Abstract:
A method of capturing image data for iris code based identification of vertebrates, including humans, comprises the steps of:
       recording a digital image of an eye with a camera equipped with at least two light sources that have a fixed spatial relationship to an object lens of the camera;   locating the eye in the digital image by detecting a specularity pattern that is created by reflection of light from said at least two light sources at a cornea of the eye; and   calculating information on the position of the camera relative to the eye on the basis of said fixed spatial relationship between the light sources and the object lens and on the basis of said specularity pattern.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to a method of capturing image data for iris code based identification of vertebrates, including humans, the method comprising the steps of:
         recording a digital image of an eye with a camera equipped with at least two light sources that have a fixed spatial relationship to an object lens of the camera; and   locating the eye in the digital image by detecting a specularity pattern that is created by reflection of light from said at least two light sources at a cornea of the eye.       

     2. Description of Background Art 
     A method of this type has been described in US 2007/0140531 A1 and is used in the context of biometric identification systems based on iris analysis. 
     A biometric personal identification system based on iris analysis has been described by John G. Daugman in U.S. Pat. No. 5,291,560 and in J. G. Daugman: “How Iris Recognition Works”, IEEE Transactions on Circuits and Systems for Video Technology, Vol. 14, no. 1, pp. 21-30, January 2004. 
     Such identification systems take advantage of the fact that the iris of the eye of an individual, which may be a human or a vertebrate, has a characteristic pattern that is unique for that particular individual, so that an iris analysis may be used for uniquely identifying the individual. To that end, an image of an eye of the individual is captured with a digital camera, and image processing algorithms are used for recognizing the pupil and the iris of the eye in the digital image. Then, the iris pattern is normalized so as to compensate the effect of varying dilation or contraction of pupil, and a filter procedure is employed for transforming the normalized image of the iris into a digital code, a so-called iris code, that is unique to the individual and may therefore be used for identification purposes. 
     Once an iris code of an individual has been created and stored, that individual may be identified by capturing again an image of its eye, creating an iris code on the basis of the new image, and checking the iris code thus obtained against the code that had been stored previously. 
     In the image capturing method that has been specified in the opening paragraph, the recognition of the eye, especially its pupil and iris, is facilitated by detecting the specular reflection that is created by reflection of light from the light sources at the cornea of the eye. When, for example, the camera is equipped with two light sources, the specularity pattern will consist of two neighboring bright spots which can easily be identified in the digital image and the positions of which will roughly correspond to the position of the pupil of the eye, when the image has been captured head-on with the camera. 
     In order for the image data and the iris codes derived therefrom to be comparable, the images of the eye should be captured under similar, preferably identical conditions. Ideally, the camera should always have the same distance from the eye when the image is taken, and it should also be aligned on the “line of sight” of the eye, i.e. the line that passes through the center of the pupil and is normal to the plane of the pupil. 
     SUMMARY OF THE INVENTION 
     It is an object of the invention to improve the reproducibility of the conditions under which the image is captured. 
     In order to achieve this object, the method according to the invention comprises calculating information on the position of the camera relative to the eye on the basis of said fixed spatial relationship between the light sources and the object lens and on the basis of said specularity pattern. 
     For an eye having a cornea with a given shape and curvature, the specularity pattern is determined by the positional relationship between the light sources and the camera and by the position of the camera relative to the eye, in accordance with the laws of geometrical optics. Since the shape and the curvature of the cornea is practically the same for all individuals, at least all adults, of a given species of vertebrates, it is possible to reconstruct the position of the camera relative to the eye by analyzing the specularity pattern. Thus, it is possible with the method according to the invention to check at the very instant when the image of the eye is captured with the camera whether the position of the camera is within a tolerable range. Consequently, it can be assured that the images of the eye are always captured from an almost ideal camera position which will essentially be the same for all images, so that the effect of the camera position on the resulting iris codes is largely eliminated and the reliability of the identification system is improved. 
     The invention is particularly advantageous for species, such as horses, where the outer boundary of the iris, i.e. the boundary between the iris and the (white) sclera is largely obscured by the eyelids, so that it is difficult to determine the absolute size of the outer iris boundary. In this case, additional information on the camera position as provided by the analysis of the specularity pattern greatly facilitates the normalization of the iris image. 
     Other objects and features of the invention will become clear as the description proceeds. 
