of the training-subset database and forming the first condensed-database using the tensor sums. In some embodiments, the first condenser is configured to construct the first condensed-database by defining a subset of values from the training-subset database, each of the values being representative of a corresponding element in the training-subset database, deriving a condensed value from the values in the subset of values, and representing the corresponding elements from the training-subset database with the condensed value. Among these are embodiments in which the condensed value is a result of averaging the values in the subset of values, embodiments in which the condensed value is one of a maximum or a minimum of the values in the subset of values, embodiments in which the condensed value is derived by summing the values in the subset of values, and embodiments in which the condensed value is derived by obtaining an image-parameter set based on information from the training-subset database. Still other embodiments are those in which the image processor is configured to automatically detect that an image of a sample has an artifact and to automatically exclude the image from being used for classifying samples. Also among the embodiments are those in which the image processor is configured to partition an image of a sample into partitions, to obtain parameters for each partition, and to define a parameter for the sample based on a media of the parameters for each partition. In another aspect, the invention features an optical-inspection system that includes an image processor that has been structurally reconfigured to acquire images and to apply a machine-learning process to train a model to classify that image based on its visible features. The apparatus relies on a database of images of several particular classes for building a machine-learning process through machine-learning training. In some embodiments, the method includes building such a database of images. Among these are embodiments in which the database includes multidimensional images. The resulting machine-learning process is trained using either a particular dimension of the image or a combination of dimensions. Among the embodiments are those that include using an optical recording device to acquire different maps corresponding to different properties of the sample and using combinations of these images, or image parameters derived from those images, to identify or classify a sample. Such embodiments carry out processes that include recording optical images of examples of samples that belong to well-defined classes, forming a database in which such images are associated with the classes to which they belong, using the images thus obtained and the combinations thereof to learn how to classify samples by splitting the database into training and testing data with the training data being used to learn how to classify, for example by building a decision tree or neural network or a combination of thereof, and using the testing data to verify that the classification thus learned is effective enough to pass a given threshold of effectiveness. Yet other embodiments include those that reduce the images provided by an optical recording device to a set of image parameters, the values of which are defined by mathematical functions or algorithms that use the pixel intensity of the images as inputs thereof. In a preferred practice, each image yields a parameter that can then be used, together with other parameters, to classify or identify the image. In such embodiments, there exists a classifier that classifies based on these parameters. However, the classifier itself is not predetermined. It is learned through the machine-learning procedure as described above. The described method is agnostic to the use of a particular machine-learning process herein. In those cases in which classification is to be carried out, a suitable machine-learning process is one that is used for supervised machine learning. Various regression and classification methods, decision trees, neural networks, KNN models, and support vector machines can also be utilized. In another aspect, the invention features using an optical recording device, acquiring a set of images associated with samples, processing the images to obtain the parameter, and using a machine-learning process applied to the images, classifying the images. Among these practices are those that include selecting the images to be images of malignant and nonmalignant bladder epithelial cells. As used herein, “parameter” refers to “image parameter” unless otherwise noted. The only methods described in this specification are non-abstract methods. Thus, the claims can only be directed to non-abstract implementations. As used herein, “non- abstract” is a deemed to mean compliant with the requirements of 35 USC 101 as of the filing of this application. These and other features of the invention will be apparent from the following detailed description and the accompanying figures, in which: BRIEF DESCRIPTION OF THE FIGURES FIG.1 shows an optical-inspection system for creating a validated model for use in detecting features embodied in an inspected sample; FIG.2 shows details of the condensers shown in FIG.1; FIG.3 shows the use of the validated model that was created using the optical- inspection system of FIG.1 FIG.4 shows a multidimensional image of a sample of database. FIG.5 shows a condenser decreasing the dimension of the data space by converting the original images into sets of parameters; FIG.6 shows the result of using reflection mode to obtain optical images of a sample that comprises cells of biological origin; FIG.7 shows the result of using bright-field mode and dark-field mode to obtain optical images of a sample that comprises cells of biological origin; FIG.8 shows parameters that have been ranked by their respective Gini importance coefficients; FIG.9 shows resulting receiver-operating-characteristic curves; FIG.10 shows average values of a confusion matrix; FIG.11 shows the distribution of probabilities for each cell to belong its class. DETAILED DESCRIPTION FIG.1 shows an optical-inspection system 10 for optically inspecting a sample 12. The optical-inspection system 10 determines, from the result of its optical inspection, one or more physical properties of the sample 12. In some examples, the sample 12 is an article of non-biological origin, such as an article that is to be implanted in a human being. In other examples, the sample 12 is an article of biological origin, such as a cell. An optical-inspection system 10 as described herein offers numerous practical applications. Among these is that of inspecting the condition of the material from which the sample 12 has been manufactured. For example, in some cases, the material from which the sample 12 is made has a defect, such as a crack or a