# Patent

## Title
Method of generating multiscale contrast enhanced image

## Abstract

A method of generating a multiscale contrast enhanced image is described wherein the shape of edge transitions is preserved. Detail images are subjected to a conversion, the conversion function of at least one scale being adjusted for each detail pixel value according to the ratio between the combination of the enhanced center differences and the combination of the unenhanced center differences.

## Background
RELATED APPLICATIONS
This application claims priority to European Patent Application No. 06125766.3, filed on Dec. 11, 2006, and claims the benefit under 35 USC 119(e) of U.S. Provisional Application No. 60/870,024, filed on Dec. 14, 2006, and is related to U.S. application Ser. No. 11/933,834, filed on Nov. 1, 2007, entitled, “Method of Generating Multiscale Contrast Enhanced Image,” by Tom Bertens and Pieter Vuylsteke, U.S. Pat. Appl. Publ. No. US 2008/0137977 A1, all three of which are incorporated herein by reference in their entirety.


BACKGROUND OF THE INVENTION
Commonly images represented by a digital signal such as medical images are subjected to image processing during or prior to displaying or hard copy recording.
The conversion of grey value pixels into values suitable for reproduction or displaying may comprise a multi-scale image processing method (also called multi-resolution image processing method) by means of which the contrast of the image is enhanced.
According to such a multi-scale image processing method an image, represented by an array of pixel values, is processed by applying the following steps. First the original image is decomposed into a sequence of detail images at multiple scales and occasionally a residual image. Next, the pixel values of the detail images are modified by applying to these pixel values at least one conversion. Finally, a processed image is computed by applying a reconstruction algorithm to the residual image and the modified detail images. Such a method is illustrated in FIGS. 2 and 3.
There are limits for the behavior of the conversion functions. Grey value transitions in the image can be distorted to an extent that the appearance becomes unnatural if the conversion functions are excessively non-linear. The distortions are more pronounced in the vicinity of significant grey level transitions, which may result in overshoots at step edges and loss of homogeneity in regions of low variance facing strong step edges. The risk of creating artifacts becomes more significant for CT images since they have sharper grey level transitions, e.g. at the interface of soft tissue and contrast media. One has to be careful using the multi-scale techniques on CT images.
In U.S. Pat. No. 6,731,790 B1 a method is described in which artifacts are corrected in an image that is represented by a digital signal. The corrected artifacts originate from any kind of non-linear modification of the components of a multi-scale image representation.
A gradient representation of the original image is generated and modified. A modification step is applied to gradient images.
A reconstruction process is applied to the modified gradient representation.
SUMMARY OF THE INVENTION
The present invention relates to a method for enhancing the contrast of an image that is represented by a digital signal.
It is an object of the present invention to provide a method for enhancing the contrast of an image that is represented by a digital signal that overcomes the prior art inconveniences.
More specifically it is an object of the present invention to provide a new multi-scale contrast enhancement algorithm which results in a contrast enhanced image while preserving the shape of the edge transitions.
The invention provides that enhanced detail pixel values are created by enhancement of the center differences.
The method of the present invention is different from and advantageous over the prior art multi-scale contrast enhancement for the following reason: the prior art algorithms amplify the detail pixel values by applying the conversion functions directly to the detail pixel values by means of look up tables or multiplicative amplification factors.
The present invention is applicable to all the multi-scale detail representation methods from which the original image can be computed by applying the inverse transform.
The invention is applicable to all the multi-scale decomposition methods wherein the detail pixel values are equivalent to the sum of translation difference images or can be computed as a center difference image.
