Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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METHOD OF CODING A MATRIX, IN PARTICULAR A
MATRIX REPRESENTATIVE OF A FIXED OR VIDEO IMAGE
BACKGROUND OF THE INVENTION
Field of the Invention
This invention relates to the field of coding digital values arranged in a
matrix, in particular in the case where this matrix is a two-dimensional
matrix,
representing the pixels of an image.
The main constraints of the methods of compression are, on the one
hand, to reduce as much as possible, by compressing it, the volume, measures
in bytes, of an initial digital file and, on the other hand, to restore a file
that is
as close as possible to the initial file.
Description of the Related Art
Certain methods of compression make it possible to restore exactly the
initial values. This is the case with DPCM modulation. According to this
method,
an original value, i.e. the first value of the initial digital file, is
retained, then
each other value is replaced with its difference with the value before it in
the
initial file. The numbers corresponding to the differences are generally
smaller
than those corresponding to the initial values, which makes it possible to
obtain
a compressed file. In order to restore an initial value, it is sufficient to
add the
difference corresponding to the previous initial value, i.e. the various
successive
values are added together with the origin value. This mode of compression
therefore applies to a linear sequence, i.e. extending according to a single
dimension, of numerical values; the same applies for a two-dimensional matrix
of numerical values, formed of lines and columns, with this mode of
compression able to be applied to each line of the matrix successively; the
same
applies regardless of the number of dimensions of a matrix, with the mode of
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compression able to be applied to each line (or the equivalent in the
corresponding dimension) of the matrix.
It is admitted that it is the most substantial reduction in the differences
between two initial values that makes it possible to obtain the highest
compression ratio possible. It is as such that DPCM modulation was introduced.
Nevertheless, the rate of compression obtained with the DPCM method remains
low. The idea to apply an additional compression to the file of the
differences
thus appears attractive. However, the errors induced by this new compression
are accumulated at the same time as, during the restitution, the successive
differences are added together with the original value. According to the ADPCM
(Adaptive DPCM) method, these errors are partially offset by using an
algorithm
that is supposed to predict these errors. This method remains unsatisfactory
with regards to the compression rates that it is desirable to achieve.
Moreover, in the case of a matrix representing a fixed or video image, the
processing of each image is done in blocks of 8x8 pixels, and in each block,
line
by line, from the first to the eighth. Such a method often results in a
lineage
and/or a pixelization of the restored image.
BRIEF SUMMARY OF THE INVENTION
The invention has for purpose to propose a simple and powerful method
of compression that makes it possible to accumulate the advantages of a
compression rate that is greater than that of the DPCM method alone, while
still
retaining therein the advantages of a differential coding, without error
propagation, at the same time that it prevents or notably reduces the risk of
lineage and/or of pixelization proper to the methods of prior art.
A method according to the invention, for the coding via successive layers
of an initial matrix into a compressed matrix and its restoring as a restored
matrix, with each cell of the initial matrix containing a respective initial
digital
value; with each cell of the compressed matrix containing a respective
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compressed digital value corresponding to the respective initial digital
value;
with each cell of the restored matrix containing a respective restored digital
value corresponding to the respective initial digital value; characterised in
that
in order to process, i.e. compress, at least one initial value of an initial
box,
among the lines passing through said box, as a path of travel for the
compression of said initial value, the one that, estimated using previously
calculated restored values, has the lowest variation, is chosen.