roughening, that may not be apparent to the naked eye. Inspecting the sample 12 with the optical-inspection system 10 prior to use would thus have the practical application of preventing the use of a defective article. Another practical application is that of inspecting a sample 12 of biological origin, such as a cell to identify abnormalities that elude visual inspection. For example, cancerous bladder cells have been found to have a visual appearance that differs from that of normal bladder cells. Nevertheless, humans appear to be unable to reliably detect these visual difference. In contrast, the optical-inspection system 10 has been found to be able to do so. This suggests that the activities described herein cannot practically be performed by a human being. The optical-inspection system 10 includes a microscope 14 that records images on a digital camera 15. The microscope 14 receives an image having values at each point thereof. These values arise from interaction of light with the sample 12 at that point. The pattern formed by such values represents a property of the sample. Changes in that property thus result in corresponding changes in the pattern of values received by the microscope 14 from the image plane. In a preferred embodiment, the microscope 14 is an optical microscope, such as a confocal optical-microscope. A typical microscope 14 has settings that affect the extent to which a change in a property results in a change in this pattern of values. In general, it is desirable to optimize these settings in an effort to maximize the extent to which the pattern of values changes in response to a change in a property of the sample 12. In the context of an optical microscope, among these settings are the power delivered by a light source that provides illumination for the microscope 14. The microscope 14 stores acquired images in an image database 16 within a memory 18 of an image processor 20. A splitter 22 within the image processor 20 divides the set of images from the memory 18 into a training-subset database 24 (hereafter “training subset”) and a testing-subset database 26 (hereafter “testing subset”) for use in connection with machine learning. In some embodiments, the image processor 20 implements supervised machine- learning for classification. This avoids the use of methods that are tuned to processing entire images and that require large databases, such as convolution neural-networks or deep neural-networks. Some embodiments rely on regression algorithms, decision trees, neural networks, k-nearest-neighbor models, and support vector machines. Examples include linear regression, logistic regression, decision trees, random forests, support vector machines (SVM), k-nearest neighbors (k-NN), naive Bayes, neural networks (including multilayer perceptrons), gradient boosting methods (such as XGBoost, LightGBM, and CatBoost), linear discriminant analysis, ordinary least squares regression, gaussian process regression, ridge regression, lasso regression, elastic net regression, kernel regression, polynomial regression, Bayesian regression, quantile regression, Poisson regression, ordinal regression, learning vector quantization (LVQ), Minimum Complexity Machines (MCM), Ensemble Methods (including Bagging and Boosting), AdaBoost, Stochastic Gradient Descent (SGD) classifiers, Passive Aggressive Classifiers, Perceptron, and various specialized neural network architectures such as Recurrent Neural Networks (RNNs)., or combinations thereof. In general, the image processor 20 implements a machine-learning process that is based on either regression or classification. To some extent, these can be viewed as interchangeable. For example, a machine-learning process that relies on regression can be converted into one that relies on classification by simply defining a threshold probability that divides two classes. Conversely, a regression-based machine-learning process can be converted into a classifier by bootstrapping a large number of classification algorithms in a probabilistic manner. An example of this method is that used to build a Random Forest decision tree regression from classification decision trees. Embodiments include those in which the images are split evenly across the training subset 24 and the testing subset 26. However, various other splits can also be carried out since in principle, machine learning should not depend significantly on the ratio used in splitting the images across the training subset 24 and the testing subset 26. Because the dimensionality of the resulting data space is high, it is useful for the image processor 20 to include first and second condensers 28, 30 to reduce the dimensionality, i.e., the number of parameters, of the data space defined by the training subset 24 the testing subset 26, respectively. The image processor 20 uses the output of the first condenser 28 to train a latent (or “unvalidated”) model 32 and the output of the second condenser 30 to validate the latent model 32, thus transforming it into a validated model 34. The resulting validated model 34 is then be used to optically inspect a sample 12 having unknown properties. A validated model 34 is characterized in part by receiver-operating-characteristic curves and a confusion matrix. To avoid a coincidentally good split of the image database 16 into training subset 24 and testing subset 26, it is preferable to have the splitter 22 repeat the splitting process many times, for example as many as a hundred times, and to randomly split each time. The receiver-operating-characteristic curves and the confusion matrices are then built for each split. Validation of the latent model 32 is complete when the accuracies have reached levels deemed acceptable by a user. Referring to FIG.2, the first and second condensers 28, 30 each include an image converter 36, a ranking circuit 38, and an optional decorrelator 40. The image converter 36 reduces the number of parameters in each image to some manageable number, for example, on the order of thirty to forty parameters. A ranking circuit 38 receives the remaining parameters and ranks them by the extent to which they are important in identifying the properties of the sample 12. A suitable ranking is one based on the Gini index. In some cases certain parameters are coupled to each other so that changes in one are reflected in the other. These parameters are said to be “correlated.” In some embodiments, a decorrelator 40 removes strongly correlated parameters. FIG.3 shows the validated model 34 being used to inspect a sample 12 whose image has been uploaded into the memory 18. The image processor 20 then uses the uploaded image to form a set of parameters upon which the validated model 34 has been trained to operate. The validated model 34 then generates an image-identification output 42. If necessary, the image processor 20 provides a suitable feedback