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BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to signal processing apparatus, such as image
processing apparatus, for providing variable-bandwidth filtering of a
D-dimensional signal (where D may have a given value equal to or larger
than one) and, more particularly, to such apparatus capable of providing a
linearly variable response over a wide range of cutoff frequencies with
linear phase.
2. Description of the Prior Art
It is known to apply various types of signal processing to signals to
extract certain features of interest for further analysis. Usually, linear
filtering is the main tool used in such applications, such as low-pass,
band-pass, or high-pass filtering a signal to remove high, mid, or low
frequencies respectively. Further, in many cases it is advantageous to
interactively vary the cutoff of the filter to isolate features of
interest, so that a variable bandwidth filter is desirable.
Typically, in one-dimensional (1D) signal enhancement, such as in enhancing
horizontal frequencies in a television picture, analog or digital filters
can be used. Variable-bandwidth analog filters are known in the art.
However, providing a linearly variable response over a wide range of
cutoff frequencies with the added desirable property of linear phase is
extremely difficult and costly in the case of variable-bandwidth analog
filters. Variable-bandwidth digital filters (which can be implemented by
switching in a different set of filter coefficients for each new cutoff
frequency) are to be preferred because they can have precisely linear
phase over their entire range of operation, and they can be made
completely stable under all conditions. However, one problem with such
implemented variable-bandwidth digital filters is that the number of
coefficients needed to represent a wide range of various cutoff
frequencies can grow extremely large depending on the degree of
incremental "fineness" of the variation from one cutoff frequency to
another.
The use of filtering in two-dimensional (2D) image enhancement applications
is known. Another problem that occurs in such 2D image enhancement
applications is the need to store multiple points vertically for
filtering. In raster-scanned images, where adjacent vertical points are
one full scan line apart, this means storing a number of successive lines
in order to access the points needed for a filtering. In analog filter
implementations, at most one to two lines are possible. This is usually
achieved using CCD (charge-coupled delay) delay lines, which are costly.
In digital filter implementations, the storage is achieved with digital
memories, which are less expensive and more robust than CCD delay lines.
It is known in signal theory that a filters' bandwidth is inversely related
to its time response. That is, as the passband is made more narrow the
corresponding time response of the filter gets longer. In the case of
vertical filtering, low frequencies can only be extracted by using many
lines of storage. This can be very expensive. The cost and complexity of
doing this with analog filters would be prohibitive.
A known technique (disclosed in U.S. Pat. No. 4,674,125) for solving such
vertical-filtering imaging problems is to use Laplacian pyramidal
processing. In Laplacian pyramidal processing, a signal is decomposed in
multiple, octave-wide, spatial-frequency bands; wherein the frequency
decomposition inherently produces bands of information containing one
octave of frequency, where adjacent bands touch on octave boundaries. This
approach relies on repetitive usage of low-pass filter-subsample
operations, so that the means for high-order low-frequency filtering is
accomplished very efficiently and cost-effectively.
A problem with octave decomposition that occurs in known Laplacian
pyramidal processing results from integer subsampling by two at each level
of the pyramid. This imposes a severe limitation on the processing of some
signals. For optimal spectral decomposition, it is desirable to produce
band-pass (or low-pass) components that are not octave wide to better
match the information of interest. For example, in image transmission a
technique called progressive transmission is sometimes used. The signal is
first put into a Laplacian pyramid format, and the lower-resolution images
are transmitted quickly due to their relatively low quantity of data. As
bandwidth permits, refinements of the image (the higher frequency
band-pass components) are sent and added in at the receiver to reconstruct
the original image. This process assures that the receiver always displays
a full image, although initially a blurred version of the original is
displayed which becomes clearer if and when later-received higher
frequency band-pass components are added to the display.
Using the Laplacian pyramid to process a 2-D image means that the amount of
data in each band increases from band-to-band by a factor of four (two per
dimension.) In moving up to the higher resolution bands, the increase in
data by four may be too much for the channel to handle, while for
instance, an increase in two might not. Thus, there is a great advantage
in scaling the quantity of data as needed, and not be limited to the fixed
octave-width sizes of the spatial-frequency bands forced by the aforesaid
known Laplacian pyramid technique.
Further, reference is made to our copending U.S. patent application Ser.
No. 08/033,503, filed Mar. 18, 1993, entitled "Resampling Apparatus
Suitable for Resizing a Video Image", which is assigned to the same
assignee as the present application, the disclosure of which is
incorporated herein by reference.
