Abstract:
A method is provided for reading distorted optical symbols using known locating and decoding methods, without requiring a separate and elaborate camera calibration procedure, without excessive computational complexity, and without compromised burst noise handling. The invention exploits a distortion-tolerant method for locating and decoding 2D code symbols to provide a correspondence between a set of points in an acquired image and a set of points in the symbol. A coordinate transformation is then constructed using the correspondence, and run-time images are corrected using the coordinate transformation. Each corrected run-time image provides a distortion-free representation of a symbol that can be read by traditional code readers that normally cannot read distorted symbols. The method can handle both optical distortion and printing distortion. The method is applicable to “portable” readers when an incident angle with the surface is maintained, the reader being disposed at any distance from the surface.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of, U.S. patent application Ser. No. 11/312,703, filed Dec. 20, 2005 now U.S. Pat. No. 7,878,402. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to reading symbols using machine vision, and particularly to enhanced location and/or decoding of distorted symbols. 
     BACKGROUND OF THE INVENTION 
     Automated identification of products using optical codes has been broadly implemented throughout industrial operations for many years. Optical codes are patterns composed of elements with different light reflectance or emission, assembled in accordance with predefined rules. The elements in the optical codes may be bars or spaces in a linear barcode, or a regular polygonal shape in a two-dimensional matrix code. The bar code or symbols can be printed on labels placed on product packaging, or directly on the product itself by direct part marking. The information encoded in a bar code or symbol can be decoded using various laser scanners or optical readers in fixed-mount installations, or portable installations. 
     Various business operations have come to rely upon the accuracy and availability of data collected from product automatic identification as a result of code reading. Therefore, the readers are required to not only deal with multiple symbologies, but also variation caused by printing errors and optical distortion. Usually there is a trade-off between the reading robustness on damaged codes and capability of tolerating distortions. When direct part marking becomes essential for tracking and traceability in highly complex and sensitive assembly systems, such as aerospace and defense systems, medical devices, and electronic assemblies, a robust decoding is the highest priority. 
     To achieve highly robust decoding, automated readers of two-dimensional images typically require the condition that the code be placed on a planar surface (so as to avoid high-order non-linear distortion), and the condition that the optical axis of a lens of the reader be placed perpendicularly with respect to the planar surface (so as to avoid perspective distortion). If a finder pattern of a symbology to be read is not distorted, it can be located according to its unique geometric characteristics (U.S. Pat. No. 6,128,414). Difficulties arise when these two conditions cannot be satisfied due either to the geometry of the product, or to a spatial limitation as to where the reader can be placed with respect to the product. The expected geometric characteristics of the finder pattern of a symbology in question may be distorted to an extent that an automated identification is difficult and time consuming, if not impossible. 
     There are two known solutions to these problems. The first solution is to use a locating and decoding method that can detect and tolerate various types of symbol damage and symbol distortion. A method for reading MaxiCode symbology with distortion is described in U.S. Pat. No. 6,340,119. A method for reading Code One symbology with perspective distortion is described in U.S. Pat. No. 5,862,267. To achieve a reader of multiple symbologies, a locating, and decoding method for each symbology needs to be devised (U.S. Pat. No. 6,097,839). To allow for reading distorted symbols of multiple symbology, each symbology-specific locating and decoding method needs to be modified so as to detect and tolerate distortion. However, this solution requires some undesirable trade-offs. It not only slows down the process of locating and decoding a symbol due to added computational complexity, but also reduces the reader&#39;s ability to handle burst noise, such as damaged codes. 