Such a method can comprise at least one layer for which, for an initial
value to be processed of said layer, the corresponding compressed value is
determined by calculating a difference between said value to be processed and
a
previously determined and neighboring restored reference value, preferably the
most neighboring, of the box provided to contain the restored value
corresponding to said value to be processed on one of the lines passing
through
said box. When several of the lines passing through the cell provided to
contain
the restored value corresponding to said value to be processed comprise a
value
that can potentially be a reference value, for all of the combinations of
potential
values taken two by two, for a first of said potential reference values,
located on
a first of said lines and a second of said potential reference values, located
on a
second of said lines, a variation is calculated equal to the difference
between
said first value and another restored value, previously calculated, located on
the
same third line as said first value, said third line being parallel to the
second
line, and said other value being at the same distance from the first value as
the
second value is from the value to be processed, the reference value chosen
being the second value for which said variation is the lowest. If the matrices
are
of two dimensions and when there are at least two possible reference values,
one on the same line, the other on the same column for the value to be
processed of the second layer, the choice of the reference value is made by:
- calculating a first variation between the first potential reference value
that has the same column number as the value processed and the restored
value that has the same line number as this first potential reference value
and
same column index as the second potential reference value; and,
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- calculating a second variation between the second potential reference
value that has the same line index as the value processed and the restored
value that has the same column number as this second potential reference
value and the same line number as said first potential reference value; then,
- choosing the reference value for which the path of travel gives the
lowest variation, i.e. the first reference value is chosen if the second
variation is
less in absolute value than the first variation, or, the second reference
value is
chosen if the first variation is less in absolute value than the second
variation.
There is advantageously at least one layer, preferably a base layer, for
which, for an initial value to be processed of said layer, the corresponding
compressed value is determined by calculating a difference between the initial
value and a reference value equal to a previously calculated restored value,
belonging either to the same line, or to the same column, as said value to be
processed.
Preferably, there is at least one layer, for which, for an initial value to be
processed, the reference value is calculated using a pair surrounding initial
values having already been processed and arranged on either side of said
value,
for which the restored value is calculated using a reference value at
decompression calculated using the equivalent surrounding pair of previously
restored values. As an alternative, there is at least one layer for which, for
an
initial value to be processed of said layer, the reference value is calculated
using
a surrounding pair of restored values that have already been processed and
arranged on either side of said value, for which the restored value is
calculated
using a reference value to the compression calculated using the same pair of
previously restored values. In terms of another alternative, there is at least
one
layer for which, for an initial value to be processed of said layer, the
corresponding compressed value is determined by calculating a difference
between the initial value and a reference value determined using a surrounding
pair of previously determined restored values, the surrounding pair chosen
being that for which the two values of said pair, i.e. the variation, is the
lowest.
In one or the other of the cases, if there are at least two surrounding pairs,
for
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calculating the reference value the pair is chosen for which the variation,
equal
to the difference between the corresponding restored values of previously
determined restored values, has the lowest absolute value.
The reference value for this layer is advantageously the mathematical
mean between the two values of the chosen surrounding pair and, where
applicable, the reference value at the decompression is the mathematical mean
between the restored values of the values of the surrounding pair; the
reference
value for this layer can alternatively be the mathematical mean between the
two initial values corresponding to that of the chosen surrounding pair.
Advantageously, according to the method, there is an initial origin value
of which the compressed value and the restored value are equal to said initial
origin value, said restored original value serving as a reference value,
either
directly or indirectly, for the processing of the other initial values.
According to a preferred embodiment of the invention, a quantification
table is applied to the difference between the initial value processed and the
reference value, in order to calculate the compressed value and the restored
value. Preferably, there are several quantification tables that can be used,
with
the quantification table used being defined using previously calculated
restored
values. Advantageously, there is a threshold, below which a first
quantification
table is applied and beyond which a second quantification table is applied.
Preferably, according to whether the initial value to be processed belongs to
one
layer or another, one table or another is used.
Each cell can represent a pixel of an image.
BRIEF DESCRIPTION OF THE DRAWINGS
Several embodiments of the invention shall be described hereinafter, by
way of non-restricted examples, in reference to the annexed drawings wherein:
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FIG. 1 partially shows an initial matrix, representing the upper left corner
of an image, as well as those of the compressed matrix and of the
corresponding error matrix;
FIGS. 2 to 5 each show a layer of cells among the cells of the initial
matrix;
FIGS. 6 and 7 show two quantification tables respectively for dark and
light values of the image, that can be used during the compression of the
values
of the base layer;
FIGS. 8 and 9 show two quantification tables respectively for dark and
light values of the image, that can be used during the compression of the
values
of the secondary layers; and,
FIGS. 10 to 14 show algorithms used in the method according to the
invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
A method according to the invention shall be described in its application
to the digital compression of an image. In this example, the original image is
shown in the figures by an initial matrix M. This matrix can be that of the
values
of a monochrome image, if the original image is monochrome, or one of the
matrices making it possible to reconstitute a colour image, if the original
image
is in colour. In the case of a colour image, the initial matrix M can show,
for
each pixel, the luminosity of Red, Green or Blue, in the case of an initial
image
with notation RGB; it can represent values composed of luminance Y, in the
case of an initial image with notation YCbCr. The values of the initial matrix
M
are between 0 and 255. As such, the matrix can be the representation of a raw
image or that of an image that has already been subjected to a colorimetric
transformation.