SUMMARY OF THE INVENTION
The present invention is directed to improved digital-filter apparatus that
incorporates principles disclosed in the aforesaid U.S. patent application
Ser. No. 08/033,503, (U.S. Pat. No. 5,355,328) which makes it possible to
achieve a controllably variable-bandwidth for the digital filter.
More specifically, the present invention is directed to an improvement in
filtering apparatus responsive to a sequence of samples of an input signal
that is digitally-sampled at a given frequency, wherein the input signal
defines information having at least one dimension. The apparatus comprises
first means for resampling the input-signal to derive a first signal at a
first frequency which is substantially equal to the reciprocal 1/C of a
given factor C times the given frequency, and second means for resampling
the first signal to derive a second signal at a second frequency which is
substantially equal to the given factor C times the first frequency. In
accordance with the improvement, the given factor C is an improper
fraction having a least-common-denominator larger than one.
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1 is a functional block diagram illustrating a first embodiment of
means for resampling the sampling period P of an input stream of
digital-signal sample values that define a given dimension of information,
where the given dimension may be either the horizontal or, alternatively,
the vertical dimension of a video image;
FIG. 2 is a functional block diagram illustrating a second embodiment of
means for resampling the sampling period P of an input stream of
digital-signal sample values that define a given dimension of information,
where the given dimension may be either the horizontal or, alternatively,
the vertical dimension of a video image;
FIG. 3 is a block diagram of a low-pass filter, having frequency
characteristics depicted in FIGS. 3a and 3b, that constitutes a first
embodiment of the present invention;
FIG. 4 is a block diagram of a high-pass filter, having frequency
characteristics depicted in FIGS. 4a and 4b, that constitutes a second
embodiment of the present invention;
FIG. 5 is a block diagram of a band-pass filter, having frequency
characteristics depicted in FIGS. 5a-5d, that constitutes a third
embodiment of the present invention;
FIGS. 6a and 6b, respectively, illustrate the analyzer and the synthesizer
of a hierarchical pyramid that constitutes a fourth embodiment of the
present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
The Ser. No. 08/033,503 application discloses an input-sample frame memory
for storing an input stream of digital-signal sample values written into
thereto that define a 2-dimensional input video image, such as a
television frame; an X,Y resampler responsive to a stream of
digital-signal sample values read out from the input-sample frame memory
applied thereto; and an output-sample frame memory for storing a resampled
stream of digital-signal sample values written into thereto from the X,Y
resampler. The samples applied to X,Y resampler spatially define a given
pixel sampling period in the X (horizontal) direction of the video image
and a given scanline sampling period in the Y (vertical) direction of the
video image. X,Y resampler operates to alter the pixel sampling period in
the X-direction in accordance with an adjustable X resample ratio applied
thereto and the scanline sampling period in the Y-direction in accordance
with an adjustable Y resample ratio applied thereto. This results in
reducing or expanding the the size of the video image in the X-direction
in accordance with the X resample ratio and independently reducing or
expanding the the size of the video image in the Y-direction in accordance
with the Y resample ratio.
FIG. 1 (which conforms to FIG. 3 of the Ser. No. 08/033,503 application) is
a functional block diagram illustrating the approach employed by a first
embodiment of the X,Y resampler that alters the input sampling period P is
by a factor equal to M/L, where M/L may be either a proper fraction (M
being a positive integer smaller than a positive integer L) for expansion
in the X or Y size of an image or an improper fraction (M being larger
than L) for reduction in the X or Y size of an image.
As indicated by block 100, interpolator I(f) 102 and block 104 (which, as
indicated in FIG. 1, may be implemented, in practice, in composite form),
the input is effectively upsampled by the factor 2L with interpolated
digital sample values and directly downsampled by the factor M', thereby
to produce a first derived sample stream having a period equal to
(M'/2L)P. M' is an integer having a value smaller than that of 2L (so that
M'/2L is always a proper fraction), in which the value of M' is chosen so
that the value of either 2.sup.n (M'/CL) or 2.sup.-n (M'/CL) is equal to
the value of M/L.
The input may be first upsampled by the factor 2L by inserting (2L-1)
zero-valued samples between each pair of consecutive input sample values
(as indicated by block 100) prior to appropriately interpolated values of
that pair of consecutive input sample values being substituted for each of
the (2L-1) zero-valued samples (as indicated by block 102), and then be
downsampled by the factor M' (as indicated by block 104). However, unless
the value of the proper fraction M'/2L happens to be a very small
fraction, this is an inefficient approach to deriving the factor M'/2L.