     The second solution is to employ camera calibration as widely used in 3D computer vision. Camera calibration is performed by observing a calibration object whose geometry in 3-D space is known with very good precision. The calibration object may consist of two or three planes orthogonal to each other, or a plane with checkerboard pattern that undergoes a precisely known translation. However, these approaches require an expensive calibration apparatus and an elaborate setup, as taught in O. Faugeras, Three-Dimensional Computer Vision: a Geometric Viewpoint, MIT Press, 1993, for example. An easy-to-use method for calibrating an image acquisition system with a camera being stationary with respect to a fixture frame of reference is disclosed in U.S. Pat. No. 6,798,925. This method requires using a non-rotationally symmetric fiducial mark having at least one precise dimension and being placed at a predetermined location on an object. These requirements are necessary for a machine vision system whose purpose is to measure or align an object. In comparison, it is not necessary to know or compute dimensions for a machine vision system whose purpose is to automatically identify an object based on reading a symbol, within which the information is encoded as different reflectance or emission of an assembly of modules, instead of the dimension of the modules. In addition, the requirement of a camera being at a fixed distance with respect to a surface of a fixture frame of reference may not be satisfied for a fixed-mount symbol reader that needs to read symbols off a variety of different surfaces of different heights, or a hand-held symbol reader that may be placed at variable distances from the objects carrying symbols. 
     SUMMARY OF THE INVENTION 
     The invention enables reading of distorted optical symbols using known locating and decoding methods, without requiring a separate and elaborate camera calibration procedure, without excessive computational complexity, and without compromised burst noise handling. The invention exploits a distortion-tolerant method for locating and decoding 2D code symbols to provide a correspondence between a set of points in an acquired image and a set of points in the symbol. Then, a coordinate transformation is constructed using the correspondence. Run-time images are then corrected using the coordinate transformation. Each corrected run-time image provides a distortion-free representation of a symbol that can be read by traditional code readers that usually are unable to read distorted symbols. The method can handle both optical distortion and printing distortion. The method is applicable to “portable” readers when an incident angle with the surface is maintained, the reader being disposed at any distance from the surface. 
     In one general aspect of the invention, a method is provided for decoding distorted symbols. The method includes, at train-time: acquiring a training image of a two-dimensional (2D) code symbol disposed on a train-time surface using a camera with an optical axis having an incident angle with respect to the train-time surface; running a 2D code symbol reader that can detect and tolerate distortion so as to provide a correspondence between at least two 2D coordinates of points within the training image and at least two 2D coordinates of points within the 2D code symbol; and using the correspondence to construct a coordinate transformation. The method includes, at run-time: disposing a symbol on a run-time surface that is substantially parallel to the train-time surface; acquiring a run-time image of a symbol disposed on the run-time surface using a camera with an optical axis having substantially the incident angle with respect to the run-time surface; correcting distortion of the run-time image using the coordinate transformation to provide a corrected image; and running a run-time symbol reader on the corrected image. 
     In a preferred embodiment, the run-time symbol reader can read damaged symbols. 
     In another preferred embodiment, the 2D code symbol is a matrix code symbol. In a further preferred embodiment, the 2D code symbol is one of a Data Matrix symbol, a QR Code symbol, a MaxiCode symbol, a Code One symbol, and an Aztec Code symbol. 
     In yet another preferred embodiment, the 2D code symbol can be read by a reader that provides at least two feature points having well-defined correspondence with expected locations in the symbol. 
     In another preferred embodiment, the coordinate transformation is at least one of a geometric transformation and a non-linear transformation. 
     In a further preferred embodiment, running a run-time symbol reader on the corrected image includes providing at least two 2D coordinates of points within the run-time symbol in the corrected image, the method further includes applying an inverse of the coordinate transformation to the at least two 2D coordinates of points to provide mapped versions of the at least two 2D coordinates of points. In a yet further preferred embodiment, the mapped versions of the at least two 2D coordinates of points are displayed within the run-time image so as to define an outline of the run-time symbol. In another further preferred embodiment, the mapped versions of the at least two 2D coordinates of points are analyzed. 
     In a further preferred embodiment, after running a symbol reader on the corrected image, the method further includes computing quality metrics of the symbol within the corrected image. 
