Abstract:
Images with closely spaced objects can be processed using a deblending procedure that includes the calculation of some moments and centroids of intensity data. Methods and apparatus for performing this processing are well-suited for use in DNA sequencing, where the locations of fluorescing nucleotides appearing in images must be compared across several images and can be very close to one another in any single image. The increased accuracy and resolution provided by embodiments of the invention reveals previously undetected or misdetected fluorescing nucleotides, thereby facilitating the sequencing process. Embodiments of the invention can be used in other applications where, for example, defects in testing apparatus and/or limitations on image resolution frustrate subsequent analyses.

Description:
TECHNICAL FIELD  
       [0001]     The present invention generally relates to image analysis.  
       BACKGROUND INFORMATION  
       [0002]     Image analysis often requires a determination of whether an observed object is a single object or whether it is made up of several overlapping objects. When objects in an image are spaced closer together than the resolving power of the optics, several closely spaced objects can erroneously appear as one large object.  
         [0003]     Software exists to process electronic (i.e., digitized) representations of images. The processing includes operations performed on the digital image data to effectively increase the resolution of the image and attempt to minimize or eliminate image artifacts. An example is a software application called Source Extractor, which is used to process and deblend astronomical images. Deblending is the process of attempting to determine whether an observed object is a single object or a collection of closely-spaced, but separate objects.  
         [0004]     Deblending in Source Extractor is performed by examining an intensity profile of the objects appearing in an image and comparing that profile to a threshold. This is described in, for example, B. W. Holwerda, Source Extractor for Dummies 32-34 (Space Telescope Science Institute, Baltimore, Md.) and also in E. Bertin, SExtractor v2.3 User&#39;s Manual 20-22 (Institue d&#39;Astrophysique &amp; Observatoire de Paris). This technique is generally unable to resolve individual objects that are closer than about four pixels.  
       SUMMARY OF THE INVENTION  
       [0005]     The invention generally relates to image processing techniques that improve the resolution of objects appearing in an image. The improved images can then be used in further analyses. In accordance with one aspect of the invention, images containing objects arranged very close together are processed and individual objects are distinguished from clusters of objects. Embodiments of the invention are useful to detect single molecules appearing in a dense field of objects. In a highly-preferred embodiment, single molecules labeled with an optically-detectable reporter are detected. The increased accuracy and resolution provided by the invention reveals previously undetected or misdetected single objects.  
         [0006]     The present invention provides, in one aspect, methods and apparatus for facilitating the accurate detection of objects appearing in an image, such as single fluorescent molecules. The invention provides resolution of closely-spaced objects without the need to perform intensive, time-consuming computations.  
         [0007]     In one particular embodiment according to the invention, a method of image analysis includes providing a representation of a sample image that contains intensity and centroid (coordinates of object centers) data for objects in the image. A deblending procedure is performed on the representation, which involves computing several moments corresponding to the intensity data. The moments allow the characteristics (e.g., position and/or intensity) of the sample objects to be computed. The number of mathematical moments that are calculated depends upon the number of objects that one wishes to resolve as taught below.  
