Abstract:
A digital image processing method includes the steps of embedding a delta function in a digital image; subjecting the digital image to an intermediate processing step, the intermediate processing step having a modulation transfer function (MTF) that blurs the image; extracting the delta function from the processed digital image; and estimating the MTF from the recovered delta function. The blur is removed from the image by generating a sharpening filter that is substantially the inverse of the MTF and applying the sharpening filter to the blurred image to produce an improved image.

Description:
FIELD OF THE INVENTION 
     The invention relates generally to the field of image processing, and in particular to image enhancement and more particularly to image sharpening. 
     BACKGROUND OF THE INVENTION 
     When images are subjected to intermediate processing steps such as printing and rescanning, the quality of the image may be reduced i.e., the sharpness of the images may be degraded, due to the limited modulation transfer function (MTF) of the intermediate processing steps. It is known to apply sharpening filters to images in an attempt to improve the appearance of the image either because they have been degraded by intermediate processing steps, or because they are being optimized for display on a particular medium. For example, digital images that are transmitted over the Internet are optimized for display on CRTs by applying a predetermined amount of sharpening. If the sharpened image is subsequently printed and rescanned, it is possible that more sharpening will be applied to the image in an attempt to improve its appearance. Unfortunately, if an image is oversharpened, its quality can be further reduced. Because of this, a digital image having an unknown processing history cannot be automatically sharpened by a predetermined amount prior to display. An operator is generally required to view the effects of different amounts of sharpening and select the one that produces the most improvement without reducing the quality of the image. 
     There is a need therefore for an improved method of sharpening digital images prior to display, and therefore to be able to know how much an image has been degraded due to the MTF of intermediate processing steps, and/or sharpened so that an optimal level of sharpening can be applied to the image when it is displayed. 
     SUMMARY OF THE INVENTION 
     The problem is solved according to the present invention by providing a digital image processing method including the steps of embedding a delta function in a digital image; subjecting the digital image to an intermediate processing step, the intermediate processing step having a modulation transfer function (MTF) that blurs the image; extracting the delta function from the processed digital image; and estimating the MTF from the recovered delta function. The blur is removed from the image by generating a sharpening filter that is substantially the inverse of the MTF and applying the sharpening filter to the blurred image to produce an improved image. 
     The processing method has the advantages of avoiding oversharpening an image and eliminating the need for an operator to select the amount of sharpening applied to an image for display. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram illustrating a digital imaging system capable of performing several steps of intermediate processing and sharpening; 
     FIG. 2 is a flow chart showing the steps of the present invention; 
     FIG. 3 is a diagram showing an image tiled with an embedded delta function, useful in describing the operation of the present invention; 
     FIG. 4 is a diagram showing the recovery of the delta function from an arbitrary region of the image in FIG. 3, useful in describing the operation of the present invention; 
     FIG. 5 is a flow chart illustrating the steps in deriving the MTF from the recovered delta function; 
     FIG. 6 is an illustration of a ramping function applied to the region containing the delta function to smooth the edges of the region; 
     FIG. 7 is a graph showing the Fourier amplitude; and 
     FIG. 8 is a graph showing the inverse Fourier amplitude. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 1, an image of a subject  10  is captured by a camera  12  employed by person A. The camera  12  may be an electronic camera of the type that directly produces a digital image. Alternatively the camera can be a conventional film camera that produces a film image that can be scanned to produce a digital image. The digital image is supplied to a first personal computer  14  operated by person A and is sent over the World Wide Web  16  to a second personal computer operated by person B. Person B enlarges the image on his computer  18 , sharpens it somewhat and makes a print  20  on his ink jet printer  22 . Person B approves of the image and would like to obtain a number of copies on a more desirable output medium, such as silver halide photographic paper. He takes the ink jet print to a photofinisher  24  and asks to have 8×10 inch copies of the image made from the ink jet print  20 . The photofinisher scans the ink jet print on a scanner  26  to produce a digital image, applies additional processing to the digital image, such as image sharpening, in an image processing computer  28  and sends the processed digital image to a silver halide digital photographic printer  30 . Alternatively, person B may have taken or sent the digital image directly from his personal computer  18  to the photofinisher without the intermediate steps of processing and printing. 