     In another embodiment, the surface includes a non-planar surface. 
     In a preferred embodiment, the coordinate transformation includes at least one of an affine transformation portion, a perspective transformation portion, and a high-order non-linear transformation portion. 
     In various preferred embodiment, the run-time symbol is one of a two-dimensional matrix code symbol, a stacked code, a linear barcode, and a text block. 
     In other embodiments, the run-time symbol is a matrix code symbol of different scale than the matrix code symbol in the training image. In yet other embodiments, the run-time symbol is a matrix code symbol having a different number of modules than included in the matrix code symbol in the training image. In still other embodiments, the run-time symbol is a matrix code symbol having different information content from the information content of the matrix code symbol in the training image. 
     In some embodiments, the run-time symbol is not a matrix code symbol. 
     In a preferred embodiment, running the 2D code reader includes 
     establishing correspondence based on multiple feature points as supported by the 2D code reader. 
     In another preferred embodiment, running the 2D code reader includes establishing correspondence based on corner points of a polygonal 2D code symbol. 
     In another preferred embodiment, running the 2D code reader includes establishing correspondence based on four corner points of a quadrilateral 2D code symbol. 
     In another preferred embodiment, the coordinate transformation is a perspective coordinate transformation constructed using the correspondence established based on four corner points of a quadrilateral 2D code symbol. 
     In another preferred embodiment, the camera is a projective camera. 
     In still another preferred embodiment, the surface is not normal with respect to an optical axis of an image sensor of the camera. In some embodiments, the method further includes, at train-time, mounting a camera at a three-dimensional position fixed relative to a train-time surface upon which run-time symbols will be presented. 
     In some embodiments, the run-time image is one of the train-time image, a copy of the train-time image, a derivative of the train-time image, a portion of the train-time image, and an equivalent of the train-time image. 
     In another embodiment, the corrected image corresponds to a portion of the run-time image. In still another embodiment, the corrected image corresponds to a full run-time image. 
     In another general aspect of the invention, a method is provided for decoding distorted symbols, the method comprising: acquiring a train-time image of a 2D code symbol, the 2D code symbol showing distortion in the train-time image; running a 2D code symbol reader on the training image, the 2D code symbol reader being able to detect and tolerate distortion so as to provide a correspondence between at least two 2D coordinates of points within the train-time image and two 2D coordinates of points within the 2D code symbol; using the correspondence to construct a coordinate transformation; acquiring a run-time image of a symbol under the same conditions as the acquiring of the train-time image of the 2D code symbol; correcting distortion of the run-time image using the coordinate transformation to provide a corrected image; and running a run-time symbol reader on the corrected image. 
     In a preferred embodiment, the run-time symbol shows the distortion of the train-time symbol; and the distortion includes at least one of an optical distortion and a printing distortion. 
     In yet another general aspect of the invention, a method is provided for decoding distorted symbols, the method including acquiring a run-time image of a symbol, the symbol showing distortion in the run-time image; obtaining a coordinate transformation that describes the distortion shown in the image of the symbol; correcting distortion shown in the run-time image using the coordinate transformation so as to provide a corrected image; and running a run-time symbol reader on the corrected image. 
     In a preferred embodiment, the coordinate transformation is constructed using a correspondence between at least two 2D coordinates of points within a train-time image and two 2D coordinates of points within a 2D code symbol. The correspondence is provided by a 2D code symbol reader that can detect and tolerate distortion of the 2D code symbol. 
     In another preferred embodiment, the distortion includes at least one of an optical distortion and a printing distortion. 