         [0008]     Determination of moments associated with an object or objects allows computation of parameter, such as a revised centroid, that allow an observed object to be “fit” to one or more known objects. For example, single fluorescent molecules in a microscopic field of view have a known point spread function. In determining whether a given observed object is a single object, moments are determined as taught below, with the result being the determination whether the point spread function matches that of the known single object.  
         [0009]     Thus, in one embodiment of the invention, a deblending procedure includes the use of a point spread function to characterize object intensity data. The intensity data are fit to the point spread function, the effect of the now fitted point spread function is subtracted from the intensity data, and then moments representative of the intensity data are computed. The moments are then used to calculate centroids of the objects. The process can be repeated one or more times to refine the intensity data. This generally improves resolution of closely spaced objects.  
         [0010]     In a particular alternative aspect, methods of the invention are used to detect the incorporation of single fluorescent-labeled nucleotides into a single surface-bound nucleic acid duplex in a template-directed sequencing-by-synthesis reaction, as detailed below.  
         [0011]     Other aspects and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating the principles of the invention by way of example only. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]     The foregoing and other objects, features, and advantages of the present invention, as well as the invention itself, will be more fully understood from the following description of various embodiments, when read together with the accompanying drawings, in which:  
         [0013]      FIG. 1  is a flowchart depicting a method for image analysis in accordance with an embodiment of the invention;  
         [0014]      FIG. 2  is a flowchart depicting a method for deblending a representation of an image in accordance with an embodiment of the invention;  
         [0015]      FIG. 3A  is a depiction of a representation of an image before deblending in accordance with an embodiment of the invention;  
         [0016]      FIG. 3B  is a depiction of a representation of an image after deblending in accordance with an embodiment of the invention;  
         [0017]      FIG. 4A  depicts a single peak intensity profile;  
         [0018]      FIG. 4B  is a theoretical projection of the intensity profile depicted in  FIG. 4A ;  
         [0019]      FIG. 4C  depicts a view of a dual peak intensity profile;  
         [0020]      FIG. 4D  depicts an alternate view of the dual peak intensity profile shown in  FIG. 4C ;  
         [0021]      FIG. 4E  is a theoretical projection of the intensity profile depicted in  FIGS. 4C and 4D ;  
         [0022]      FIG. 4F  depicts another dual peak intensity profile;  
         [0023]      FIG. 4G  depicts a planar view of the dual peak intensity profile shown in  FIG. 4F ;  
         [0024]      FIG. 4H  is a theoretical projection of the intensity profile depicted in  FIGS. 4F and 4G ;  
         [0025]      FIG. 5  is a block diagram depicting image analysis apparatus in accordance with an embodiment of the invention;  
         [0026]      FIG. 6  is a representation of image analysis apparatus in accordance with an embodiment of the invention; and  
         [0027]      FIG. 7  depicts a series of intensity peaks for correlation in accordance with an embodiment of the invention. 
     