signal 21 to adjust the microscope’s settings to increase the visibility of changes in the pattern of light received by the microscope in response to different properties of the sample 12. In those cases in which the machine-learning process relies on a regression type of algorithm, the image-identification output 42 includes the probability of that the sample 12 belongs to a particular class of samples. In those cases in which the machine- learning process relies on a classification algorithm, the image-identification output 42 is a Boolean variable that indicates whether the image of the sample 12 indicates that the sample 12 belongs to a particular class. Referring to FIG.4, the image database 16 includes images 44, each of which is represented as a three-dimensional image array 46. Two of the image array’s dimensions define a spatial location on the sample 12. The array’s third dimension corresponds to different properties of the sample 12. Thus, the array 46 defines a map corresponding to different properties of the sample 12 at the same location on the sample 12. This is similar to how a weather map might show both temperature and barometric pressure at different locations on the Earth’s surface. The properties that define the array’s third dimension are thus “mapped properties” because they have been mapped to spatial locations on the sample 12. Each of these properties defines a “channel.” The following equation represents a K-dimensional image array M(k), where the dimension index, k, is an integer in the closed interval [1, K]. For convenience, the geometrical location of pixels of the image 44 can be defined by Cartesian coordinates (xi, yj). The value of the kthdimension measured at a pixel located (xi, yj) is a pixel intensity, zi,j(k). intensity” is the total signal sensed by the camera 15 coupled to the microscope 14. This is defined by hardware parameters that are difficult to change. However, some control can be had by varying the intensity of illumination light and by controlling exposure time, or swell time. With this in mind, an image array 46 that represents a map or image 44 of the kthdimension, which is sometimes referred to as the “kthchannel”, can be formally represented as: M(k)={xi, yj, zi,j(k)} where “i” and “j” are integers in the intervals [1, Ni] and [1, Nj], respectively, and where “Ni” and “Nj” are the numbers of pixels available for recording an image 44 in first and second orthogonal directions, respectively. Although the values of “Ni” and “Nj” can be different, for purposes of discussion, Ni = Nj = N. The number of elements in a sample’s image array 46 would be the product of the number of dimensions and the number of pixels. Sometimes, it is efficient to use only a part of the image 44. This is useful when the image has stochastic properties that render the image signal spatially stationary. By way of analogy, if one wishes to inspect the images of the water in a harbor, it is most likely only necessary to inspect one region of an image 44 because other regions would likely be similar. On the other hand, if one wishes to inspect the city that the harbor serves, it would be prudent to image multiple regions of the image 44. This is because different parts of a city have markedly different properties. With this in mind, the image array 46 acquires another index to identify the particular region that is being imaged. This increases the array’s dimensionality. A formal representation of an image array with this additional index is thus: M(k; s)= {xi(s),yj(s),zi,j(k; s)} where the imaged index “s” [1, S] that identifies a particular imaged region within a sample. Note that this causes the number of elements in the image array 46 for a particular sample 12 to grow by a factor equal to the number of imaged regions. Preferably, the number of such imaged regions is large enough to represent the sample 12 as a whole. One way to converge on an appropriate number of imaged regions is to compare the distribution of deviations between two such imaged regions. If incrementing the number of imaged regions does not change this in a statistically significant way, then the number of imaged regions is likely to be enough to adequately represent the sample 12 as a whole. Another way is to divide what is considered to be a reasonable testing time by the amount of time required to scan each imaged region and to use that quotient as the number of regions. In some cases, it is useful to split each of the imaged regions into partitions. An example of circumstances that make it desirable to split an image region into partitions is the presence, within a partition, of an abnormality that, if included, would skew the resulting validated model 34. For the case in which there are P such partitions in each scanned region, the array can be defined as: M(k;s;p)= {xi(s;p),yj(s;p),zi,j(k;s;p)} where the partition-index . In the case of a square imaged area, it is convenient to divide the square into four square partitions, thus setting P to be equal to four. The ability to divide an imaged region into partitions provides a useful way to exclude image abnormalities or artifacts. This is particularly important because the process of preparing biological cells for inspection sometimes introduces artifacts. These artifacts should be excluded from the analysis. This makes it possible to compare one partition against the others to identify which, if any, deviate significantly enough to be excluded. To identify a class to which a sample belongs based on the image arrays M(k,s)acquired, the method of building a validated model 34 relies in part on building a suitable image database 16 that includes images of samples 12 that are known a priori to belong to particular classes C(l). A formal representation for such an image database 16 is: Dn(l;k;s;p)={Mn(k;s;p),C(l)} where k is a dimension index, a that identifies a particular imaged region, “p” is a partition index that represents a particular partition of the “sth” imaged region, “n” is a sample index that identifies a particular sample (n=1...NN), and “l” is a class index that identifies a particular class from a set of L classes. The overall of the image array 46 is thus the product of the number of classes, the number of samples, the number of imaged regions, the number of partitions per scanned region, and the number of image dimensions. It should be noted that multiple images can be taken for the same object. As an example, the image database 16 can be presented as:D (1; k ; s ; p ) = { M ( k ; s ; p ) , C (1) }, D (1; k ; s ; p ) = { M ( k ; s ; p ) , C (1) } .. D (1; k ; s ; p ) ( k ; s ; p ) (1)1 1 2 2 Ndata 1 = { M Ndata 1 , C }(2; k ; s ; p ) ( k ; s ; p ) (2) (2; k ; s ; p ) ( k ; s ; p ) (2) (2; k ; s ; p ) ( k ; s ; p ) (2) } objects that are in a second class, and “s” is the number of images taken for each object. It is not necessary