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Claims  |
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What is claimed is:
1. A non-linear and linear method of scale-up, scale-down, or mixed mode
scale-up/scale-down image resolution conversion, the steps of the method
being performed by a data processor, the method comprising the steps of:
(a) receiving an input image featuring a plurality of pixels, said input
image plotted in an input image grid, said input image grid featuring an
input image grid coordinate system;
(b) providing pixel position control functions, said pixel position control
functions used to defined and set up a connection grid with a connection
grid coordinate system, whereby said pixel position control functions and
said connection grid with said connection grid coordinate system each
relate an output image grid with an output image grid coordinate system to
said input image grid with said input image grid coordinate system;
(c) calculating real position coordinates, located in said connection grid,
of each of a plurality of output pixel positions, located in said output
image grid, from said pixel position control functions;
(d) determining position coordinates of neighbor pixels, located in said
input image grid, surrounding each said real position coordinates of said
each of a plurality of output pixel positions;
(e) calculating differences between each said real position coordinates of
said each of a plurality of output pixel positions and said position
coordinates of said neighbor pixels, located in said input image grid;
(f) calculating for said each of a plurality of output pixel positions, a
new set of local coefficients from known values of said neighbor pixels
surrounding each said real position coordinates of said each of a
plurality of output pixel positions;
(g) calculating a value for said each of a plurality of output pixels
located in said output image grid from a differential prescription for a
two dimensional image featuring said pixels and featuring n.sup.2 said
neighbor pixels, said differential prescription comprising an inner
multiplication between two vectors, first of said two vectors featuring
one-times dot multiplication of said differences between each said real
position coordinates defined over a two-dimensional said connection grid
coordinate system of each of a plurality of output pixel positions and
said position coordinates of said n.sup.2 neighbor pixels defined over a
two-dimensional said input image grid coordinate system, and second of
said two vectors featuring said set of local coefficients calculated from
said known values of said n.sup.2 neighbor pixels; and
(h) displaying an output image featuring said a value for said each of a
plurality of said output pixels located in said output image grid.
2. The method of claim 1, wherein said pixel position control functions are
non-linear functions of output pixel position coordinates, image scaling
factors, and free parameters, said free parameters are real numbers used
for controlling extend of non-linearity of the non-linear image resolution
conversion from said input grid to said output grid.
3. The method of claim 1, wherein said pixel position control functions are
linear functions of output pixel position coordinates, image scaling
factors, and free parameters, said free parameters are real numbers not
affecting the linear image resolution conversion from said input grid to
said output grid.
4. The method of claim 1, wherein said connection grid with said connection
grid coordinate system is embedded within said input image grid coordinate
system, said connection grid with said connection grid coordinate system
is used for locating said real pixel position coordinates corresponding to
said output image pixel position coordinates.
5. The method of claim 1, wherein said output image grid initially features
an empty set of said values of said plurality of output image pixels.
6. The method of claim 1, wherein scaling of said input image is selected
from the group consisting of non-linear scaling, non-linear scaling and
linear scaling, and linear scaling.
7. The method of claim 1, wherein the step of calculating said value for
said each of a plurality of output pixels located in said output image
grid is from a differential prescription for a u dimensional image
featuring said pixels and featuring v.sup.u said neighbor pixels, said
differential prescription comprising
##EQU1##
whereby .degree. represents said inner multiplication between two vectors,
said dx.sub.1 to dx.sub.u are said differences between said real valued
output image positions defined over a u-dimensional said connection grid
coordinate system and said input image positions defined over a
u-dimensional said input grid coordinate system, said A.sub.j, for j=1,2,
. . .,v.sup.u are said local coefficients calculated from said known
values of said v.sup.u neighbor pixels defined over said u-dimensional
input image grid coordinate system, and said vector .PI..sub.p=1 to u (1,
dx.sub.p, dx.sub.p.sup.2, . . .,dx.sub.p.sup.v-1) is defined as
(u-1)-times dot multiplication .PI..sub.p=1 to u (1, dx.sub.p,
dx.sub.p.sup.2, . . .,dx.sub.p.sup.v-1)=(1, dx.sub.1, dx.sub.1.sup.2, . .