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In the description which shall follow, "line" shall refer to the lines
represented horizontally in the figures and "columns" shall refer to the lines
represented vertically; of course, regardless of whether they are horizontal
or
vertical, the lines are treated indifferently according to the method.
In the description which shall follow, each cell Cmn of the initial matrix M
is index by its line number m and its column number n and contains a
corresponding initial value Vmn, indexed in the same way. To the initial
matrix
M corresponds a compressed matrix MC and a restored matrix MR after
decompression of the compressed matrix MC. To each value Vmn of the initial
matrix M corresponds a respective compressed value VCmn and a restored
value VRmn, each one in a cell CCmn, CRmn respective of the same indices. In
order to simplify the description, the method according to the invention shall
be
applied only to the upper left corner of the initial matrix M, therefore to
the
upper left corner of the corresponding image; by facility of language, in what
follows the corner of each matrix is assimilated with the corresponding
matrix,
of which it is the illustration. The FIG. 1 therefore shows the initial matrix
M, the
compressed matrix MC and the restored matrix MR obtained, using the initial
matrix M, by the method according to the invention described in reference to
FIGS. 10 to 14; FIG. 1 also shows an error matrix ME constituted of the
differences between the restored values and the initial values.
The method according to the invention allows for the successive coding of
successive layers of values, using an original value V00 contained in an
original
cell COO the highest on the left of the initial matrix M. The encoding of a
value of
a given layer depends solely on the previously encoded layers or on the
previously encoded values of its own layer. In the example shown, the method
utilise four layers, a base layer and three secondary layers.
In FIG. 2, the values of the cells that belong to the base layer are shown
in bold in the matrix M; in FIG. 3, the values of the cells belonging to the
first
secondary layer are shown in bold in the matrix M; in FIG. 4, the values of
the
cells belonging to the second secondary layer are shown in bold in the matrix
M;
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and, in FIG. 5, the values of the cells belonging to the third secondary layer
are
shown in bold in the matrix M. Note that, for each layer, the cells that it is
comprised of are regularly distributed in the matrix.
In the example shown, the base layer is encoded using a first lossless
differential encoding algorithm, followed by a first quantification; the
secondary
layers are encoded using a second predictive algorithm, itself followed by a
second quantification. Two quantification tables TB1, TB2 are used for the
quantification of the values of the base layer. Two other tables TS1, TS2 are
used for the quantification of the values of the secondary layers. These
tables
are partially shown in FIGS. 6 to 9. The tables are only partially shown in
these
figures. In particular, they only show the values for positive differences and
less
than 13 or 14, according to the case; nevertheless, a complete table includes
more preferably negative values and, in the case of an image coded over eight
bits, allows for the encoding of differences D of which the values are between
-255 and +255.
For each type of layer, a first table T31, TS1 is allocated to the
quantification of the dark values; with the values being considered as dark
below a threshold value equal to 40, out of 255. The second tables TB2, TS2
are
allocated to the light values, i.e. starting from 40 up to 255. The choice of
the
value 40 for the threshold value is arbitrary, determined by a better
rendering
of the darkest colours. The first tables TB1 and TS1 assign to the dark values
quantifications that are less severe, corresponding to a division by 2 for the
base layer and to a division by 4 for the secondary layers, compared to a
division by 3 (TB2) and 5 or 8 (TS2) respectively for the light values. The
degradations, i.e. the errors between the restored value and the initial value
are
generally more perceptible in the dark zones than in the light zones; such an
arrangement, that makes it possible to have less losses in the dark zones is
therefore particularly advantageous. The rest of this description explains, in
reference to FIGS. 11 to 14, how it is determined whether a value is deemed
light or dark.
