Method and apparatus for compressing the dynamic range of an image

An original image is transformed into a multi-resolution space and is thereby decomposed into images, each of which is of one of a plurality of different frequency bands. An image of the lowest frequency band, which is lowest among the plurality of the different frequency bands, is processed with the formula EQU g.sub.L '=g.sub.L +f.sub.1 (g.sub.L)=f.sub.2 (g.sub.L) wherein f.sub.1 (g.sub.L) represents a function, the value of which decreases monotonically as the signal value g.sub.L of the image of the lowest frequency band increases. A processed image of the lowest frequency band is obtained from the processing. An inverse multi-resolution transform is then carried out on the processed image of the lowest frequency band and the images of the other frequency bands, and a processed image is thereby obtained.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to an image processing method and apparatus for 
carrying out image processing on an image of a predetermined frequency 
band in an original image. 
2. Description of the Prior Art 
Techniques for obtaining an image signal, which represents an image, 
carrying out appropriate image processing on the image signal, and then 
reproducing a visible image by use of the processed image signal have 
heretofore been known in various fields. For example, in Japanese 
Unexamined Patent Publication No. 55(1980)-163772, the applicant proposed 
a method for carrying out frequency emphasis processing, such as unsharp 
mask processing, on an image signal, such that a visible radiation image 
may be obtained, which has good image quality and can serve as an 
effective tool in, particularly, the efficient and accurate diagnosis of 
an illness. With the frequency processing, an unsharp mask signal is 
subtracted from an image signal representing an original image, the 
resulting difference value is multiplied by an emphasis coefficient, and 
the thus obtained product is added to the image signal. In this manner, 
predetermined frequency components in the image are emphasized. 
A different method for carrying out frequency processing on an image signal 
has also been proposed. With the proposed frequency processing method, an 
image is transformed into multi-resolution images by a Fourier transform, 
a wavelet transform, a sub-band transform, or the like, and the image 
signal representing the image is thereby decomposed into signals falling 
within a plurality of different resolutions or frequency bands. 
Thereafter, of the decomposed signals, a signal falling within a desired 
frequency band is subjected to predetermined image processing, such as 
emphasis. 
Further, recently in the field of image processing, a novel technique for 
transforming an image into a multi-resolution space, which is referred to 
as the Laplacian pyramid technique, has been proposed in, for example, 
Japanese Unexamined Patent Publication No. 6(1994)-301766. With the 
proposed Laplacian pyramid technique, mask processing is carried out on 
the original image by using a mask having characteristics such that it may 
be approximately represented by a Gaussian function. A sub-sampling 
operation is then carried out on the resulting image in order to thin out 
the number of the picture elements to one half along each of 
two-dimensional directions of the array of the picture elements in the 
image, and an unsharp image having a size of one-fourth of the size of the 
original image is thereby obtained. Thereafter, a picture element having a 
value of 0 is inserted into each of the points on the unsharp image, which 
were eliminated during the sampling operation, and the image size is 
thereby restored to the original size. Mask processing is then carried out 
on the thus obtained image by using the aforesaid mask, and an unsharp 
image is thereby obtained. The thus obtained unsharp image is subtracted 
from the original image, and a detail image of a predetermined frequency 
band of the original image is thereby obtained. This processing is 
iterated with respect to the obtained unsharp image, and n number of 
unsharp images having sizes of 1/2.sup.2n of the size of the original 
image are thereby formed. As described above, the sampling operation is 
carried out on the image, which has been obtained from the mask processing 
with the mask having characteristics such that it may be approximately 
represented by the Gaussian function. Therefore, though the Gaussian 
filter is actually used, the same processed image as that obtained when a 
Laplacian filter is used is obtained. Also, in this manner, the images of 
low frequency bands, which have the sizes of 1/2.sub.2N of the size of the 
original image are successively obtained from the image of the original 
image size. Therefore, the group of the images obtained as a result of the 
processing is referred to as the Laplacian pyramid. 
The Laplacian pyramid technique is described in detail in, for example, 
"Fast Filter Transforms for Image Processing" by Burt P. J., Computer 
Graphics and Image Processing, Vol. 16, pp. 20-51, 1981; "Fast Computation 
of the Difference of Low.cndot.Pass Transform" by Growley J. L., Stern R. 
M., IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 6, No. 