. , dx.sub.1.sup.v-1)*(1,dx.sub.2, dx.sub.2.sup.2, . . .,
dx.sub.2.sup.v-1)***(1, dx.sub.u,dx.sub.u.sup.2, . . . ,
dx.sub.u.sup.v-1), whereby said (u-1)-times dot multiplication results in
a vector of length v.sup.u.
8. The method of claim 1, wherein said input image is selected from the
group consisting of black and white, gray scale, color, and video.
9. A non-linear and linear method of scale-up, scale-down, or mixed mode
scale-up/scale-down image resolution conversion, featuring calculating a
value for each of a plurality of output pixels located in an output image
grid from a differential prescription for a two dimensional image
featuring pixels and featuring n.sup.2 neighbor pixels, said differential
prescription comprising an inner multiplication between two vectors, first
of said two vectors featuring one-times dot multiplication of differences
between each real position coordinates coordinates defined over a
two-dimensional connection grid coordinate system of each of a plurality
of output pixel positions and positions coordinates of said n.sup.2
neighbor pixels defined over a two-dimensional input image grid coordinate
system, and second of said two vectors featuring a set of local
coefficients calculated form known values of said n.sup.2 neighbor pixels.
10. The method of claim 9 wherein said output image grid initially features
an empty set of said values of said plurality of output image pixels.
11. The method of claim 9 wherein a new said set of local coefficients is
calculated for said each of a plurality of output pixels.
12. The method of claim 9 wherein calculating said value for said each of a
plurality of output pixels located in said output image grid is from a
differential prescription for a u dimensional image featuring said pixels
and featuring v.sup.u said neighbor pixels, said differential prescription
comprising
##EQU2##
whereby .degree. represents said inner multiplication between two vectors,
said dx.sub.1 to dx.sub.u are said differences between said real valued
output image positions defined over a u-dimensional said connection grid
coordinate system and said input image positions defined over a
u-dimensional said input grid coordinate system, said A.sub.j, for j=1,2,
. . . ,v.sup.u are said local coefficients calculated from said known
values of said v.sup.u neighbor pixels defined over said u-dimensional
input image grid coordinate system, and said vector .PI..sub.p=1 to u (1,
dx.sub.p, dx.sub.p.sup.2, . . . ,dx.sub.p.sup.v-1) is defined as
(u-1)-times dot multiplication .PI..sub.p=1 to u (1, dx.sub.p,
dx.sub.p.sup.2, . . . ,dx.sub.p.sup.v-1)=(1, dx.sub.1, dx.sub.1.sup.2, . .
. , dx.sub.1.sup.v-1)*(1,dx.sub.2, dx.sub.2.sup.2, . . . ,
dx.sub.2.sup.v-1)***(1, dx.sub.u,dx.sub.u.sup.2, . . . ,
dx.sub.u.sup.v-1), whereby said u-times dot multiplication results in a
vector of length v.sup.u. |
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Claims |
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Description |
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FIELD AND BACKGROUND OF THE INVENTION
The present invention relates to digital image processing. In particular,
this invention relates to a non-linear and linear method of scaling up or
scaling down the resolution of a digital input image to a defined output
window.
Digital displays are characterized by their scan rate and pixel resolution.
Standard non-interlaced displays have scan rate of at least 60 HZ and
resolution of at least 480 lines (rows) by 640 pixels (columns) in each
line. Non-interlaced displays are typically formatted as VGA, SVGA, XGA,
SXGA and UGA, where each one has a different resolution and scan rate. It
often occurs that various display systems are mixed together and
transformation from one resolution to other is needed. For example,
de-interlaced video images are usually of size 480 lines by 640 pixels
resolution (VGA format). Such images are visualized relatively small when
displayed on a monitor with pixel resolution capacity of 1200 lines by
1600 pixels. There is a need for a method of scaling up or scaling down
the resolution of a digital input image to a defined output window, in
order to display a video image over the entire resolution capacity of a
display monitor having different resolution from the video image.
