Patent Publication Number: US-6990221-B2

Title: Automated DNA array image segmentation and analysis

Description:
RELATED APPLICATION 
     This is a Continuation Application of application Ser. No. 09/020,155, filed Feb. 7, 1998, now U.S. Pat. No. 6,674,882. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to DNA array image analysis, and, image analysis, and, in particular, to automatically segmenting DNA array images into individual DNA spot images for quantification. 
     BACKGROUND 
     Cellular behavior is primarily dictated by the selective expression of a subset of genes. Normal growth and differentiation depends on the appropriate genes being expressed in a desired context. Various disease states alter the normal expression of genes as compared to normal tissue. For example, malignant transformation of cancer tissues involves or induces altered gene expression. Through signal transduction cascades and transcriptional networks, alterations of one gene can impact a large number of genes and result in global effects on cell behavior. Regulation of translation and post-transcriptional modification play significant roles, but, invariably, signal transduction pathways lead to the nucleus and changes in gene transcription. 
     Therefore, there has been enormous interest in the development of techniques that allow the analysis of differential gene expression between different tissues or cell lines. One such technique includes use of ordered micro-arrays that allow two color fluorescence detection of hybridization signals. Individual DNA targets are arrayed on a small glass surface and hybridized with fluorescently labeled heterogeneous DNA probes derived from cDNA. The amount of fluorescence at each DNA spot correlates with the abundance of that DNA fragment in the probe mixture. 
     Using micro-arrays, gene expression levels can be quantitated at up to thousands of genes simultaneously. As hundreds of the same array can be printed, numerous tissues can be easily analyzed for relative expression levels. As such, the technique provides a powerful new tool for analyzing differential gene expression in numerous biologic problems. In addition to the determination of gene expression differences between tissues, genomic micro-arrays are useful for genomic mapping, genomic ploidy measurements and as hybridization targets for genomic mismatch scanning. Such techniques require rapid quantitative analysis of fluorescent hybridization for hundreds to tens of thousands of DNA spots. As such, there is a severe bottleneck in gene expression data collection due to inadequate methods for processing of individual DNA spot images for determining the quantitative fluorescent hybridization levels. 
     Some existing methods include manual processing of DNA spot images using a generic image processing tool, such as NIH image. Using such a tool a user visually locates each DNA spot image in a micro-array image, and moves a display pointer to each spot image, and manually defines a small area around the spot image. The image processing tool then reports image intensity values within the small area. The user then manually records the intensity values and continues this process for other visually located DNA spot images in the micro-array image. 
     However, such manual methods are impractical for micro-arrays with more than a handful of spot images. Further such methods are tedious and repetitive, requiring considerable time and effort. For example, with a micro-array image having about 600 DNA image spots, such manual methods can take about 8 hours of work, and resulting in quantification of only a limited number of image spots which visually seem to have a “good” expression level. As the micro-array density increases and becomes more complex, use of such methods becomes even more prohibitive. For example, current micro-array sizes range from several hundred to 1,200 genes, arrayed in a 1.8×1.8 cm area. As tip fabrication has improved, arrays with greater than 50,000 genes are viable. Such methods are also prone to various errors, including errors in manually recording the intensity values. Further such methods provide inconsistent quantification of intensity values, both for different spot images measured by a single individual, and for multiple individuals making measurements from the same micro-array image. 
     To alleviate the shortcomings of manual methods, some existing methods automate the process of locating DNA spot images from micro-array images and quantifying corresponding expression values. Such methods utilize a computer to manually position a cell grid on an area of the micro-array image containing an array of DNA spot images. The grid can be resized and individual columns and rows of the grid can be manually adjusted to better fit the arrayed pattern of DNA spot images. The grid position is then used by the computer to quantify the expression values using the intensity levels at each cell in the grid. However, such methods are inflexible since the grid placement requires extensive user interaction to fine-tune the grid. Further, the grid used in such methods is either completely fixed in shape, or has limited global flexibility (e.g., resizing and rotating the entire grid). 