     In another general aspect of the invention, a method is provided for decoding distorted symbols. The method includes, at train-time: acquiring a training image of a two-dimensional (2D) code symbol disposed on a train-time surface using a camera with an optical axis having an incident angle with respect to the train-time surface; running a 2D code symbol reader that can detect and tolerate distortion so as to provide a correspondence between at least two 2D coordinates of points within the training image and at least two 2D coordinates of points within the 2D code symbol; and using the correspondence to construct a coordinate transformation. The method includes, at run-time: disposing a symbol on a run-time surface that is substantially parallel to the train-time surface; acquiring a run-time image of a symbol disposed on the run-time surface using a camera with an optical axis having substantially the incident angle with respect to the run-time surface; correcting distortion of the run-time image using the coordinate transformation to provide a corrected representation of the symbol; and running a run-time symbol reader on the corrected representation of the symbol. 
     In a preferred embodiment, the corrected representation of the symbol is a corrected image of the symbol. In another preferred embodiment, the corrected representation of the symbol is a corrected feature of the symbol. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
       The invention will be more fully understood by reference to the detailed description, in conjunction with the following figures, wherein: 
         FIG. 1  is an illustration of a projective camera model, wherein a quadrilateral in world plane is mapped to a quadrilateral in an image plane; 
         FIG. 2  is a flow diagram of the method of the invention; 
         FIG. 3  is a representation of a two-dimensional DataMatrix code that is used to establish a homography between a world plane and an image plane, showing four corner points that have been detected in the image plane of the DataMatrix code, with four respective coordinates p i (x i ,y i ), i=1, 2, 3, 4, the homography describing a perspective transformation; 
         FIG. 4  is a representation of the two-dimensional DataMatrix code in  FIG. 3  after the homography matrix is applied, mapping the coordinates p i (x i ,y i ) to P i (X i , Y i ), and thereby correcting any image that is acquired with the same camera model; 
         FIG. 5A  shows an example of a train-time image of a DataMatrix code symbol showing perspective distortion as a result of using a camera with an optical axis having a non-zero incident angle with respect to a train-time planar surface; 
         FIG. 5B  shows a corrected image obtained by applying the perspective transformation to a run-time image that is an equivalent of the train-time image in  FIG. 5A ; 
         FIG. 6A  shows another example of a run-time image of the DataMatrix code symbol in  FIG. 5A , disposed with a second orientation on the train-time surface, showing perspective distortion; 
         FIG. 6B  shows a corrected image obtained by applying the perspective transformation to the run-time image of  FIG. 6A , providing a symbol with no distortion; 
         FIG. 7A  shows another example of a run-time image of a DataMatrix code symbol with different symbol size than that shown in  FIG. 5A , disposed with yet another orientation on the train-time surface, the symbol showing perspective distortion; 
         FIG. 7B  shows a corrected image obtained by applying the perspective transformation to the run-time image of  FIG. 7A , the symbol showing no distortion; 
         FIG. 8A  shows yet another example of a run-time image of a QRCode symbol, disposed with yet another orientation on a run-time surface parallel to the train-time surface, the symbol showing perspective distortion; 
         FIG. 8B  shows a corrected image obtained by applying the perspective transformation to the run-time image of  FIG. 8A , the symbol showing no distortion; 
         FIG. 9A  shows an example of a train-time image of a DataMatrix code symbol, a QRCode symbol, and two text blocks of human readable strings that are disposed on a planar surface, the symbols and text blocks showing perspective distortion in the image, as a result of using a camera with an optical axis having a non-zero incident angle with respect to the surface; and 
         FIG. 9B  shows a corrected image obtained by applying a perspective transformation to a run-time image that is an equivalent of the train-time image in  FIG. 9A , the symbols and text blocks showing no distortion in the corrected image. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , a preferred embodiment of the invention provides methods for calibrating a projective camera model of a camera  100 , for which a perspective transformation  105  exists, between a world plane  102  and an image plane  104 . The world plane  102  bears a code symbol  106 . 
     In general, the method of the invention can be used with other camera models, such as a simplified model with variable zoom, or a more complicated model including a lens with barrel or pin-cushion distortion, and with transformations other than geometric transformations and perspective transformations, such as a polynomial transformation, as long as a correspondence can be established using multiple feature points, as will be explained further below. 