Specifically, because the downsampling in FIG. 1 is direct (i.e., no
prefiltering is required prior to downsampling by the factor M in the X,Y
resampler approach of the present invention shown in FIG. 1), makes it
possible to divide a longer period interval, that is equal in length to M
times the input period P, into a series of oversampled periods equal in
length to 1/2L of this longer period and then insert appropriately
interpolated values for each oversampled period of this series.
For instance, assume that M=5 and L=4, so that M/L=5/4. Therefore, in this
case, M'/2L=5/8. Assume further that six successive samples of the input
sample stream, occurring with a sample period P have the respective sample
values v.sub.1, v.sub.2, v.sub.3, v.sub.4, v.sub.5 and v.sub.6. In this
case, the respective upsampled interpolated sample values, occurring with
a sample period 5P/8 (assuming linear interpolation), are v.sub.1, v.sub.1
+5/8(v.sub.2 -v.sub.1), v.sub.2 +1/4(v.sub.3 -v.sub.2), v.sub.2
+7/8(v.sub.3 -v.sub.2), v.sub.3 +1/2(v.sub.4 -v.sub.3), v.sub.4
+1/8(v.sub.5 -v.sub.4), v.sub.4 +3/4(v.sub.5 -v.sub.4), v.sub.5
+3/8(v.sub.6 -v.sub.5) and v.sub.6. Thus, this process converts each group
of six successive samples of the input sample stream into a group of nine
successive interpolated-value samples, which occur serially at the same
single clock rate as the group of six successive samples, in accordance
with the aforesaid illustrative assumption. However, it should be
understood that, in practice, the interpolation function need not be
linear.
In FIG. 1, the first derived stream of sample values, which have a sample
period equal to (M'/2L)P, are prefiltered by digital octave filter H(f)
106 and multiplied by 2.sup.n means 108, where n has an absolute value of
at least one, thereby producing as an output a second derived stream of
sample values having a period equal to (M/L)P. As indicated in FIG. 1, the
separate functions performed by digital octave filter H(f) 106 and 2.sup.n
means 108, in practice, may be combined in a single composite structure.
Further, as indicated by the arrows situated above 2.sup.n means 108,
2.sup.n means 108 performs the function (1) of decreasing (downsampling)
the number of samples in the second derived stream of sample values in the
case of reduction in the size of an image when n has a positive value,
thereby causing the sample period to be increased, and (2) of increasing
(upsampling) the number of samples in the second derived stream of sample
values in the case of expansion in the size of an image when n has a
negative value, thereby causing the sample period to be decreased.
As discussed above, in the first embodiment shown in FIG. 1 the resampling
ratio M/L may be either a proper fraction (in the expansion of the size of
an image) or may be an improper fraction (in the reduction of the size of
an image). Further, in the case of image expansion (M<L), in which the
insertion of interpolation coefficients involves oversampling, no problem
of aliasing exists. Therefore, it is not necessary to upsample by the
factor 2L with interpolated digital sample values before directly
downsample by the factor M', as described above in connection with FIG. 1.
The fact is that upsampling by the factor 2L doubles the number of
interpolated pixel values that need to be computed and inserted into the
data stream during each scanline period, which number may be quite large
when the image size defined by a small portion of each successive scanline
is expanded to the size of each entire successive scanline. In the case of
real-time processing, this creates a practical problem in implementation.
One obvious solution is to employ a system clock at twice the frequency so
that all required computations can be made within the time span of each
successive scanline period. However, this causes additional heating of the
circuitry, which is particularly undesirable in a VLSI implementation.
Another obvious solution is to employ additional computer elements
operating in parallel. However, this increases the cost of implementation.
Because upsampling by the factor 2L is not required for image size
expansion (but only for image size reduction), doubling the number of
interpolated pixel values that need to be computed and inserted into the
data stream during each scanline period and the real-time processing
problem in implementation created thereby is avoided in the expansion case
by only upsampling by a factor of L, rather than by a factor of 2L. FIG. 2
(which conforms to FIG. 3a of the Ser. No. 08/033,503 application) is a
functional block diagram illustrating the approach employed by a second
embodiment of the X,Y resampler that is limited to the expansion case in
which M<L.