    
     DESCRIPTION  
       [0028]     As shown in the drawings for the purposes of illustration, the invention may be embodied in methods and apparatus for analyzing images acquired during DNA sequencing. Embodiments of the invention are useful for minimizing or eliminating image artifacts that compromise the accuracy of detection. Application of methods of the invention to nucleic acid sequencing is used to demonstrate the utility of the invention. The skilled artisan understands that the principles of the invention are useful in any application in which high-resolution single object detection is desired, e.g., including applications involving diffraction limited or other symmetrical objects.  
         [0029]     In brief overview,  FIG. 1  is a flowchart depicting a method  100  for image analysis in accordance with an embodiment of the invention.  
         [0030]     In the context of DNA sequencing, embodiments of the invention are used to identify the incorporation into a template/primer duplex of single, labeled nucleotide at a discrete location on a surface. The basic process includes attaching nucleic acid duplex (comprising a template hybridized to a primer) to a surface, such as glass or fused silica (the specific type of surface is immaterial to the present invention, but should be selected to be compatible with the type of label used). The attached duplex is then exposed to an optically-labeled nucleotide that hybridizes to the next available nucleotide in the template (available meaning just 3′ of the template terminus) and a polymerizing enzyme capable of incorporating the labeled nucleotide into the primer. Incorporation is determined by observing the optically-detectable label at the known location of the duplex. For example, if the optically-detectable label is a fluorescent label, then illumination at the appropriate wavelength is used to stimulate fluorescence of the label. The invention allows one to determine whether a single optically-labeled nucleotide has been incorporated or whether there are multiple duplexes, non-specific label, dirt, etc. that overlap.  
         [0031]     An image acquired after each incorporation step (i.e., a sample image  118 ) shows the location of each specific fluorescing nucleotide (i.e., sample objects  120  ). DNA sequencing includes comparing the location of each sample object  120  with the location of each template object  104  (i.e., the expected object location). If the locations correspond, an “incorporation event” occurred. In other words, there is confirmation that a specific nucleotide is present in that part of the DNA strand. If the locations do not correspond (e.g., the fluorescence of the sample object  120  is due to a defect in the testing apparatus), then the specific nucleotide is not considered present in that part of the DNA strands. The process of incorporation is repeated until a desired number of incorporations has been reached. At the end of this process the sequence of the nucleotides in the template is known. This is discussed below in connection with  FIG. 7 .  
         [0032]     Defects in the testing apparatus and limitations on image resolution can hide or misidentify single fluorescent objects, thereby compromising the accuracy of the data.  
         [0033]     In embodiments of the invention, an image  102  is acquired using, for example, a personal computer with an image capture card. The image is recorded in one or more electronic files, typically in the “FITS” (Flexible Image Transport System) format. A photometry program then operates on the FITS files. One such program is Source Extractor, which is typically used in astronomical studies. The photometry program detects the intensities and locations of the fluorescence (i.e., the template objects  104 ) and generates a representation of the image  106  that includes a table or catalog containing intensity data  108  and the centroids  110  of the objects  104 . The intensity data  108  generally follow a Gaussian distribution, and the centroids  110  are typically the coordinates of the centers of the identified objects  104 .  
         [0034]     A problem with the representation of the image  106  is that photometry programs generally have a limited ability to identify or resolve a number of closely spaced objects  104 . For example, the photometry programs can erroneously interpret two discrete, closely spaced objects  104  as single large object. This can occur if the objects  104  are closer than, for example, four pixels. To minimize or eliminate this problem, embodiments of the invention subject the representation of the image  106  to post-processing known as deblending  112 .  
         [0035]     Deblending  112 , described more fully below in connection with  FIG. 2 , examines the intensity data  108  (collectively, the intensity flux), and computes several axially-specific, zero-, and higher-order moments  114  of the intensity flux. A result is a series of equations that are solved simultaneously to yield a template parameter  116  that, in some embodiments, includes corrected values for the centroids  110 . The corrections have the effect of revealing locations of additional objects  104  that were previously unresolvable.  
         [0036]      FIG. 2  is a flowchart depicting a method for deblending  200  in accordance with an embodiment of the invention. A representation of the image  202  includes, as described above, intensity data  204  and centroids  206  of the fluorescing objects therein. The fluorescing objects generally appear in a constellation-like form  203 . When the representation of the image  202  includes many large and closely spaced fluorescing objects, for example, as shown in illustration  302  in  FIG. 3A , deblending  200  operates to minimize or eliminate artifacts that could prevent a proper analysis.  
         [0037]     The intensity data  204  for each fluorescing object are typically follow a curve that can be approximated by a known point spread function  208 , such as a Gaussian function or a sine cardinal (“sinc”) function. In the case of the Gaussian function, the intensity data  204  (collectively, the intensity flux “F(x, y)”) for a fluorescing object is given by Equation 1:  
               F   ⁡     (     x   ,   y     )       =       F     π   ⁢           ⁢     σ   2         ⁢     ⅇ         -       (     x   -     μ   1       )     2       -       (     y   -     μ   2       )     2         2   ⁢           ⁢     σ   2                     Equation   ⁢           ⁢   1             
 