     Such limitations cause a major handicap in most DNA array image analysis applications since DNA spots are never perfectly formed in a regular grid pattern in a micro-array such as shown in FIG.  1 . Although a robot used in spotting DNA fragments on a glass surface has positional accuracy to within +/−5 um, larger variations in the precise spacing of the arrayed DNA spots occur due to surface interactions of the solution with the silanized surface and tip variations. Moreover, printing tips are difficult to fabricate and many do not work uniformly. Therefore, as shown in  FIG. 2 , not only are DNA spots occasionally placed out of the regular grid pattern, but they also vary in size. It is therefore rare to have a fixed grid that can match exactly the pattern in the micro-array. Though in existing methods the grid can be manually resized, rotated, and a column or a row of the grid can be moved, the individual grid cells cannot be manipulated. Therefore, such methods are impractical for most DNA array image analysis applications, and specially for high density micro-arrays 
     Further, DNA spot image signals derived from the micro-arrays are susceptible to surface noise and laser reflection, due to surface dust. And, nonspecific DNA binding to the silanized surface occurs in a non-uniform pattern creating a varying background of fluorescence over the surface. Existing methods are unable to cope with irregular micro-array pattern, search for DNA image spots, and accurately quantify specific signals while accounting for the local background. 
     Other existing methods do not use a grid at all but apply a “spot” filter to detect locations in the micro-array image which “look-like” DNA spot images. However, using such methods it is difficult to define what a spot should look like. Furthermore, extensive noise and variations in the spot shape, due to the processing and scanning mechanisms, significantly reduce the signal to noise ratio (SNR) of the spot images. Thus, the detection scheme misses many real spots and processes many false patches in the image as real DNA spot images. 
     Another disadvantage of existing systems is their inability to display micro-array image pixel intensities, corresponding to gene expression values in related DNA spots for example, in an intuitive manner. As such, the user cannot easily determine gene properties in such DNA spots. 
     There is, therefore, a need for a DNA array image analysis method for automatically segmenting DNA array images into individual DNA spot images for quantification. There is also a need for such method to process irregular micro-array patterns, search for DNA image spots, and accurately quantify, and intuitively display, specific signals while accounting for the local background. 
     SUMMARY 
     The present invention satisfies these needs. In one embodiment, the present invention provides a method for segmentation of a frame of image information including a plurality of spaced DNA spot images corresponding to a plurality of DNA spots, the image information including image intensity level and intra frame position information corresponding to said DNA spots. The method of the present invention comprises the steps of: (a) transferring the frame of image information into a memory device; (b) selecting a set of image information within said frame including a selected set of the DNA spot images; (c) generating a grid in said memory device, the grid including a plurality of spaced grid points corresponding to said selected DNA spot images, each grid point including position information indicating the position of the grid point within said frame; and (d) modifying a current position of at least one grid point corresponding to a spot image to shift the grid point toward the corresponding spot image. Step (d) can be repeated for said grid point and for all the grid points of the grid. 
     The step of modifying said current position includes: (i) selecting a first bounding area in the frame around the current position of the grid point; (ii) generating a first position update including position information for updating a current position of said grid point to a first new position within the first bounding area, the location of said first new position relative to said current position being a function of intensity level of at least a portion of the image within the first bounding area; (iii) generating a second position update including position information for updating said current position to a second new position in the frame, said second new position being in a geometric arrangement with the position of one or more grid points around said grid point; and (iv) updating said current position with the position-information of the first and the second position updates, thereby shifting said grid point toward the corresponding spot image. The DNA spot images can be in a substantially two dimensional array arrangement, and generating the grid can include generating a two dimensional array of grid points spaced according to a predetermined criteria. 