According to the present invention the pixel-wise amplification function of at least one scale is adjusted for each detail pixel value according to the ratio between the combination of the enhanced center differences and the combination of the unenhanced center differences.
The detail pixel values are then modified with the adjusted conversion function.
In general, according to one aspect, the invention features a method for enhancing the contrast of an image that is represented by a digital signal. The method comprises decomposing said digital signal into a multi-scale representation comprising at least two detail images representing detail at multiple scales and approximation images of which the detail images are derived, an approximation image at a scale representing the grey values of said image in which all details at that scale have been omitted, computing translation difference images of at least one approximation image, non-linearly modifying the values of said translation difference images, computing an amplification image at at least one scale as the ratio of two images wherein the first image is computed by combining said modified translation difference images at the same or smaller scale and the second image is created by combining unenhanced translation difference images at the same or smaller scale, computing an enhanced multi-scale detail representation by modifying at at least one scale the detail image according to the amplification image at that scale, and computing an enhanced image representation by applying a reconstruction algorithm to the enhanced multi-scale detail representation.
In embodiments, the method further comprises computing one of the translation difference images at a specific scale out of an approximation image at the same scale. A translation image at a scale k is computed out of an approximation image at scale m, wherein m represents a scale between scale 1 and scale k−1. The center difference images are identical to the multi-scale detail images or a close approximation of the multi-scale detail images.
In one example, the image is a mammographic image. The image is a computed tomography (CT) image, other cases.
In general, according to another aspect, the invention features, a computer software for enhancing the contrast of an image that is represented by a digital signal, the software, when executed by a computer, causes the computer to: decompose said digital signal into a multi-scale representation comprising at least two detail images representing detail at multiple scales and approximation images of which the detail images are derived, an approximation image at a scale representing the grey values of said image in which all details at that scale have been omitted, compute translation difference images of at least one approximation image, non-linearly modify the values of said translation difference images, compute an amplification image at at least one scale as the ratio of two images wherein the first image is computed by combining said modified translation difference images at the same or smaller scale and the second image is created by combining unenhanced translation difference images at the same or smaller scale, compute an enhanced multi-scale detail representation by modifying at at least one scale the detail image according to the amplification image at that scale, and compute an enhanced image representation by applying a reconstruction algorithm to the enhanced multi-scale detail representation.
In general, according to another aspect, the invention features, a computer software product for enhancing the contrast of an image that is represented by a digital signal, the product comprising a computer-readable medium in which program instructions are stored, which instructions, when read by a computer, cause the computer to execute the above described method.
The above and other features of the invention including various novel details of construction and combinations of parts, and other advantages, will now be more particularly described with reference to the accompanying drawings and pointed out in the claims. It will be understood that the particular method and device embodying the invention are shown by way of illustration and not as a limitation of the invention. The principles and features of this invention may be employed in various and numerous embodiments without departing from the scope of the invention.