2, March 1984; "A Theory for Multiresolution Signal Decomposition; The 
Wavelet Representation" by Mallat S. G., IEEE Trans. on Pattern Analysis 
and Machine Intelligence, Vol. 11, No. 7, July 1989; "Image Compression by 
Gabor Expansion" by Ebrahimi T., Kunt M., Optical Engineering, Vol. 30, 
No. 7, pp. 873-880, July 1991; and "Multiscale Image Contrast 
Amplification" by Pieter Vuylsteke, Emile Schoeters, SPIE, Vol. 2167, 
Image Processing (1994), pp. 551-560. 
Japanese Unexamined Patent Publication No. 6(1994)-301766 mentioned above 
discloses a method, wherein processing for emphasizing image values is 
carried out on the images of all of the frequency bands in the Laplacian 
pyramid, which images have been obtained in the manner described above, 
and the image of each frequency band, which has been obtained from the 
emphasis processing, is then subjected to an inverse transform, and a 
processed image is thereby obtained. In the image obtained from such 
processing, the image has been emphasized in each frequency band. 
Therefore, an image is obtained such that unsharp mask processing might 
have been carried out substantially with masks having a plurality of sizes 
in the aforesaid unsharp mask processing. 
Also, "Multiscale Image Contrast Amplification" mentioned above discloses a 
method comprising the steps of: (i) carrying out processing for 
multiplying the density of the lowest resolution image, which has the 
lowest resolution among the images having been decomposed with the 
Laplacian pyramid technique into a plurality of different frequency bands, 
by a factor of a (a&lt;1), and (ii) carrying out an inverse multi-resolution 
transform on the lowest resolution image, which has been obtained from the 
processing, and the images of the other frequency bands, a processed image 
being thereby obtained. With the disclosed method, the contrast of the 
lowest resolution image is restricted, and the processed image can be 
obtained such that portions of the image covering a wide range of image 
density can be used. Therefore, it is possible to obtain substantially the 
same processed image as that obtained when a dynamic range compressing 
process is carried out on the original image. 
However, with the method disclosed in "Multiscale Image Contrast 
Amplification" mentioned above, the image of the lowest frequency band is 
merely multiplied by a factor of a, and therefore all of the signal values 
of the image of the lowest frequency band are processed equally. 
Therefore, the image information of a signal range, which it is not 
necessary to process, in the image of the lowest frequency band is 
processed together with the image information which is to be processed. 
Accordingly, the degree of freedom of image processing cannot be kept 
high, and a processed image having a desired quality cannot be obtained. 
For example, in cases where processing is carried out on a radiation image 
of the chest of a human body, if the processing described in "Multiscale 
Image Contrast Amplification" mentioned above is carried out on the image 
of the lowest frequency band such that the change in density in the 
mediastinum region may become perceptible, the mediastinum region will 
become perceptible, but the lung field regions having a high density will 
be affected adversely. As a result, the thus obtained image will become 
imperceptible as a whole. 
SUMMARY OF THE INVENTION 
The primary object of the present invention is to provide an image 
processing method, wherein the degree of freedom of image processing is 
kept high, and a processed image, which is perceptible, is obtained. 
Another object of the present invention is to provide an apparatus for 
carrying out the image processing method. 
The present invention provides a first image processing method, comprising 
the steps of: 
i) transforming an original image into a multi-resolution space, the 
original image being thereby decomposed into images, each of which is of 
one of a plurality of different frequency bands, 
ii) processing an image of the lowest frequency band, which is lowest among 
the plurality of the different frequency bands, with the formula 
EQU g.sub.L '=g.sub.L +f.sub.1 (g.sub.L)=f.sub.2 (g.sub.L) 
wherein f.sub.1 (g.sub.L) represents a function, the value of which 
decreases monotonically as the signal value g.sub.L of the image of the 
lowest frequency band increases, a processed image of the lowest frequency 
band being obtained from the processing, and 
iii) carrying out an inverse multi-resolution transform of the processed 
image of the lowest frequency band and the images of the other frequency 
bands, a processed image being obtained from the inverse multi-resolution 
transform. 