As indicated in FIG. 2 by block 200, interpolator I(f) 202 and block 204
(which, as indicated in FIG. 2 may be implemented, in practice, in
composite form), the input is effectively upsampled by the factor L with
interpolated digital sample values and directly downsampled by the factor
M', thereby to produce a first derived sample stream having a period equal
to (M'/L)P. M' is an integer having a value smaller than that of L (so
that M'/L is always a proper fraction), in which the value of M' is chosen
so that the value of 2.sup.-n (M'/L) is equal to the value of M/L.
More specifically, in FIG. 2, the first derived stream of sample values,
which have a sample period equal to (M'/L)P, are prefiltered by digital
octave filter H(f) 206 and multiplied by 2.sup.-n means 208, where n has
an absolute value of at least zero, thereby producing as an output a
second derived stream of sample values having a period equal to (M/L)P. As
indicated in FIG. 2, the separate functions performed by digital octave
filter H(f) 206 and 2.sup.n means 208, in practice, may be combined in a
single composite structure. Further, as indicated by the arrow situated
above 2.sup.n means 208, 2.sup.n means 208 performs the function of only
increasing (upsampling) the number of samples in the second derived stream
of sample values because means 208 is used only in the case of expansion
in the size of an image. In this case n always has a negative value.
As known, a digital octave filter is a symmetrical multitap filter having a
low-pass kernel weighting function characteristic defined by the
respective multiplier coefficient values thereof. In principle, the number
of taps of the symmetrical multitap filter may be either odd or even.
However, in practice, it is-preferred that the multitap filter have an odd
number of taps so that the respective multiplier coefficient values can be
symmetrically disposed about a central multiplier coefficient value of the
kernel weighting function. It is usual for the value of each multiplier
coefficient of a low-pass kernel weighting function to become smaller in
accordance with the distance of that multiplier coefficient from the
central multiplier coefficient.
For illustrative purposes, assume that in FIGS. 1 and 2 the symmetrical
multitap filter is a 5-tap digital filter having a low-pass kernel
weighting function characteristic defined by the five multiplier
coefficient values c, b, a, b and c. Generally, in both FIGS. 1 and 2,
these multiplier coefficient values meet both of the two above-described
constraints. One filter that meets these two constraints has coefficients
a,b,c that satisfy unity gain at DC or zero frequency, that is a+2b+2c=1,
and a+2c=2b. One case of this, by way of example, would be c=1/16, b=1/4
and a=3/8. However, in the special case in which the second embodiment of
FIG. 2 is employed to provide an expansion greater than 1 but less than 2
(i.e., 1/2<M/L<1), so that the n value of 2.sup.n means 208 is zero (i.e.,
no upsampling is required) the five multiplier coefficient values c, b, a,
b and c have the respective values 0, 0, 1, 0 and 0.
The Ser. No. 08/033,503 application discloses a 5-tap digital octave filter
that requires only two one-pixel delay means in the X-direction or,
alternatively, two scanline delay means regardless of the value of n. This
5-tap digital octave filter may be implemented on a VLSI chip. Further, an
increase in the number of taps of the digital octave filter requires only
a small increase in the number of delay means (three delay means for a
7-tap digital octave filter, four delay means for a 9-tap digital octave
filter, etc.).
A purpose of the present invention is not to resize a video image. On the
contrary, it is to spatially filter a video image without altering the
size of the video image. Specifically, the implementation of the present
invention makes use of at least one pair of X,Y resamplers in which a
first of each pair is used to independently reduce the size of one or both
of the dimensions of the video image by a certain X and/or Y ratio factor
and a second of each pair is used to expand the size of the aforesaid one
or both of the dimensions of the video image by the same certain factor.
Therefore, one feature of the overall result is that the size of the image
at the output of the second of each pair of X,Y resamplers remains the
same as the size of the image at the input of the first of each pair of
X,Y resamplers. However, another feature of the overall result is that the
spatial cutoff frequency in each dimension of the image at the output of
the second of each pair of X,Y resamplers is lower than the spatial cutoff
frequency in each dimension of the image at the input of the first of each
pair of X,Y resamplers by an amount determined by the value of the certain
ratio factor in each dimension of the image.
