Title: Palettized image compression
Abstract: An adaptive entropy coder is coupled with a localized conditioning context to provide efficient compression of images with localized high frequency variations. In one implementation, an arithmetic coder can be used as the adaptive entropy coder. The localized conditioning context includes a basic context region with multiple context pixels that are adjacent the current pixel, each of the context pixels having an image tone. A state is determined for the basic context region based upon a pattern of unique image tones among the context pixels therein. An extended context region that includes the basic context region is used to identify a non-local trend within the context pixels and a corresponding state. A current pixel may be arithmetically encoded according to a previously encoded pixel having the same tone or as a not-in-context element. In one implementation, a not-in-context element may be represented by a tone in a color cache that is arranged as an ordered list of most recent not-in-context values.
Patent Number: 6,968,089 Issued on 11/22/2005 to Wang
| Inventors:
|
Wang; Albert Szu-chi (Palo Alto, CA)
|
| Assignee:
|
Microsoft Corporation (Redmond, WA)
|
| Appl. No.:
|
974108 |
| Filed:
|
October 27, 2004 |
| Current U.S. Class: |
382/239; 329/246 |
| Intern'l Class: |
G06K 009/36; G06K 009/46 |
| Field of Search: |
382/239-240,244-247
241/51,65,106
|
References Cited [Referenced By]
U.S. Patent Documents
Other References
Paul Ausbeck, "Content Models for Palette Images," Data Compression Conference,
DCC 1998, Mar. 30-Apr. 1, 1998, Snowbird, Utah, USA. IEEE Computer Society, 1998.
"Introduction to Data Compression," Khalid Sayood, Morgan Stanley Publishers,
Inc., San Francisco, CA, pp. 87-94, 336-348, 1996.
|
Primary Examiner: Mancuso; Joseph
Assistant Examiner: Dang; Duy M.
Attorney, Agent or Firm: Lee & Hayes, PLLC
Parent Case Text
RELATED APPLICATIONS
This application is a continuation of and claims priority to U.S. patent application
Ser. No. 09/577,544, filed May 24, 2000, now U.S. Pat. No. 6,856,700 the disclosure
of which is incorporated by reference herein.
Claims
1. An image encoding system for compressing image data representing plural pixels
of plural nonzero image tones, the system comprising:
designation means for designating a current pixel to be encoded;
defining means for defining a context region that includes multiple context pixels
that are adjacent the current pixel, each of the context pixels having an image tone;
first identification means for identifying a pattern of unique image tones among
the context pixels in the context region;
assignment for assigning a state to the context region according to the pattern
of unique image tones therein;
coding means for adaptive entropy coding the current pixel with reference to
the state of the context region; and
second identification means for identifying a non-local trend within the context
pixels in which identification of each non-local trend references a trend context
pixel in addition to the context pixels in which the pattern of unique tones are identified.
2. The system of claim 1, wherein the second identification means is also for
identifying non-local trends that are in horizontal or vertical alignment with
the current pixel.
3. The system of claim 1, wherein the identification of each non-local trend
references a trend context pixel in addition to the context pixels in which the
pattern of unique tones are identified.
4. The system of claim 1, wherein the coding means is also for arithmetic coding.
5. The system of claim 1, wherein the pattern of unique image tones is identified
with reference only to context pixels that are immediately adjacent the current pixel.
6. The system of claim 1, wherein the pattern of tones is identified with reference
to only four context pixels.
7. The system of claim 1, wherein the coding means is also for arithmetic coding
in which the current pixel may be encoded according to a previously encoded pixel
having the same tone or as a not-in-context element corresponding to a tone in
a color cache representing an ordered list of most recent not-in-context values.
8. An image encoding system for compressing image data representing plural pixels
of plural nonzero image tones, the system comprising:
designation means for designating a current pixel to be encoded;
defining means for defining a context region that includes multiple context pixels
that are adjacent the current pixel, each of the context pixels having an image tone;
first identification means for identifying a pattern of unique image tones among
the context pixels in the context region, wherein the pattern of unique image tones
is identified with reference only to context pixels that are immediately adjacent
the current pixel;
assignment means for assigning a state to the context region according to the
pattern of unique image tones therein;
coding means for adaptive entropy coding the current pixel with reference to
the state of the context region; and
second identification means for identifying a non-local trend within the context
pixels, identification of each non-local trend referencing a trend context pixel
in addition to the context pixels in which the pattern of unique tones are identified.