     Several of the steps described above had the potential for degrading the image due to an imperfect MTF, and/or sharpening the image using digital image processing. If the photofinisher knows how much image degradation and/or sharpening was carried out on the image after the original capture by person A, he can calculate the optimal level of sharpening to be applied to the digital image prior to printing on the silver halide printer  30 . 
     This information is supplied according to the present invention by embedding a delta function in the original image, either at the time of capture by the camera  12 , or shortly thereafter in personal computer  14 . The delta function is an image of a spot (preferably one pixel) that has, for example a magnitude of one in a bed of zeros. The delta function is effectively convolved with a carrier having a substantially flat Fourier amplitude and random phase to disperse the information contained in the delta function over a finite region of the image, thereby rendering the delta function invisible to the human eye when added to the image. 
     A method for constructing such a carrier having a substantially flat Fourier amplitude random phase is shown and described in U.S. Pat. No. 6,044,156, issued on Mar. 28, 2000, by Honsinger et al., entitled “Method for Generating An Improved Carrier For Use In An Image Data Embedding Application.” The carrier is designed in the Fourier frequency domain. In the Fourier domain, the value of the carrier at each frequency is characterized by a complex number that can be represented as either a real/imaginary pair or as an amplitude/phase pair. The carrier is designed in the Fourier domain in such a way that the carrier&#39;s amplitude at each frequency is a constant and the carrier&#39;s phase at each frequency is a random number that is uniformly distributed between 0 and 360 degrees. The autocorrelation of such a carrier has a shape resembling a delta function with small sidelobes. It should be noted that if there is only one delta function, the carrier itself is equivalent to the convolution of the carrier with the delta function. 
     Each step of intermediate processing and/or image sharpening will affect the envelope of the delta function. The processing history of the image can be determined by recovering the delta function and deriving the Fourier amplitude of the processed delta function, which is equivalent to the combined MTF of the intermediate processing steps. 
     Turning to FIG. 2, the invention includes the following steps. First a delta function is embedded ( 32 ) in an image. Next, the image having the embedded delta function is processed ( 34 ) through a number of intermediate processing steps such as sharpening, printing and scanning. Prior to a further step of printing, the delta function is extracted ( 36 ) from the image. An estimate of the combined MTF of the intermediate processing steps is then made ( 38 ) from the extracted delta function. A sharpening filter is generated ( 40 ) that is the inverse of the combined MTF. Finally, the sharpening filter is applied ( 42 ) to the processed image prior to the further step of printing the image. 
     In a preferred embodiment of the invention, the carrier (which is equivalent to a single delta function convolved with the carrier) is a 128×128 block of random numbers having the properties of flat Fourier amplitude and random phase. Turning to FIG. 3, 128×128 blocks  44  of carrier are added to a digital image  46  in a tile like fashion to cover the image. 
     As shown in FIG. 4, the delta function  48  is recovered from the image by taking an arbitrary 128×128 block  50  of image data and correlating the block  50  with the carrier  44 . The location of the delta function in the block of recovered data will depend upon the location of the arbitrary block  50  with respect to the boundaries of the tiled carriers, but is not important for the following description. The recovered delta function will exhibit degradation due to the intermediate processing steps. 