     In a preferred embodiment, the camera is equipped with two light sources, e.g. near infrared light sources, which are disposed symmetrically on opposite sides of the object lens of the camera. Then, the specularity pattern will consist of two bright spots. Based on a realistic estimate for the curvature of the cornea, the distance from the camera to the eye can be calculated from the spacing between the two bright specularity spots in the digital image. Further, when the image has been taken head-on, the mid-point between the two spots should coincide with the center of the pupil. An offset of the specularity pattern relative to the center of the pupil indicates that the image has been taken from a somewhat oblique angle. 
     When the pupil is elongated in a certain direction, the specularity pattern, when displayed on a display of the camera, helps to check the alignment of the camera relative to the direction of largest elongation of the pupil. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will become more fully understood from the detailed description given hereinbelow and the accompanying drawings which are given by way of illustration only and thus are not limitative of the present invention, and wherein: 
         FIG. 1  is a schematic front view of an eye of a vertebrate; 
         FIG. 2  is an overall flow diagram of a method for creating an iris code from a captured image of the eye; 
         FIGS. 3 and 4  are top plan views of the eye and a camera for taking an image of the eye; 
         FIG. 5  is a diagram illustrating a relation between a camera-to-eye distance and a spacing of specularity spots; 
         FIG. 6  is a top plan view similar to  FIGS. 3 and 4  for an oblique aspect angle of the camera; 
         FIG. 7  is a flow diagram of an image capturing method according to the invention; 
         FIG. 8  is a flow diagram of a method for segmenting a pupil in the image of the eye; 
         FIG. 9  is an example of a histogram used in the method that has been illustrated in  FIG. 8 , 
         FIG. 10  is an example of a set of pixels obtained in the pupil segmentation process; 
         FIG. 11  illustrates the contour of the pupil obtained as a result of the segmentation process; 
         FIG. 12  is a diagram illustrating a first embodiment of a method for normalizing an image of the iris of the eye; 
         FIG. 13  is a diagram illustrating another embodiment of the method for normalizing the iris image; 
         FIGS. 14 and 15  illustrate examples of normalized iris images; 
         FIG. 16  is a block diagram of an identification system for horses, based on iris analysis; and 
         FIG. 17  shows an example of a record in a database used in the identification system shown in  FIG. 16 . 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     As an example of an image of an eye of a vertebrate,  FIG. 1  shows an image of a (left) eye  10  of a horse. An upper lid  12 , a lower lid  14 , a conjunctiva  14 , a pupil  18  and an iris  20  of the eye have been shown schematically. As is typical for horses, the pupil  18  is elongated in lateral direction. A bright sclera  22  of the eye is obscured almost completely by the eyelids, so that only small fractions of an outer boundary  24  of the iris (iris/sclera boundary) are visible. 
       FIG. 2  illustrates essential steps of a method for creating an iris code from an image of the type shown in  FIG. 1 . 
     In a step S 1 , an image of the eye is captured with a digital camera  26  (shown in  FIG. 3 ). 
     In step S 2 , the digital image is subjected to image processing algorithms for delineating a boundary  28  of the pupil  18 . 
     In step S 3 , the image is subjected to further image processing for creating a normalized iris image, i.e. an image of the iris that is normalized to a standard size of the outer iris boundary  24  and a standard size of the pupil  18 . Such image normalization is necessary because, in practice, the pupil  18  dilates and contracts in response to varying illumination conditions, so that, when two images of the same iris are compared, the position and shape of the pupil boundary  28  will normally not be the same. 
     Finally, in step S 4 , the normalized iris image is filtered with suitable filter for obtaining a binary iris code which has a reasonable number of bits and is nevertheless capable of encoding the characteristic structural features of the iris  20 . 
     As is shown in  FIG. 3 , the camera  26  that is used for capturing the image of the eye  10  in step S 1  as a casing  30  and an object lens  32 . Two light sources  34  are rigidly mounted on the casing  30  and are disposed symmetrically on both sides of the object lens  32 . Preferably, the light sources  34  emit light in the near infrared to which the camera  26  is sensitive, so that the light sources provide good illumination conditions without blinding the horse and causing the pupil  18  to contract excessively. Near infrared illumination is used also to more effectively reveal iris structure because it penetrates iris pigment better than visible wavelengths. 
     As has schematically been shown in  FIG. 3 , ingoing light rays  36  propagate from each of the light sources  34  to the eye  10  and outgoing rays  38  propagate from the eye  10  to the object lens  32  after having been reflected at a cornea  40  of the eye. 
     As a result, the image captured with the camera  26  includes a specularity pattern formed by two bright specular spots  42  (see also  FIG. 1 ), which are reduced mirror images of the two light sources  34 . Although the light sources  34  have identical sizes and brightnesses, the spots  42  may be different in size, dependent upon the local curvature of the cornea  40 . 