 Where F(x, y) is the flux at a location given by coordinates (x, y), μ 1  and μ 2  are the x- and y-coordinates (i.e., centroid) of the fluorescing object, σ is the standard deviation, and F is the maximum intensity. In the case where there are two nearby fluorescing objects, Equation 2 gives the flux:  
               F   ⁡     (     x   ,   y     )       =           F   1       π   ⁢           ⁢     σ   2         ⁢     ⅇ         -       (     x   -     μ     1   ⁢   x         )     2       -       (     y   -     μ     1   ⁢           ⁢   y         )     2         2   ⁢           ⁢     σ   2             +         F   2       π   ⁢           ⁢     σ   2         ⁢     ⅇ         -       (     x   -     μ     2   ⁢   x         )     2       -       (     y   -     μ     2   ⁢           ⁢   y         )     2         2   ⁢           ⁢     σ   2                       Equation   ⁢           ⁢   2             
 
 Where (μ 1x , μ 1y ) and (μ 2x , μ 2y ) are the (x, y) coordinates (i.e., centroid) of the first and second fluorescing objects, respectively. 
 
         [0038]     The intensity data  204  and centroid  208  for each fluorescing object are then fit  210  to the known point spread function  208 . Data are fit according to Equation 2A:  
               L     2   -   fit       =     ∫     ∫         (           F   image     ⁡     (     x   ,   y     )       -   E     E     )     2     ⁢     ⅆ   x     ⁢     ⅆ   y                   Equation   ⁢           ⁢   2   ⁢           ⁢   A             
 
 (Where “E” is either Equation (1) or Equation (2), depending on whether there are one or two objects, and F image (x, y) is the actual image data.) A result is a series of fitted point spread functions  212 , one for each fluorescing object in the representation of the image  202 . Next, the effect of a quantity of the fitted point spread functions  212  is subtracted  214  from the representation of the image  202 . In other words, intensity data generated by a quantity of the fitted point spread functions  212  is subtracted  214  from the intensity data  204  in the representation of the image  202 . The number of fitted point spread functions  212  used to generate the data to be subtracted can be based on a pixel distance between the centroids of the fluorescing objects or, in the alternative, a fixed pixel distance (e.g., six pixels). Also, the number can be based on a characteristic of the object intensity data, such as the full-width half-maximum (“FWHM”) of the known point spread function  208 . In the case of the Gaussian function, the FWHM is given by Equation 3: 
 
 FWHM=   2σ√{square root over (2 ln 2)}≈2.3548σ   Equation 3 
 
         [0039]     The subtraction  214  yields a revised representation of the image  216  that includes revised intensity data  218 . In some embodiments, several axially-specific, zero-, and higher-order moments of the revised representation of the image  216  (i.e., moments of the revised intensity data  218  associated with each fluorescing object) are computed, as shown in Equations 4 through 13: 
 
 M   0   =∫∫F ( x,y ) dxdy   Equation 4 
 
 M   1x   =∫∫xF ( x,y ) dxdy   Equation 5 
 
 M   1y   =∫∫yF ( x,y ) dxdy   Equation 6 
 
 M   2xx   =∫∫x   2   F ( x,y ) dxdy   Equation 7 
 
 M   2xy   =∫∫xyF ( x,y ) dxdy   Equation 8 
 
 M   2yy   =∫∫y   2   F ( x,y ) dxdy   Equation 9 
 
 M   3xxx   =∫∫x   3   F ( x,y ) dxdy   Equation 10 
 
 M   3yxx   =∫∫yx   2   F ( x,y ) dxdy   Equation 11 
 
 M   3yyx   =∫∫y   2   xF ( x,y ) dxdy   Equation 12 
 
 M   3yyy   =∫∫y   3   F ( x,y ) dxdy   Equation 13 
 
 Equation 4 represents the zero-order moment, and Equations 5 and 6 represent the first-order moments of the intensity data  218  having a single peak, as shown in  FIG. 4A , with the corresponding theoretical projection shown in  FIG. 4B . Equations 7, 8, and 9 represent second order moments, which can be important in instances where the intensity data  218  have two peaks, as shown in  FIG. 4C  and, in alternate view,  FIG. 4D , with the corresponding theoretical projection shown in  FIG. 4E . Equations 10, 11, 12, and 13 represent third order moments, which can also be important in instances where the intensity data  218  have two peaks arranged, for example, as shown in  FIGS. 4F and 4G , with the corresponding theoretical projection shown in  FIG. 4H . The area of integration for Equations 4 through 13 is typically limited to the FWHM value of each corresponding fluorescing object. In some embodiments, the area of integration is limited to a fixed number of pixels, such as six pixels. 
 
         [0040]     Note that it may be necessary to rotate the coordinate system used in Equations 7 through 13 by an angle “theta” (θ) to align with another coordinate system. This is accomplished using the well-known coordinate transformation matrix for tensors. Consequently, Equations 7 through 13 can be restated as follows: 
 
 M   2xx (θ)= M   yy  sin 2 θ+2 M   xy  sin θ cos θ+ M   xx  cos 2 θ  Equation 7A 
 
 M   2xy (θ)=( M   yy   −M   xx )sin θ cos θ+ M   xy (cos 2 θ−sin 2 θ)  Equation 8A 
 