BRIEF DESCRIPTION OF THE DRAWINGS
In the accompanying drawings, reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale; emphasis has instead been placed upon illustrating the principles of the invention. Of the drawings:
FIG. 1 schematically illustrates the steps of the two embodiments of the present invention,
FIG. 2 illustrates a multi-resolution image processing method according to the prior art,
FIG. 3 illustrates the image enhancement step of the multi-resolution image processing method illustrated in FIG. 2,
FIGS. 4, 6, 8 illustrate different implementations of the multi-resolution image processing method according to the present invention,
FIG. 5 illustrates the image enhancement step of the multi-resolution image processing method illustrated in FIG. 4,
FIG. 7 illustrates the image enhancement step of the multi-resolution image processing method illustrated in FIG. 6,
FIG. 9 illustrates the image enhancement step of the multi-resolution image processing method illustrated in FIG. 8,
FIG. 10 is a legend pertaining to the symbols used in the above figures.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
In the context of the present invention specific terms are defined as follows:
Multi-scale decomposition mechanism: A multi-scale (or multi-resolution) decomposition of an image is a process that computes detail images of the image at multiple scales of a grey value image. A multi-scale decomposition mechanism generally involves filter banks for computing the detail images. Well-known techniques are for example: the Laplacian pyramid, the Burt pyramid, the Laplacian stack, the wavelet decomposition, QMF filter banks.
Approximation image: An approximation image is a grey value image that represents the original grey value image at the same or a larger scale, or at the same or a lower resolution. An approximation image at a specific scale is equivalent to the original grey value image in which all details at that scale have been omitted (Mallat S. G., “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation”, IEEE Trans. On Pattern Analysis and Machine Intelligence, vol. 11, no. 7, July 1989).
Detail image: A detail image is defined as the difference of information between an approximation image at a certain scale and an approximation image at a smaller scale.
Conversion operator: A conversion operator is operator which generates the pixel-wise modification of the detail pixel values as an intermediate step to create a contrast enhanced version of the grey value image. Such an operator has been described in European patent EP 527 525. The modification is defined by a conversion function and can e.g. be implemented as a look up table or as a multiplicative amplification.
Translation difference image: The translation difference images at a scale s are a measurement of elementary contrast in each pixel of an approximation image at scale s. They can be computed by taking the difference of the approximation image at that scale s and a translated version. The difference of the approximation images can represent other computations of elementary contrast, e.g. the ratio of a pixel with a neighboring pixel in case the processing steps are preceded by an exponential transform and followed by a logarithmic transform.
Center difference image: A center difference image is computed by applying a combining operator (for example the summation) to translation difference images. The combining operator can be a linear or non-linear function of corresponding pixel values in the translation difference images. An example of a linear combining function is the weighted sum. An example of a non-linear combining function is the median.
According to the present invention the pixel-wise amplification function of at least one scale is adjusted for each detail pixel value according to the ratio between the combination of the enhanced center differences and the combination of the unenhanced center differences.
The detail pixel values are then modified with the adjusted conversion function. This is illustrated in FIGS. 4, 6 and 8 with corresponding enhancement steps being illustrated in FIGS. 5, 7 and 9 respectively.
The characteristics of the method of the present invention are shown in FIG. 1.
The present invention is generally implemented as a computer program product adapted to carry out the method of any of the claims when run on a computer and is stored on a computer readable medium, such as optically-read disk.
This contrast enhancement algorithm is applicable to all multi-scale detail representation methods from which the original image can be computed by applying the inverse transformation.
It is applicable to the reversible multi-scale detail representation that can be computed as a weighted sum of translation difference images.
The weighing factors and the translation offsets of the translation difference images can be deducted from the multi-scale decomposition in such a way that the resulting weighted sum of the translation difference images is either identical or an approximation of the detail pixel values.
For these multi-scale detail representations the contrast can be enhanced by applying the conversion operator to the center differences before the weighted sum is computed.
To compute the weighted sum of translation difference images, the approximation image at the same scale (or resolution level) or the approximation images at the smaller scales (or finer resolution levels) can be used.
State-of-the-art multi-scale contrast enhancement algorithms decompose an image into a multi-scale representation comprising detail images representing detail at multiple scales and a residual image.
Some of the important multi-scale decompositions are the wavelet decomposition, the Laplacian-of-Gaussians (or LoG decomposition), the Difference-of-Gaussians (or DoG) decomposition and the Burt pyramid.
The wavelet decomposition is computed by applying a cascade of high-pass and low-pass filters followed by a subsampling step.
The high-pass filter extracts the detail information out of an approximation image at a specific scale.
In the Burt pyramid decomposition the detail information is extracted out of an approximation image at scale k by subtracting the upsampled version of the approximation image at scale k+1.
In a state of the art methods as the one disclosed in EP 527 525 a contrast enhanced version of the image is created by conversion of the pixel values in the detail images followed by multi-scale reconstruction.
All above implementations of multiscale decomposition have a common property. Each pixel value in the detail images can be computed out of an approximation image by combining the pixel values in a moving neighborhood.
In the above cases the combining function is a weighted sum.
For the wavelet decomposition the pixel values in the detail image at scale k are computed as:

dk+1=↓(hd*gk)

gk+1=↓(ld*gk)

with hd a high-pass filter, ld a low-pass filter, * the convolution operator and ↓ the subsampling operator (i.e. leaving out every second row and column).
For the wavelet reconstruction the enhanced approximation image at scale k is computed as:

hk=lx*(↑hk+1)+hx*(↑f(dk+1))

with hr a high-pass filter, lr a low-pass filter and ↑ the upsampling operator (i.e. inserting pixels with value 0 in between any two rows and columns).
For the Burt decomposition the pixel values in the detail image at scale k are computed as:

dk=gk−4g*(↑gk+1)

or

dk=gk−4g*(↑(↓(g*gk)))

or

dk=(1−4g(↑(↓g)))*gk 

with g a Gaussian low-pass filter and 1 the identity operator.
For the Burt reconstruction the enhanced approximation image at scale k is computed as:

hk=4g*(↑hk+1)+f(dk)

with f(x) the conversion operator.
The multi-scale detail pixel values as weighted sums
Suppose that in the Burt multi-scale decomposition a 5×5 Gaussian filter is used with coefficients wk,l with k=−2, . . . 2 and l=−2, . . . , 2, the subsampling operator removes every second row and column and the upsampling operator inserts pixels with value 0 in between any two rows and columns.
The pixel at position i,j in the approximation image gk+1 is computed as:




  
    
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The pixel at position i,j in the upsampled image uk is computed as:




  
    
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Finally, the pixel at position i,j in the detail image dk is computed as:




  
    
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              ⁢
              
                
                  ∑
                  
                    m
                    =
                    
                      {
                      
                        
                          -
                          2
                        
                        ,
                        0
                        ,
                        2
                      
                      }
                    
                  
                  
                    
                  
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      
                        {
                        
                          
                            -
                            1
                          
                          ,
                          1
                        
                        }
                      
                    
                    
                      
                    
                  
                  ⁢
                  
                    
                      w
                      
                        m
                        ,
                        n
                      
                    
                    ⁢
                    
                      
                        ∑
                        
                          s
                          =
                          
                            -
                            2
                          
                        
                        2
                      
                      ⁢
                      
                        
                          ∑
                          
                            t
                            =
                            
                              -
                              2
                            
                          
                          2
                        
                        ⁢
                        
                          
                            w
                            
                              s
                              ,
                              t
                            
                          
                          ⁢
                          
                            
                              g
                              k
                            
                            ⁡
                            
                              (
                              
                                
                                  i
                                  +
                                  s
                                  +
                                  m
                                
                                ,
                                
                                  j
                                  +
                                  t
                                  +
                                  n
                                
                              
                              )
                            
                          
                          ⁢
                          
                            
                          
                          ⁢
                          if
                          ⁢
                          
                            
                          
                          ⁢
                          i
                          ⁢
                          
                            
                          
                          ⁢
                          is
                          ⁢
                          
                            
                          
                          ⁢
                          even
                          ⁢
                          
                            
                          
                          ⁢
                          and
                          ⁢
                          
                            
                          
                          ⁢
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          is
                          ⁢
                          
                            
                          
                          ⁢
                          odd
                        
                      
                    
                  
                
              
            
          
        
      
      
        
          
            
              
                g
                k
              
              ⁡
              
                (
                
                  i
                  ,
                  j
                
                )
              
            
            -
            4
            +
            
              
                ∑
                
                  m
                  =
                  
                    {
                    
                      
                        -
                        1
                      
                      ,
                      1
                    
                    }
                  
                
                
                  
                
              
              ⁢
              
                
                  ∑
                  
                    n
                    =
                    
                      {
                      
                        
                          -
                          1
                        
                        ,
                        1
                      
                      }
                    
                  
                  
                    
                  
                
                ⁢
                
                  
                    w
                    
                      m
                      ,
                      n
                    
                  
                  ⁢
                  
                    
                      ∑
                      
                        s
                        =
                        
                          -
                          2
                        
                      
                      2
                    
                    ⁢
                    
                      
                        ∑
                        
                          t
                          =
                          
                            -
                            2
                          
                        
                        2
                      
                      ⁢
                      
                        
                          w
                          
                            s
                            ,
                            t
                          
                        
                        ⁢
                        
                          
                            g
                            k
                          
                          ⁡
                          
                            (
                            
                              
                                i
                                +
                                s
                                +
                                m
                              
                              ,
                              
                                j
                                +
                                t
                                +
                                n
                              