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For each table, the first column contains a difference to be quantified D,
the second column contains, for each difference D, the corresponding
compressed value VC, and, the third column contains the corresponding
restored value DR of the difference D.
The number of layers defines a pitch p, q of the base layer, i.e. a distance
between the cells that belong to the first layer. In the example shown, the
pitch
p according to the lines and the pitch q according to the columns are equal,
with:
q=p=2(I-2), where "i" is the number of layers of the method.
In the example described, there are four layers, namely the base layer
and the three secondary layers, i.e.:
p=q=2(4-2)=4.
As such, the cells of the base layer have for indices:
m=4y, with
n=4z, with and,
(y,z) (0,0).
The base cells therefore constitute a meshing among the cells of the
initial matrix M, starting with which are calculated the compressed values of
the
other cells. By using for the values of the base cells an encoding that is
little or
not destructive with respect to the encoding of the other cells, regularly
distributed throughout the entire image, restored values are thus retained
that
are sufficiently close to the initial values in order to retain a desired
printing
quality, while still allowing for a higher compression of the values of the
secondary layers.
In the example shown, the upper left corner shown, corresponds to a
mesh; with for each one of the cells shown:
rri4 and n5.4.
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The method shall now be described according to the invention in
reference to FIGS. 10 to 14. Each one of these figures shows the calculation
of a
compressed value VCmn, i.e. a step in the constitution of the compressed
matrix MC, in particular according to the initial values Vmn, of the initial
matrix
M, but also according to the restored values VR of previously compressed
values. FIGS. 11 and 12 each show the compression of a respective value
among those of the cells of the base layer. The FIGS. 13 and 14 each show the
compression of a respective value among those of the cells of the first
secondary layer.
The method of compression/restitution according to the invention, retains
the value V00 of the original cell COO, identified in FIG. 10, in such a way
that in
the example shown, there is:
VOO=VCOO=VRO0=25.
The restored original value VROO is a reference, directly or indirectly, for
the calculation of the other compressed VCmn or restored VRmn values.
In reference to FIG. 11, the application of the method shall now be
described according to the invention to the cell CO4 of the initial matrix M,
more
particularly to the value VO4=32 that the cell CO4 contains. The cell C04
belongs
to the base layer. Other than the particular case of the value VOO, the value
VO4
is the first to be compressed.
In an embodiment of the invention, the restored value is taken for the
reference value, already calculated, with the closest lower index on the same
line or the same column. In the case here, the reference value is necessarily
the
value VRO0=25. As the reference value is less than 40, the value VO4 is
processed as a dark value and the first table TB1 is therefore used. The
difference D04=VO4-VRO0=+7 is then calculated between the initial value to be
processed VO4 and the reference value VROO; the compressed value VC04=+3
and the restored difference DR04=+6 are deduced from the table TB1 and from
the difference D04=+7. The restored value VRO4=VROO+DR04=25+6=31 is
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then obtained, by adding the restored difference DRO4 to the reference value
VROO.
The same procedure is applied to the initial value V40 of the cell C40 of
the initial matrix M. The same procedure can then be applied to all of the
initial
values V0,4z and V4y,O.
In reference in FIG. 12, the application of the method shall now be
described according to the invention to the cell C44 of the initial matrix M,
more
particularly to the value V44=55 that cell C44 contains. The cell C44 belongs
to
the base layer.
In an embodiment of the invention, the restored value is taken as the
reference value, already calculated, with the closest lower index on the same
line or the same column. In the case here, two values potentially respond to
this
definition, one VRO4 in the box CR04, the other VR40 in the box CR40 of the
matrix MR.
In order to make a choice between the two potential reference values:
- the variation DVm=VR04-VRO0=+6 is calculated between the first
potential reference value VRO4 that has the same column index n=4 as the
value V44 processed and the restored value VROO that has the same line index
m=0 as this first potential reference value VRO4 and the same column index
n=0 as the second potential reference value VR40; and,
- the variation DVn=VR4O-VRO0=-1-24 is calculated between the second
potential reference value VR40 that has the same line index m=4 as the value
V44 processed and the restored value VROO that has the same column index
n=0 as this second potential reference value VR40 and the same line index m=0
as the first potential reference value VRO4; then,
- a direction of travel of the matrix is determined, i.e. a direction
according to which the reference value will be chosen, parallel to the lowest
variation; in the case here, the lowest variation is that of DVm, according to
the
index line m=0, in such a way that the reference value of the same line index
m
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is chosen as the value V44 processed, in such a way that the reference value
chosen is the value VR40, in the box CR40 of the restored matrix MR.
