SYSTEM AND METHOD FOR MINIMIZING BLOCKING ARTIFACTS IN A FILTERED IMAGE

BACKGROUND OF THE INVENTION

1. Field ofthe Invention

The invention relates generally to an improved method and apparatus for digital image processing. More particularly, the invention relates to a novel method and apparatus for removing or at least minimizing blocking artifacts perceptible in a block processed image.

2. Description ofthe Prior Art

A scene can be perceived as some visual reality that is distributed in space and/or time. Ordinarily, a scene is what the human visual system perceives as variations in light-dependent stimuli such as brightness, contrast, color and depth cues.

A scene can be captured by an electronic imaging device and represented as a multi-dimensional digitized image of picture elements, i.e. pixels. The image can be displayed in many different ways, e.g. a photograph, on a computer monitor, etc. The image is composed of various parts which represent scene characteristics. For instance, a color photograph of a scene is typically a collection of red, green, blue and luminance images ofthe same scene.

An image can be electronically processed by segmentation into MxN blocks of pixels, where M and N are preselected integers. This is done to provide compatibility ofthe block sizes with the processing limitations of commercially available chips. For instance, 8x8 blocks conform to international compression standards set by JPEG (Joint Photographic Experts Group) and MPEG (Motion Picture Experts Group).

Block processing is utilized by many known processing routines, such as the one taught in U.S. Patent Application No. 08/440.639 filed May 15, 1995 by the present inventors and others, incoφorated herein by reference. There, a pyramid image representation of the image is segmented into MxN overlapped blocks, and subjected to a variant Wiener filter.

The above and other methods of digital image processing, which are based on block processing, sometimes exhibit visible blocking artifacts due to discontinuities in the block boundaries of a reproduced image. One type of image discontinuity comes from independent processing (e.g. filtering) of each block which causes images that can be visually unpleasant to human observers who tend to see the discontinuities as artificial tiling. The overall quality ofthe observed image drops dramatically.

The blocking artifacts problem can sometimes be adequately dealt with by overlapping adjacent pixel blocks in both the horizontal and vertical directions. For instance, Figure 2 shows a portion of an image containing 144 pixels which is segmented into MxN blocks 200 and 210 where M=N=8. Notice that block 210 overlaps block 200 by 4 pixels in the horizontal direction, i.e. the horizontal overlapping coefficient k_h = 4. Of course, the size of the blocks and the amount of overlap between blocks can be selected to meet whatever design criteria is specified. In this case, filtering of each overlapped block yields a 4x4 section of filtered pixels for each block as shown by the crosshatched regions. The remaining 2 pixel wide perimeter of each 8x8 block is discarded. Further details concerning the overlapping of adjacent pixel blocks is disclosed in U.S. Patent Application No. 08/427,457 filed April 24, 1995 by Wober & Reisch (see particularly Figure 7 and the accompanying text on pages 32-33 which are incoφorated herein by reference).

When each block is processed in a different manner, such as being filtered differently from an adjacent block, the discontinuities evident from independent processing sometimes cannot be overcome by any amount of overlapping. For instance in the variant Wiener filtering method mentioned above, each overlapped block at each pyramid level is independently filtered with one of many predetermined variant Wiener filters, which may result in the appearance of unacceptable blocking artifacts along the borders of adjacent blocks.

U. S. Patent No. 5,454,051 issued 26 September 1995 to Smith discloses a method of reducing blocking artifacts created by block transform compression algorithms by applying a variable lowpass filter (blur) operation on block boundaries that is based on the frequency coefficients of the transformed data. However, several limitations are evident in the Smith method. First, his method is applicable only to unoverlapped blocks. Second, his method processes each side of a block individually. Third, his corrections are determined only in the frequency domain. And fourth, his method uses a two point filter limited to blurring only boundary pixels.

Consequently, the primary object of the present invention is to overcome the above and other problems by providing an improved method and system for removing or at least minimizing blocking artifacts in an image subsequent to independent processing of each block. This and other objects of the invention will, in part, appear hereinafter and, in part, be obvious when the following detailed description is read in conjunction with the drawings.

SUMMARY OF THE INVENTION

In order to prevent or minimize blocking artifacts from appearing in an image due to independent processing of each overlapped block of an image by one of many different filters, true pixel correction values are calculated, then added to each pixel of the image so that the transition between adjacent blocks of pixels will be smooth. This corrective method coined "stitching" can be applied in either the spatial or the frequency domain to each block of filtered pixels in the image and generally includes the steps of:

(i) choosing measurement points within a given block, so that the measurement points reside in areas overlapped by adjacent blocks and are situated in between pixels which have been saved (i.e. the saved region) and pixels which have been discarded during filtering;

(ii) determining measurement point values at each measurement point by pixel measurement or approximation from neighboring pixels, as necessary;

(iii) calculating measurement point correction values which will be non¬ zero when the measurement points are situated between pixels;

(iv) calculating true pixel correction values for pixels situated in the saved region by inteφolating between the measurement point correction values; and

(v) modifying pixel values within the saved region in accordance with the true pixel correction values, respectively.