     The positions of the specularity spots  42  in the image are determined by the positions of the light sources  34  relative to the camera  26  ( FIG. 3 ) and by the position of the camera  26  relative to the eye  10 , in accordance with the laws of geometrical optics. The ingoing ray  36  from each light source and the corresponding outgoing ray  38  are symmetric with respect to the axis of incidence, i.e. the normal to the cornea  40  at the reflection point of the rays  36 ,  38 . 
     More specifically, as has been illustrated in  FIG. 4 , the spacing s between the two spots  42  becomes smaller when the distance D between the camera  26  and the eye  10  becomes larger. Thus, since the distances of the light sources  34  from the object lens  32  are known, it is possible to calculate the camera-to-eye-distance from the spacing between the specularity spots  42  when the shape of the cornea  40  is known. 
     In a first approximation, the cornea  40  can be assumed to be spherical with a constant curvature that will be known for a given species, at least for adult individuals. For non-adults, there will be a known relation between the curvature of the cornea  40  and the age of the individual. In this first approximation, the camera-to-eye-distance D can be calculated on the basis of straightforward geometrical considerations. 
     In a more realistic approach, the local curvature of the cornea  40  will be a function of the distance of the respective incidence point from the center of the pupil  18 . Then, for a given configuration of the camera  26  and the light sources  34  and a given animal species, the relation between the spacing s of the specular spots  42  and the camera-to-eye-distance D will be given by a function that can be determined empirically. An example of a graph  44  of such a function has been shown in a diagram in  FIG. 5 , where the specularity spacing s, as measured in units of pixels in the digital image, is indicated on the abscissa, and the camera-to-eye-distance D is indicated on the ordinate. 
     For certain species, e.g. for horses, the cornea typically has different (but constant) curvatures in the vertical and horizontal direction. Then, the assumption of a spherical cornea is realistic as long as the specularity spots  42  are separated along a roughly horizontal section. 
     In a processor for processing the digital image obtained with the camera  26  (the processor may be implemented in the camera  26  and has not been shown here), the function represented by the graph  44  may be stored in the form of a look-up table or in the form of an algebraic expression, so that the camera-to-eye-distance D can readily be derived from the spacing s between the spots  42 . 
       FIG. 6  illustrates a situation in which the camera  26  captures the image of the eye  10  from a slightly inclined position, so that an aspect axis A that passes through the eye  10  and the camera  26  forms an angle α (aspect angle) with a line of sight S of the eye  10 , the line of sight S being defined as a line that passes through the center of the pupil  18  and is normal to the plane of that pupil. In this case, one of the specular spots  42  is closer to the line of sight S and hence to the center of the pupil  18  than the other spot. 
     In practice, the optical axis A of the camera  26  may deviate from the line of sight S of the eye  10  in both, horizontal direction (as shown in  FIG. 6 ) and vertical direction (not shown). In  FIG. 1 , a common center or mid-point of the spots  42  has been designated as  46 . A deviation of the camera  26  from the line of sight S in horizontal direction translates into a horizontal offset a of the mid-point  46  from a centroid or center  48  of the pupil  18 , and a deviation of the camera from the line of sight S in vertical direction translates into a vertical offset b. 
     When the camera-to-eye-distance D is known, the aspect angles such as the angle α can be calculated from the offsets a and b. In order to measure these offsets in the digital image, the position of the center  48  of the pupil  18  must be known. To that end, as is generally known in the art of image processing and has been illustrated in  FIG. 1 , a rectangular bounding box  50  may be drawn around the relatively dark area of the pupil  18 , and the center of that bounding box  50  may be taken as the center  48  of the pupil. 
     Thus, in summary, an analysis of the specularity pattern (spots  42 ) permits to determine four of the six degrees of freedom of the position of the camera  26  relative to the eye  10 . The two remaining degrees of freedom are rotations of the camera about a horizontal and a vertical axis, respectively, which, however, lead only to a shift of the image in horizontal and vertical direction in  FIG. 1  and can easily be compensated by moving the image such that the center  48  of the pupil will be in the center of the image. Knowledge of the four relevant degrees of freedom of the camera  26  permits to check the camera position at the very instant when the image of the eye is captured. 
     An example of a method of image capturing utilizing the principles that have been described above will now be explained in conjunction with a flow diagram shown in  FIG. 7 . This flow diagram expands the step S 1  in  FIG. 2 . 