     The method can further include the step of segmenting the selected set of image information by selecting at least one image segment defining a segment area around a grid point and including a spot image with minimum distance from said grid point, said segment area being a function of the spacing between said grid point and one or more neighboring grid points. The selected set of image information can further be segmented into a plurality of image segments corresponding to the plurality of grid points in the grid, each image segment defining a segment area around a corresponding grid point and including a corresponding spot image with minimum distance from said grid point, said segment area being a function of the spacing between said grid point and one or more neighboring grid points, wherein each spot image is contained in a corresponding image segment. 
     The method of the present invention can further include quantifying at least a portion of image information in said image segment to obtain image characteristic values for said image segment. The image characteristic values can include DNA information for a DNA spot corresponding to the DNA spot image in said image segment, said DNA information including gene expression values. 
     In another aspect, the present invention provides a method of displaying image information corresponding to a plurality of DNA spot images of at least one DNA spot, the image information including image characteristic values including background and signal intensity levels. In one embodiment, the display method includes the steps of: (a) for each DNA spot image: (1) extracting said background and signal intensity levels from the image characteristic values for the spot image, and (2) determining difference values between the background intensity levels and signal intensity levels; and (b) for each DNA spot: (1) relating the corresponding difference values to a range of graphic values, (2) selecting a graphic value for each difference value, and (3) displaying the selected graphic values. The steps of relating and selecting can include associating each difference value to a segment of a pie chart having multiple segments, and the step of displaying the selected graphic values can include displaying said segments as a pie chart. The area of each segment of each pie chart can be a function of the magnitude of the associated difference value. 
     In another aspect, the present invention provides a software system for configuring a computer system comprising a processor, and a memory device, to perform the steps of the methods of the present invention described above. The present invention also provides a computer system including means for performing the steps of the method of the present invention. 
     As such, the present invention provides a method, software system and computer system for automatically deforming a grid to locate individual DNA spot images and to quantify the spot images for measuring the local signal and background intensity values for the spot images, and to display such values. The method and software system of the present invention automate data quantification and extraction in DNA array image analysis applications. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features, aspects and advantages of the present invention will become better understood with regard to the following description, appended claims and accompanying drawings where: 
         FIG. 1  is a graphic representation of a frame of image information including DNA images spots corresponding to an ideal micro-array of DNA spots; 
         FIG. 2  is a graphic representation of a frame of image information including DNA images spots corresponding to a typical micro-array of DNA spots; 
         FIG. 3   a  illustrates the steps of an embodiment of a DNA array image analysis according the present invention; 
         FIG. 3   b  illustrates the steps of an embodiment of adjusting the position of a grid point in the method of  FIG. 3   a;    
         FIG. 4  is a graphic representation of a grid with uniform spacing used to locate DNA spots in a typical example micro-array according to the method of  FIG. 3   a;    
         FIG. 5  is a graphic representation of the grid of  FIG. 4  deformed according to the method of  FIG. 3   a  to substantially match placement of DNA spot images in a micro-array; 
         FIG. 6  is a graphic illustration of updating the position of a grid point in a grid according to the method of  FIG. 3   b;    
         FIG. 7  is a graphic illustration of segmenting a frame of image information including DNA images spots according to the method of  FIG. 3   a;    
         FIG. 8  illustrates an example flow diagram for program instructions for implementing the DNA array image analysis method of  FIG. 3   a;    
         FIG. 9  illustrates the steps of an embodiment of a display method according the present invention for displaying quantified image information corresponding to DNA spots; 
         FIG. 10  illustrates differential gene expression levels for different images of a micro-array displayed as pie charts according to an embodiment of a display method of  FIG. 9 ; 
         FIGS. 11   a-d  illustrates differential gene expression levels for different images of a micro-array displayed as bar graphs according to another embodiment of a display method of  FIG. 9 ; 
         FIG. 12  illustrates an example flow diagram for program instructions for implementing the display method of  FIG. 9 ; and 
         FIG. 13  is an example block diagram of a computer system for implementing the present invention. 
     