that “Ndata1” and “Ndata2” be equal. Because the classification process can be considered as a regression process, it is sufficient to describe the flow of work using a regression method. In this case, the machine-learning process, which is represented below as “AI,” outputs a probability that a particular sample “n” belongs to a particular class “l”: (k;s Probn;p)(l)= AI(Mn|C(l)) where “Probn(k;s;p)(l) ” is the defined by “Mn(k;s;p)” belongs to class “C(l)”. This is used to build the latent model 32. After having been built, the image processor 20 uses the testing subset 26 to verify that the latent model 32 is, in fact, sufficiently effective. In one embodiment described herein, the image processor 20 evaluates the effectiveness of the latent model 32 based at least in part on a receiver-operating-characteristic and on a confusion matrix. The robustness of the latent model 32 is then verified by repeating the random splitting of the image database 16 to thereby generate a different testing subset 26 and a different training subset 26. The latent model 32 is then used to repeat the classification procedure. To the extent the outcome of classification no longer changes appreciably, the latent model 32 is ready to use as a validated model 34. If the latent model 32 turns out to be insufficiently effective, the image processor 20 changes the parameters of the process and generates a new latent model 32. This cycle continues until the latent model 32 eventually attains threshold of effectiveness required to become a validated model 34. The process of building a validated model 34 is hindered to some extent by the computational load that arises when there exists more than one probability value associated with a sample n. In fact, as a result of the multidimensional nature of the image array 46, for any one sample 12, there would be K·S·P probabilities, Probn(k;s;p)(l), to process. The required computational load would be impractically high for a large image database 16. Another bottleneck in dealing with such large arrays 46 of data is the large number of samples 12 used to provide reasonable training for the latent model 32. When building decision trees, a rule of thumb requires that the number of samples 12 be at least six times larger than the dimension of the database. In many cases, it is impractical to obtain such a large database. For this reason, it is useful to have condensers 28, 30 to condense the arrays 46. FIG.5 shows the role of the condenser 28, 30 in decreasing the dimensionality of the data space. The condenser 28, 30 converts original images 44 from the image database 16 into sets of parameters. The condenser 28, 30 condenses information provided by a particular dimension of the image 44 into a space of parameters that embodies information about that dimension. The condenser 28, 30 uses the image database 16 to generate a condensed database 48. In effect, this amounts to projecting a multidimensional array that is in a fairly high-dimensional space, i.e., the image arrays 46 from the image database 16, into an array of lower dimensionality, i.e., corresponding matrices in the condensed database 48. The condenser 28, 30 can carry out several database-reduction procedures. Among these are procedures that combine one or more of the database-reduction procedures described herein. These have in common deriving, from a set of data, an image parameter that embodies at least some of the information embodied in that set. In some practices, the condenser 28, 30 carries out a first database-reduction procedure. This first database-reduction procedure relies on the observation that each image 44 is represented by an array 46 that can be combined with other such arrays in a way that yields an object that preserves enough aspects of the information from the arrays 46 that went into it so as to be useful in classifying a sample 12. For example, tensor addition “⊕” can be used to combine a set of images Mn(k;s;p)along a slice corresponding to one of its indices. In one specific implementation, the slice corresponds to the index k. In that case, the tensor sum of the images is given by: Mn(1;s;p)⊕ Mn(2;s;p)⊕ Mn(3;s;p)⊕… Mn(K;s;p)Thus, each element of the condensed database 48 that is to be used for machine learning becomes the following: Dn(l;s;p)={Mn(1;s;p)⊕ Mn(2;s;p)⊕ Mn(3;s;p)⊕… Mn(K;s;p)} In this particular example, the condenser 28, 30 has decreased the dimensionality of the image database 16 by a factor of K. Therefore, the validated model 34 defines the probability as follows: Probn(s;p)(l)=AI(Mn(1;s;p)⊕ Mn(2;s;p)⊕ Mn(3;s;p)⊕… Mn(K;s;p)|C(l)) It is also possible to carry out a similar procedure for the remaining indices. Ultimately: Probn(l)=AI(⊕⊕⊕Mn(k;s;p)|C(l)) where “⊕⊕⊕” represents a tensor summation over the indices k, s, and p. In other practices, the condenser 28, 30 instead carries out a second database- reduction procedure. This second database-reduction procedure relies on geometrical or algebraic averaging on each of the indices k, s, p separately or in combination. Examples of particular ways to carry out this second procedure include the following averaging procedures over all indices k, s, p: Prob (l )1( k ; s ; p )( l )n =K× S × P Probk ^ n, s , pProb (l )1( k ; s ; p )( l )n =3K× S × P Prob nk ∏ , s , pProb (l )1( k ; s ; p )( l )n =K× S × P k ^ (1-Prob n ), s , pProb (l ) =1(1- ( k ; s ; p )( l )n3K× S × P Prob n )k ∏ , s , pIn yet other practices, the condenser 28, 30 instead carries out a third database- reduction procedure. This third database-reduction procedure relies on assigning the highest or lowest probability of the entire series to a particular index. For example, considering scanned-region index s, one can use one of the following relationships: Prob (k ; p )( l ) =Max {Prob ( k ; s ; p )( l )n s n }Prob (k ; p )( l ) =Min ( k ; s ; p )( l )n s {Prob n }Ultimately, if all indices are reduced this way: Prob (l ) = Max {Pr ( k ; s ; p )( l )n k , s , p ob n } orProb (l ) = ( k ; s ; p )( l )n M , si ,n p {Prob } In some practices, the condenser 28, 30 reduces the dimensionality of the database Dn(l;s)by passing each image through a parameter extractor Am to obtain a parameter set, Pnm(k,s). This can be represented formally by: Pnm(k,s) =Am{Mn(k;s;p)} where the parameter index m interval [1, M], the dimension index k identifies a particular physical or geometric parameter, the sample index n identifies the sample, the scanned-region index s identifies the particular scanned region within a sample, and the partition index p identifies the particular partition within a scanned region. This procedure provides a compact way to represent a multidimensional tensor Mn(k;s;p)as a reduced dimension parameter tensor Pnm(k,s,p). The parameter tensor includes enough residual information concerning the dimension from which it was derived to be usable as a basis for