The present invention also provides a second image processing method, 
comprising the steps of: 
i) transforming an original image into a multi-resolution space, the 
original image being thereby decomposed into images, each of which is of 
one of a plurality of different frequency bands, 
ii) processing an image of the lowest frequency band, which is lowest among 
the plurality of the different frequency bands, with the formula 
EQU g.sub.L '=g.sub.L +.alpha..multidot.f.sub.3 (g.sub.L) 
wherein f.sub.3 (g.sub.L) represents a function, the value of which 
decreases monotonically as the signal value g.sub.L of the image of the 
lowest frequency band increases, and .alpha. represents the degree of 
emphasis, a processed image of the lowest frequency band being obtained 
from the processing, and 
iii) carrying out an inverse multi-resolution transform of the processed 
image of the lowest frequency band and the images of the other frequency 
bands, a processed image being obtained from the inverse multi-resolution 
transform. 
The present invention further provides a first image processing apparatus, 
comprising: 
i) a multi-resolution decomposing means for transforming an original image 
into a multi-resolution space, the original image being thereby decomposed 
into images, each of which is of one of a plurality of different frequency 
bands, 
ii) an operation means for processing an image of the lowest frequency 
band, which is lowest among the plurality of the different frequency 
bands, with the formula 
EQU g.sub.L '=g.sub.L +f.sub.1 (g.sub.L)=f.sub.2 (g.sub.L) 
wherein f.sub.1 (g.sub.L) represents a function, the value of which 
decreases monotonically as the signal value g.sub.L of the image of the 
lowest frequency band increases, a processed image of the lowest frequency 
band being obtained from the processing, and 
iii) an inverse transform means for carrying out an inverse 
multi-resolution transform of the processed image of the lowest frequency 
band and the images of the other frequency bands, a processed image being 
obtained from the inverse multi-resolution transform. 
The present invention still further provides a second image processing 
apparatus, comprising the steps of: 
i) a multi-resolution decomposing means for transforming an original image 
into a multi-resolution space, the original image being thereby decomposed 
into images, each of which is of one of a plurality of different frequency 
bands, 
ii) an operation means for processing an image of the lowest frequency 
band, which is lowest among the plurality of the different frequency 
bands, with the formula 
EQU g.sub.L '=g.sub.L +.alpha..multidot.f.sub.3 (g.sub.L) 
wherein f.sub.3 (g.sub.L) represents a function, the value of which 
decreases monotonically as the signal value g.sub.L of the image of the 
lowest frequency band increases, and .alpha. represents the degree of 
emphasis, a processed image of the lowest frequency band being obtained 
from the processing, and 
iii) an inverse transform means for carrying out an inverse 
multi-resolution transform of the processed image of the lowest frequency 
band and the images of the other frequency bands, a processed image being 
obtained from the inverse multi-resolution transform. 
The term "transforming an original image into a multi-resolution space" as 
used herein means decomposing the image signal, which represents the 
original image, into image signals representing the images of a plurality 
of different frequency bands by using a predetermined filter for the 
Laplacian pyramid technique, the wavelet transform, the sub-band 
transform, or the like. 
With the first image processing method and apparatus in accordance with the 
present invention, the image of the lowest frequency band, which is among 
the images of the plurality of the different frequency bands having been 
obtained from the transform into the multi-resolution space, is processed 
with the formula 
EQU g.sub.L '=g.sub.L +f.sub.1 (g.sub.L)=f.sub.2 (g.sub.L) 
wherein f.sub.1 (g.sub.L) represents the function, the value of which 
decreases monotonically as the signal value g.sub.L of the image of the 
lowest frequency band increases. The processed image of the lowest 
frequency band is obtained from the processing. Therefore, the dynamic 
range of the entire image of the lowest frequency band can be compressed, 
and the contrast of an image portion, at which the signal values are 
comparatively large, can be kept high. Accordingly, the processed image of 
the lowest frequency band can be obtained such that the portions of the 
image covering a wide range of image density can be used and may have good 
image quality. The inverse multi-resolution transform is then carried out 
on the processed image of the lowest frequency band and the images of the 
other frequency bands. From the inverse multi-resolution transform, a 
processed image can be obtained, in which the dynamic range compressing 
process has been carried out in accordance with different regions of the 
image. 
With the second image processing method and apparatus in accordance with 
the present invention, the image of the lowest frequency band is processed 
with the formula 
EQU g.sub.L '=g.sub.L +.alpha..multidot.f.sub.3 (g.sub.L) 
wherein f.sub.3 (g.sub.L) represents the function, the value of which 
decreases monotonically as the signal value g.sub.L of the image of the 
lowest frequency band increases, and .alpha. represents the degree of 
emphasis. The processed image of the lowest frequency band is obtained 
from the processing. Therefore, the extent of the dynamic range 
compressing process carried out on the image of the lowest frequency band 
can be altered. Accordingly, the dynamic range compressing process can be 
carried out with a high degree of freedom.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The present invention will hereinbelow be described in further detail with 
reference to the accompanying drawings. 