     In step S 1 - 1 , the image of the eye  10  is “recorded” with the camera  26 . This means that the camera is operating in a video mode in which the image data are continuously transmitted from a CCD array of the camera to a processing module where they are processed further. Simultaneously, the image may continuously be displayed on a display of the camera, but the image data are not yet saved in a memory as long as the user of the camera does not actuate a trigger button of the camera. 
     In step S 1 - 2 , the processing software searches for the specularity pattern, i.e. for the bright spots  42 , in the digital image. These spots will have the highest intensity values in the entire image, so that they are easy to find and can then serve as a guide indicating the image area where the pupil ( 18 ) of the eye should be expected. 
     In step S 1 - 3 , the distance between the spots  42  is measured (in units of pixels), and the camera-to-eye-distance D is calculated on the basis of a function of the type shown in  FIG. 5 . 
     In step S 1 - 4 , the processing algorithm searches a region with very low intensity values in the vicinity of the spots  42 . This region is a candidate for the pupil  18  and is enclosed in the bounding box  50 . This provides at least a rough estimate for the position of the center  48  of the pupil. 
     Then, in step S 1 - 5 , the offsets a and b ( FIG. 1 ) are measured and the aspect angles (the angle α and its counterpart for a vertical offset) are calculated on the basis of the camera-to-eye-distance D that has been calculated before in step S 1 - 3 . 
     Optionally, the angular offsets may be used for refining the calculation of the camera-to-eye-distance D. When the cornea  40  is not spherical, the exact shape of the graph  44  in  FIG. 5  will also depend upon the angular offsets, so that an appropriate function for deriving the distance D from the specularity spacing should be selected dependent upon the actual values of the angular offsets. 
     In step S 1 - 6 , the calculated distance D and the angular offsets are checked against predetermined tolerance ranges. When the calculated values are within their respective tolerance ranges (Y), this means that the camera is in a suitable (or almost optimal) position for capturing the image of the eye  10 . Then, the camera is unlocked in step S 1 - 7 , and a corresponding “ok” sign is shown on the display of the camera, signaling to the user that he may push the trigger button. When the camera is triggered, in step S 1 - 8 , the image is scaled to a standard size on the basis of the calculated distance D, so that eyes of equal size will also have the same size in the digital image, regardless of the exact camera-to-eye-distance. Further, the image is clipped to a standard height and width which are selected such that the image will contain only the relevant image part, i.e. the region around the iris  20 . Finally, the scaled and clipped image is saved in a memory for further processing. 
     When it is found in step S 1 - 6  that at least one of the distance D and the angular offsets is not admissible (N), corresponding correction instructions are shown on the camera display in step S 1 - 9 , showing the user how he has to move the camera in order to bring the distance and the angular offsets into the respective tolerance ranges. From step S 1 - 9 , the program loops back to step S 3 , and the steps S 1 - 3  to S 1 - 6  are repeated until a suitable camera position has been reached. 
     In a modified embodiment of this method, calculations corresponding to those in steps S 1 - 3  to S 1 - 5  will be performed only after the camera has been triggered and the image has been saved. Depending on the result of a check that is comparable to step S 1 - 6 , the user will then be advised whether the image is accepted or rejected. In this case, the processing does not have to be done in the camera but may done in a multi-purpose computer to which the camera  26  is connected after the image has been taken. 
       FIG. 8  is a flow diagram expanding the step S 2  ( FIG. 2 ) of delineating the pupil boundary  28  ( FIG. 1 ). 
     In this example, the image that has been saved in step S 1 - 8  is a monochromatic (infrared) intensity image, wherein an intensity value is assigned to each pixel of the image. Of course, a straightforward extension to color images with, for example, three intensity values per pixel would be possible. 
     In the intensity image, the area of the pupil  18  is a low intensity area which, however, is “pierced” by the specularity spots  42 . In order to reconstruct the original pupil area, the specularity pattern is removed in step S 2 - 1 . This can be achieved by means of an inpainting algorithm which fills in the area of the spots  42  using information from the surrounding area of the pupil  18 . Mathematically, the problem is equivalent to solving a system of Navier-Stokes equations in classical fluid dynamics, when the image intensity is considered as a “stream function” for a two-dimensional incompressible flow. The Laplacian of the image intensity plays the role of the vorticity of the fluid and is trans-ported into the region of the spots  42  by a vector field defined by the stream function. Details of the algorithm are described by Bertalmio, M.; Bertozzi, A. L.; Sapiro, G.: “Navier-Stokes, Fluid Dynamics and Image and Video Inpainting” Computer Vision and Pattern Recognition, 2001, CVPR 2001, Proceedings of the 2001 IEEE Computer Society Conference, vol. 1, pp. I-355-I-362. Of course, any other known inpainting method may used. 