classification. However, its dimensionality is smaller than that of the image. As such, a classification procedure that relies on the parameter tensor sustains a much lower computational load but without a corresponding loss of accuracy. A variety of parameters can be extracted from each image dimension. These include: average roughness, root mean square, image skew, image kurtosis, peak-peak, ten-point height, maximum valley-depth, maximum peak-height, mean value, mean summit-curvature, texture index, root-mean-square gradient, area, root-mean-square slope, 2D to 3D image-area ratio, projected area, image area, image-bearing index, core fluid-retention index, valley fluid-retention index, reduced summit-height, core roughness-depth, reduced valley-depth, l-h% height intervals of bearing curve, density of summits, texture direction, texture-direction index, dominant radial wave length, radial wave index, mean half wavelength, fractal dimension, correlation length at twenty percent, correlation length at thirty-seven percent, texture aspect ratio at twenty percent, texture aspect ratio at thirty-seven percent, and parameters listed in standards ISO 21178, ASME B46.1, EUR 15178N, EUR 16145 EN, or a combination of thereof. It is also possible to further extend the parameter list by introducing the algorithms or mathematical formulas. For example, one can normalize the parameters to the area of the images, which can be different for different images. The quality of an optical image acquired by the microscope 14 frequently depends on the intensity of the microscope’s light source. In that case, it is important to relate the calculated parameters to the intensity of the microscope’s light source. In one embodiment, such a relation is built by normalizing each calculated parameter by the light source’s intensity. In another embodiment, all optical images used in the analysis are multiplied by a factor that is determined by the maximizing the gradient of the parameters with respect to the change of the value of the optical intensity of the pixels of the image. If the factor thus found differs for different image parameters, the parameter is restricted to the range of the parameter values calculated for the most important parameters. In one example, if the factor found for the ten most important parameters ranges between four and ten, the factor is chosen to be in the middle of this interval, i.e. to have a value of seven. In some embodiments, this parameter can further be optimized by calculating the important statistical parameters like area under the receiver-operating- characteristic curve or accuracy of classification for a set of the factor values within the range. The example described herein relies on three parameters: valley fluid retention index (“Svi”), the 2D-3D image Area Ratio (“Sdr”), and the 3D image Area, (“S3A”). The valley fluid retention index is a parameter that indicates the existence of large voids in a valley zone. It is defined by: where “N” is the number of pixels in the “x” direction, “M” is the number of pixels in the “y” direction, “V(hx)”, is a void area over the bearing area ratio curve and under the horizontal line hx, and “Sq” is the root mean square (RMS), which is defined by the following expression: The 2D to 3D image area ratio (“Sdr”) is an image parameter that expresses an artificial 3D-image in which each height is equal to the intensity of the optical image Aij (hereafter “image intensity”) at each particular pixel area relative to the area of the projected x, y plane. This image parameter is defined by: where “N” is the number of pixels in the “x” direction, and “M” is the number of pixels in the “y” direction. As noted above, the value of zi,j(k)(and hence that of Akl, corresponds to an intensity of light reaching the 15. A difficulty arises from a constraint inherent in a digital camera 15, namely that values of zi,j(k)must be expressed within a finite number of bits. For example, given N bits, the intensity must be an integer between zero and 2N–1. However, light intensity is a continuous variable with a broad dynamic range. This can make it difficult to represent variations in intensity when only a finite number of bits is available to represent an intensity. It is therefore important to ensure that intensity zi,j(k)is neither too low nor too high. With this in mind, it is useful to provide calibration circuitry 50 that ensures that intensity of the optical image Aijis within appropriate bounds. The calibration circuitry 50 operates as an image preprocessor that determines the operating settings of the microscope 14 to be used for controlling the rate at which the pixel intensity changes as a function of changes in properties of the sample 12. These operating settings include brightness of the microscope’s illumination and exposure time. The particular values to optimize these settings depend in part on the nature of the sample 12 itself. The calibration circuitry 50 determines the optimal settings iteratively while the sample 12 is being inspected. In general, the optimal settings will depend on exactly which features of the sample 12 are most important to inspect and on information from the image processing system 20 concerning which parameters are the most important to make visible. This information is available from the image processor 20 having evaluated such properties as the Gini importance index or the entropy index. When a property of the sample 12 changes, zi,j(k)will likewise change. The only question is by how much. In some cases, a change in a property of the sample 12 causes zi,j(k)to change by only a small amount, so small as to be imperceptible given the finite number of bits available to represent values. To avoid this difficulty, it is useful for the calibration circuitry 50 to ensure that even small changes in a property of the sample 12 cause a detectable change in the observable quantities, namely the ratio between a change in the value of zi,j(k)and a change in the property of the sample 12 be as great as possible. This maximizes the sensitivity of the optical-inspection system 10 to detecting that change at the digital camera 15. One solution is to simply multiply all values of the intensity zi,j(k)by a constant. However, because of the limited number of bits available in the camera 15, this approach can easily result in loss of resolution at either high values or low values of the intensity. For example, when dealing with fluorescence imaging, one uses low intensity excitation light to avoid photobleaching. This leads to small values of intensity, which in turn makes small variations of that intensity undetectable because of roundoff error caused by having a limited number of bits. It may therefore be necessary to amplify or attenuate intensities by different amounts depending on the value of the intensity being amplified or attenuated. In