One of the most important characterizations of advanced, interlaced or
non-interlaced, video screens is the ratio between the width (number of
columns) and the height (number of rows) of the actual display area,
commonly called the aspect ratio of the display screen. Currently, the
most popular aspect ratio is 4:3 (for example, de-interlaced video images
of size 480 rows by 640 columns or pixels (VGA format), or 1200 rows by
1600 columns). New screens are now available in the market with aspect
ratios such as 16:9 or 21:9. High Definition TV screens typically have an
aspect ratio of 16:9. In order to present images of one aspect ratio, for
example 4:3, on displays having a different aspect ratio, for example
16:9, a sophisticated transformation that converts the image between
aspect ratios is needed.
In such non-linear image resolution conversion cases, where the input and
output conversion ratio is not 1:1, i.e., 4:3 ? 16:9, using standard
linear resolution conversion methods on digital input images results in
distortions within the corresponding output images. Various methods of
video image resolution conversion and scaling have been developed, for
non-linear or linear cases, most of which either feature or include linear
interpolation processing for the purpose of either adding pixels by
estimating values of missing pixels, or deleting pixels with known values,
in the input image, for producing a converted output image. Using standard
interpolation methods for adding missing pixels to an input image as part
of forming an output image during scale-up resolution conversion, or for
deleting pixels from an input image as part of forming an output image
during scale-down resolution conversion, results in an output image either
containing additional pixels in, or missing deleted pixels from, the
initial input image, according to whether the image resolution conversion
is scale-up, or scale-down, respectively. In such methods, input image
data is simply used as a template for forming the output image. A more
sophisticated method of image resolution conversion, and one in which
higher quality results are obtained, is one which includes the formation
of an entirely new output image, by calculating each output image pixel,
in principle, from scratch, using input image pixels only as a starting
point of resolution conversion, and not where all, or portions, of input
image data simply become part of the output image. Moreover, many standard
linear interpolation methods may not be computationally efficient for
producing high quality resolution conversion images.
There is thus a need for a sophisticated, yet computationally efficient,
non-linear transformation that minimizes distortions resulting from
scale-up or scale-down resolution conversion with non-linear changes in
display screen aspect ratios. There is also a need for, and it would be
useful to have a sophisticated, yet computationally efficient linear
transformation for performing scale-up or scale-down image resolution
conversion, in cases where there is no change in aspect ratios between the
video input image and the display output image.
Relative suitability of known methods of image resolution conversion
ultimately depends on the resulting image quality. Moreover, different
methods of image resolution conversion work better under different
conditions.
U.S. Pat. No. 5,513,120 issued to Berlad, is based on a four-point linear
interpolation method, using nearest neighbor grid points and the next
nearest neighbor grid points that are in a line with the grid location
point requiring interpolated data, for estimating missing pixels required
for conversion of video images. Interpolation involves the use of Lagrange
polynomials for determination of four interpolation coefficients and each
output pixel value, whereby the texture of the image does not vary as a
function of pixel location. The interpolation method can be extended to an
n-dimensional display grid.
U.S. Pat. No. 5,574,572 issued to Malinowski et al., describes various
configurations of a video scaling method and device featuring a linear
interpolator and decimating FIR filter with constant coefficients for
horizontal or vertical scaling of video images.
U.S. Pat. No. 5,119,082 issued to Lumelsky et al., features a pixel rate
expansion circuit with a linear scaling method for video expansion, along
with a means of defining a window as a subset of an entire display and
scaling a video image to fit. The circuit includes a linear scaling
mechanism, which causes selected adjacent scan lines to be repeated as
they are read out of a frame buffer, for vertically and horizontally
expanding an input image.
U.S. Pat. No. 5,559,905 issued to Greggain et al., describes a digital
image resizing apparatus operating with a linear combination of
interpolation filters. Filter coefficients are multiplied by input data
and the results are shifted and sign extended to compensate for reduced
precision of resizing the image.