 M   2yy (θ)= M   xx  sin 2 θ−2 M   xy  sin θ cos θ+ M   yy  cos 2 θ  Equation 9A 
 
 M   3xxx (θ)= M   3xxx  cos 3 θ+3 M   3xxy  sin θ cos 2 +3 M   3xyy  sin 2 θ cos θ+ M   3yyy  sin 3 θ  Equation 10A 
 
 M   3xxy (θ)= M   3yyy  sin 2 θ cos θ− M   3xyy (sin 3 θ−2 sin θ cos 2 θ)+ M   3xxy (cos 3 θ−2 sin 2 θ cos θ)− M   3xxx  sin θ cos 2 θ  Equation 11A 
 
 M   3xyy (θ)= M   3xxx  sin 2 θ cos θ+ M   3xxy (sin 3 θ−2 sin θ cos 2 θ)+ M   3xyy (cos 3 θ−2 sin 2 θ cos θ)+ M   3yyy  sin θ cos 2 θ  Equation 12A 
 
 M   3yyy (θ)= M   3yyy  cos 3 θ−3 M   3xyy  sin θ cos 2 θ+3 M   3xxy  sin 2 θ cos θ− M   3xxx  sin 3 θ  Equation 13A 
 
         [0041]     Assuming the flux F(x, y) is given by Equation 2, Equations 4 through 13 simplify to the following due to symmetry with respect to the x-axis that is a result of the coordinate transformation described above: 
 
 M   0   =F   1   +F   2   Equation 14 
 
 M   1   =M   1x   =μ   1   F   1   +μ   2   F   2   Equation 15 
 
 M   2   =M   xx =σ 2 ( F   1   +F   2 )+ F   1 μ 1   2   +F   2  μ 2   2   Equation 16 
 
 M   3   =M   xxx =¾μ 1 σ 2   F   1 +¾μ 2 σ 2   F   2 +μ 1   3   F   1 +μ 2   3   F   2   Equation 17 
 
         [0042]     To solve the system of Equations 14-17, first define the following quantities:  
             C   ≡         M     3   ⁢           ⁢   x   ⁢           ⁢   x   ⁢           ⁢   x       ⁢     σ   2         2   ⁢           ⁢       M     y   ⁢           ⁢   y       ⁡     (       σ   2     2     )       ⁢     (         M     x   ⁢           ⁢   x         M     y   ⁢           ⁢   y         -   1     )     ⁢         (       σ   2     2     )     ⁢     (         M     x   ⁢           ⁢   x         M     y   ⁢           ⁢   y         -   1     )                     Equation   ⁢           ⁢   18               X   ≡         σ   2     2     ⁢     (         M     x   ⁢           ⁢   x         M   0       -   1     )               Equation   ⁢           ⁢   19               f   ≡       F   1       F   2               Equation   ⁢           ⁢   20             
 
         [0043]     Combining Equations 14-23 yields the revised centroid  220  of a fluorescing object:  
               μ   1     =       X     f             Equation   ⁢           ⁢   24                 μ   2     =       -     μ   1       ⁢   f             Equation   ⁢           ⁢   25             
 