     As the pupil  18  is a low intensity area, the intensities are compared to a threshold in step S 2 - 2 , and pixels having an intensity above the threshold are masked-off, so that only low intensity areas remain which should include the pupil area. The threshold value may for example be 25% of the highest intensity value (after the specularity spots  42  have been eliminated). 
     The pupil area is not only characterized by low intensity values but also a low texture area, i.e. an area that is almost free of substantial high-frequency intensity variations. 
     This is why, in addition to the intensity criterion, the method for identifying the pupil area uses also a texture image that is constructed in step S 2 - 3 . 
     The texture image can be derived from the intensity image by computing an edge contrast for each pixel. For example, a Sobel first derivative filter may be used for that purpose, and the output may be smoothened with a spatial averaging filter. 
     Step S 2 - 4  is a step of forming a pointwise product of the masked intensity image obtained in step S 2 - 2  and the texture image obtained in step S 2 - 3 , i.e. the intensity value of each pixel is multiplied by the contrast value of that pixel. Thus, image areas in the masked intensity image which have both, a low intensity and low texture are characterized by particularly low values in the product image. The pixels of the pupil area can be expected to have the lowest product values in the entire image, and, moreover, these product values will be almost identical, since the pupil area is essentially uniform in both, intensity and texture. Consequently, a good estimate for the real pupil area will be obtained by comparing the product values to a suitably selected threshold. 
     To that end, a histogram of the product image is computed in step S 2 - 5 . An example of such a histogram has been illustrated in  FIG. 9 , showing the frequency of occurrence of each product value (i.e. the number of pixels having that product value) as a function of the product value. The pixels of the pupil  18  will form a distinct peak  52  at the low end of the histogram. 
     In step S 2 - 6 , a threshold T ( FIG. 9 ) is selected such that it marks the high end of the peak  52 . Consequently, all the pixels having product values below the threshold T can be expected to form the pupil area. 
     The set of pixels that fulfils this threshold criterion is selected in step S 2 - 7 . An example of such a set  54  has been shown in  FIG. 10 . In practice, there may of course be outliers, e.g. “islands”  56  of pixels which are located outside of the area of the pupil  18  but have product values below the threshold T, and “bays”  58  and “lakes”  60  of pixels inside the pupil area which have product values above the threshold T. 
     In step S 2 - 8 , the islands  56  are eliminated, using well known image processing techniques such as morphological dilation and erosion operations. The bays  58  and lakes  60  are eliminated by forming the convex hull of the remaining set  54 , as has been shown in  FIG. 11 . Normally, this convex hull will be a good guess for the real boundary  28  of the pupil  18 . 
     There may however be cases where the pupil area obtained in this way is unrealistically or unacceptably large or unrealistically or unacceptably small. Reasons for this may be for example an inappropriate choice of the threshold T or an extreme dilation or contraction of the pupil of the horse as a result of abnormal illumination conditions. The latter case will not actually be “unrealistic”, but should nevertheless be excluded, because extreme dilations or contractions of the pupil would imply that the iris  20  is distorted to an extent that makes the match of iris codes impossible even for images taken from the same individual. For this reason, it is checked in step S 2 - 9  whether the dimensions of the iris  20 , e.g. the total height, as determined on the basis of the convex hull is within an acceptable range. The upper and lower limits of this range can be determined empirically for the given species of vertebrates. It should be noted in this context that the height of the pupil area in the digital image can be taken as a measure for the actual height of the pupil because the image capturing process (step S 1 ) assures that the images are always taken from approximately the same distance and remaining distance variations have been compensated by image scaling. 
     If the result of the check in step S 2 - 9  is negative (N), it is checked in step S 2 - 10  whether a flag has been set. If the flag has not been set (N), the flag is set in step S 2 - 11 , and the program loops back to step S 2 - 6 . It will then be attempted in step S 2 - 6  to obtain a pupil with reasonable size by correcting the threshold T. When the dimension of the pupil was too large, the threshold T will be shifted to lower values, and it will be shifted to higher values when the dimension of the pupil was too small. When the steps S 2 - 6  to S 2 - 8  have been run-through a second time, and it is still found in step S 2 - 9  that the dimensions of the pupil are not acceptable, it is found in step S 2 - 10  that the flag is set (Y) which indicates that an attempt to correct the threshold T has already been made and has failed. In this case, the image is rejected in step S 2 - 12  and the user is invited to capture a new image. 