FIG. 1 is a block diagram showing an apparatus for carrying out an 
embodiment of the image processing method in accordance with the present 
invention. As illustrated in FIG. 1, the apparatus for carrying out the 
embodiment of the image processing method in accordance with the present 
invention comprises an image input means 1 for feeding an image signal, 
which represents an original image, into the apparatus, and a 
multi-resolution decomposing process means 2 for carrying out a 
multi-resolution decomposing process on the original image and thereby 
obtaining decomposed images of a plurality of different frequency bands or 
resolutions. The apparatus also comprises an emphasis processing means 3 
for carrying out emphasis processing, which will be described later, on an 
image of a predetermined frequency band, which is among the decomposed 
images of the plurality of the different frequency bands having been 
obtained from the multi-resolution decomposing process means 2. The 
apparatus further comprises a restoration processing means 4 for restoring 
the image of the predetermined frequency band, which has been obtained 
from the emphasis processing carried out by the emphasis processing means 
3, and the images of the other frequency bands into a processed image. The 
apparatus still further comprises an image output means 5 for reproducing 
the processed image, which has been restored by the restoration processing 
means 4, as a visible image. The apparatus also comprises a residual image 
processing means 6 for carrying out a dynamic range compressing process, 
which will be described later, on a residual image, which is the image of 
the lowest frequency band obtained from the multi-resolution decomposing 
process means 2. 
How the embodiment of the image processing method in accordance with the 
present invention operates will be described hereinbelow. FIG. 2 is a 
block diagram showing how the processing is carried out by the 
multi-resolution decomposing process means 2 shown in FIG. 1. In this 
embodiment, by way of example, the Laplacian pyramid technique is utilized 
in order to decompose an image signal S, which represents the original 
image, into multi-resolution images. As illustrated in FIG. 2, the digital 
image signal S, which represents the original image, is fed into a first 
filtering means 101 of the multi-resolution decomposing process means 2. 
In the multi-resolution decomposing process means 2, the digital image 
signal S is fed into a first filtering means 101, which carries out a 
filtering process on the digital image signal S by using a low pass 
filter. By way of example, as illustrated in FIG. 3, the low pass filter 
approximately corresponds to a two-dimensional Gaussian distribution on a 
5.times.5 grid. As will be described later, the same types of low pass 
filters as that shown in FIG. 3 are utilized for all of the 
multi-resolution images. 
Also, in the filtering means 101, the image signal S, which has been 
obtained from the filtering process carried out with the low pass filter, 
is subjected to a sampling process. The filtering means 101 samples the 
signal components of the image signa S at every second row and every 
second column in the array of picture elements of the original image. An 
image signal representing a low-resolution approximate image g.sub.1 is 
thus obtained from the filtering means 101. The low-resolution approximate 
image g.sub.1 has a size of one-fourth of the size of the original image. 
Thereafter, in a first interpolating operation means 111, a single picture 
element having a value of 0 is inserted into each of the points on the 
low-resolution approximate image g.sub.1, which were eliminated during the 
sampling process. Specifically, a single picture element having a value of 
0 is inserted between every set of two adjacent picture elements located 
along each row and each column in the array of picture elements of the 
low-resolution approximate image g.sub.1. The low-resolution approximate 
image g.sub.1, into which the picture elements having a value of 0 have 
thus been inserted at intervals of a single picture element, is unsharp, 
and the change in the signal value of the low-resolution approximate image 
g.sub.1 is not smooth due to the picture elements having a value of 0, 
which have been inserted at intervals of a single picture element. 
Further, in the first interpolating operation means 111, the low-resolution 
approximate image g.sub.1, into which the picture elements having a value 
of 0 have been inserted in the manner described above, is subjected to a 
filtering process with the low pass filter shown in FIG. 3. An image 
signal representing a low-resolution approximate image g.sub.1 ' is thus 
obtained from the first interpolating operation means 111. The change in 
the signal value of the image signal representing a low-resolution 
approximate image g.sub.1 ' is smoother than the change in the signal 
value of the aforesaid low-resolution approximate image g.sub.1, into 
which the picture elements having a value of 0 have been inserted. Also, 
the low-resolution approximate image g.sub.1 ' has the characteristics 
such that the image information of the frequency band higher than the 
middle frequency in the frequency band of the original image have been 
eliminated from the original image. This is because, as described above, 
the size of the low-resolution approximate image g.sub.1 has been reduced 
to one-fourth of the size of the original image, the picture elements 
having a value of 0 have been inserted at intervals of a single picture 
element into the low-resolution approximate image g.sub.1, and the 
filtering process has then been carried out on the low-resolution 
approximate image g.sub.1 by using the low pass filter shown in FIG. 3. As 
a result, the image is obtained such that the image information of the 
frequency band higher than the middle frequency in the frequency band of 
the original image might have been blurred with the Gaussian function. 