9. The system of claim 8, wherein the second identification means is also for
identifying non-local trends that are in horizontal or vertical alignment with
the current pixel.
10. The system of claim 8, wherein the identification of each non-local trend
references a trend context pixel in addition to the context pixels in which the
pattern of unique tones are identified.
11. The system of claim 8, wherein the coding means is also for arithmetic coding.
12. The system of claim 8, wherein the pattern of unique image tones is identified
with reference only to context pixels that are immediately adjacent the current pixel.
13. The system of claim 8, wherein the pattern of tones is identified with reference
to only four context pixels.
14. The system of claim 8, wherein the coding means is also for arithmetic coding
in which the current pixel may be encoded according to a previously encoded pixel
having the same tone or as a not-in-context element corresponding to a tone in
a color cache representing an ordered list of most recent not-in-context values.
15. In a computer readable medium, image encoding software for compressing image
data representing plural pixels of plural nonzero image tones, comprising:
designation means for designating a current pixel to be encoded;
first identification means for identifying within a basic context region that
includes multiple context pixels that are adjacent the current pixel, each of the
context pixels having an image tone, a pattern of unique image tones among the
context pixels in the context region;
second identification means for identifying within an extended context region
that includes the basic context region a non-local trend within the context pixels;
assignment means for assigning a state according to identifications made within
the basic and extended context regions; and
coding means for adaptive entropy coding the current pixel with reference to
the state of the context region.
16. The system of claim 15, wherein the second identification means is also for
identifying non-local trends that are in horizontal or vertical alignment with
the current pixel.
17. The system of claim 15, wherein the coding means is also for arithmetic coding.
18. The system of claim 15, wherein the pattern of unique image tones is identified
with reference only to context pixels that are immediately adjacent the current pixel.
19. The system of claim 15, wherein the pattern of tones is identified with reference
to only four context pixels.
20. The system of claim 15, wherein the coding means is also for arithmetic coding
in which the current pixel may be encoded according to a previously encoded pixel
having the same tone or as a not-in-context element corresponding to a tone in
a color cache representing an ordered list of most recent not-in-context values.
Description
FIELD OF THE INVENTION
The present invention relates to data compression and, in particular, to compression
of digital image data.
BACKGROUND AND SUMMARY OF THE INVENTION
A wide range of methods and algorithms are available for compression of digital
images and, particularly, the image data corresponding to the pixels in a digital
image. The different available methods and algorithms are typically suited to particular
types of digital images. An example of such particularized suitability is the JPEG
compression standard, which is a widely-adopted standard compression algorithm
that is based upon the discrete cosine transform (DCT). JPEG compression and the
DCT are described in, for example,
Introduction to Data Compression by Khalid
Sayood, Morgan Kaufmann Publishers, Inc., San Francisco, Calif., 336-348, 1996.
JPEG compression applies the DCT to image data corresponding to successive 8×8
blocks of pixels. The DCT is effective and efficient with regard to linear correlations
that arise over each 8×8 block of pixels. Digital images with these characteristics
might include images that correspond to photographs or images with relatively large
regions of similar color or tone. Images corresponding to photographs typically
include a substantially continuous range of image tones represented by binary values
of 24-bits or more. In many such continuous-tone digital images, the variations
within the range of image tones are typically well accommodated by the DCT in JPEG
compression. Images with relatively large regions of the same color or tone have
no changes in tone over those regions and may be effectively compressed by JPEG
compression, as well as other compression methods.
It will be appreciated, however, that continuous-tone images are not the only
types of digital images. In some applications, digital images may include a smaller
range of discrete image colors or tones (e.g., represented by 8-bits, or fewer)
or localized high frequency variations such as text elements or other image discontinuities.
These types of discrete-tone images, sometimes called palettized images, arise
in a variety of applications including, for example, training or help-screen images
for software that uses widowed or other graphical user interfaces, shared whiteboards
or application sharing, online training, simple animations, etc. The images that
arise in such applications are often inefficiently encoded by JPEG compression
due to the spatially localized high frequency and discontinuous features in the images.
The present invention includes an adaptive entropy coder coupled with a localized
conditioning context to provide efficient compression of discrete-tone images with
localized high frequency variations. In one implementation, an arithmetic coder
can be used as the adaptive entropy coder.