     Of course, in a modified embodiment, the flag checked in step S 2 - 10  may be replaced by a count value counting the number of times that the loop S 2 - 6  to S 2 - 11  has been run-through, so that a larger number of correction attempts for the threshold T can be made. 
     When the check in step S 2 - 9  has the result that the dimensions of the pupil are acceptable (Y), the process of delineating the pupil boundary is completed, and the program continues with in step S 2 - 13  for calling the procedure for normalizing the iris image (step S 3 ). 
     In a modified embodiment, the calculation the angular offsets (as in step S 1 - 5  in  FIG. 7 ) or a more exact calculation of these offsets may be performed subsequent to the delineation of the pupil boundary so that the more exact pupil boundary may be used for determining the position of the center  48  of the pupil. 
     As is shown in  FIG. 11 , the iris  20  is a ring shaped area that is delimited at the inner periphery by the pupil boundary  28  and at the outer periphery by the iris/sclera boundary  24 . When the pupil  18  dilates or contracts while the outer boundary  24  of the iris remains unchanged, each point of the iris  20  will be shifted in a generally radial direction by an amount that is large when the point is close to the pupil boundary  28  and becomes smaller when the point is closer to the stationary outer boundary  24 . The purpose of the normalization step S 3  is to obtain a normalized iris image that is not affected by the dilations and contractions of the pupil  18 , so that the iris images and the resulting iris codes can be compared to one another. 
     The approach is to transform the coordinates of the pixel of the iris area from a Cartesian xy-coordinate system (shown in  FIG. 11 ) into a coordinate system that may be called a “generalized polar coordinate system”. 
     If the pupil  18  could be assumed to be circular, a true polar coordinate system could be used, as is known for iris analysis for humans. In that case, normalization for varying pupil radii could easily be achieved by setting the radius coordinate of the pixel in proportion to the difference between the radius of the iris/sclera boundary and the radius of the pupil. However, in the method that is discussed here, the pupil boundary  28  is not defined as a circle but as a more complex geometrical line object which can only be described by a larger number of parameters. In the simplest case, the pupil boundary  28  may be considered as an ellipse or an any other simple type of oval, and in the most general (and most practical) case, the boundary  28  will be a polygon with a very large number of corners connected by straight line segments which will approximate the smooth contour of the true boundary. Such object can only be described by defining the coordinate positions of each vertex of the polygon. This makes the identification system more robust against irregular pupil shapes but, on the other hand, requires a non-trivial coordinate transformation for normalization purposes. 
     In order to obtain a suitable new coordinate system, the ring-shaped area of the iris  20  is divided into a sequence of radial spokes  62 , as has symbolically been shown in  FIG. 12 . In practice, the number of spokes will be significantly larger than in  FIG. 12 , preferably so large that each pixel of the image lies on one of the spokes  62 . This may involve a redimensioning and re-shaping of the pixels. For at least some of the spokes  62 , the spacing from spoke to spoke is larger near the outer boundary  24  than near the pupil boundary  28 . Near the outer boundary  24 , larger pixels may be formed by sampling or averaging over a plurality of pixels of the original image, which means a loss of resolution. Conversely, when the original pixel size is approximately retained near the outer boundary  24 , two or more of the spokes  62  may pass over the same original pixel near the pupil boundary  28 , which means that the image information becomes redundant. The number and density of the spokes  62  is therefore selected to be a reasonable compromise between resolution and redundancy. 
     The spokes  62  are numbered sequentially along the boundary of the pupil  28 . In the simplified example in  FIG. 12  (20 spokes), the spoke numbers are running from 1 through 20. For a pixel located on a given spoke  62 , the running number of that spoke will be the first coordinate “a” in the new coordinate system. As an example,  FIG. 12  shows a pixel  64  on spoke number  13 , so that the first coordinate “a” of this pixel will be a=13. A second coordinate r of the pixel  64  is determined by its location on the spoke, normalized to the entire length of the corresponding spoke, so that a pixel located on the pupil boundary  28  would have the second coordinate r=0 and a pixel located on the outer boundary  24  of the iris would have the coordinate r=1. 
     Thus, when the pupil boundary  28  is dilated while the (a, r)-coordinates are kept constant, the pixel  64  designated by these coordinates will move outwardly along its spoke. This movement of the pixel will at least approximately simulate the movement of the corresponding point on the iris when the iris is physically distorted by the dilation of the pupil. 