U.S. Pat. No. 5,796,879 issued to Wong et al., teaches of using the
technique of area-based interpolation for performing image interpolation,
emphasizing scaling-up of images. Pixel values are determined from
integrals of curves over an area proportional to a sampling size of an
input image. Two integrators and two interpolation steps, including the
use of a linear filter and evaluation of coefficients by solving linear
polynomial equations, are required to achieve the desired image
conversion.
U.S. Pat. No. 5,532,716 issued to Sano, describes a resolution conversion
system for scaling-down images. The system operates with scaling factors
proportional to input and output image sizes, and provides linear image
conversion in both horizontal and vertical directions.
U.S. Pat. No. 5,446,831 issued to Yamashita et al., describes an image data
processor for scaling-down an image. A base 2 logarithmic expression is
used for changing the amount of data required for performing the desired
resolution conversion. The image processor converts and reduces binary
image data in both vertical and horizontal direction.
Additional methods of digital image resolution conversion include using an
error diffusion technique, U.S. Pat. No. 5,208,871 issued to Eschbach, and
an area mapping technique using reference clusters of a digitized input
image, U.S. Pat. No. 5,758,034 and 5,689,343, issued to Loce et al.
SUMMARY OF THE INVENTION
The present invention relates to a non-linear and linear method of scale-up
or scale-down image resolution conversion.
The method of non-linear and linear scale-up or scale-down image resolution
conversion of the present invention features a new and unique method of
relating image pixels of an output grid to image pixels of an input grid,
by using non-linear or linear pixel position control functions. Moreover,
output images are formed by generating entirely new sets of output pixel
data, while being appropriately related to input image pixel data, in
contrast to current standard methods of image resolution conversion
featuring linear interpolation using input image pixel data as a template
for forming an output image.
The method of the present invention allows one to maintain the aspect ratio
of the output image equal to the aspect ratio of the input image during
non-linear scale-up or scale-down image resolution conversion, featuring
unequal aspect ratios of output and input images. For linear scale-up or
scale-down image resolution conversion, aspect ratios of the output image
and input image are the same. The present invention is a sophisticated,
yet computationally efficient method of scale-up or scale-down image
resolution conversion of video images. Resulting output images using the
method of the present invention are of high quality and closely
representative of original input images.
A preferred embodiment of a method of non-linear and linear scale-up or
scale-down image resolution conversion of the present invention features
the following principle steps: (1) Characterize an input image and its
target output image. (a) Define and set up input and output image grids.
(b) Determine scaling mode of the input image. (c) Determine if non-linear
or linear image resolution conversion. (2) Convolute the input image with
an FIR filter. (3) Define pixel position control functions relating pixel
positions in output image grid to input image grid. Define and set up a
connection grid using the position control functions. (4) Calculate real
position coordinates of an output image pixel, embedded within the input
image grid, using pixel position control functions and the connection
grid. (5) Identify position coordinates of neighbor pixels in the input
image grid, surrounding the real valued position of the output image pixel
located in the connection grid. (6) Define and evaluate (delta) functional
differences between real valued position coordinates of the output pixel
located in the connection grid, and neighbor pixel position coordinates
located in the input image grid. (7) Assign values to neighbor pixels in
the input image grid, surrounding the real position of the output pixel
located in the connection grid. (8) Define and calculate local
coefficients from values of neighbor pixels in the input image grid,
surrounding the real position of the output pixel located in the
connection grid. (9) Calculate preliminary value of the output pixel. (10)
Calculate and assign final value to the output pixel. (11) Calculate and
assign a value to next output pixel by repeating steps (1) through (10).
(12) Display completed resolution converted image.