Thereafter, in a first subtracter 121, the image signal representing the 
low-resolution approximate image g.sub.1 ' is subtracted from the image 
signal S representing the original image, and an image signal representing 
a detail image b.sub.0 is thereby obtained. Specifically, the image signal 
components of the image signal representing the low-resolution approximate 
image g.sub.1 ' and the image signal S representing the original image, 
which image signal components represent corresponding picture elements in 
the two images, are subtracted from each other. As described above, the 
low-resolution approximate image g.sub.1 ' has the characteristics such 
that the image information of the frequency band higher than the middle 
frequency in the frequency band of the original image might have been 
blurred. Therefore, the detail image b.sub.0 represents only the image 
information of the frequency band higher than the middle frequency in the 
frequency band of the original image. Specifically, as illustrated in FIG. 
4, the detail image b.sub.0 represents the image information of the 
frequency band of N/2 to N, where N represents the Nyquist frequency of 
the original image. 
Thereafter, the image signal representing the low-resolution approximate 
image g.sub.1 is fed into a second filtering means 102 and subjected to 
the filtering process using the low pass filter shown in FIG. 3. Also, in 
the filtering means 102, the image signal representing the low-resolution 
approximate image g.sub.1, which has been obtained from the filtering 
process, is subjected to a sampling process. The filtering means 102 
samples the signal components of the image signal, which represents the 
low-resolution approximate image g.sub.1, at every second row and every 
second column in the array of picture elements of the low-resolution 
approximate image g.sub.1. An image signal representing a low-resolution 
approximate image g.sub.2 is thus obtained from the filtering means 102. 
The low-resolution approximate image g.sub.2 has a size of one-fourth of 
the size of the low-resolution approximate image g.sub.1, i.e. a size of 
one-sixteenth of the size of the original image. Thereafter, in a second 
interpolating operation means 112, a single picture element having a value 
of 0 is inserted into each of the points on the low-resolution approximate 
image g.sub.2, which were eliminated during the sampling process. 
Specifically, a single picture element having a value of 0 is inserted 
between every set of two adjacent picture elements located along each row 
and each column in the array of picture elements of the low-resolution 
approximate image g.sub.2. The low-resolution approximate image g.sub.2, 
into which the picture elements having a value of 0 have thus been 
inserted at intervals of a single picture element, is unsharp, and the 
change in the signal value of the low-resolution approximate image g.sub.2 
is not smooth due to the picture elements having a value of 0, which have 
been inserted at intervals of a single picture element. 
Further, in the second interpolating operation means 112, the 
low-resolution approximate image g.sub.2, into which the picture elements 
having a value of 0 have been inserted in the manner described above, is 
subjected to a filtering process with the low pass filter shown in FIG. 3. 
An image signal representing a low-resolution approximate image g.sub.2 ' 
is thus obtained from the first interpolating operation means 112. The 
change in the signal value of the image signal representing a 
low-resolution approximate image g.sub.2 ' is smoother than the change in 
the signal value of the aforesaid low-resolution approximate image 
g.sub.2, into which the picture elements having a value of 0 have been 
inserted. Also, the low-resolution approximate image g.sub.2 ' has the 
characteristics such that the image information of the frequency 
components higher than the middle frequency in the frequency band of the 
low-resolution approximate image g.sub.1 has been eliminated from the 
low-resolution approximate image g.sub.1. 
Thereafter, in a second subtracter 122, the image signal representing the 
low-resolution approximate image g.sub.2 ' is subtracted from the image 
signal representing the low-resolution approximate image g.sub.1, and an 
image signal representing a detail image b.sub.1 is thereby obtained. 