     Thus, when two images of the same iris are captured for different dilation states of pupil  18 , pixels having the same (a, r)-coordinates will at least approximately have the same intensity values. 
     In the scheme that has been described above, there is still some choice in the exact arrangement of the spokes  62 . In the example shown, the spokes are arranged to be normal to the pupil boundary  28  (i.e. normal to the tangent to this boundary at the point where the spoke meets the boundary). 
     In a modified embodiment, a number of equidistant points may be defined on the pupil boundary  28 , and a like number of equidistant points might be defined on the outer boundary  24 , and the spokes may be formed by connecting corresponding points on the two boundaries. 
     Other arrangement of the spokes  62  are also possible as long as the way how the pixels are shifted in response to dilations and contractions of the pupil correspond with sufficient accuracy to the actual distortion of the iris. 
     When the iris/sclera boundary  24  or at least a substantial part thereof is visible in the captured image, so that any obscured parts of the boundary can readily be interpolated on the basis of the assumption that the boundary has a regular (e.g. circular) shape (as is typically the case for humans), the length of each spoke  62  is determined by the requirement that the outer end of the spoke must be located on the boundary  24 . However, when the boundary  24  is largely obscured as in the example shown in  FIG. 1 , a suitable way must be found to “reconstruct” the boundary  24  or, more precisely, to construct an imaginary boundary that will be similar to the real boundary. 
     In the example shown in  FIG. 12 , it is assumed that the height of the iris  20 , i.e. the distance between the lower apex and the upper apex of the boundary  24 , is essentially the same for all adult individuals of the same species. For horses, it has been confirmed that this assumption is fulfilled with sufficient accuracy. 
     Since the image that has been obtained in step S 1 - 8  is scaled to a standard camera-to-eye-distance D, the above assumption implies that the vertical dimension of the boundary  24  has a fixed value, e.g. 150 pixel in the x-y coordinate system shown in  FIG. 11 . Then, a reasonable value for the length of the spokes  62  can be obtained by subtracting the vertical dimension of the pupil  18  (measured in pixels in  FIG. 11 ) from the vertical dimension of the boundary  24  and dividing the difference by two. In the example shown in  FIG. 12 , all the spokes  62  are assumed to have the same length which is calculated pursuant to this formula. Together with the requirement that the spokes are normal to the pupil boundary  28 , this defines the shape of the outer boundary  24 . 
     At least for horses, this way of constructing the boundary  24  is realistic. When the dilation and contraction of the pupil  18  is not isotropic, the horizontal dimension of the boundary  24  (distance from the left apex to the right apex in  FIG. 12 ) will not be exactly constant. However, the resulting deviations from the physical shape of the iris are found to be acceptable. 
       FIG. 13  illustrates a modified embodiment wherein it is assumed that not only the height but also the width of the iris  20  (its outer boundary  24 ) is constant, and the shape of the boundary  24  can be approximated by a suitable oval, such as an ellipse or a Cassini oval. In the example shown in  FIG. 13 , the height of the iris is assumed to be 150 pixel and the width is assumed to be 250 pixel. Again, the spokes  62  are arranged to be normal to the pupil boundary  28 . Further, in this example, the spokes  62  have been arranged such that their outer end points (on the boundary  24 ) are equidistant. As an alternative, the inner end points (on the pupil boundary  28 ) may be made equidistant (as in  FIG. 12 ), or equal distances may be required for corresponding points on the spokes  62  for any given coordinate value r between 0 and 1. 
       FIG. 14  gives an example of a normalized iris image  66  resulting from the coordinate transformation that has been explained in conjunction with  FIG. 12 . Here, the (a, r)-coordinates are represented as Cartesian coordinates, with the a-coordinates on the abscissa and the r-coordinates on the ordinate, so that the ring-shaped area of the iris  20  is evolved into a rectangular strip  68 . 
     Ideally, two normalized iris images  66  obtained from two photographs of the same eye should be identical. In practice, however, the absolute position of, e.g., spoke number  1  on the pupil boundary  28  is somewhat arbitrary, so that the a-coordinates in one image may be slightly shifted relative the a-coordinates in the other image. This effect may be compensated by a slight “rotation” of the spoke pattern along the boundary  28  or, equivalently, a cyclic permutation of the spokes in the normalized image  66 , as has been illustrated in  FIG. 15 . 
     Such a shift of the a-coordinates might also be caused by a slight rotation of the camera  26  about the aspect axis A ( FIG. 6 ) when the image is captured. In this case, an alternative possibility to compensate the shift is to rotate the digital image (prior to the coordinate transformation) until the axis of largest elongation of the pupil is horizontal in the image. 