According to the present invention, there is provided a non-linear and
linear method of scale-up, scale-down, or mixed mode scale-up/scale-down
image resolution conversion, the steps of the method being performed by a
data processor, the method comprising the steps of: (a) receiving an input
image featuring a plurality of pixels, the input image plotted in an input
image grid, the input image grid featuring an input image grid coordinate
system; (b) providing pixel position control functions, the pixel position
control functions used to define and set up a connection grid with a
connection grid coordinate system, whereby the pixel position control
functions and the connection grid with the connection grid coordinate
system each relate an output image grid with an output image grid
coordinate system to the input image grid with the input image grid
coordinate system; (c) calculating real position coordinates, located in
the connection grid, of each of a plurality of output pixel positions,
located in the output image grid, from the pixel position control
functions; (d) determining position coordinates of neighbor pixels,
located in the input image grid, surrounding each real position
coordinates of each of a plurality of output pixel positions; (e)
calculating differences between each real position coordinates of each of
a plurality of output pixel positions and position coordinates of the
neighbor pixels, located in the input image grid; (f) calculating for each
of a plurality of output pixel positions, a new set of local coefficients
from known values of the neighbor pixels surrounding each real position
coordinates of each of a plurality of output pixel positions; (g)
calculating a value for each of a plurality of output pixels located in
the output image grid from a differential prescription for a two
dimensional image featuring the pixels and featuring n.sup.2 neighbor
pixels, the differential prescription comprising an inner multiplication
between two vectors, first of the two vectors featuring one-times dot
multiplication of the differences between each real position coordinates
defined over a two-dimensional connection grid coordinate system of each
of a plurality of output pixel positions and position coordinates of the
n.sup.2 neighbor pixels defined over a two-dimensional input image grid
coordinate system, and second of the two vectors featuring the set of
local coefficients calculated from the known values of the n.sup.2
neighbor pixels; and (h) displaying an output image featuring a value for
each of a plurality of the output pixels located in the output image grid.
According to the present invention, there is provided a non-linear and
linear method of scale-up, scale-down, or mixed mode scale-up/scale-down
image resolution conversion featuring the use of pixel position control
functions, the pixel position control functions used to define and set up
a connection grid with a connection grid coordinate system, whereby the
pixel position control functions and the connection grid with the
connection grid coordinate system each relate an output image grid with an
output image grid coordinate system to an input image grid with an input
image grid coordinate system.
According to the present invention, there is provided a non-linear and
linear method of scale-up, scale-down, or mixed mode scale-up/scale-down
image resolution conversion, featuring calculating a value for each of a
plurality of output pixels located in an output image grid from a
differential prescription for a two dimensional image featuring pixels and
featuring n.sup.2 neighbor pixels, the differential prescription
comprising an inner multiplication between two vectors, first of the two
vectors featuring one-times dot multiplication of differences between each
real position coordinates defined over a two-dimensional connection grid
coordinate system of each of a plurality of output pixel positions and
position coordinates of the n.sup.2 neighbor pixels defined over a
two-dimensional input image grid coordinate system, and second of the two
vectors featuring a set of local coefficients calculated from known values
of the n.sup.2 neighbor pixels.
The present invention could be implemented by hardware or by software on
any operating system of any firmware or a combination thereof. For
example, as hardware, the invention could be implemented as a chip or a
circuit. As software, the invention could be implemented as a plurality of
software instructions being executed by a computer using any suitable
operating system. In any case, the steps of the method of the invention
could be described as being performed by a data processor, such as a
computing platform for executing a plurality of instructions, regardless
of the implementation of the present invention.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention is herein described by way of example only, with reference to
the accompanying drawings, wherein:
FIG. 1A is an illustration of an input grid, used for plotting a digitized
video image (not shown), relating to the preferred embodiment of
non-linear scale-up or scale-down image resolution conversion, according
to the method of the present invention;
FIG. 1B is an illustration of an output grid, used for plotting the
resolution converted digitized video image (not shown) of FIG. 1A,
relating to the preferred embodiment of non-linear scale-up or scale-down
image resolution conversion, according to the method of the present
invention;
FIG. 1C is an illustration of a connection grid, showing the macro-level
relationship between the input grid of FIG. 1A and the output grid of FIG.
1B, relating to the preferred embodiment of non-linear scale-up or
scale-down image resolution conversion, according to the method of the
present invention;
FIG. 2A is an illustration of an input grid, used for plotting a digitized
video image (not shown), relating to the preferred embodiment of linear
scale-up or scale-down image resolution conversion, according to the
method of the present invention;
FIG. 2B is an illustration of an output grid, used for plotting the
resolution converted digitized video image (not shown) of FIG. 2A,
relating to the preferred embodiment of linear scale-up or scale-down
image resolution conversion, according to the method of the present
invention;
FIG. 2C is an illustration of a connection grid, showing the macro-level
relationship between the input grid of FIG. 2A and the output grid of FIG.