     The method of the invention is applicable to mounted cameras for reading symbols, as well as to “portable” symbol readers, provided that the incident angle θ between an optical axis  108  of the camera (or the symbol reader) and a normal vector  110  of the surface  102  is substantially maintained. Thus, the distance of the camera (or the symbol reader)  100  relative to the surface  102  does not need to be “fixed”; the camera or reader  100  can move along the optical axis  108  and operate at any point away from the surface  102 , but not too far away, as limited by the focal length and resolution of the camera or reader  100 . 
     Referring to  FIG. 2 , the method of the invention is divided into train-time steps and run-time steps, wherein the train-time steps are performed before the run-time steps, and the run-time steps are typically repeated  214  after the train-time steps. 
     At train-time, a training image is acquired  200  that includes a two-dimensional (2D) code symbol  300  (as shown in  FIGS. 3 ,  5 ,  7 ,  9 , and  11 ) disposed on a train-time surface  310  using a camera  100  with an optical axis  108  having an incident angle θ with respect to the train-time surface  310 . The surface  310  can be flat, or it can be curved. 
     Next, a 2D code symbol reader is run  202  that can detect and tolerate distortion so as to provide a correspondence between at least two 2D coordinates of points within the training image and at least two 2D coordinates of points within the 2D code symbol. The complexity of the transformation to be constructed at train-time decides the number of points that need to be detected and involved in the correspondence. A correspondence between at least four 2D coordinates of points within the training image and at least four 2D coordinates of points within the 2D code symbol is required to construct a perspective transformation, for example. A correspondence between fewer points is needed for constructing a simpler transformation, for example, an affine transformation. Most conventional code readers that can read distorted 2D codes require implementing symbology-specific locating and decoding methods that can tolerate distortion. Such techniques are disclosed in U.S. Pat. No. 6,340,119 He, et. al, Techniques for Reading Two Dimensional Code, including MaxiCode, and U.S. Pat. No. 5,862,267 Liu, Method and Apparatus for Locating Data Regions in Stored Images of Symbols for Code One symbology, for example. 
     Then, using the correspondence, a coordinate transformation is constructed  204 , as will be explained in detail below. The coordinate transformation can be a geometric transformation, a perspective transformation, or it could be a non-linear transformation, for example. 
     At run-time, a symbol is placed  206  on a run-time surface that is substantially parallel to or the same as the train-time surface  310 . 
     Then, a run-time image is acquired  208  of a symbol disposed on the run-time surface using a camera with an optical axis having substantially the same incident angle θ with respect to the run-time surface. The symbol can be of a code of a different symbology with respect to the symbol used at train-time, or the symbol can be of the same symbology, but of different scale and/or dimensions. Further, the symbol is not limited to being selected from a two-dimensional code. The symbol can be selected from a stacked code, or from a linear barcode, or from a text block, for example. 
     Next, distortion of the run-time image is corrected  210  using the coordinate transformation so as to provide a corrected image, as will be explained further below. Alternatively, the symbol can be represented by one or more features, and if so-represented, then distortion of the run-time image is corrected  210  using the coordinate transformation so as to provide at least one corrected feature. 
     Then, a run-time symbol reader is run  212  on the corrected image. Alternatively, if the symbol is represented by one or more features, then the run-time symbol reader is run on the corrected features. 
     Then, a next symbol is to be read, returning to step  206 . 
     Referring again to  FIG. 1 , when a projective camera is used, a straight line in the world plane  102  is mapped to a straight line in the image plane  104 . The transformation  105  between the model plane and its image is often called a perspective transformation or a homography. When the train-time “surface” is a plane  102  that is not normal to the optical axis  108  of the image sensor  100 , the nominal grid of a two-dimensional matrix code that is a square in world plane is mapped to an arbitrary quadrilateral in image plane. When at least four corner points of the two-dimensional matrix code can be located, the homography between the model plane and its image can be estimated using a method described in (A. Criminisi, I. Reid, and A. Zisserman, A Plane Measuring Device, Image and Vision Computing, Vol. 17, No. 8, pp 625-634, 1999.):
 