    
    
     DESCRIPTION 
     In one embodiment, the present invention provides a method for automatically locating an array of DNA spot images  10  within a scanned image frame  12  of a DNA micro-array or a DNA macro-array, shown in  FIGS. 1 and 2 , wherein each spot corresponds to a particular gene or gene fragment. The method of the present invention is applicable to both high-density micro-arrays, where spots are closely packed together on a solid surface, such as glass, with several thousands of spots placed in about 1 cm square area, and to macro-arrays with larger spacing of spots on surfaces such as membrane surfaces. 
       FIG. 2  is a graphic representation of the frame  12  of image information for a micro-array of DNA spots, including the DNA spot images  10 . Typically, the image frame  12  is generated by scanning a micro-array with a particular laser frequency. The spot images  10  are not in perfect alignment to each other, and there are large fluctuations in intensity, shape, and size of each spot in the micro-array. The image information includes intensity levels for the spots corresponding to the level of expression of a particular gene 
     Referring to FIG. a, an embodiment of the method of the present invention comprises the steps of: (a) storing the frame  12  of image information in a memory device  14  (step  16 ); (b) selecting a set  18  of image information within said frame  12  including a selected set of the DNA spot images  10  (step  20 ); (c) generating a grid  22  in said memory device  14 , the grid  22  including a plurality of spaced grid points  24  corresponding to said selected DNA spot images  10 , each grid point  24  including position information indicating the position of the grid point within said frame  12  (step  26 ); and (d) modifying a current position of at least one grid point  24  corresponding to a spot image  10  to shift the grid point  24  toward the corresponding spot image  10  (step  28 ). Step  28  can be repeated for said grid point  24  and for all the grid points  24  of the grid  22 . 
     The method of the present invention can be implemented as program instructions for configuring a computer system  34 , further described below, to perform the steps of the method of the present invention described herein. The computer system  34  includes a processor  36 , the memory device  14 , an input device  38  and a display  40 . Using the computer  34 , a user selects an image file containing the image frame  12  (control image) for processing, stores the image frame  12  in the memory  14  and displays it on the display  40  as the control image  12 . The control image  12  includes a plurality of pixels each having an intensity level and a position within the control image  12 . The user then selects an image region  18  in the control image  12  by defining approximate four corners  42  of the image region  18  using the input device  38 . If not all corners  42  are visible, due to lack of DNA product at a particular location, the user can guess at a rough placement for a missing corner. Anchor spots can be used depending on the experiment to guarantee that all corners are visible. 
     The user then specifies the number of columns, C, and rows, R, of arrayed image spots  10  in the selected region  18 . The computer  34  then automatically generates the grid  22  with equal spacing between each pair of corners having R rows and C columns within the specified region  18 . The grid  22  comprises R×C grid points  24 , one grid point  24  for each intersection of a row with a column. Each gird point  24  in the grid  22 , except for those along the edges of the grid  22 , is displayed as connected to its four neighbors to the right, let, up, and down, through an elastic connection  46 . This placement of the grid points  24  establishes the starting configuration of the dynamic grid  22  as shown in FIG.  4 . The grid  22  can be represented in the memory  14  using two matrices: (i) a first matrix comprising an adjacency matrix of size R×C×4 where each row number refers to a particular intersection point in the grid  22  and each column number refers to the neighboring intersection points arranged in a North, West, South, East fashion, and (ii) a second matrix comprising a position matrix of size R×C×2 specifying the absolute location of each grid point  24  in the control image  12 . 
     Since it is assumed that the pixel intensity corresponding to DNA spots images  10  in the image region  18  are greater than their surrounding background  50  intensity values, the computer  34 , according to the above steps, automatically shifts each grid point  24  towards local regions with the highest intensity values in subsequent iterations of said steps, wherein each grid point&#39;s location in the image frame  12  is modified.  FIG. 5  illustrates an example representations of the grid  22  with grid points  24  so shifted. A similar process can be applied to the image frame  12  in reverse video. Referring to  FIG. 3   b , an embodiment of the step of modifying (step  28 ) comprises: (i) selecting a first bounding area  52  in the control image  12  around the current position of a grid point  24  (step  54 ); (ii) generating a first position update including position information for updating a current position of said grid point  24  to a first new position  48  within the first bounding area  52 , the location of said first new position  48  relative to said current position being a function of intensity level of at least a portion of the image within the first bounding area  52  (step  56 ); (iii) generating a second position update including position information for updating said current position to a second new position  49  in the control image  12 , said second new position  49  being in a geometric arrangement with the position of one or more grid points  24  around said grid point  24  (step  58 ); and (iv) updating said current position with the position information of the first and the second position updates, thereby shifting said grid point  24  toward the corresponding spot image  10  (step  60 ). 
     The position matrix elements are modified and updated by the computer  34  during multiple iterations of the above steps.  FIG. 6  is a graphic illustration of updating the position of a grid point  24  in the grid  22  according to the above steps. In the embodiment of the invention described herein, the first position update comprises a normalized direction vector d, based on the pixel intensity values within the first bounding area  52  around the grid point  24 . The first bounding area  52  can comprise a bounding box of size r×r, or a circle of radius r centered on the current position of the grid point  24 . The direction vector d can comprise an average or a weighted sum of vectors defining arrows originating at the center of the first bounding area  52  and ending at a plurality of the pixel locations within the first bounding area  52 . The intensity value at each such pixel location can be used as the weight coefficient for calculating the weighted sum of said vectors. The direction vector d can be based on the direction of the local intensity gradient. Other weighting coefficients can also be utilized. 
     An example calculation of the direction vector d for said bounding box of size r×r is described below. The bounding box is represented as a matrix P in the memory  14  with n columns and m rows, and elements p ij  corresponding to image intensity values at a location (i,j) in the bounding box. The direction vector d is calculated as: 
             T   =       ∑     i   =   1     n     ⁢           ⁢       ∑     j   =   1     m     ⁢           ⁢     p   ij                   s   j     =         ∑     i   =   1     n     ⁢     P   ij       T               t   i     =         ∑     j   =   1     m     ⁢     P   ij       T               
 x L ≡Number of pixels from the left edge to the center of P
 
x R ≡Number of pixels from the right edge to the center of P
 
y t ≡Number of pixels from the lop edge to the center of P
 
y b ≡Number of pixels from the bottom edge to the center of P
 
 X=[−x   L −( x   L +1). . . −1 0 1 2 . . . ( x   R +1) x   R ]
 