2B, relating to the preferred embodiment of linear scale-up or scale-down
image resolution conversion, according to the method of the present
invention;
FIG. 3 is a flow diagram of a preferred embodiment of the non-linear and
linear method of scale-up or scale-down image resolution conversion,
according to the present invention; and
FIG. 4 is an illustration showing either the micro-level relationship
between the input grid of FIG. 1A, featuring nine nearest neighbor pixel
positions, and the connection grid of FIG. 1C, featuring the real valued
pixel position of the output pixel, or, the micro-level relationship
between the input grid of FIG. 2A, featuring nine nearest neighbor pixel
positions, and the connection grid of FIG. 2C, featuring the real valued
pixel position of the output pixel, relating to the preferred embodiment
of non-linear and linear scale-up or scale-down image resolution
conversion, according to the method of the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention is of a non-linear and linear method of scaling-up or
scaling-down the resolution of a digital image to a defined output window.
Scale-up image resolution conversion is described as follows. An input
digital image (moving or still, color or not), I, of size M lines (rows)
by N pixels (columns) per line, is to be converted into an output image,
O, of size M1 lines by N1 pixels per line, where M1>M and/or N1>N, by
increasing or scaling-up the total number of pixels in a portion of, or
the entire input image, I.
Scale-down image resolution conversion is described as follows. An input
digital image (moving or still, color or not), I, of size M lines (rows)
by N pixels (columns) per line, is to be converted into an output image,
O, of size M1 lines by N1 pixels per line, where M1<M and/or N1<N, by
decreasing or scaling-down the total number of pixels in a portion of, or
the entire input image, I.
Combination scale-up and scale-down image resolution conversion involves
scaling-up lines and scaling-down columns of an input image, I, or,
scaling-down lines and scaling-up columns of an input image, I, in order
to generate an output image, O, of different resolution.
The method of the present invention is applicable to either non-linear or
linear, scale-up or scale-down, image resolution conversion. The present
method featuring non-linear scale-up or non-linear scale-down image
resolution conversion is preferably applied to an input image when the
output image aspect ratio, M1:N1, is not equal to the input image aspect
ratio, M:N. The present method featuring linear scale-up or linear
scale-down image resolution conversion is preferably applied to an input
image when the output image aspect ratio, M1:N1, is equal to the input
image aspect ratio, M:N.
Steps and implementations of a non-linear and linear method of scale-up or
scale-down image resolution conversion, according to the present invention
are better understood with reference to the drawings and the accompanying
description. It is to be noted that illustrations of the present invention
shown here are for illustrative purposes only and are not meant to be
limiting.
Referring now to the drawings, FIG. 1A is an illustration of a graphical
input grid 10, used for plotting a digitized video image, I, (not shown),
relating to the preferred embodiment of non-linear scale-up or scale-down
image resolution conversion, according to the method of the present
invention. The input grid 10 features rows (lines) 12, and columns
(pixels) 14, with each input grid location identifiable by coordinates of
row number i, and column number j. I(i,j) represents the value of a pixel
16 of a digitized input image (not shown) which can be plotted in input
grid 10, and whose position coordinates in input grid 10 are indicated by
row i, and column j. For a digital input image, I, of size M rows by N
columns, position indices (i,j) are limited to the input image size as
follows: i; 0,1,2, . . . M-1; and j: 0,1,2, . . . N-1. In general, indices
i and j can be real or integer. In this preferred embodiment of the
present invention, position coordinates row i and column j, and
corresponding position indices (i,j), are integers (i.e., not real),
translating to integer valued position indices of a pixel 16 in input grid
10. Digitized video image, I, having a known resolution, is to undergo
non-linear scale-up or scale-down image resolution conversion, in order to
enable its display on a digitized output grid having a different
resolution.