                            
                            )
                          
                        
                        ⁢
                        
                          
                        
                        ⁢
                        if
                        ⁢
                        
                          
                        
                        ⁢
                        i
                        ⁢
                        
                          
                        
                        ⁢
                        and
                        ⁢
                        
                          
                        
                        ⁢
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        are
                        ⁢
                        
                          
                        
                        ⁢
                        odd
                      
                    
                  
                
              
            
          
        
      
    
  




Generally, the pixel at position i,j in the detail image dk can be computed as a weighted sum of pixels in the approximation image at the same or smaller scale k, k−1, k−2, . . . :




  
    
      d
      k
    
    ⁡
    
      (
      
        i
        ,
        j
      
      )
    
  
  =
  
    
      
        g
        l
      
      ⁡
      
        (
        
          ri
          ,
          rj
        
        )
      
    
    -
    
      
        ∑
        m
      
      ⁢
      
        
          ∑
          n
        
        ⁢
        
          
            v
            
              m
              ,
              n
            
          
          ⁢
          
            
              g
              l
            
            ⁡
            
              (
              
                
                  ri
                  +
                  m
                
                ,
                
                  rj
                  +
                  n
                
              
              )
            
          
        
      
    
  




with 1ε{0, . . . , k} and r=subsampling_factor(1−k) 
Because




  
    
      ∑
      m
    
    ⁢
    
      
        ∑
        n
      
      ⁢
      
        v
        
          m
          ,
          n
        
      
    
  
  =
  1




the pixel at position i,j in the detail image dk can be computed as:



  
    
      
        d
        k
      
      ⁡
      
        (
        
          i
          ,
          j
        
        )
      
    
    =
    
      
        
          g
          l
        
        ⁡
        
          (
          
            ri
            ,
            rj
          
          )
        
      
      -
      
        
          ∑
          m
        
        ⁢
        
          
            ∑
            n
          
          ⁢
          
            
              v
              
                m
                ,
                n
              
            
            ⁢
            
              
                g
                l
              
              ⁡
              
                (
                
                  
                    ri
                    +
                    m
                  
                  ,
                  
                    rj
                    +
                    n
                  
                
                )
              
            
          
        
      
    
  




  
    
      
        d
        k
      
      ⁡
      
        (
        
          i
          ,
          j
        
        )
      
    
    =
    
      
        
          ∑
          m
        
        ⁢
        
          
            ∑
            n
          
          ⁢
          
            
              v
              
                m
                ,
                n
              
            
            ⁢
            
              
                g
                l
              
              ⁡
              
                (
                
                  ri
                  ,
                  rj
                
                )
              
            
          
        
      
      -
      
        
          ∑
          m
        
        ⁢
        
          
            ∑
            n
          
          ⁢
          
            
              v
              
                m
                ,
                n
              
            
            ⁢
            
              
                g
                l
              
              ⁡
              
                (
                
                  
                    ri
                    +
                    m
                  
                  ,
                  
                    rj
                    +
                    n
                  
                
                )
              
            
          
        
      
    
  




  
    
      
        d
        k
      
      ⁡
      
        (
        
          i
          ,
          j
        
        )
      
    
    =
    
      
        
          c
          k
        
        ⁡
        
          (
          
            i
            ,
            j
          
          )
        
      
      =
      
        
          ∑
          m
        
        ⁢
        
          
            ∑
            n
          
          ⁢
          
            
              v
              
                m
                ,
                n
              
            
            ⁡
            
              (
              
                
                  
                    g
                    l
                  
                  ⁡
                  
                    (
                    
                      ri
                      ,
                      rj
                    
                    )
                  
                
                -
                
                  
                    g
                    l
                  
                  ⁡
                  
                    (
                    
                      
                        ri
                        +
                        m
                      
                      ,
                      
                        rj
                        +
                        n
                      
                    
                    )
                  
                
              
              )
            
          
        
      
    
  