In the case of FIG. 12, the lowest variation is DVm=+6; the reference
value is therefore the value VR40=49. As the reference value is greater than
40,
the value V44 is processed as a light value and the second table TB2 is
therefore used. The difference D44=V44-VR40=+6 is calculated between the
initial value to be processed V44 and the reference value VC 44; the
compressed value VC04=+2 and the restored difference DR44=+6 are deduced
from the table TB2 and from the difference D44=+6. The restored value
VR44=VR4O+DR44=55 is then obtained, by adding the restored difference
DR44 to the reference value VR40.
In reference to FIGS. 13 and 14, the application of the method shall now
be described according to the invention to cells of a secondary layer of the
initial
matrix M. The cells of each secondary layer are all framed by cells of the
layer
with a lower index (case of FIG. 13), or by cells of the same layer which
themselves are framed by cells of the layer with a lower index (case of FIG.
14).
For the processing of the secondary layers, an average value between the
values of a surrounding pair is chosen for the reference value; a surrounding
pair being a pair of previously calculated restored values contained in the
two
most neighbouring boxes, on either side of the cell being processed, in the
restored matrix MR, aligned on the same line m or on the same column n. This
average is in this example rounded to the nearest integer.
FIG. 13 shows more particularly the processing of the value V02=29 that
cell CO2 contains, belonging to the first secondary layer MS1 of the initial
matrix
M.
In the case here, the average value W02 is calculated between the
previously calculated original values V00, VO4 contained in the two most
neighbouring boxes COO, C04, on either side of the cell being processed CO2,
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aligned on the same index line m=0; with no surrounding pair existing on the
index column n=2. From this reasoning is deduced the reference value:
W02=(V00+VO4)/2=28.
In the same way, the reference value is calculated at the decompression
WR02, i.e. used during the restitution, between the corresponding restored
values VROO and VRO4 contained in the cells CROO and CR04, in order to obtain
the reference value at decompression:
WRO2=(VROO+VR04)/2=28.
As the reference values at the compression and at the decompression
were obtained with different values, the difference D02=V02-W02=+1 is
calculated between the initial value V02 being processed and the reference
value at the decompression WR02. As the reference value WRO2 is less than 40,
it is processed as a dark value, using the first table TS1; the compressed
value
VCO2=0 is deduced from the table TS1; then the restored difference DR02=+0
and then the restored value:
VRO2=WRO2+DR02=28+0= +28.
FIG. 14 shows more particularly the processing of the value V22=41 that
the cell C22 contains, also belonging to the first secondary layer SM1 of the
initial matrix M.
In the case here, there are two potential surrounding pairs (VR02, VR42)
and (VR20, VR24) of restored values. In a manner similar to what was
described in reference to FIG. 12, in order to choose the reference value, the
direction of travel is first determined according to the previously calculated
neighbouring restored values that have the lowest variation DV; in the case of
secondary layers, the surrounding pair is chosen for which the values have the
lowest variation DV. In the case here:
DVm=VR24-VR20= +10, and
DVn=24-Vr02= +24,
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where DVm shows the variation according to the index line m=2 and DVn
according to the index column n=2.
The variation DVm, according to the line, being the lowest, it is therefore
the surrounding pair (VR20, VR24) of the values located on the same index line
m=2 as the value being processed which is chosen for calculating the reference
value at the decompression WR22:
WR22=(VR2O+VR24)/2=(33+43)/2=38.
The reference value at the compression W22 is then calculated using
original values located in the equivalent cells:
W22=(V20+V24)/2=(33+42)/2=37.5 rounded to 38.