Specifically, the image signal components of the image signal representing 
the low-resolution approximate image g.sub.2 ' and the image signal 
representing the low-resolution approximate image g.sub.1, which image 
signal components represent corresponding picture elements in the two 
images, are subtracted from each other. As described above, the 
low-resolution approximate image g.sub.2 ' has the characteristics such 
that the image information of the frequency band higher than the middle 
frequency in the frequency band of the low-resolution approximate image 
g.sub.1 might have been blurred. Therefore, the detail image b.sub.1 
represents only the image information of the frequency band higher than 
the middle frequency in the frequency band of the low-resolution 
approximate image g.sub.1. Specifically, as illustrated in FIG. 4, the 
detail image b.sub.1 represents only the image information of the 
frequency band higher than the middle frequency in the frequency band of 
the low-resolution approximate image g.sub.1, i.e. the image information 
of the frequency band of N/4 to N/2, where N represents the Nyquist 
frequency of the original image. In this manner, the detail image is 
obtained by carrying out the filtering process with the low pass filter 
having the Gaussian distribution. However, since the image having been 
obtained from the filtering process is subtracted from the low-resolution 
approximate image, substantially the same results as those obtained when 
the filtering process is carried out with a Laplacian filter can be 
obtained. 
The processing described above is carried out successively for 
low-resolution approximate images g.sub.k, where k=1 to N, which have been 
respectively filtered and sampled with the corresponding filtering means 
101-104. In this manner, as illustrated in FIG. 4, n number of detail 
images b.sub.k, wherein k=0 to L-1, and a residual image g.sub.L of the 
low-resolution approximate image are obtained. The levels of the 
resolution of the detail images b.sub.k successively become lower, 
starting with the resolution of the detail image b.sub.0. Specifically, 
the frequency bands of the detail images b.sub.k successively become 
lower. The detail images b.sub.k respectively represent the frequency 
bands of N/2.sup.k+1 to N/2.sup.k with respect to the Nyquist frequency N 
of the original image, and the sizes of the detail images b.sub.k become 
1/2.sup.2k times as large as the size of the original image. Specifically, 
the size of the detail image b.sub.0, which has the highest resolution, is 
equal to the size of the original image, and the size of the detail image 
b.sub.1, which has a high resolution next to the resolution of the detail 
image b.sub.0, is one-fourth of the size of the original image. The sizes 
of the detail images thus successively become smaller, starting with the 
size equal to the size of the original image. Also, the detail images are 
substantially identical with the images obtained from the process using 
the Laplacian filter. Therefore, the multi-resolution transform in this 
embodiment is referred to as the Laplacian pyramid. The residual image 
g.sub.L may be regarded as being an approximate image having a very low 
resolution with respect to the original image. In extreme cases, the 
residual image g.sub.L is constituted of only a single piece of image 
information, which represents the mean value of the signal values of the 
original image. The information representing the detail images b.sub.k and 
the residual image g.sub.L, which have thus been obtained, is stored in a 
memory (not shown). 
Thereafter, in the emphasis processing means 3, predetermined emphasis 
processing is carried out on a detail image b.sub.k of a desired frequency 
band, which is among the detail images b.sub.k having been obtained in the 
manner described above. The emphasis processing is carried out by 
multiplying the detail image b.sub.k of the desired frequency band by a 
predetermined emphasis coefficient. 
Also, in the residual image processing means 6, the dynamic range 
compressing process is carried out on the residual image g.sub.L. How the 
dynamic range compressing process is carried out will be described 
hereinbelow. 
FIG. 5A is a graph showing an example of a monotonically decreasing 
function, in which the value of the residual image signal g.sub.L serves 
as a variable. (As an aid in facilitating the explanation, the same 
reference character is used for both the residual image and the residual 
image signal.) The maximum value of the residual image signal g.sub.L is 
1,023. A function f.sub.1 (g.sub.L) shown in FIG. 5A has the 
characteristics such that the value of the function f.sub.1 (g.sub.L) 
changes when the residual image signal g.sub.L takes a small value, and 
such that the value of the function f.sub.1 (g.sub.L) is equal to zero 
when the value of the residual image signal g.sub.L is larger than d. For 
each picture element (i,j), a calculation using the function f.sub.1 
(g.sub.L) is carried out with Formula (1). 
##EQU1## 
In this manner, an image signal representing a processed residual image 
g.sub.L ', which image signal corresponds to all of the picture elements 
in the residual image, is obtained. 