More particularly, reduction in the X size of an original image by the
first of the pair of X,Y resamplers causes there to be fewer pixel samples
in each scanline of the resampled reduced image than the number of pixel
samples in each scanline of the original image. Similarly, reduction in
the Y size of the original image by the first of the pair of X,Y
resamplers causes there to be fewer scanlines of pixel samples in the
resampled reduced image than the number of scanlines of pixel samples in
the original image. Thus, in the case of image size reduction, the first
of the pair of X,Y resamplers between its input and output performs of a
sample-decreasing function. This sample-decreasing function causes a
permanent loss of the higher-frequency information defined by the omitted
samples of the original image, leaving only lower-frequency information
remaining. Thus, while the expansion in the X size of the reduced-sized
image by the second of the pair of X,Y resamplers causes there to be the
same number of pixel samples in each scanline of the resampled expanded
image as the number of pixel samples in each scanline of the original
image and the expansion in the Y size of the reduced-sized image causes
there to be more scanlines of pixel samples in the resampled expanded
image than the number of scanlines of pixel samples in the original image,
such expansion in number of samples, which is derived by interpolation of
the respective sample values of the reduced-sized image samples, which
results in oversampling the remaining lower-frequency information, is not
able to restore the higher-frequency information defined by the omitted
samples of the original image.
Referring now to FIG. 3, there is shown a low-pass filter that constitutes
a first embodiment of the present invention. Specifically, FIG. 3 shows
1/C reduce-size X,Y resampler 300 and C expand-size X,Y resampler 302. A
stream of digital sample values defining an input image having a given
pixel period P.sub.x in the X-direction and a given scanline period
P.sub.y in the Y-direction is applied to the input of resampler 300.
Resampler 300 includes first means for decreasing the number of pixels in
each scanline of the input image by a factor 1/x while increasing their
original pixel period P.sub.x of the pixels in each scanline by an
improper fraction M.sub.Rx /L.sub.Rx and second means for independently
decreasing the number of scanlines of the input image by a factor 1/y
while increasing their original scanline period P.sub.y of the scanlines
by an improper fraction M.sub.Ry /L.sub.Ry, where the structure of each of
the first and second means may take the form shown in FIG. 1 (with n
having the positive value +n). Therefore, the total number of pixels in
the reduced-size output image from resampler 300 is equal to 1/C of the
total number of pixels in the input image to resampler 300, where 1/C is
equal to the product of 1/x times 1/y.
The reduced-size output image from resampler 300 is applied as an input to
resampler 302. Resampler 302 includes third means for increasing the
number of pixels in each scanline of the image input thereto by a factor x
while decreasing their original pixel period M.sub.Rx /L.sub.Rx *P.sub.x
of the pixels in each scanline by a proper fraction M.sub.Ex /L.sub.Ex and
second means for independently increasing the number of scanlines of the
image input thereto by a factor 1/y while decreasing their original
scanline period M.sub.Ry /L.sub.Ry *P.sub.y of the scanlines by a proper
fraction M.sub.Ey /L.sub.Ey, where the structure of each of the first and
second means may take either the form shown in FIG. 1 (with n having the
negative value -n) or the form shown in FIG. 2 (with the form shown in
FIG. 2 being preferable). The proper fractions M.sub.Ex /L.sub.Ex and
M.sub.Ey /L.sub.Ey, respectively, are substantially reciprocals of the
improper fractions M.sub.Rx /L.sub.Rx and M.sub.Ry /L.sub.Ry. Thus, the
size of the output image front resampler 302 is substantially the same as
the size of the input image to resampler 300. However, for the reasons
discussed above, the output-image spatial spectra from resampler 302,
shown in FIG. 3b, comprises only the lower-frequency information of the
input-image spatial spectra to resampler 300, shown in FIG. 3a. Therefore,
the pair of resamplers 300 and 302 operate as a low-pass filter. A
low-pass filter comprising such a pair of serially connected 1/C
reduce-size and C expand-size X,Y resamplers has a cutoff frequency which
is substantially proportional to the value of the factor C.
It is old in the resampling art, after reducing the size of an input image
by a factor 1/C, to then expand its size by a factor C, where the factor C
is an integer. Therefore, while resamplers 300 and 302 will operate as a
low-pass filter regardless of whether C is an improper fraction having a
lowest-common-denominator equal to one (i.e., C is an integer) or is an
improper fraction having a lowest-common-denominator larger than one
(i.e., C is a non-integer), the present invention is limited to the case
in which C is a non-integral improper fraction.