 Y=[−y   b −( y   b +1). . . −1 0 1 2 . . . ( y   t +1) y   t ]
 
             dx   =       ∑     j   =   1     m     ⁢           ⁢       s   j     ⁢     X   j                 dy   =       ∑     i   =   1     n     ⁢           ⁢       t   i     ⁢     Y   i                   
 d=[dx dy]
 
     Using a priori information about the location of DNA spot images  10  in the frame  12 , i.e., almost a uniform 2-D array, the second position update is generated to place an additional constraint on the movement of the grid points  24 . In the embodiment described herein, the constraint maintains the position of a grid point  24  in a linear geometric arrangement relative to position of one or more of neighboring grid points  24  in vertical and horizontal directions. Other geometric arrangements such as curves can also be selected. The neighboring grid points  24  can be selected by the user, or automatically selected by the computer  34 , to include one or more of first and second order neighbors of the grid point  24 . In this embodiment, the second position update comprises another direction vector e, defining an arrow pointing at the mean location of the mid point between the first order neighbors in the horizontal direction to the left and right of the grid point  24 , and the mid point between the first order neighbors in the vertical direction to the top and bottom of the grid point  24 . The direction vector, e, attempts to keep the spacing between adjacent grid points  24  equal by using a linear geometric arrangement discussed above. 
     An example calculation of the direction vector e for a grid point  24  with a spatial position vector L having elements L x  and L y  is described below. Eight first and second order neighboring grid points around said grid point include spatial vectors: (1) A with elements A x  and A y , (2) B with elements B x  and B y , (3) C with elements C x  and C y , (4) D with elements D x  and D y , (5) E with elements E x  and E y , (6) F with elements F x  and F y , (7) G with elements G x  and G y , and (8) H with elements H x  and H y , as shown in diagram 1. 
                 
 
     The vector e is calculated as: 
     When said first order neighbors are used:
 
 {tilde over (X)} =( A   x   +B   x )/2+( C   x   +D   x )/2
 
 {tilde over (Y)} =( A   y   +B   y )/2+( C   y   +D   y )/2
 
 dx={tilde over (X)} /2 −L   x    dy={tilde over (Y)} /2 −L   y 
 
     When first and second order neighbors are used:
 
 {tilde over (X)} =[( A   x   +B   x )+( C   x   +D   x )]+( F   x   +E   x )/2+( G   x   +H   x )/2
 
 {tilde over (Y)} =[( A   y   +B   y )+( C   y   +D   y )]+( F   y   +E   y )/2+( G   y   +H   y )/2
 
 dx={tilde over (X)} /6 −L   x    dy={tilde over (Y)} /6 −L   y 
 
e=[dx dy]
 
     The computer  34  then linearly combines the direction vectors d and e to obtain a direction vector t for updating the position of the grid point  24 :
 
 t=αd+βe 
 
     Where α and β are weighting coefficient parameters, with an example α or β range 0 to 10. The larger the value of β relative to α, the stiffer are connections  46  between adjacent grid points  24 . 
     The spatial position L of said grid point  24  is then updated as:
 