The localized conditioning context includes a basic context region with multiple
context pixels that are adjacent the current pixel, each of the context pixels
having an image tone. A state is determined for the basic context region based
upon the pattern of unique image tones among the context pixels therein. An extended
context region that includes the basic context region is used to identify a non-local
trend within the context pixels and a corresponding state. The current pixel is
then encoded as having one of the tones in the context or as a not-in-context element.
In one implementation, a not-in-context element may be represented by a tone in
a color cache that is arranged as an ordered list of most recent not-in-context values.
Statistics for conditional probabilities are gathered for each context
during encoding. Many traditional context-based coders choose contexts that are
based on the values present in the surrounding context. Since the number of states
in the coder grows exponentially with the size of the context, traditional context-based
coders work well only when the possible set of values is small (e.g. black and
white or binary images), or when the context is very small (one element).
The present invention allows the use of a large context (e.g., up to at least
six elements) with elements that can take on many values. This is performed by
quantizing the huge number of fundamental states (about 300 trillion) into a set
of meaningful patterns (e.g., 60) that are based on the number of unique image
tones or values. These patterns model palettized images well. Quantizing the states
into this set of meaningful patterns, rather than scalar quantizing the values
of the elements, as is traditionally done, greatly increases the efficiency with
which palettized images can be encoded or compressed.
Additional objects and advantages of the present invention will be apparent
from the detailed description of the preferred embodiment thereof, which proceeds
with reference to the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a computer system that may be used to implement
the present invention.
FIG. 2 is an illustration of a first exemplary palettized image.
FIG. 3 is an illustration of a second exemplary palettized image.
FIG. 4 is a flow diagram of a palettized image compression method for compressing
or encoding data representing palettized images.
FIG. 5 is diagram illustrating a causal context region that is in the vicinity
of a current pixel being encoded.
FIG. 6 is a diagram of a predefined encoding pattern or sequence for encoding
a palettized image.
FIG. 7 is a flow diagram of a method of determining a state for causal context
region in the vicinity of a current pixel.
FIG. 8 illustrates a universe of image tone pattern classifications for a basic
context region according to the present invention.
FIG. 9 illustrates four possible trend tone patterns of a pair of supplemental
context pixels.
FIG. 10 is a flow diagram of an entropy coding method employed in one implementation
of the present invention.
FIGS. 11 and 12 are diagrams illustrating operation of a color cache employed
in the arithmetic coding method of FIG. 10.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
FIG. 1 illustrates an operating environment for an embodiment of the present
invention as a computer system
20 with a computer
22 that comprises
at least one high speed processing unit (CPU)
24 in conjunction with a memory
system
26, an input device
28, and an output device
30. These
elements are interconnected by at least one bus structure
32.
The illustrated CPU
24 is of familiar design and includes an ALU
34
for performing computations, a collection of registers
36 for temporary
storage of data and instructions, and a control unit
38 for controlling
operation of the system
20. The CPU
24 may be a processor having
any of a variety of architectures including Alpha from Digital, MIPS from MIPS
Technology, NEC, IDT, Siemens, and others, x86 from Intel and others, including
Cyrix, AMD, and Nexgen, and the PowerPC from IBM and Motorola.
The memory system
26 generally includes high-speed main memory
40
in the form of a medium such as random access memory (RAM) and read only memory
(ROM) semiconductor devices, and secondary storage
42 in the form of long
term storage mediums such as floppy disks, hard disks, tape, CD-ROM, flash memory,
etc. and other devices that store data using electrical, magnetic, optical or other
recording media. The main memory
40 also can include video display memory
for displaying images through a display device. Those skilled in the art will recognize
that the memory
26 can comprise a variety of alternative components having
a variety of storage capacities.
The input and output devices
28 and
30 also are familiar. The input
device
28 can comprise a keyboard, a mouse, a physical transducer (e.g.,
a microphone), etc. The output device
30 can comprise a display, a printer,
a transducer (e.g., a speaker), etc. Some devices, such as a network interface
or a modem, can be used as input and/or output devices.
As is familiar to those skilled in the art, the computer system
20 further
includes an operating system and at least one application program. The operating
system is the set of software which controls the computer system's operation and
the allocation of resources. The application program is the set of software that
performs a task desired by the user, using computer resources made available through
the operating system. Both are resident in the illustrated memory system
26.