FIG. 6 shows the image signal representing the processed residual image 
g.sub.L ', which is obtained when the value of the residual image signal 
g.sub.L changes along a straight line with respect to the x direction on 
the residual image. As illustrated in FIG. 6, the dynamic range of the 
region in which the value of the residual image signal g.sub.L is small, 
i.e. the region in which the mean density is low, is compressed. Also, the 
contrast of a portion, at which the signal value is comparatively high, in 
each region is kept at the same level as that prior to the compression. 
Thereafter, an inverse transform is carried out on the detail image b.sub.k 
of the predetermined frequency band, which image has been obtained from 
the emphasis processing, the detail images of the other frequency bands, 
and the processed residual image g.sub.L '. The restoration processing 
means 4 carries out the inverse transform processing in the manner 
described below. 
FIG. 7 shows how the inverse transform is carried out. Firstly, the image 
signal representing the processed residual image g.sub.L ', is fed into a 
first interpolating operation means 141. In the first interpolating 
operation means 141, picture elements are inserted between adjacent 
picture elements of the processed residual image g.sub.L ', and an image 
signal representing an image g.sub.L ", which has a size four times as 
large as the size of the processed residual image g.sub.L ', is thereby 
obtained. The image signal representing the image g.sub.L " having been 
obtained from the interpolating operation is then fed into a first adder 
151. In the first adder 15, the image signal components of the image 
signal representing the image g.sub.L " and the image signal representing 
a lowest resolution detail image b.sub.n-1, which image signal components 
represent corresponding picture elements in the two images, are added to 
each other. An image signal representing an addition image (g.sub.L 
"+b.sub.n-1) is thereby obtained. The image signal representing the 
addition image (g.sub.L "+b.sub.n-1) is then fed into a second 
interpolating operation means 142. In the second interpolating operation 
means 142, picture elements are inserted between adjacent picture elements 
of the addition image (g.sub.L "+b.sub.n-1), and an image signal 
representing an image b.sub.n-1 ', which has a size four times as large as 
the size of the detail image b.sub.n-1, is thereby obtained. 
Thereafter, the image signal representing the image b.sub.n-1 ' is fed into 
a second adder 152. In the second adder 152, the image signal components 
of the image signal representing the image b.sub.n-1 ' and the image 
signal representing a detail image b.sub.n-2 of a resolution higher by a 
single level than the resolution of the detail image b.sub.n-1, which 
image signal components represent corresponding picture elements in the 
two images, are added to each other. An image signal representing an 
addition image (b.sub.n-1 '+b.sub.n-2) is thereby obtained. The image 
signal representing the addition image (b.sub.n-1 '+b.sub.n-2) is then fed 
into a third interpolating operation means 143. In the third interpolating 
operation means 143, picture elements are inserted between adjacent 
picture elements of the addition image (b.sub.n-1 '+b.sub.n-2), and an 
image signal representing an image b.sub.n-2 ', which has a size four 
times as large as the size of the detail image b.sub.n-2, is thereby 
obtained. 
The processing described above is iterated, and the same processing is 
carried out also for the emphasized image b.sub.kp. Specifically, in an 
adder 153, the image signal representing the emphasized image b.sub.kp and 
the image signal representing an image b.sub.k-1 ', which is of a 
resolution lower by a single level than the resolution of the emphasized 
image b.sub.kp and has been obtained from the processing described above, 
are added to each other. An image signal representing the addition image 
(b.sub.kp +b.sub.k-1 ') is thereby obtained. Thereafter, in an 
interpolating operation means 143, picture elements are inserted between 
adjacent picture elements of the addition image (b.sub.kp +b.sub.k-1 '), 
and an image signal representing an interpolation image b.sub.kp ' is 
thereby obtained. The processing is successively carried out for the 
detail images of higher frequency bands. Finally, in an adder 155, an 
image signal representing an interpolation image b.sub.1 ' and an image 
signal representing the detail image b.sub.0 having the highest resolution 
are added to each other, and a processed image signal S' is thereby 
obtained. 
The processed image signal S' having thus been obtained is fed into the 
image output means 5 and used in the reproduction of a visible image. The 
image output means 5 may be constituted of a display means, such as a 
cathode ray tube (CRT) display means, a recording apparatus for recording 
an image on photographic film by a light beam scanning operation, or a 
device for storing an image signal in an image file on an optical disk, a 
magnetic disk, or the like. 
In this manner, the visible image can be reproduced from the processed 
image signal S' such that the contrast of fine structures in the high 
density region may be kept high, and such that the dynamic range of the 
entire image may be compressed. 