L←L+ηt
 
     Where η is the update rate with an example range of 0 to 1. The upper limit of said range for α or β is inversely proportion to an upper limit of η. 
     The local neighborhood size defined by the first bounding area  52  for each grid point  24  can be gradually reduced after each iteration, or every few iterations, of the modification step  28  described above. The number of iterations is typically around forty and can be increased or decreased by the user to optimize the grid position appropriate for the image spots  10 . 
     After a number of iterations, the user can instruct the computer  34  to perform further tasks according to the present invention, including: (1) executing more iterations to optimize the location of the grid points  24 , (2) redrawing the grid  22 , (3) canceling out of the grid placement, or (4) accepting the current grid placement and proceed to segmentation and quantification steps  30 ,  32  described below. All of the above steps can be implemented using program instructions to be executed by a computer. 
     Referring to  FIG. 7 , once the user is satisfied with the grid position, the method of the present invention further includes the step of segmenting the selected region  18  into a plurality of image segments  62  corresponding to the plurality of grid points  24  in the grid (step  32 ). Each image segment  62  defines an area around a corresponding grid point  24  and includes a corresponding spot image  10  with minimum distance from said grid point  24 . The size and shape of each segment  62  for each grid point  24  is a function of the spacing between said grid point  24  and one or more neighboring grid points  24 . 
     As an example, for the two-dimensional grid  22 , the programmed computer automatically segments the image region  18  into the segments  62  each having: (a) a width substantially equal to the smaller of: (i) the distance between the positions of the grid point  24  in the image segment  62  and the midpoint between said grid point  24  and an adjacent grid point to the left of said grid point  24 , and (ii) the distance between the positions of said grid point  24  and the midpoint between said grid point  24  and an adjacent grid point to the right of said grid point  24 ; and (b) a height substantially equal to the smaller of: (i) the distance between the positions of a said grid point  24  and the midpoint between said grid point  24  and an adjacent grid point to the left of said grid point  24 , and (ii) the distance between the positions of said grid point  24  and the midpoint between said grid point  24  an adjacent grid point to the right of said grid point  24 . 
     The method of the present invention can further include the step of quantifying at least a portion of image information in each image segment  62  to obtain image characteristic values for the image segment  62  (step  34 ). Each spot image  10  in an image segment  62  can be used to measure the gene expression signal value and local background intensity levels according to a number of different user selected quantification methods. Five example quantification methods are described below. 
     Segmented Intensities: This method includes sorting all the pixel intensities within an image segment  62 , selecting a portion, for example the top 10%, of said intensity values, and calculating the mean of the selected intensity values as a signal value. A similar portion, for example the bottom 10%, of intensity values is also selected and its mean value is provided as the local background intensity level. 
     Fixed Circle Mean Intensity: In this method, a fixed circle of user specified size is centered at each grid point  24  in the image segment  62 . The mean intensity value of all pixels within the circle is provided as the signal value of the image spot  10  in the image segment  62  and the mean intensity value of the surrounding pixels are reported as the background intensity levels. 
     Fixed Circle Total Intensity: This method is similar to the Fixed Circle. Mean Intensity method described above, except, total sum of all intensity values is provided in place of the mean values. 
     Fixed Circle Segmented Intensity: This method is a combination of the above three methods where the mean of certain predefined portion of the intensity values within the circle is provided as the signal value and the mean of another predefined portion of the intensity values outside the circle is provided as the background intensity level. 
     Automatic Circle Detection: This method is similar to Fixed Circle Segmented Intensity method except, an automatic spot detection method is used to localize each image spot  10  in the image segment  62 . Such a detection method can comprise a Hough transform for circle detection, a match-filter approach for optimum match between filters of various sizes to the data, or other detection methods. 
     Other quantification methods can also be utilized and are contemplated by the present invention. As such, the present invention provides an automatic method for refining the position of grid points  24  to optimally match the arrayed spot images  10  in micro-array images  12 , using the dynamic elastic grid  22 . The user need only specify the four corners  42  of a region  18  in a micro-array image  12 , and the number of rows and columns of the image spots  10  in the micro-array. Non-rectangular griddling patterns are also contemplated by the present invention. 
     In another aspect, the present invention provides a computer system  34 , described further below, for segmentation of the frame  12  of image information including the plurality of spaced DNA spot images  10  corresponding to the plurality of DNA spots, said image information including image intensity level information corresponding to said DNA spots. In one embodiment, the computer system comprises means for performing the above steps of the method of the present invention described herein and shown in FIGS. a and  3   b . Said means include program instructions for configuring a general purpose, or dedicated computer, to perform said steps. The present invention further provides a software system including program instructions for configuring a computer system to perform the above steps described herein and shown in FIGS. a and  3   b.    