The term gl(ri, rj)−gl(ri+m, rj+n) is called a translation difference.
It expresses the difference in pixel value between a central pixel and a neighboring pixel in an approximation image. It is a measure of local contrast.
The weighted sum of the translation differences is called a centre difference ck(i,j).
In a similar way it can be proven that the detail images in other multi-scale decomposition methods can also be represented as a combination of translation difference images.
The Conversion Operation
In state-of-the-art methods like the one disclosed in EP 527 525 contrast enhancement is obtained by applying a conversion operator ƒ(x) to the detail image dk or, equivalently:




  
    f
    ⁡
    
      (
      
        
          d
          k
        
        ⁡
        
          (
          
            i
            ,
            j
          
          )
        
      
      )
    
  
  =
  
    f
    (
    
      
        
          g
          l
        
        ⁡
        
          (
          
            ri
            ,
            rj
          
          )
        
      
      -
      
        
          ∑
          m
        
        ⁢
        
          
            ∑
            n
          
          ⁢
          
            
              v
              
                m
                ,
                n
              
            
            ⁢
            
              
                g
                l
              
              ⁡
              
                (
                
                  
                    ri
                    +
                    m
                  
                  ,
                  
                    rj
                    +
                    n
                  
                
                )
              
            
          
        
      
    
    )
  




An example of such a conversion operator is the sigmoid function. Another example of such conversion operator is the contrast enhancement function like the one disclosed in EP 525 527.
The shape of the conversion operator depends on the specific requirements of the enhancement which is intended to amplify the low-value detail pixel more than the high-value detail pixels.
The conversion step may cause deformations of the shape of the edge transitions in the reconstructed, contrast enhanced image.
The reason is the non-linearity of the conversion function.
Generally, the following applies to non-linear functions:



  
    
      f
      ⁡
      
        (
        
          x
          +
          y
        
        )
      
    
    ≠
    
      
        f
        ⁡
        
          (
          x
          )
        
      
      +
      
        f
        ⁡
        
          (
          y
          )
        
      
    
  




  or




  
    
      f
      (
      
        
          ∑
          i
        
        ⁢
        
          x
          i
        
      
      )
    
    ≠
    
      
        ∑
        i
      
      ⁢
      
        f
        ⁡
        
          (
          
            x
            i
          
          )
        
      
    
  



State-of-the-art algorithms first compute the pixel values in the detail image dk as weighted sums and apply the conversion step afterwards.
By rewriting the pixel values in the detail image dk as a weighted sum of translation differences, it is possible to apply the conversion step before the summation instead of afterwards.
Contrast enhancement is now obtained by applying the conversion step to the translation differences:




  
    f
    ⁡
    
      (
      
        
          d
          k
        
        ⁡
        
          (
          
            i
            ,
            j
          
          )
        
      
      )
    
  
  =
  
    
      ∑
      m
    
    ⁢
    
      
        ∑
        n
      
      ⁢
      
        
          v
          
            m
            ,
            n
          
        
        ⁢
        
          f
          ⁡
          
            (
            
              
                
                  g
                  l
                
                ⁡
                
                  (
                  
                    ri
                    ,
                    rj
                  
                  )
                
              
              -
              
                
                  g
                  l
                
                ⁡
                
                  (
                  
                    
                      ri
                      +
                      m
                    
                    ,
                    
                      rj
                      +
                      n
                    
                  
                  )
                
              
            
            )
          
        
      
    
  