some embodiments, the calibration circuitry 50 processes all intensities or the entire image, or a region of interest. In such a case, the intensity of each pixel is transferred into a new parameter as shown below: 1^ 2 22 2 ^A kl = ^^ δ y + z ( x k , y l ) − z ( x k , y l + 1 ) + δ y + z ( x k + 1 , y l ) − z ( x k + 1 , y l + 1 ) ^^ ⋅^ of length, is being added to z, which is dimensionless. However, the optical-inspection system 10 takes advantage of the fact that machine learning is, by nature, remarkably insensitive to the physical meaning of variables. This approach makes it possible to find the optimum intensity of the excitation light to maximize the change in a particular parameter when changing the intensity as alluded in the description of work of calibration circuitry 50. To avoid dealing with potential image artifacts in images provided by an optical recording device 40, in one of the embodiments, one can calculate each of the above- mentioned three parameters by first splitting, each image into four partitions. Thus, each image yielded four sets of the image parameters, one for each quadrant. The presence of possible artifacts in an image can be addressed in any one of three different ways. A first way is to have an operator inspect the images for artifacts and exclude, from further processing, any image that had one or more such artifacts. This requires human intervention to identify artifacts. A second way is to provide an artifact-recognition module that is able to recognize an artifact and automatically exclude the cell that contains that artifact. This renders the procedure more operator-independent. A third way is to use the median value of the parameters for each cell instead of the mean values. The results described herein were virtually unchanged when the median value was used instead of the mean value. Using the same example of just two classes, the condensed database 48 will look as followsD (1; k ; s ; p ) = { P ( k ; s ; p ) , C (1) }, D (1; k ; s ; p ) = { P ( k ; s ; p ) , C (1) } .. D (1; k ; s ; p ) = { P ( k ; s ; p ) , C (1)1 1 2 2 Ndata 1 Ndata 1 }} between different classes even though these parameters are not directly related to the images. It can be any digital information associated with the class. For example, there are other factors that are not related to parameters but are nevertheless pertinent to classification. These other parameters can include characteristics of patients, like age, smoking, and family history, all of which may be relevant to the probability of that patient having a potential pathology. There exist yet other ways to use the parameters to reduce the size of the database. One such procedure is that of excluding parameters that are sufficiently correlated with each other. Some parameters depend strongly on various other parameters. Hence, little additional information is provided by including parameters that are correlated with each other. These redundant parameters can be removed with little penalty. One way to find the correlation matrix between parameters is to generate various augmented images. A nonrestrictive example of such generated images is to use a generator of random numbers to simulate the image value at each pixel of the image. Another example is the assignment of the image value at each pixel using the following formula: c⋅sin(x⋅a1 + b1) ⋅sin(y⋅a2+b2), where c, a1, a2, b1, b2 are the randomly chosen numbers. This random choice of numbers can be done for each pixel. Alternatively, c, a1, a2, b1, b2 are randomly chosen but stay the same for all pixels of the entire image. However, at each pixel, the values of c, a1, a2, b1, b2 are changed by an addition of the randomly chosen number, which values are limited by X% of the values of c, a1, a2, b1, b2, correspondingly. As a nonrestrictive example, the random generator can be either produced by a uniform distribution between fixed boundaries or by using a Gaussian distribution. In addition to the methods that rely on the database-reduction procedures identified above, it is also possible to use a machine-learning process 24 that combines different parameters of the same kind from the same sample. Formally, this type of machine-learning process 24 can be represented formally as: Probn(l)= AI(Pn|C(l)) where Pn=F(Pnm(k;s;p)) and of different parameters identified by the parameter index m and belonging to the sample identified by the sample index n. A related machine-learning process 24 is one that combines different parameters of the same kind m of the same sample n from the images of the same properties. Such a machine-learning process 24 can be represented formally as: Probn(k)(l)= AI(Pnm(k)|C(l)) where Pnm(k)= F(Pnm(k;s;p)) and F(Pnm(k;s;p)) is a combination of different parameters identified by the same parameter index m of the sample identified by the sample index n and from the channel identified by the channel index k. Yet another machine-learning process 24 is one that does not combine all parameters but instead combines image parameters by only one index. One such machine-learning process 24 assigns one image parameter to an entire series of partitions p within the same image. Such a machine-learning process 24 is formally represented as: Probn(k;s)(l)= AI(Pnm(k;s)|C(l)) where Pnm(k;s)= F(Pnm(k,s;p)) of image parameters, examples of which include a parameter associated with a statistical distribution of Pnm(k;s;p)over the partition index. Examples include the average: NP (k ; s ) = 1 ^ P ( k ; s ; p )m and the median: Pnm(k,s)= median{Pn(k;s;p)} for p=1…N When used in connection with the collecting multiple images / samples from each patient, the machine-learning process 24 relies on either the average or the median. However, it is preferable for the machine-learning process 24 to rely on the median rather than the average because the median is less sensitive to artifacts. In the particular embodiment described herein, the machine-learning process 24 implements any of a variety of machine-learning methods. However, when confronted with multiple image parameters, a machine-learning process 24 can easily become over- trained. It is thus useful to use three methods that are least prone to overtraining, namely various tree-based models. As an example, the Random Forest, Extremely Randomized Forest, and Gradient Boosting Trees can successfully be used. Another way to reduce the dimension of the data space is to identify the parameters that are most important for image identification. Some practices include use of a Gini importance index to further decrease the data space’s dimensionality. Such practices include ranking parameters based on their importance for classification. Other similar methods include Mean Decrease Accuracy and Greedy methods. The Gini index, which is a measure of variance across all K classes, is defined as follows: ^ ^= ^ ^^^ −The Gini index remains