     Referring to FIG. 5, the combined MTF is determined from the recovered delta function as follows. A region surrounding the delta function is selected ( 52 ) and the remaining pixels in the recovered block are set to zero. In a preferred embodiment with a carrier of 128×128 pixels, the region containing the delta function will generally be about 12 pixels in diameter with the delta function at its center. The Fourier amplitude of the block containing the zeros and the delta function is then computed ( 56 ) preferably by applying a fast Fourier transform to the 128×128 block of pixels representing the recovered delta function. The Fourier amplitude is the square root of the sum of the real squared plus the imaginary squared Fourier coefficients. The result is equivalent to the combined MTF of the intermediate processing steps. In a preferred mode of practicing the invention, the region surrounding the delta function is smoothed ( 54 ) at its edges by applying a ramping function to the delta function data that ramps up from zero to one over about 3 pixels at the edge of the region containing the delta function. FIG. 6 illustrates the ramping function  58 , the region including the delta function  60 , and the smoothed region  62  after applying the ramping function. This processing step has the effect of reducing ringing in the MTF estimate. 
     FIG. 7 shows a plot  64  of a typical Fourier amplitude. FIG. 8 shows a plot  66  of the inverse Fourier amplitude, which is the specification for a sharpening filter that is applied to the image prior to printing on silver halide printer  30  (see FIG.  1 ). The sharpening filter as shown in FIG. 8 can be applied to the image in the frequency domain. Alternatively, a simple sharpening filter having approximately the same frequency response shown in FIG. 8 can be applied to image in the spatial domain by convolving the filter with the image. 
     According to a further alternative, the sharpening filter is derived using Wiener estimation techniques. If the noise characteristics of the intermediate processing apparatus are known, a Wiener filter can be derived in the frequency domain by dividing the MTF by the sum of the square of the MTF plus the square of the noise. The resulting Wiener filter is substantially the inverse of the MTF and maximizes the signal to noise ratio of the sharpening process. 
     Although the invention has been described with reference to embedding one delta function in the image for the purposes of tracking the changes to the image due to the MTF of intermediate processing steps and then generating an optimum sharpening filter based on the MTF, there are several known techniques where data is embedded in images for other purposes such as digital signatures, water marks, etc. Some of these techniques employ carriers that can be used in the present invention. See for example the techniques disclosed in U.S. Pat. No. 5,850,481 issued Dec. 15, 1998 to Rhoads, entitled “Steganographic System,” or in U.S. Pat. No. 6,044,156, issued on Mar. 28, 2000, by Honsinger et al., entitled “Method ForGenerating An Improved Carrier For Use In An Image Data Embedding Application.” In the technique described by Rhoads, a plurality of carriers are employed, each carrier representing one bit of data. In the technique described by Honsinger, a pattern of data bits is convolved with a single carrier. Individual bits that were embedded in an image using either of these techniques can be recovered and employed according to the present invention to generate the MTF of intermediate processing steps, and to design an optimum sharpening filter that is substantially the inverse of the MTF. 
     The delta function embedding step of the present invention can be employed in a digital camera to embed the delta function at the time of image capture. One application that is envisioned is to embed the delta function in an image captured by a satellite born camera in space. Alternatively, the embedding step can be performed in a digital image processing program in a personal computer or other digital image processing apparatus that receives the digital image after capture. In any event, the method can be implemented by a computer program and stored on a computer readable storage medium. 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention. 
     Parts List 
       10  photographic subject 
       12  camera 
       14  personal computer 
       16  World Wide Web 
       18  personal computer 
       20  ink jet print 
       22  ink jet printer 
       24  photofinisher 
       26  scanner 
       28  image processing computer 
       30  digital photographic printer 
       32  embed delta function step 
       34  intermediate processing step 
       36  extract delta function step 
       38  estimate MTF step 
       40  generate sharpening filter step 
       42  apply sharpening filter to image step 
       44  128×128 carrier block 
       46  digital image 
       48  delta function 
       50  arbitrary 128×128 block from image 
       52  select region surrounding delta function step 
       54  smooth edge of region step 
       56  compute Fourier amplitude step 
       58  ramping function 
       60  region containing delta function 
       62  smoothed region containing delta function 
       64  typical Fourier amplitude plot 
       66  inverse Fourier amplitude plot