Referring now to FIG. 4, there is shown a high-pass filter that constitutes
a second embodiment of the present invention. Specifically, FIG. 4 shows
1/C reduce-size X,Y resampler 400, C expand-size X,Y resampler 402, delay
means 404 and subtraction means 406. Serially connected resamplers 400 and
402, which correspond in structure and function to resamplers 300 and 302
of FIG. 3, operate in the manner described above to low-pass filter the
spatial spectra of the digitally-sampled input image applied as an input
to resampler 400. Also, the digital samples of the input image, after
being delayed by delay means 404, are applied as a minuend to the plus (+)
input of subtraction means 406. The output digital samples from resampler
402 are applied as a subtrahend to the minus (-) input of subtraction
means 406. The sample delay provided by delay means 404 is equal to the
sample delay inserted by resamplers 400 and 402. Therefore, corresponding
minuend and subtrahend samples are applied isochronously to each of the
inputs of subtraction means 406, so that each sample at the output of
subtraction means 406 has a value equal to the difference in the
respective values of the corresponding minuend and subtrahend samples.
Thus, the high-pass spatial spectra of the output image from subtraction
means 406, shown in FIG. 4b, is achieved by subtracting the low-pass
spatial spectra of the output from resampler 402 from the input-image
spatial spectra, shown in FIG. 4a.
Referring now to FIG. 5, there is shown a band-pass filter that constitutes
a third embodiment of the present invention. Specifically, FIG. 5 shows a
first pair of serially connected resamplers comprising 1/C.sub.1
reduce-size X,Y resampler 500-1 and C.sub.1 expand-size X,Y resampler
502-1, a second pair of serially connected resamplers comprising 1/C.sub.2
reduce-size X,Y resampler 500-2 and C.sub.2 expand-size X,Y resampler
502-2, and subtraction means 506. Each of first pair of serially connected
resamplers 500-1 and 502-1 and second pair of serially connected
resamplers 500-2 and 502-2, which correspond in structure and function to
resamplers 300 and 302 of FIG. 3, operate in the manner described above to
low-pass filter the spatial spectra of the digitally-sampled input image
applied as an input to each of resamplers 500-1 and 500-2. The digital
samples of the output from resampler 502-1 are applied as a minuend to the
plus (+) input of subtraction means 506 and the output digital samples
from resampler 502-2 are applied as a subtrahend to the minus (-) input of
subtraction means 506. Each sample at the output of subtraction means 506
has a value equal to the difference in the respective values of the
corresponding minuend and subtrahend samples.
As stated above, a low-pass filter comprising a pair of serially connected
1/C reduce-size and C expand-size X,Y resamplers has a cutoff frequency
which is substantially inversely proportional to the value of the factor
C. In FIG. 5, the relative value of the factor C.sub.1 is small with
respect to the value of the factor C.sub.2. FIG. 5b shows the relatively
high cutoff-frequency spatial spectra of the minuend input to subtraction
means 506 with respect to the input-image spatial spectra of FIG. 5a, and
FIG. 5c shows the relatively low cutoff-frequency spatial spectra of the
subtrahend input to subtraction means 506 with respect to the input-image
spatial spectra of FIG. 5a. Therefore, as shown in FIG. 5d, the
output-image spatial spectra derived at the output of subtraction means
506, (which is the difference between the FIGS. 5b and 5c spatial spectra)
constitutes a band-pass filter output.
Referring now to FIGS. 6a and 6b, there is shown a hierarchical pyramid
that constitutes a fourth embodiment of the present invention.
Specifically, FIG. 6a shows the analyzer of the hierarchical pyramid of
the present invention, which is a modification of the prior-art Laplacian
pyramid analyzer disclosed in the aforesaid U.S. Pat. No. 4,674,125, and
FIG. 6b shows the synthesizer of the hierarchical pyramid of the present
invention, which is a modification of the prior-art Laplacian pyramid
synthesizer disclosed in the aforesaid U.S. Pat. No. 4,674,125.
The analyzer of FIG. 6a, like the prior-art Laplacian pyramid analyzer,
comprises a hierarchical pyramid of high-pass filter stages 608-1, 608-2 .
. . 608-N for deriving a group of Laplacian outputs L.sub.0, L.sub.1, . .
. L.sub.N-1 and Gaussian remnant G.sub.N in response to successive digital
samples of a Gaussian high-resolution input image G.sub.O applied as an
input to stage 608-1. As exemplified by stage 608-1, the high-pass filters
of each of stages 608-1, 608-8 . . . 608-N comprises reduce-size and
expand-size resamplers 600 and 602, delay means 604, and subtraction means
606 that are structurally and functionally interconnected and operate in
the manner described above in connection with FIG. 4. Fu | | |