FIG. 1B is an illustration of, initially empty valued, graphical output
grid 18, used for plotting the resolution converted digitized video image
(not shown) of FIG. 1A, relating to the preferred embodiment of non-linear
scale-up or scale-down image resolution conversion, according to the
method of the present invention. The output grid 18 features rows (lines)
20, and columns (pixels) 22, with each output grid location identifiable
by coordinates of row number s, and column number t. O(s,t) represents the
value of a pixel 24 of a digitized output image (not shown) which can be
plotted in output grid 18, and whose position coordinates in output grid
18 are indicated by row s, and column t. For a digital output image, O, of
size M1 rows by N1 columns, the position indices (s,t) are limited to the
output image size as follows: s: 0,1,2, . . . M1-1; and t: 0,1,2, . . .
N1-1. In general, indices s and t can be real or integer. In this
preferred embodiment of the present invention, position coordinates row s
and column t, and corresponding position indices (s,t), of exemplary pixel
24, are integer (i.e., not real) valued in output grid 18.
FIG. 1C is an illustration of a graphical connection grid 26, showing the
macro-level relationship between output grid 18 (FIG. 1B), and input grid
10 (FIG. 1A), relating to the preferred embodiment of non-linear scale-up
or scale-down image resolution conversion, according to the method of the
present invention. The utility of connection grid 26 is to relate pixel
positions of output grid 18 (FIG. 1B) to pixel positions of input grid 10
(FIG. 1A), taking into account non-linear effects during image resolution
conversion. Connection grid 26 features rows (lines) 28, and columns 30,
with each connection grid location identifiable by coordinates of row
number y.sub.i, and column number x.sub.j. In general, indices y.sub.i,
and x.sub.j can be real or integer. In this preferred embodiment of the
present invention, position coordinates row y.sub.i, and column x.sub.j,
and corresponding position indices (y.sub.i,x.sub.j) of an exemplary pixel
position 32, are real (i.e., not integer) valued in connection grid 26.
In connection grid 26 (FIG. 1C), subscript i of row y, and subscript j of
column x, are used in order to relate or connect between position
coordinates, or indices, of output image, O(s,t) (not shown), which can be
plotted in output grid 18 (FIG. 1B), and position coordinates, or indices,
of input image, I(i,j), which can be plotted in input grid 10 (FIG. 1A).
Exemplary pixel position indices (y.sub.i,x.sub.j) 32, in connection grid
26, are real position indices, pointing out to the exact position of a
pixel 16 of input image, I(i,j), which can be plotted in input grid 10
(FIG. 1A).
In the non-linear case of the preferred embodiment of the method of
scale-up or scale-down image resolution conversion of the present
invention, the non-linear relationship between output indices (s,t), of
output grid 18 (FIG. 1B), and input indices, (i,j), of input grid 10 (FIG.
1A), is represented functionally as follows: y.sub.i =F.sub.i
(s,t,a,b,.lambda..sub.1,.mu..sub.l), and x.sub.j =F.sub.j
(s,t,a,b,.lambda..sub.2,.mu..sub.2). F.sub.i and F.sub.j are non-linear
pixel position control functions, .lambda..sub.1, .mu..sub.1,
.lambda..sub.2, and .mu..sub.2 are free parameters that control the extent
of non-linearity during image resolution conversion from input grid 10
(FIG. 1A), to output grid 18 (FIG. 1B), and, a and b are scale factors
(ratios), relating output to input image sizes, where a=M1/M, or (number
of rows of output image, O) divided by (number of rows of input image, I),
and b=N1/N, or (number of columns of output image, O) divided by (number
of columns of input image I), where a>0 and b>0 are real positive numbers.