In this way the shape of the edge transitions is better preserved in the contrast enhanced, reconstructed image.
If for every scale k the detail image at that scale is computed out of the full resolution image g0, and enhancement is applied to the center differences, then the shapes of the edge transitions are best preserved after reconstruction.
Different implementations of the present invention are illustrated in FIGS. 4, 6 and 8. Corresponding enhancement steps are shown in FIGS. 5, 7 and 9.
In the present invention, the center differences (i.e. the weighted sum of the translation differences) only approximate the pixel values in the detail image as would be generated by a multi-scale decomposition.
For example, in case of a 5×5 Gaussian filter in the Burt decomposition and given the fact that the approximation image at the same scale as the detail image is used, 9×9=81 translation difference images and 9×9=81 weights need to be computed according to the first embodiment.
By using an approximating summation of e.g. 7×7=49 terms instead, only 49 translation difference images and 49 weights have to be computed.
The number of terms used in the summation generates a trade-off between the speed of the multi-scale decomposition/reconstruction and the degree of preservation of the shape of the edge transitions after contrast enhancement.
The first step is to compute the multi-scale decomposition in the conventional way, resulting in a multi-scale representation of detail images dk.
The next step is to compute for each detail image dk an image of amplification coefficients ak, based on the center difference images computed out of an approximation image at scale lε{0, . . . , k}.
The number of translation difference images and the corresponding translations depends on the number of terms used in the approximating summation.
To obtain contrast enhancement, the translation images are converted.
The amplification coefficients image ak are computed as the ratio of the weighted sum of the enhanced translation difference images and the weighted sum of the unenhanced translation difference images.
For the amplification coefficient at scale k at position i,j following formula is applied:




  
    
      a
      k
    
    ⁡
    
      (
      
        i
        ,
        j
      
      )
    
  
  =
  
    
      
        ∑
        
          m
          ~
        
      
      ⁢
      
        
          ∑
          
            n
            ~
          
        
        ⁢
        
          
            
              v
              ~
            
            
              
                m
                ~
              
              ,
              
                n
                ~
              
            
          
          ⁢
          
            f
            ⁡
            
              (
              
                
                  
                    g
                    l
                  
                  ⁡
                  
                    (
                    
                      ri
                      ,
                      rj
                    
                    )
                  
                
                -
                
                  
                    g
                    l
                  
                  ⁡
                  
                    (
                    
                      
                        ri
                        +
                        
                          m
                          ~
                        
                      
                      ,
                      
                        rj
                        +
                        
                          n
                          ~
                        
                      
                    
                    )
                  
                
              
              )
            
          
        
      
    
    
      
        ∑
        
          m
          ~
        
      
      ⁢
      
        
          ∑
          
            n
            ~
          
        
        ⁢
        
          
            
              v
              ~
            
            
              
                m
                ~
              
              ,
              
                n
                ~
              
            
          
          ⁡
          
            (
            
              
                
                  g
                  l
                
                ⁡
                
                  (
                  
                    ri
                    ,
                    rj
                  
                  )
                
              
              -
              
                
                  g
                  l
                
                ⁡
                
                  (
                  
                    
                      ri
                      +
                      
                        m
                        ~
                      
                    
                    ,
                    
                      rj
                      +
                      
                        n
                        ~
                      
                    
                  
                  )
                
              
            
            )
          
        
      
    
  




The detail images dk are enhanced by multiplication of dk by the amplification coefficients ak.
The set of amplification coefficients is called amplification image.
The reconstructed, contrast enhanced version of the image is computed by applying the multi-scale reconstruction to the enhanced detail images.
Remark: If the conversion function ƒ(x) is the identity function, all the amplification factors will be equal to 1. This results in a reversible multi-scale decomposition/reconstruction.
While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.

## Claims

1. A method for enhancing the contrast of an image that is represented by a digital signal, the method comprising:
a computer decomposing said digital signal into a multi-scale representation comprising at least two detail images representing detail at multiple scales and approximation images from which the detail images are derived, an approximation image at a scale representing the grey values of said image in which all details at that scale have been omitted,
the computer computing translation difference images of at least one approximation image,
the computer non-linearly modifying the values of said translation difference images,
the computer computing an amplification image at least one scale as the ratio of two images wherein the first image is computed by combining said modified translation difference images at the same or smaller scale and the second image is created by combining unenhanced translation difference images at the same or smaller scale,
the computer computing an enhanced multi-scale detail representation by modifying at least one scale the detail image according to the amplification image at that scale, and
the computer computing an enhanced image representation by applying a reconstruction algorithm to the enhanced multi-scale detail representation.

2. A method according to claim 1, further comprising computing one of the translation difference images at a specific scale out of an approximation image at the same scale.