In accordance with the practices of persons skilled in the art of computer programming,
the present invention is described below with reference to acts and symbolic representations
of operations that are performed by computer system
20, unless indicated
otherwise. Such acts and operations are sometimes referred to as being computer-executed
and may be associated with the operating system or the application program as appropriate.
It will be appreciated that the acts and symbolically represented operations include
the manipulation by the CPU
24 of electrical signals representing data bits
which causes a resulting transformation or reduction of the electrical signal representation,
and the maintenance of data bits at memory locations in memory system
26
to thereby reconfigure or otherwise alter the computer system's operation, as well
as other processing of signals. The memory locations where data bits are maintained
are physical locations that have particular electrical, magnetic, or optical properties
corresponding to the data bits.
FIGS. 2 and 3 are simplified diagrams illustrating palettized images
46
and
48, which are sometimes called discrete-tone images. One way to characterize
a palettized image is that the number of colors in the image is small compared
to the number of pixels in the image (i.e., the image size). Another way to characterize
a palettized image is that the number of colors in the image is represented by
N-number or fewer binary bits, with N having a value of about 8. Generally, a palettized
image is contrasted with a continuous tone image, such as a photograph, that potentially
includes large numbers of colors or tones in comparison to the number of pixels
in the image. As an example, palettized images are commonly used in various computer
user interfaces, including those for desktop software applications, Internet (e.g.,
World Wide Web) network sites, etc. It will be appreciated, however, that palettized
images can arise in various other computer applications.
FIG. 4 is a flow diagram of a palettized image compression method
50
for compressing or encoding image data representing palettized images. Palettized
image compression method
50 compresses palettized images with high efficiency
and no loss of information, and so may be referred to as a lossless compression
method. Palettized image compression method
50 compresses palettized images
on a pixel-by-pixel basis.
Process block
52 indicates that a "current" pixel
54 (FIG.
5) is designated for encoding. Successive adjacent pixels of a palettized image
are encoded in a predefined encoding pattern or sequence
56 (FIG. 6). In
the illustrated implementation, the pixels of a palettized image are encoded left-to-right
across successive horizontal rows of pixels, beginning with a start pixel
58
at the upper left corner of the image. It will be appreciated that other encoding
patterns or sequences could alternatively be applied.
Process block
60 indicates that a state is determined for a causal
context region
62 (FIG. 5), sometimes referred to as extended causal context
region
62, that includes a predefined set of previously encoded pixels that
are in the vicinity of current pixel
54, as described below in greater detail.
In accordance with the present invention, quantization of causal context region
62 into patterns greatly reduces the number of possible states in comparison
to prior encoding processes, thereby supporting the high efficiency of palettized
image compression method
50.
Process block
64 indicates that current pixel
54 is adaptively
entropy coded with regard to the predefined set of previously encoded pixels within
causal context region
62. In one implementation, the adaptive entropy coding
includes arithmetic coding, which is known in the art and described in
Introduction
to Data Compression by Khalid Sayood, Morgan Kaufmann Publishers, Inc., San
Francisco, Calif., 1996. Other suitable adaptive entropy coding methods include
adaptive Huffman codes.
FIG. 7 is a flow diagram of a state determination method
70 for determining
a state for causal context region
62 in the vicinity of current pixel
54.
Process block
72 indicates that a basic causal context region
74
(FIG. 5) is defined with regard to current pixel
54 to be encoded. Basic
causal context region
74 corresponds to context pixels
76-
1,
76-
2,
76-
3, and
76-
4 in the palettized
image that have been previously encoded and are immediately adjacent (i.e., contact)
current pixel
54. The illustrated implementation corresponds to an image
in which pixels are arranged in a conventional rectangular array, which results
in basic context region
74 having only four context pixels
76 that
are immediately adjacent current pixel
54. Also, the arrangement of context
pixels
76 relates to the illustrated left-to-right, top-to-bottom encoding
pattern
56. It will be appreciated that a different pixel arrangement and
a different encoding pattern could result in a different basic context region.