A projective camera model can be written as M=Hm, where
 
             M   =     [         XW           YW           W         ]           
is a vector of world plane coordinates,
 
             m   =     [         x           y           1         ]           
is the vector of image plane coordinates, and H is a matrix transformation. This transformation can be written in more detail as:
 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           XW 
                         
                       
                       
                         
                           YW 
                         
                       
                       
                         
                           W 
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             a 
                           
                           
                             b 
                           
                           
                             c 
                           
                         
                         
                           
                             d 
                           
                           
                             e 
                           
                           
                             f 
                           
                         
                         
                           
                             g 
                           
                           
                             h 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             x 
                           
                         
                         
                           
                             y 
                           
                         
                         
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     With W=gx+hy+1, equation (1) is equivalent to 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           1 
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               a 
                             
                             
                               b 
                             
                             
                               c 
                             
                           
                           
                             
                               d 
                             
                             
                               e 
                             
                             
                               f 
                             
                           
                           
                             
                               g 
                             
                             
                               h 
                             
                             
                               1 
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               x 
                             
                           
                           
                             
                               y 
                             
                           
                           
                             
                               1 
                             
                           
                         
                         ] 
                       
                     
                     
                       
                         [ 
                         
                           
                             
                               g 
                             
                             
                               h 
                             
                             
                               1 
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               x 
                             
                           
                           
                             
                               y 
                             
                           
                           
                             
                               1 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     By reorganizing the two sides and group the X and Y terms, we have
 
 X=ax+by+ 1 c+ 0 d+ 0 e+ 0 f−Xxg−Xyh  
 
 Y= 0 a+ 0 b+ 0 c+xd+yd+ 1 f−Yxg−Yyh   (3)
 
     Or in matrix form: 
     
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             x 
                           
                           
                             y 
                           
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               - 
                               Xx 
                             
                           
                           
                             
                               - 
                               Xy 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             x 
                           
                           
                             y 
                           
                           
                             1 
                           
                           
                             
                               - 
                               Yx 
                             
                           
                           
                             
                               - 
                               Yy 
                             
                           
                         
                         
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                           
                             … 
                           
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             a 
                           
                         
                         
                           
                             b 
                           
                         
                         
                           
                             c 
                           
                         
                         
                           
                             d 
                           
                         
                         
                           
                             e 
                           
                         
                         
                           
                             f 
                           
                         
                         
                           
                             g 
                           
                         
                         
                           
                             h 
                           
                         
                       
                       ] 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           X 
                         
                       
                       
                         
                           Y 
                         
                       
                       
                         
                           … 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     The problem of estimating matrix H becomes solving equation Ax=B. A correspondence between two sets of at least four coordinates of points is needed to estimate the parameter vector x, which has eight unknown variables. Using the correspondence, this equation can be solved by several methods that achieve least-square estimation of the vector x; among these solutions, the simplest although not the most mathematically stable one is to use the pseudo-inverse:
 
 Ax=B  
 
 A   T   Ax=A   T   B  
 
 x =( A   T   A ) −1   A   T   B  
 
     Other more robust solutions can be found in W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C, 2 nd  edition, Cambridge University Press, 1992. With four corner points in a two-dimensional matrix code being detected, a correspondence can be established between four coordinates of corner points within the observed image, and their known coordinates in the world plane. When the purpose of this camera calibration is for code reading or quality assessment purpose only, it is not necessary to know the accurate dimension of the code in world plane, as long as a predetermined scale is used to set an expected location for each detected feature point. For example,  FIG. 3  shows a two-dimensional DataMatrix code that can be used for establishing the homography between world plane and image plane. In  FIG. 3 , four corner points are detected in the image plane of the DataMatrix code, with coordinates p i (x i ,y i ), i=1, 2, 3, 4. Without knowing the exact dimension of the code in the world plane, one can use a predetermined scale, e.g., a nominal module size in image coordinates (referred to as s), to set up imaginary coordinates in world plane. For example, the following correspondence can be set up for a numRow*numCol DataMatrix code:
 
 p   1 ( x   1   ,y   1 ) map to  P   1 ( X   1   ,Y   1 )=(0,0);
 
 p   2 ( x   2   ,y   2 ) map to  P   2 ( X   2   ,Y   2 )=(0,numCol* s );
 
 p   3 ( x   3   ,y   3 ) map to  P   3 ( X   3   ,Y   3 )=(numRow* s, 0);
 
 p   4 ( x   4   ,y   4 ) map to  P   4 ( X   4   ,Y   4 )=(numRow* s ,numCol* s ).
 