3. A method according to claim 1, wherein a translation image at a scale k is computed out of an approximation image at scale m, wherein m represents a scale between scale 1 and scale k−1.

4. A method according to claim 1, wherein center difference images are identical to the multi-scale detail images or a close approximation of the multi-scale detail images.

5. A method according to claim 1, wherein said image is a mammographic image.

6. A method according to claim 1, wherein said image is a computed tomography (CT) image.

7. A method for enhancing the contrast of an image that is represented by a digital signal, the method comprising:
a computer decomposing said digital signal into a multi-scale representation comprising at least two detail images representing detail at multiple scales and approximation images from which the detail images are derived, an approximation image at a scale representing the grey values of said image in which all details at that scale have been omitted,
the computer computing translation difference images out of the original image,
the computer non-linearly modifying the values of said translation difference images,
the computer computing an amplification image at least one scale as the ratio of two images wherein the first image is computed by combining said modified translation difference images at the same or smaller scale and the second image is created by combining unenhanced translation difference images at the same or smaller scale,
the computer computing an enhanced multi-scale detail representation by modifying at least one scale the detail image according to the amplification image at that scale, and
the computer computing an enhanced image representation by applying a reconstruction algorithm to the enhanced multi-scale detail representation.

8. Computer software stored on a non-transitory computer-readable medium for enhancing the contrast of an image that is represented by a digital signal, the software, when executed by a computer, causes the computer to:
decompose said digital signal into a multi-scale representation comprising at least two detail images representing detail at multiple scales and approximation images from which the detail images are derived, an approximation image at a scale representing the grey values of said image in which all details at that scale have been omitted,
compute translation difference images of at least one approximation image,
non-linearly modify the values of said translation difference images,
compute an amplification image at least one scale as the ratio of two images wherein the first image is computed by combining said modified translation difference images at the same or smaller scale and the second image is created by combining unenhanced translation difference images at the same or smaller scale,
compute an enhanced multi-scale detail representation by modifying at least one scale the detail image according to the amplification image at that scale, and
compute an enhanced image representation by applying a reconstruction algorithm to the enhanced multi-scale detail representation.

9. A computer software product for enhancing the contrast of an image that is represented by a digital signal, the product comprising a non-transitory computer-readable medium in which program instructions are stored, which instructions, when read by a computer, cause the computer to:
decompose said digital signal into a multi-scale representation comprising at least two detail images representing detail at multiple scales and approximation images from which the detail images are derived, an approximation image at a scale representing the grey values of said image in which all details at that scale have been omitted,
compute translation difference images of at least one approximation image,
non-linearly modify the values of said translation difference images,
compute an amplification image at least one scale as the ratio of two images wherein the first image is computed by combining said modified translation difference images at the same or smaller scale and the second image is created by combining unenhanced translation difference images at the same or smaller scale,
compute an enhanced multi-scale detail representation by modifying at least one scale the detail image according to the amplification image at that scale, and compute an enhanced image representation by applying a reconstruction algorithm to the enhanced multi-scale detail representation.

10. A method according to claim 7, wherein a translation image at a scale k is computed out of an approximation image at scale m, wherein m represents a scale between scale 1 and scale k−1.

11. A method according to claim 7, wherein center difference images are identical to the multi-scale detail images or a close approximation of the multi-scale detail images.

12. A method according to claim 7, wherein said image is a mammographic image.

13. A method according to claim 7, wherein said image is a computed tomography (CT) image.

14. Computer software according to claim 8, that further causes the computer to compute one of the translation difference images at a specific scale out of an approximation image at the same scale.

15. Computer software according to claim 8, wherein a translation image at a scale k is computed out of an approximation image at scale m, wherein m represents a scale between scale 1 and scale k−1.

16. Computer software according to claim 8, wherein center difference images are identical to the multi-scale detail images or a close approximation of the multi-scale detail images.

17. Computer software according to claim 8, wherein said image is a mammographic image.

18. Computer software according to claim 8, wherein said image is a computed tomography (CT) image.