       FIG. 8  illustrates an example general flow diagram for the program instructions of the computer system  34  and the software system of the present invention described above. Referring to the flow diagram, the program instructions include steps for: receiving and storing the image frame  12  in memory  14  (step  64 ); displaying the image frame  12  on the display  40  (step  66 ); obtaining four corners  42  of the image region  18  selected by user via the input device  38  (step  68 ); generating the grid  22  of R rows and C columns in the memory  14  as described above (step  70 ); forming a bounding box  52  of size r×r around a grid point (step  72 ); calculating the direction vector d as described above (step  74 ); calculating the direction vector e as described above (step  76 ); adjusting position of said grid point  24  with direction vectors d and e (step  78 ); displaying the adjusted grid  22  on the display  40  (step  80 ); determining if user is satisfied with the adjusted grid  22  (step ( 82 ); if not, proceeding to step  72  to adjust other grid point positions, otherwise, proceeding to step  84  to segment the selected image  18  into segments  62  as described above; and quantifying DNA spot image information for spot images  10  in the segments  62  as described above (step  86 ). 
     The program instructions can be implemented utilizing a program language such as MatLab™, C, Fortran, C++, and executed by a computer system  34  described below. Mathematical calculations and image display can be implemented utilizing a simulation package or a math library such as MatLab, from Mathworks™, located in Natick. The program instructions and related data are stored in the memory of the computer, to be executed by the processor to interact with the display, input device and storage in performing the steps described above. Alternatively, the program instructions and related data can be used to program a dedicated graphics system to perform the above steps, the graphics system including a processor, a memory device, display, input device, storage and image input means such as a scanner. In such a system, DNA micro-arrays are scanned into the memory device as image frames for processing as described above. 
     The values provided by one or more of the above quantification methods can be stored, as an ASCII file for example, and also saved in the memory  14  for comparison and display with similar quantified values corresponding to one or more other DNA micro-array images  12  according to another aspect of the present invention. In addition to the control image  12 , the user can also select one or more non-control images. The grid position determined in steps described above can be applied, with any user defined translation or transformation, to the non-control image to quantify expression values according to the quantification methods described above. Typically, the control image  12  is generated by scanning a micro-array with one particular laser frequency, and the non-control image is generated by scanning the same micro-array with a different frequency laser. Different tags, each sensitive to one of the two laser frequencies are used to label DNA fragments from two different tissue types, e.g., healthy and diseased tissue. It is one of the main goals of micro-array data analysis to identify those sets of genes that are differentially expressed in different tissues. Extracted signal and background intensity levels for each gene (each DNA spot in the micro-array) can be displayed according to the present invention to visualize the differential gene expression levels between the control and non-control images. 
     Referring to  FIG. 9 , an embodiment of the steps of such a display method for displaying image information corresponding to a plurality of DNA spot images  10  of at least one DNA spot, the image information including image characteristic values including background and signal intensity levels, comprises the steps of: (a) receiving image characteristic values for DNA spot images  10  in said control and non-control images (step  88 ); (b) for each DNA spot image  10 : (1) extracting said background and signal intensity levels from the image characteristic values for the spot image  10 , and (2) determining difference values between the background intensity levels and signal intensity levels (step  90 ); and (c) for each DNA spot: (1) relating the corresponding difference values to a range of graphic values, (2) selecting a graphic value for each difference value; and (3) displaying the selected graphic values (step  92 ). The graphic values can include graphic objects  93  and color characteristic values as described below. 
     Applying said display method to the control and non-control images described above, includes the steps of: (a) determining difference values between the background intensity levels and the signal intensity levels for both the control and non-control images, (b) displaying both difference values for all spots in the micro-array using a plurality of graphic objects  93  such as pie charts  94  or bar graphs  96 , each graphic object corresponding to a DNA spot, (c) probing each graphic object  93  to examine the expression levels, ratios, and other similar information, including displaying corresponding image segments form the control and non-control images for a selected graphic object  93 . 
     Referring to  FIG. 10 , each difference value is associated to a segment  98  of a pie chart  94  having multiple segments, and the segments  98  as displayed a pie chart. The area of each segment  98  of each pie chart  94  can be a function of the magnitude of the associated difference value. Further, color characteristic values can be assigned to the pie segments  98  by: (1) relating the corresponding difference values to a range of color characteristic values; (2) selecting a color characteristic value for each difference value; and (3) displaying the selected color characteristic value in the corresponding pie chart segments  98 . As such, each pie chart segment  98  among a plurality of pie segments can have a different color characteristic value. The color characteristic values can include color, hue, brightness, intensity, and texture. 