Each pixel has associated with it a value, called an image value, which corresponds
to the color or tone, or other image characteristics of the pixel. Process block
80 indicates that the image values of context pixels
76 are compared
to determine the pattern of unique image values among the four context pixels,
thereby to classify basic context region
74 by the pattern of unique image
values or tones among the four pixels. For example, basic context region
74
is referred to as one-tone context if all four context pixels have the same image
value. If there are two unique values, basic context region
74 is called
a two-tone context, and so on. With only four context pixels
76, the image
values within basic context region
74 can correspond to one-, two, three,
or four-tone contexts.
Process block
82 indicates that a tone pattern of basic context region
74 is assigned a state according to the arrangement of unique image values
or tones among the four context pixels
76. FIG. 8 illustrates the universe
of fifteen tone patterns classifications for basic context region
74.
In particular, a one-tone pattern has only one possible classification
90
that is designated as "tone
1, pattern
0" corresponding to all context
pixels
76 having the same image value or tone (e.g., designated "a"). A
two-tone pattern may be any of seven classifications
92-
104 that
are designated as patterns 0-6, respectively. A three-tone pattern may be any of
six classifications
106-
116 as patterns
0-
5, respectively.
A four-tone pattern has only one possible classification
118 that is designated
as "tone
4, pattern
0."
This classification of basic context region
74 by the number tones and
their arrangement is based upon context pixels
76 having equal image values,
or not. Other than this equality or inequality of the image values or tones, the
classification of basic context region
74 is independent of the actual image
values. The pattern classification is only concerned with spatial distribution
of the pattern, and not the values themselves. In contrast, conventional encoding
methods base regional contexts on the actual image values, not the pattern of unique
values. Even with a relatively simple color spectrum of 256 colors (i.e., 8-bit
colors), a conventional regional context of four pixels would encompass many millions
of possible patterns, rather than the 15 patterns shown in FIG. 8. As a result,
classification of basic context region
74 according to the arrangements
of unique image values or tones, rather than actual tones, provides a greatly reduced
set of possible context patterns, thereby providing a significant increase in encoding efficiency.
Process block
120 indicates that supplemental context pixels
76-
5
and
76-
6 (FIG. 5) are appended to basic causal context region
74
to complete the extended context region
62 and to detect any non-local trend
extending through region
62. Supplemental context pixels
76-
5
and
76-
6 are horizontally- and vertically-aligned with current pixel
54 and detect horizontal and vertical trends, respectively. As shown in
FIG. 2, for example, many palettized images may include image features with horizontal
or vertical boundaries that would correspond to non-local trends through overall
context region
62. A horizontal trend is indicated when context pixel
76-
4
has an image value or tone equaling that of context pixel
76-
5. A
vertical trend is indicated when context pixel
76-
3 has an image
value or tone equaling that of context pixel
76-
6.
FIG. 9 illustrates the four possible trend tone patterns
124-
130
of supplemental context pixels
76-
5 and
76-
6. In trend
tone pattern
124, neither of supplemental context pixels
76-
5
and
76-
6 has the same tone as either of respective context pixels
76-
4 and
76-
2, thereby corresponding to no trends.
In trend tone pattern
126, supplemental context pixel
76-
5
has the same tone context pixel
76-
4, but pixels
76-
6
and
76-
2 differ from each other, thereby corresponding only to a
horizontal trend. In trend tone pattern
128, supplemental context pixel
76-
6 has the same tone context pixel
76-
2, but pixels
76-
5 and
76-
4 differ from each other, thereby corresponding
only to a vertical trend. In trend tone pattern
130, both of supplemental
context pixels
76-
5 and
76-
6 have the same tones as
respective context pixels
76-
4 and
76-
2, thereby corresponding
to both horizontal and vertical trends.
The presence or absence of horizontal or vertical trends classifies each pattern
into another four trend states
124-
130. In combination the fifteen
possible states or patterns of basic context region
74, the six context
pixels
76-
1 through
76-
6 can represent a total of sixty
states into which the overall context region can be classified.
Process block
132 indicates that a trend state is assigned to context
region
62.
FIG. 10 is a flow diagram of an entropy coding method
150 employed in
one implementation of the present invention.
Process block
152 indicates that method
150 is initialized
that a first current pixel
54 is designated.
Process block
154 indicates that a context region
62 is classified
into a selected state by, for example, state determination method
70.
Process block
156 indicates that each of the unique values of the
pixels or elements in the context region
62 is indexed, as known in the
art of entropy coding.