Based on the assignment of scale factor a, and in its use in the equations
for calculating values of connection grid indices (y.sub.i x.sub.j) 32,
for a >1, there is an increase in the number of rows in converting from
input to output image, as such, rows 12 of input image, I, in input grid
10 (FIG. 1A), are non-linearly scaled-up to rows 20 of output image, O, in
output grid 18 (FIG. 1B). For 0<a<1, there is a decrease in the number of
rows in converting from input to output image, and rows 12 of input image,
I, in input grid 10 (FIG. 1A), are non-linearly scaled-down to rows 20 of
output image, O, in output grid 18 (FIG. 1B). In a similar way, based on
the assignment of scale factor b, for b>1, there is an increase in the
number of columns in converting from input to output image, as such,
columns 14 of input image, I, in input grid 10 (FIG. 1A), are non-linearly
scaled-up to columns 22 of output image, O, in output grid 18 (FIG. 1B).
For 0<b<1, there is a decrease in the number of columns in converting from
input to output image, and columns 14 of input image, I, in input grid 10
(FIG. 1A), are non-linearly scaled-down to columns 22 of output image, O,
in output grid 18 (FIG. 1B).
FIG. 2A is an illustration of a graphical input grid 34, used for plotting
a digitized video image, I, (not shown), relating to the preferred
embodiment of linear scale-up or scale-down image resolution conversion,
according to the method of the present invention. The input grid 34
features rows (lines) 36, and columns (pixels) 38, with each input grid
location identifiable by coordinates of row number i, and column number j.
I(i,j) represents the value of a pixel 40 of a digitized input image (not
shown) which can be plotted in input grid 34, and whose position
coordinates in input grid 34 are indicated by row i, and column j. For a
digital input image, I, of size M rows by N columns, position indices
(i,j) are limited to the input image size as follows: i: 0,1,2, . . . M-1;
and j: 0,1,2, . . . N-1. In general, indices i and j can be real or
integer. In this preferred embodiment of the present invention, position
coordinates row i and column j, and corresponding position indices (i,j),
are integers (i.e., not real), translating to integer valued position
indices of a pixel 40 in input grid 34. Digitized video image, I, having a
known resolution, is to undergo linear scale-up or scale-down image
resolution conversion, in order to enable its display on a digitized
output grid having a different resolution.
FIG. 2B is an illustration of, initially empty valued, graphical output
grid 42, used for plotting the resolution converted digitized video image
(not shown) of FIG. 2A, relating to the preferred embodiment of linear
scale-up or scale-down image resolution conversion, according to the
method of the present invention. The output grid 42 features rows (lines)
44, and columns (pixels) 46, with each output grid location identifiable
by coordinates of row number s, and column number t. O(s,t) represents the
value of a pixel 48 of a digitized output image (not shown) which can be
plotted in output grid 42, and whose position coordinates in output grid
42 are indicated by row s, and column t. For a digital output image, O, of
size M1 rows by N1 columns, the position indices (s,t) are limited to the
output image size as follows: s: 0,1,2, . . . M1-1; and t: 0,1,2, . . .
N1-1. In general, indices s and t can be real or integer. In this
preferred embodiment of the present invention, position coordinates row s
and column t, and corresponding position indices (s,t), of exemplary pixel
48, are integer (i.e., not real) valued in output grid 42.
FIG. 2C is an illustration of a graphical connection grid 50, showing the
macro-level relationship between output grid 42 (FIG. 2B), and input grid
34 (FIG. 2A), relating to the preferred embodiment of linear scale-up or
scale-down image resolution conversion, according to the method of the
present invention. The utility of connection grid 50 is to relate pixel
positions of output grid 42 (FIG. 2B) to pixel positions of input grid 34
(FIG. 2A), taking into account linear effects during image resolution
conversion. Connection grid 50 features rows (lines) 52, and columns 54,
with each connection grid location identifiable by coordinates of row
number y.sub.i, and column number x.sub.j. In general, indices y.sub.i,
and x.sub.j can be real or integer. In this preferred embodiment of the
present invention, position coordinates row y.sub.i, and column x.sub.j,
and corresponding position indices (y.sub.i,x.sub.j) of an exemplary pixel
position 56, are real (i.e., not integer) valued in connection grid 50.
In connection grid 50 (FIG. 2C), subscript i of row y, and subscript j of
column x, are used in order to relate or connect between position
coordinates, or indices, of output image, O(s,t) (not shown), which can be
plotted in output grid 42 (FIG. 2B), and position coordinates, or indice | | |