         [0044]     The coordinates (μ 1 , μ 2 ) given by Equations 24 and 25 represent the revised (x, y) location of a fluorescing object in the revised representation of the image  216 . In other words, each fluorescing object subjected to deblending  200  has its initial centroid  206  recomputed to yield a revised centroid  220 , thereby reducing the effects of image artifacts.  
         [0045]     Next, in some embodiments, a revised object set is determined for each fluorescing object by replacing the original centroid  206  with a pair of centroids (μ 1 , μ 2 ). In the case of the Gaussian function (i.e., Equations 1 and 2), the x 0  coordinate is changed to the values computed by Equations 24 and 25 for each fluorescing object.  
         [0046]     The revised intensity data  218  and revised centroid  220  for each fluorescing object are then fit  224  to the revised point spread function  222 . A result is a series of fitted revised point spread functions  226 , one for each fluorescing object in the revised representation of the image  216 . Next, the effect of a quantity of the fitted revised point spread functions  226  is subtracted  228  from the revised representation of the image  216 . Similar to that described above, intensity data generated by a quantity of the fitted revised point spread functions  226  is subtracted  228  from the revised intensity data  218  in the revised representation of the image  216 . The number of fitted revised point spread functions  226  used to generate the data to be subtracted can be based on a pixel distance between the revised centroids of the fluorescing objects or, in the alternative, a fixed pixel distance (e.g., six pixels). Also, the number can be based on a characteristic of the object revised intensity data, such as the FWHM of the revised point spread function  222 .  
         [0047]     The subtraction  228  yields a final representation of the image  230  that includes final intensity data  232 . In some embodiments, several axially-specific, zero-, and higher-order moments of the final representation of the image  230  (i.e., moments of the final intensity data  232  associated with each fluorescing object) are computed, as shown in Equations 4 through 13. Proceeding as described above in connection with Equations 14 through 23, a new set of coordinates (μ 1 , μ 2 ) is computed for each fluorescing object. These new coordinates (μ 1 , μ 2 ) are the final centroid  234  for each fluorescing object. In some embodiments, the final centroid  234  becomes the parameter  236  used in the comparison of the template and sample objects.  
         [0048]     An illustration  231  of the final representation of the image  230  lacks many of the image artifacts present in the initial representation of the image  202 . In particular,  FIG. 3B  shows several instances  231 A,  231 B,  231 C,  231 D,  231 E where two fluorescing objects appear. Before deblending  200 , many closely spaced pairs of fluorescing objects, such as those shown in  FIG. 3B , would be erroneously rendered as single large objects, thereby preventing a proper analysis of, for example, chemical incorporations in DNA sequencing.  
         [0049]     The process of fitting a point spread function to intensity data, subtracting the effect of the function from the data, and computing new centroids by the calculation of moments can be performed more than the two times described above. In theory, repeating the process will refine the image data, thereby reducing artifacts and allowing for the resolution of more (e.g., three or greater) closely spaced objects.  
         [0050]     In brief overview,  FIG. 5  is a block diagram depicting image analysis apparatus  500  in accordance with an embodiment of the invention. The apparatus  500  includes an image capture subsystem  502  that acquires images of fluorescing objects (i.e., template objects  104 , or sample objects  120 , or both), digitizes them, and generates corresponding optical data  504  that can be stored in computer files, typically in the FITS format. First software code  506  processes the optical data  504  and generates field pattern data  508  that includes original centroids  510  of the fluorescing objects. In the context of DNA sequencing, at least some of the original centroids  510  are associated with a single molecule of one of the nucleic acid sequences (i.e., DNA strands) adhered to a surface.  
         [0051]     Second software code  512  processes the optical data  504 , or the field pattern data  508 , or both, computes the moments  514  of the intensity data corresponding to each fluorescing object, and generates a replacement field data pattern  516 . From the computation of the moments  514 , the second software code  512  also calculates replacement centroids  518 . The apparatus  500  can repeat this process any number of times to refine the data.  
         [0052]     The second software code  512  determines if any of the original centroids  510  should be replaced by two or more replacement centroids  518 . This can occur when, for example, the moments  514  suggest that what was thought to be a single fluorescing object is actually two (or more) closely spaced fluorescing objects, each having its own centroid. For example, compare the fit of the image with a two centroid configuration with a fit of the image with a single centroid configuration. Apply a tolerance (e.g., 0.7-0.9) to the fit of the image with a single centroid configuration and choose which represents the better overall fit, typically still giving preference to the single centroid configuration. Consequently, the replacement field data pattern  516  typically includes both the replacement centroids  518  and any remaining centroids  520  (i.e., original centroids  510  left unchanged by the second software code  512  ).  