     In the example pie chart embodiment  94  of the graphic objects  93  shown in  FIG. 10 , each pie chart  94  includes at least two segments: (1) a segment representing difference values between the background and signal intensity levels of a spot image  10  in the control image, corresponding to a DNA spot, and (2) another segment representing difference values between the background and signal intensity levels of a spot image  10  in the non-control image, corresponding to said DNA spot. Each pie chart  94  can include additional segments for visualizing other differences associated with images  10  of a DNA spot in additional non-control images. As shown in  FIG. 10  the graphic objects  93  can be arranged, for example, in the order in which their corresponding DNA spot images  10  appear in the control and non-control images. The user can also specify a different desired grouping of the graphic objects. The display arrangement can also be different from that of DNA spots 
     Referring to  FIGS. 11   a-d , the graphic objects  93  are shown as the bar graphs  96 , wherein each difference value is associated to a segment  98  of a bar graph having multiple segments, and the segments are displayed as a bar graph. The arrangement, segment size and segment attributes of the bar graphs  96  can be identical to those of the pie charts  94  described above. Further, one or more type of the bar graphs  96  can be displayed in the same arrangement as shown for the pie charts  94  in FIG.  10 . 
     In another aspect, the present invention provides a computer system  34  for displaying image information corresponding to the plurality of DNA spot images  10  of at least one DNA spot, the image information including image characteristic values including background and signal intensity levels. In one embodiment, the computer system  34  comprises means for performing the steps of the display method described above. Said means include program instructions for configuring a general purpose or dedicated computer to perform said steps. The present invention further provides a software system including program instructions for configuring a computer system to perform the steps of said display method. 
       FIG. 12  illustrates a general flow diagram for the program instructions of the display computer system and the display software system of the present invention described above. Referring to the flow diagram, the program instructions include steps for: receiving and storing said characteristic values in memory  14  (step  100 ); selecting a DNA spot and corresponding DNA spot images&#39; characteristic values (step  102 ); extracting background and signal intensity values for a image spot  10  (step  104 ); determining difference values between said background and intensity values (step  106 ); determining in step  108  if all spot images corresponding to said DNA spot have been so processed; if not, proceeding to step  104  to other spot images corresponding to said DNA Spot, otherwise, relating the difference values to graphic values as described above (step  110 ); selecting a graphic value for each difference value as described above (step  112 ); displaying the selected graphic values as described above (step  114 ); and determining, in step  116  if all images for all DNA spots have been so processed, if not, proceeding to step  102  to process images for other DNA spots. 
     The program instructions can be implemented utilizing a program language such as MatLab, AVS/Expert, and Java, and executed by a computer system described below. Mathematical calculations can be implemented utilizing a simulation package or a math library such as MatLab, from Mathworks. The program instructions and related data are stored in the memory of the computer, to be executed by the processor to interact with the display, input device and storage in performing the steps described above. Alternatively, the program instructions and related data can be used to program a dedicated graphics system to perform the above steps, the graphics system including a processor, a memory device, display, input device, storage and image input means such as a scanner. In such a system, DNA micro-arrays are scanned into the memory device as image frames for processing as described above. Alternatively, the program instructions and related data can be used to program a dedicated graphics system to perform the above steps, the graphics system including a processor, a memory device, display, input device, storage and image input means such as a scanner. In such a system, DNA micro-arrays are scanned into the memory device as image frames for processing as described above. 
     A suitable computer system  34  for executing said program instructions can be a dedicated computer such as a computer dedicated to scanning micro-arrays and processing micro-array images, or a general purpose computer system such as a personal computer or a dedicated computer system.  FIG. 13  shows a functional block diagram of the computer system  34  embodying the present. A central processing unit (CPU)  36  operates on program instructions in the memory  14  using a processing unit  118 . The CPU  36  also has a clock/calendar logic circuit  120  for maintaining an internal time/date clock. A storage device  122  for storing information pertaining to micro-array images is connected to the CPU  36  over a bus  124 . The micro-array images can be located on a file server  126  over a LAN or local to the CPU. A keyboard  128  or mouse  38  receives instructions from the user concerning the DNA image micro-array analysis as necessary. A scanner  130  allows scanning micro-arrays and obtaining images frames for processing as described above, and a printer  132  allows printing of images and data. The main memory  14  stores the program instructions implementing the method of the present invention. An example of a computer system suitable is a microcomputer equipped with a Pentium II™ microprocessor running at 266 MHZ. Such a system is preferably equipped with at least 64 MB megabytes of random access memory and a 2.0 GB hard drive. The system preferably runs an operating system such as the Windows™ operating environment. Windows™ is manufactured by Microsoft Corporation, Redmond, Wash. 
     Although the present invention has been described in considerable detail with regard to the preferred versions thereof, other versions are possible. Therefore, the appended claims should not be limited to the descriptions of the preferred versions contained herein.