In the embodiment described above, the transform of the original image into 
the multi-resolution images is carried out by utilizing the Laplacian 
pyramid technique. However, the image processing method in accordance with 
the present invention is not limited to the use of the Laplacian pyramid 
technique. For example, the transform of the original image into the 
multi-resolution images may be carried out by utilizing one of other 
techniques, such as a wavelet transform or a sub-band transform. 
The wavelet transform has recently been developed as a frequency analysis 
method and has heretofore been applied to stereo pattern matching, signal 
compression, and the like. The wavelet transform is described in, for 
example, "Wavelets and Signal Processing," by Olivier Rioul and Martin 
Vetterli, IEEE SP Magazine, pp. 14-38, October 1991; and "Zero-Crossings 
of a Wavelet Transform," by Stephane Mallat, IEEE Transactions on 
Information Theory, Vol. 37, No. 4, pp. 1019-1033, July 1991. 
With the wavelet transform, a signal is transformed into frequency signals, 
each being of one of a plurality of different frequency bands, in 
accordance with the formula 
##EQU2## 
wherein f(t): the signal having an arbitrary wave form, W(a,b): the 
wavelet transform of f(t), 
##EQU3## 
a: the degree of contraction of the function, b: the amount of movement in 
the horizontal axis direction. 
Specifically, the filtering process is carried out by changing the period 
and the degree of contraction of the function h and moving the original 
signal. In this manner, frequency signals adapted to desired frequencies 
ranging from a fine frequency to a coarse frequency can be prepared. 
The sub-band transform includes the technique for obtaining the images of 
two frequency bands by utilizing a single kind of filter as in the wavelet 
transform, and the technique for obtaining the images of a plurality of 
frequency bands with a single simultaneous operation by utilizing a 
plurality of kinds of filters. 
In the embodiment described above, the dynamic range of the residual image 
is compressed by using the function f.sub.1 (g.sub.L) shown in FIG. 5A. 
However, the image processing method in accordance with the present 
invention is not limited to the use of the function f.sub.1 (g.sub.L) 
shown in FIG. 5A, and any of other functions may be utilized. 
FIG. 5B is a graph showing a different example of the monotonically 
decreasing function, in which the value of the residual image signal 
g.sub.L serves as a variable. The function f.sub.1 (g.sub.L) shown in FIG. 
5B has the characteristics such that the value of the function f.sub.1 
(g.sub.L) is zero when the value of the residual image signal g.sub.L 
falls within the range of zero to e, and such that the function f.sub.1 
(g.sub.L) takes values lying on the inclined straight line when the value 
of the residual image signal g.sub.L is larger than e. 
As another alternative, as illustrated in FIG. 5C, a function composed of 
the combination of the function shown in FIG. 5A and the function shown in 
FIG. 5B may be employed. 
As a further alternative, one of functions illustrated in FIGS. 8A, 8B, and 
8C may be employed as the function f.sub.1 (g.sub.L). The functions 
illustrated in FIGS. 8A, 8B, and 8C have the characteristics such that the 
line representing the function may not be folded sharply, and such that 
the differential coefficient of the function may be continuous. In cases 
where the functions shown in FIGS. 5A, 5B, and 5C are used, which have 
characteristics such that the line representing it folds sharply at the 
point, d or e, even if no particular contour is present in the original 
image, an artificial contour will occur at the part having the image 
density corresponding to the point, d or e, in the visible image 
reproduced from the processed image signal S'. In cases where the function 
f.sub.1 (g.sub.L) is employed which has characteristics such that the 
differential coefficient is continuous, no artificial contour occurs in 
the reproduced visible image. 
In the aforesaid embodiment, the image signal representing the processed 
residual image g.sub.L ' is obtained with Formula (1) shown above. 
Alternatively, the image signal representing the processed residual image 
g.sub.L ' may be obtained with Formula (3) shown below. 
EQU g.sub.L '=g.sub.L +.alpha..multidot.f.sub.3 (g.sub.L) (3) 
wherein f.sub.3 (g.sub.L) represents the function, the value of which 
decreases monotonically as the value of the residual image signal g.sub.L 
increases, and .alpha. represents the degree of emphasis. In such cases, 
the extent of the dynamic range compressing process carried out on the 
residual image g.sub.L can be altered. Accordingly, the dynamic range 
compressing process can be carried out with a high degree of freedom.