remain close to zero or unity. As a result, the Gini index measures the extent to which a particular node contains mostly samples from a single class. This is referred to as the extent of “node purity.” Thus, to avoid overgrowing, each tree is grown only until the Gini-index results in the complete separation of classes. This occurs when two descendant nodes yield a Gini-index that is less than that of the parent node. There is no pruning of the growing branches in these Random Forest methods. The cross-entropy, which also provides a metric for node purity, is defined as: ^ Like the Gini index, values of pmk are close to zero. This is indicative of a pure node. The Gini index also provides a way to obtain an “importance coefficient” that is indicative of the importance of each image parameter. One such measure comes from adding all values of the decrease of the Gini index at the tree nodes for each of the variables and averaging over all the trees. Another method to reduce the number of image parameters is based on principal component analysis. Only the first principle components, which are the linear combinations of the use parameters, are used as the most important parameters. Another method for doing the same thing is based on the known method of calculation of greedy functions, in which the importance of each parameter is estimated. Further embodiments include those in which the images in the image database 16 come from a microscope 14 that records multiple optical images of the sample 12. Among these are microscopes 14 that use multiple optical techniques such as one or more of: phase imaging, differential interference contrast microscopy, dark-field imaging, fluorescence imaging, reflection imaging, cross-polarized imaging, fluorescence polarized imaging, fluorescence cross-polarized imaging, and transmission imaging and those that implement various spectroscopic imaging techniques, such as Raman, Brillouin microscopy, and infrared microscopy. In this case, each image has multiple dimensions. Each dimension is produced by a corresponding imaging technique and represents a particular property of the sample. In some cases, the mapped properties are related to physical properties. In other cases, the properties are related to geometrical properties. In still other cases, the mapped properties are related to a combination of physical and geometrical properties. An example of such a combination is shown in FIG.6, which presents an example of optical images of biological cells collected in a reflection mode. The cells on the left are non-malignant bladder cells whereas the cells on the right are malignant bladder cells. The images of cells were obtained using a video recording device of an optical microscope 14. Specifically, the images were recorded in the reflection of light using a scanning confocal microscope 14. In reflection mode, the image forms as a result of reflection from geometrically optically dense regions of cells. The image is therefore a result of optical density. This optical density is influenced by both geometrical properties and physical properties. The reflection image shown in FIG.6 arises from a superposition of layers within the sample 12 but dominated by layers that are first to receive incident light. FIG.7 shows the sample shown in FIG.6 but imaged in transmission mode instead of reflection mode. In this image, the malignant bladder cells are on the left and the non-malignant cells are on the right. In transmission mode, image formation mechanism results from residual light that remains after much of the light provided for illumination has been reflected or scattered. The light scattered by the sample can be measured, for example, in the dark-field mode. FIG.5 shows images of biological cells collected in the bright field and dark field modes. For simplicity, we consider only the reflection images, thereby having the dimension of each image equal to 1. The number of pixels per image is N=512. The spatial dimension of each image is fifteen microns on a side. Thirty cells of each class were studied. So the image database 16 contained sixty images. Each sample was split into four quadrants of equal size (of 256× 256 pixels). The condenser 28, 30 was applied to each quadrant to calculate the parameters listed in the specifications. The parameters assigned to each image were found by averaging the parameters over the four quadrants. An alternative would have been to use the median instead of the average value. No substantial difference was found, thereby indicating the absence of artifacts. The optional parts of the condenser and were applied to the obtained parameters. Parameters were declared correlated if the coefficient of correlation was greater than ¾ by absolute value. Only one of two correlated parameters was kept. FIG.8 shows the topmost important parameters identified using the Gini importance coefficient. The names of these parameters are: Radial wave index, mean summit curvature, correlation length (tolerance value 20), mean half wavelength, root mean square gradient, texture aspect ratio, density of summits, correlation length (tolerance value 37), image bearing index parameter, dominating radial wavelength. The Random forest and Gauss process machine-learning algorithms 24 were used as an example. No substantial differences were observed between the results obtained using these machine-learning algorithms. The validation of the latent model 32 was done applying it to testing subsets 26 condensed by the second condenser 30 as described above to the most important ten parameters for each image. The entire procedure was repeated a hundred times. FIG.9 shows the resulting receiver-operating-characteristic curves and the average of these curves obtained for the multiple repetitions. For comparison, a “no classification” line is also shown. The area under the curve is sufficiently high to suggest that the latent model 32 has become a validated model 34. FIG.10 shows the average values of the confusion matrix. These values were obtained using 0.5 as the threshold of probability, i.e., the image was declared to belong to class “A” if the probability of this image being processed through the validated model 34 was more than 0.5. Using the values of the confusion matrix, one, for example, can calculate the accuracy of the validated model 34. FIG.11 shows such probabilities for each cell. The probability was calculated as average when the particular cell was in the testing subset. Assuming the probability threshold of 0.5, the overall accuracy was found to be seventy-nine percent. For applications in which this level of accuracy is sufficient, this implies the creation of the validated model 34 for use in analysis of an unknown sample 12. Having described the invention and a preferred embodiment thereof, what is claimed as new and secured by letters patent is:

Claims

CLAIMS 1. An apparatus comprising an optical-inspection system (10) for inspecting a sample (12), said optical-inspection system comprising a microscope (14) that receives light that has interacted with said sample to form an image, a camera (15) that receives said image, an image database (16) comprising images collected by said camera, and an image processor (20) that comprises: a splitter (22) that builds a training subset (24) and a testing subset (26) from said image database (16), first and second condensers (28, 30) for constructing corresponding first and second condensed-databases from said training and testing subsets, respectively, and a validated model (34) that has been developed by training a latent model (32) using a machine-learning process and said first and second condensed-databases.

2. The apparatus of claim 1, wherein said microscope is a confocal microscope.

3. The apparatus of claim 1, wherein said image processor controls illumination of said sample by said microscope based on information in an image provided by said microscope.

4. The apparatus of claim 1, further comprising calibration circuitry in communication with said image processor and said microscope for controlling illumination by said microscope to promote visibility of features in said sample.

5. The apparatus of claim 1, wherein said first condenser is configured to construct said first condensed-database by projecting said training data into a subspace of dimensionality lower than that of said training-data database, whereby said firstcondensed-database has a lower dimensionality than that of said training-data database.

6. The apparatus of claim 1, wherein said first condenser is configured to construct said first condensed-database by carrying out tensor addition to generate tensor sums that combine information from said training-subset database along one or more slices corresponding to one or more indices of said training-subset database and forming said first condensed-database using said tensor sums.

7. The apparatus of claim 1, wherein said first condenser is configured to construct said first condensed-database by defining a subset of values from said training- subset database, each of said values being representative of a corresponding element in said training-subset database, deriving a condensed value from said values in said subset of values, and representing said corresponding elements from said training-subset database with said condensed value, said condensed value being a result of averaging said values in said subset of values.

8. The apparatus of claim 1, wherein said first condenser is configured to construct said first condensed-database by defining a subset of values from said training- subset database, each of said values being representative of a corresponding element in said training-subset database, deriving a condensed value from said values in said subset of values, and representing said corresponding elements from said training-subset database with said condensed value, wherein said condensed value is one of a maximum or a minimum of said values in said subset of values.

9. The apparatus of claim 1, wherein said first condenser is configured to construct said first condensed-database by defining a subset of values from said training- subset database, each of said values being representative of a corresponding element in said training-subset database, deriving a condensed value from said values in said subset of values, and representing said corresponding elementsfrom said training-subset database with said condensed value, wherein deriving said condensed value comprises summing said values in said subset of values.

10. The apparatus of claim 1, wherein said first condenser is configured to construct said first condensed-database by defining a subset of values from said training- subset database, each of said values being representative of a corresponding element in said training-subset database, wherein deriving said condensed value comprises obtaining an image-parameter set based on information from said training-subset database.

11. The apparatus of claim 1, wherein said image processor is configured to automatically detect that an image of a sample has an artifact and to automatically exclude said image from being used for classifying samples.

12. The apparatus of claim 1, wherein said image processor is configured to partition an image of a sample into partitions, to obtain parameters for each partition, and to define a parameter for said sample based on a media of said parameters for each partition.

13. The apparatus of claim 1, further comprising calibration circuitry in communication with said image processor and said microscope for controlling exposure time of said camera to promote visibility of features in said sample.

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