Inquiry block
158 represents an inquiry as to whether current element
54 has a value equal to that of a previously indexed pixel or element of
the selected state. Inquiry block
158 proceeds to process block
160
whenever current element
54 has a value equal to that of a previously indexed
pixel or element of the selected state. Inquiry block
158 proceeds to process
block
162 whenever current element
54 has a value that is not equal
to that of a previously indexed pixel or element of the selected state.
Process block
160 indicates that an entropy code symbol corresponding
to the value of the previously indexed element is written, stored, or otherwise sent.
Process block
164 indicates that an estimated probability mass function
for each of the indices in the selected state is updated to reflect the symbol
written in process block
160. As is known in the art of entropy coding,
a probability mass function is maintained for each symbol being encoded. This allows
the entropy coding to be adaptively trained to the statistics of each source, and
sends shorter symbols for the tone indices that are popular for each state. This
adaptation allows the coder to improve its efficiency by using knowledge of previous
patterns in the image to code future similar patterns. Some examples include line
or checkerboard patterns that are quick to learn. Other more complicated phenomena
may include a particular font for text.
Process block
162 indicates that an entropy code symbol is sent or
designated indicating a not-in-context element.
Inquiry block
170 represents an inquiry as to whether current element
54 has a value equal to one maintained in a color cache
172 (FIGS.
11 and 12). Color cache
172 maintains an ordered list of the most recently
used values that were out of context. The ordered list of color cache
172
is different from a conventional list of the most commonly used values, which does
not work as well due to poor local adaptation. Inquiry block
170 proceeds
to process block
174 whenever current element
54 has a value equal
to one maintained in color cache
172. Inquiry block
170 proceeds
to process block
176 whenever current element
54 does not have a
value equal to one maintained in color cache
172.
Process block
174 indicates that the index for the cache entry is
determined, and the symbol for the index is written or stored. The index is determined
by sequentially searching the cache from most recently used values to least recently
used values, ignoring any values that may have already appeared in the tones for
the context.
It will be appreciated that the logical state of cache
172 is a subset
of elements in the physical cache. Since the value being coded was out of context,
it by definition cannot have the same value as any of the tones in the context.
Therefore, any elements in cache
172 that have the same value as any of
the tones are not useful, and are removed from the logical state of cache
172.
The remaining values are indexed and the probability mass function for the indices
are estimated and adapted every time a value is coded out of context.
Process block
178 indicates that color cache
172 and its estimated
probability mass function are updated to reflect the symbol written in process
block
172. As illustrated in FIG. 11, this updating of color cache
172
includes rotating to the top the value of the symbol being written.
Process block
176 indicates that an entropy code symbol is sent or
designated indicating a not-in-cache element.
Process block
180 indicates that the index for a color histogram entry
is determined, and the symbol for the index is written or stored. The color histogram
contains all the possible values for an element and keeps track of the probabilities
of all the out of cache values. This distribution is used to write the symbol for
the out of cache value.
Process block
182 indicates that the color histogram and its estimated
probability mass function are updated to reflect the symbol written in process
block
180. In addition, the symbol value is placed (pushed) at the top of
color cache
172, and the least recently used value drops (pops) out of the
bottom of cache
172 as in a queue (FIG. 12).
Inquiry block
184 represents an inquiry as to whether there is another
element or pixel to be coded. Inquiry block
184 proceeds to process block
186 whenever there is another element or pixel to be coded. Inquiry block
184 proceeds to termination block
188 whenever there is not another
element or pixel to be coded.
Process block
186 indicates that the method advances to the next pixel
or element. Process block
186 returns to process block
154.
Having described and illustrated the principles of our invention with reference
to an illustrated embodiment, it will be recognized that the illustrated embodiment
can be modified in arrangement and detail without departing from such principles.
It should be understood that the programs, processes, or methods described herein
are not related or limited to any particular type of computer apparatus, unless
indicated otherwise. Various types of general purpose or specialized computer apparatus
may be used with or perform operations in accordance with the teachings described
herein. Elements of the illustrated embodiment shown in software may be implemented
in hardware and vice versa.
In view of the many possible embodiments to which the principles of our invention
may be applied, it should be recognized that the detailed embodiments are illustrative
only and should not be taken as limiting the scope of our invention. Rather, we
claim as our invention all such embodiments as may come within the scope and spirit
of the following claims and equivalents thereto.
*