         [0053]     The apparatus  500  includes third software code  522  for processing the replacement field data pattern  516  to determine if each of the centroids  518 ,  520  in the replacement field data pattern  516  is associated with a single molecule of one of the nucleic acid sequences. The third software code  522  generally does this by comparing the centroids of the template image with the centroids of the sample images. If the comparison reveals that the centroids are substantially equal (e.g., within an acceptance radius of about 0.8 pixel; of course, this value can vary depending on the quality of the optics and the amount of noise present, i.e., signal integrity), it can be concluded that an incorporation event  528  occurred. If the comparison reveals no substantial equality, it can be concluded that no incorporation event  526  occurred. As described above, repeating this process on images obtained after each chemical wash of the DNA strands allows the user to compile a list of the sequence of nucleotides in the strands.  
         [0054]      FIG. 6  is a representation of image analysis apparatus  600  in accordance with an embodiment of the invention. The apparatus  600  includes a pulsed laser  602  that produces a beam that is passed through a series of mirrors  604 , mirrors coupled to galvanometers  606 , correction optics  608 , and an objective  610  to illuminate a sample  612  (e.g., the DNA strands attached to a surface). The laser beam is reflected by the sample and returns along its initial path and through a partially silvered mirror to a filter  614  and confocal pinhole  616 . At this point, the reflected beam is separated into two beams based on polarization or wavelength by a separator  618 . Each beam is then passed through dedicated avalanche photodiodes (“APDs”)  620  and image capture boards  622 . Data from the image capture boards  622  are sent to a computer  624  for further processing (e.g., deblending) by one or more software programs running on the computer  624 . The program(s) perform the processing operations describe herein, and all or some portions of the program(s) can be stored in the computer  624  on its hard drive and/or in its permanent and/or temporary memory. All or some portions of the program(s) can be stored on any program storage medium that is readable by a computer such as, for example, one or more of RAM, ROM, removable memory/storage devices, hard drives, CDs, etc. The computer  624  is depicted in  FIG. 6  as a desktop personal computer, but it can be any other type of computer and in fact any type of computing device now known or later developed (e.g., handheld, laptop, server, workstation, supercomputer, networked device, etc.) running any operating system as long as it is capable of performing the processing operations described herein such as the deblending described herein.  
         [0055]      FIG. 7  depicts a series of intensity peaks  700  for correlation in accordance with an embodiment of the invention. The representation of the template image  106  shows four intensity peaks representing the locations of the DNA strands on a surface. After a first series of chemical washes directed to a specific location  702  along the strands, one intensity peak is revealed. This intensity peak corresponds to one of the nucleotides and, because its location correlates (within a reasonable range of uncertainty) with the location of an intensity peak on the representation of the template image  106 , it can be concluded that an incorporation event occurred. In other words, at this point on the DNA strand, a specific nucleotide is present.  
         [0056]     A second series of chemical washes is then directed to the next location  704  along the DNA strands. At this point, three intensity peaks are revealed that have locations corresponding to the locations of intensity peaks on the representation of the template image  106 . Accordingly, these incorporation events indicate that a specific nucleotide is present. The process repeats with a third series of chemical washes is then directed to the next location  706  along the DNA strands, and continues until the last location  708  in the DNA strands is subjected to the sequential washes and the locations of the fluorescing objects are compared. At this point the user has compiled a list of the sequence of nucleotides, and the DNA strands have been “sequenced.” 
         [0057]     Note that embodiments of the invention can be used to analyze images unrelated to DNA sequencing. For example, any image that includes objects oriented in such a way to make resolution of them difficult may be subjected to the deblending process described herein. Performing one or more deblending “passes” on the image reduces artifacts and helps resolve the locations of the objects. When multiple images are to be compared, subjecting them to deblending before the comparisons increases accuracy.  
         [0058]     Note that in  FIGS. 1 through 7  the enumerated items are shown as individual elements. In actual implementations of the invention, however, they may be inseparable components of other electronic devices such as a digital computer. Thus, actions described above may be implemented in software that may be embodied in an article of manufacture that includes a program storage medium. The program storage medium includes, for example, data signals embodied in one or more of a carrier wave, a computer disk (magnetic, or optical (e.g., CD or DVD), or both), non-volatile memory, tape, a system memory, and a computer hard drive.  
         [0059]     From the foregoing, it will be appreciated that methods and apparatus according to the invention afford a simple and effective way to analyze images used in DNA sequencing or in any other application where images must be examined or compared with accuracy and can be difficult to obtain due to, for example, defects in the testing apparatus and/or limitations on image resolution.  
         [0060]     The invention may be embodied in other specific forms than what is particularly disclosed herein without departing from the spirit or scope of the invention. The foregoing disclosed embodiments are in all respects illustrative rather than limiting on the invention.