     After the homography matrix is estimated, every pixel in the run-time image or a derivative of the run-time image can be mapped to an imaginary plane that is parallel to the world plane. This step can correct any image that is acquired with the same camera model to assume that the image is acquired on a plane normal to the optical axis of the camera. Such an image is shown in  FIG. 4 . 
     After step  212 , i.e., after a symbol (one of two dimensional code, stacked code, or linear barcode) is detected and decoded in the corrected image, its coordinates in the original image can be obtained using the pseudo-inverse of the homography or other nonlinear transformation obtained in step  204 :
 
 M=Hm  
 
 H   T   M=H   T   Hm  
 
 m =( H   T   H ) −1   H   T   M  
 
     Thus, the detected and decoded symbol is mapped back to the train-time image plane for display and analysis. 
       FIG. 5A  shows an example of a train-time image of a DataMatrix code symbol  500  showing perspective distortion, as a result of using a camera with an optical axis having a non-zero incident angle with respect to a train-time planar surface upon which the DataMatrix code symbol is disposed with an orientation, such as shown in  FIG. 1 . After running a DataMatrix reader that can detect and tolerate distortion, the symbol  500  can be decoded, and 2D coordinates of four corner points  502 ,  504 ,  506 ,  508  of the symbol  500  can be obtained in the train-time image space, i.e., p i (x i ,y i ), i=1, 2, 3, 4. 
       FIG. 5B  shows a corrected image obtained by applying a perspective transformation, H, to a run-time image that is an equivalent of the train-time image in  FIG. 5A . The perspective transformation is constructed by a correspondence between the coordinates of the four corner points  502 ,  504 ,  506 ,  508  in train-time image space shown in  FIG. 5A  and the coordinates of the four transformed corner points  512 ,  514 ,  516 ,  518  in the transformed symbol  510  as shown in the run-time image space, i.e., p i (x i ,y i ) corresponds to P i (X i ,Y i ), i=1, 2, 3, 4. 
       FIG. 6A  shows another example of a run-time image, acquired at the incident angle with respect to the train-time surface, of the DataMatrix code symbol  500  in  FIG. 5A . The symbol  600  is an equivalent of symbol  500  being disposed with a second orientation on the train-time surface. The symbol  600  shows the perspective distortion, and has corner points  602 ,  604 ,  606 , and  608 . 
       FIG. 6B  shows a corrected image obtained by applying the perspective transformation, H, to the run-time image of  FIG. 6A . The transformed symbol  610  shows no distortion. After running a DataMatrix reader on the corrected image, coordinates of four corner points  612 ,  614 ,  616 , and  618  in the symbol  610  are obtained in the corrected image space: P 1i (X 1i ,Y 1i ), i=1, 2, 3, 4. After applying an inverse of the perspective transformation, (H T H) −1  H T , to P 1i , i=1, 2, 3, 4, their mapped versions are coordinates of four corner points  602 ,  604 ,  606 , and  608  in the symbol in the run-time image space, i.e., p 1i (x 1i ,y 1i ), i=1, 2, 3, 4. These mapped versions define an outline (not shown) of the DataMatrix symbol  600  in the run-time image, as shown in  FIG. 6A . 
       FIG. 7A  shows another example of a run-time image of a DataMatrix code symbol  700  with different symbol size than the size of the symbol  500  shown in  FIG. 5A , disposed in yet another orientation on the train-time surface. The symbol  700  exhibits perspective distortion, and has four corner points  702 ,  704 ,  706 ,  708 . 