As in the previously described case in reference to FIG. 13, the difference
D22=V22-W22=+3 is calculated between the initial value V22 being processed
and the reference value W22. As the reference value at the decompression
WR22 is less than 40, it is processed as a dark value, using the first table
TS1;
the compressed value VC22=+1 is deduced from the table TS1; then the
restored difference DR22=+4 and then the restored value:
VR22=WR22+DR22=38+4= +42.
The same procedures, described previously in reference to FIGS. 13 and 14,
apply to each of the values of the secondary layers.
Note that for each value to be restored VR, the reference values and the
condition of clarity being determined using previously restored values VR of
the
restored matrix MR. In other words, the restored values are used to calculate
the following restored values, to determine if applicable the direction of
travel of
the decompression for each value to be restored, and, to determine the
quantification table which will be used according to the threshold value
chosen.
The compressed matrix MC therefore contains in itself all of the information
needed for the restitution.
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Furthermore, as shown particularly in FIGS. 2 and 3, it is possible to carry
out the compression layer after layer. As such, as soon as each of the values
of
a layer is compressed, it is possible to transmit them, for example in the
form of
a sub-matrix SMCO to a device for their restitution, for example a computer
screen. This makes it possible to display, although it is with a lesser
definition,
the entire image, without waiting for all of the layers to have been
processed.
This allows the user who wants to view a fixed image to have the impression of
a faster processing; for the user watching a video, this allows for greater
fluidity. Particularly in the case of a video viewed as streaming, in
particular
when the bandwidth is occasionally insufficient for the complete processing of
an image before the display of the next one, this avoids the effect of
pixelization
that appears with a processing, as in certain encoding methods, such as H264.
Such an arrangement can also be advantageously used for a video game,
particularly for a game played "on line", wherein rapid sessions can be
sequenced at a high frequency; a processing of only one zone of the image, or
a
slowing down in the action, would be detrimental to the pleasure of the
player,
and even to the success of his actions; the processing of successive layers
distributed in the image, with each layer being transmitted then displayed as
soon as it is treated, makes it possible to prevent these disadvantages.
In the cases shown by the processing of the value V02, in reference to
FIG. 13, or of the value V22, in reference to FIG. 14, and as an alternative,
the
corresponding compressed values can be calculated using the average of the
restored values of the same indices mn as the surrounding pair, and, the
restored values using these same values. In this embodiment of the invention,
there is therefore:
for V02: W02=WRO2=(VROO+VR04)/2=(25+31)/2=28
then, D02=V02-W02=+1 and DR02=0
where, VRO2=WRO2+DR02=28+0=+28
and, for V22: W22=WR22=(VR2O+VR24)/2=(33+43)/2=38
then, D22=V22-W22=+3 and DR22=+4
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where, VR22=WR22+DR22=38+4=+42
with the values W02 and W22 being calculated as described previously in
reference to FIGS. 13 and 14.
Of course, the invention is not limited to the examples that have just
been described.
As such, instead of being in the upper left corner of the initial matrix, the
original cell can be any other cell whatsoever of the initial matrix, in such
a way
that the line and/or column numbers can take negative values, with the
principle of compression according to the invention not being affected
thereof.
In addition, if the previously given example describes the compression of
a matrix of which each cell shows a pixel of an image, a method of compression
according to the invention is applicable to any type of matrix, in particular
to
that corresponding to large quantities of data, for example statistical data.
Likewise, if the example corresponding to a two-dimensional matrix, symbolised
one by the lines, and the other by columns, the invention is applicable to
matrices of higher dimensions; in particular, a video can be represented by a
three-dimensional matrix, with the third dimension representing time. Such a
method of compression is, moreover, particularly suited for being used for the
processing of massive amounts of data, for example meteorological data, that
can be represented in the form of a two-dimensional matrix or higher.
In the example shown, the base layer has its own quantification tables
and the quantification tables used for the compression of the secondary layers
are identical for all the secondary layers. Of course, without these examples
being restricted, it is also possible to provide quantification tables that
are
proper to each secondary layer, or even a single quantification table valid
for all
of the layers, including the base layer.
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The order of processing of the initial values in each layer can be changed.
It can be processed by successive lines or columns, or in another order. It
can
also be provided that a processing of a layer begins before the processing of
the
preceding layer is finished.
=
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