     Another type of differences between two normalized images taken from the same eye may be caused by different positions of the upper and lower eyelids  12 ,  14  at the instant when the photos are taken, so that smaller or larger parts of the iris  20  are obscured. Consequently, when comparing two normalized images, the areas of the iris that may be affected by slight movements of the eyelids should be ignored. In  FIG. 12 , these areas have been delimited by straight lines  70 ,  72  in the top and bottom parts of the iris  20 . In 
       FIG. 14 , the ignored parts of the strip  68  in the normalized image  66  are delineated by corresponding lines  70 ′,  72 ′. 
     In order to facilitate and speed up the identification of individuals, the normalized images  66  are not directly compared to one another, but are subjected to a filter procedure resulting in a more compressed iris code (step S 4  in  FIG. 2 ). Such filtering procedures are known in the art. Examples are described by Daugman in U.S. Pat. No. 5,291,560 and in the article “How Iris Recognition Works” that has been cited in the introductory part of the present description. In brief, the process may include filtering horizontal slices through the normalized iris image  66  with logarithmic Gabor filters. This filter process provides a complex number of each point along the slice. The phases of these complex numbers may then be quantized into a two-bit representation specifying the quadrant in the complex plane in which the phase angle lies. These bits, together, form the iris code. 
     In order to identify an individual, the iris codes thus obtained are matched to one another. Preferably, the code match is repeated for several “rotated” versions of the normalized image  66  ( FIG. 15 ), and the portions delineated by the lines  70 ′,  72 ′ in  FIG. 14  are excluded from the code match. 
     The code match basically comprises computing the number of non-matching bits (Hamming Distance) by subjecting the two codes to be matched to an exclusive OR logical operation (XOR). The fraction of the non-matching bits in relation to the total number of bits indicates the probability that the two codes represent different eyes. When this fraction is smaller than a certain threshold, the code match is considered to have been successful. 
       FIG. 16  is a block diagram of an example of an identification system employing the method according to the invention and designed for identifying horses. A provider  74  of the identification services maintains a database  76  and communicates with a number of clients  78  via a communication network, e.g. the Internet. 
     Each client  78  can rent or purchase an iris code capturing kit  80  from the provider  74 . Each kit  80  includes the camera  26  as well as the software and hardware necessary for performing the method that has been described above. 
     An example of a record  82  that is kept in the database  76  and describes an individual horse has been given in  FIG. 17 . The record  82  includes an iris code field  84  and several other fields for other relevant data about the horse, such as its name, race, color, and the like. 
     When a client  78  wants to register a horse in the database  76 , he uses his kit  80  for capturing an image of one or both eyes of the horse and sends the iris code that has been created on the basis of this image to the database  76  along with other information to be entered into the record  82 . Preferably, the client generates a plurality of iris codes for the same eye of the horse, and a software in the kit  80  or in the premises of the provider  74  checks whether these codes are consistent, i.e. whether code matches between these codes are successful. When a code match is not successful, another attempt may be made after having performed a cyclic shift of the bits in one of the codes to be compared, this bit shift reflecting a cyclic permutation of the spokes or a-coordinates as has been described in conjunction with  FIGS. 14 and 15 . When a sufficient number of iris codes has been obtained that can mutually be matched to one another, one of these codes or an average over all these codes may be transmitted to the database  76  to be entered into the iris code field  84 . 
     When a client  78  wants to retrieve data about an individual horse from the database  76 , he uses the kit  80  for creating an iris code for this horse and sends the iris code to the database  76 , if possible together with other information for identifying the horse, such as the name, the owner, and the like. In order to find the pertinent record in the database, it may be more expedient to search for the name or other ID information rather than searching for a matching iris code. When a pertinent record has been found, the iris code sent by the client  78  may be checked against the iris code stored in the record in order to confirm the identity of the horse. Again, the code match may be repeated for a bit-shifted version of the code if the first attempt was not successful. Moreover, in order to improve the robustness of the identification, it is possible that the client  78  captures a plurality of images of the same eye of the same horse and sends the corresponding iris codes to the database  76 , where they are matched against the stored code. Then, identity will be confirmed when at least one of the codes matches. The required number of codes may however be smaller than in the case that a new record is entered into the database. 
     When a client  78  tries to find out the identity of an unknown horse, he may send the iris code of that horse to the database  76 , and this code may be checked against the codes that are stored in all the records  82  in the database, in order to determine the identity of the horse.