       FIG. 7B  shows a corrected image obtained by applying the perspective transformation, H, to the run-time image of  FIG. 7A . The transformed symbol  710  shows no distortion. After running a DataMatrix reader on the corrected image, coordinates of four corner points  712 ,  714 ,  716 , and  718  in the symbol  710  are obtained in the corrected image space: P 2i (X 2i ,Y 2i ), i=1, 2, 3, 4. After applying an inverse of the perspective transformation, (H T H) −1  H T , to P 2i , i=1, 2, 3, 4, their mapped versions are coordinates  702 ,  704 ,  706 , and  708  of four corner points in the symbol in the run-time image space, i.e., p 2i (x 2i ,y 2i ), i=1, 2, 3, 4. These mapped versions define an outline of the DataMatrix symbol  700  in the run-time image, as shown in  FIG. 7A . 
       FIG. 8A  shows yet another example of a run-time image of a QRCode symbol  800 , disposed in yet another orientation on a run-time surface that is parallel to, but not co-planar with respect to, the train-time surface. The symbol  800  shows the perspective distortion, and includes corner points  802 ,  804 ,  806 , and  808 . 
       FIG. 8B  shows a corrected image obtained by applying the perspective transformation, H, to the run-time image of  FIG. 8A . The symbol  810  shows no distortion. After running a QRCode reader on the corrected image, coordinates of four corner points  812 ,  814 ,  816 , and  818  in the symbol may be obtained in the corrected image space: P 3i (X 3i ,Y 3i ), i=1, 2, 3, 4. After applying an inverse of the perspective transformation, (H T H) −1  H T , to P 3i , i=1, 2, 3, 4, their mapped versions are coordinates of four corner points  802 ,  804 ,  806 , and  808  in the symbol  800  in the run-time image space, i.e., p 3i (x 3i ,y 3i ), i=1, 2, 3, 4. These mapped versions define an outline of the QRCode symbol  800  in the run-time image, as shown in  FIG. 8A . 
       FIG. 9A  shows an example of a train-time image of a DataMatrix code symbol  900 , a QRCode symbol  920 , and two text blocks  940 ,  942  of human readable strings that are disposed on a planar surface. The symbols  900 ,  920  and text blocks  940 ,  942  show perspective distortion in the image, as a result of using a camera with an optical axis having a non-zero incident angle with respect to the surface. After running a DataMatrix reader that can detect and tolerate distortion, the DataMatrix symbol  900  can be decoded, and 2D coordinates of four corner points of the symbol  902 ,  904 ,  906 ,  908  can be obtained in the train-time image space, i.e., p 4i (x 4i ,y 4i ), i=1, 2, 3, 4. 
       FIG. 9B  shows a corrected image obtained by applying a perspective transformation, H 1 , to a run-time image that is an equivalent of the train-time image in  FIG. 9A . The symbols  910 ,  930  and text blocks  941 ,  943  show no distortion in the corrected image. The perspective transformation is constructed by a correspondence between the coordinates of the four corner points  902 ,  904 ,  906 ,  908  of the DataMatrix symbol  900  in train-time image space and the coordinates of the four corner points  912 ,  914 ,  916 ,  918  in the symbol  910  as shown in the run-time image space, i.e., p 4i  (x 4i ,y 4i ) corresponds to P 4i (X 4i ,Y 4i ), i=1, 2, 3, 4. After running a QRCode reader on the corrected image, coordinates of four corner points  932 ,  934 ,  936 ,  938  in the QRCode symbol  930  are obtained in the corrected image space: P 5i (X 5i ,Y 1 ), i=1, 2, 3, 4. After applying an inverse of the perspective transformation, (H 1   T H 1 ) −1  H 1   T , to P 5i , i=1, 2, 3, 4, their mapped versions are coordinates of four corner points  922 ,  924 ,  926 ,  928  in the symbol  920  in the run-time image space, i.e., p 5i (x 5i ,y 5i ), i=1, 2, 3, 4. These mapped versions define an outline of the QRCode symbol  920  in the run-time image, as shown in  FIG. 9A . 
     Other modifications and implementations will occur to those skilled in the art without departing from the spirit and the scope of the invention as claimed. Accordingly, the above description is not intended to limit the invention except as indicated in the following claims.