BRIEF DESCRIPTION OF THE DRAWINGS

The aforementioned aspects and other features ofthe invention are described in detail in conjunction with the accompanying drawings in which the same reference numerals are used throughout for denoting corresponding elements and wherein:

Figure IA is a block diagram of a first variation preferred embodiment of the inventive method applied to a system using variant Wiener noise filtering;

Figure 1 B is a block diagram of a second variation preferred embodiment of the inventive method applied to a system using variant Wiener noise filtering;

Figure 2 is a diagrammatic representation of two overlapped 8x8 blocks of image data;

Figure 3 is a graphical representation of a sixteen point one-dimensional segment of an image;

Figure 4A is a graphical representation of the sixteen point one-dimensional segment of Figure 3 broken into three 8-point blocks with a four point overlap;

Figure 4B is a graphical representation of the measurement point correction values δ and true pixel correction values σ featured in an 8 point image segment;

Figure 5 is a diagrammatic representation showing the saved and discarded regions of an 8x8 pixel block 11 in a 16x16 pixel image segment;

Figure 6 is a diagrammatic representation of all of the 8x8 pixel blocks which overlap block 11 in the image segment of Figure 5;

Figures 7A, 7B and 7C illustrate horizontal overlapping of blocks from Figure 6;

Figures 8A, 8B and 8C illustrate vertical overlapping of blocks from Figure 6;

Figure 9 illustrates overlapping of all the blocks of Figure 6 in both the horizontal and vertical directions; Figure 10 is an expansion of the drawing of Figure 5 showing the selected locations used with the inventive method;

Figure 1 1 is a graphical representation of the measurement point correction values δ and the true pixel correction values σ featured in an 8x8 point image segment labeled block 1 1 ;

Figure 12A is an illustration of a general puφose computer used to implement the inventive stitching method of Figures IA and IB programmed therein; and

Figure 12B is a block diagram of selected parts of the system of Figure 12A necessary to implement the stitching method.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following description is provided to enable any person of ordinary skill in the art of digital image processing to make and use the present invention. It sets forth the best modes contemplated by the inventors for carrying out their invention. Various modifications, however, will remain readily apparent to those skilled in the art in keeping with the scope ofthe invention as claimed.

In both the following one-dimensional and two-dimensional preferred embodiments, the inventive stitching method is applied to blocks of pixels which have been subjected to the variant Wiener filtering of U. S. Patent Application No. 08/440,639 as shown in Figure 1. The inventive stitching method eliminates or at least minimizes blocking artifacts which occurs from independent processing of each block in an image. The following examples in one and two dimensions could readily be applied by those skilled in the art to any number of dimensions in any system or method which causes or exacerbates blocking artifacts due to independent processing of blocks.

Following Figure IA, a one-dimensional image, such as the 16 point segment shown in Figure 3, is captured and digitized in step 100. The image is then saved and segmented into MxN blocks of pixels in step 102 where M=8 and N=l . Adjacent pixel blocks are horizontally overlapped according to the predetermined overlapping coefficient k =4 in step 104. The amount of overlap is determined to meet desired visual effects. Since the image blocks of interest are one-dimensional, the vertical overlapping coefficient k_v =0. Block 0 consists of points 0-7, block 1 consists of points 4-1 1, and block 2 consists of points 8-15. The overlapped region between blocks 0 and 1 consists of points 4, 5, 6 and 7; and the overlapped region between blocks 1 and 2 consists of points 8, 9, 10 and 1 1.

MxN blocks of discrete cosine transform (DCT) coefficients corresponding to the MxN blocks of pixels are generated in step 106 by performing a DCT on the overlapped blocks of pixels.

Variant Wiener filtering of each block of DCT coefficients is performed in step 108 to generate corresponding blocks of filtered DCT coefficients. Further details of the variant Wiener filtering method are outlined in the inventors' earlier filed U.S. Patent Application No. 08/440,639 incoφorated herein by reference in its entirety. Of course, the use of a variant Wiener filter is illustrated only as one preferred embodiment. It is not necessary in the operation of the inventive stitching method. Any independently filtered blocks of image data resident in either the spatial or frequency domain can be input into the inventive stitching routine 125.

Continuing with the example of Figure IA, the next step in the variant Wiener filtering method is to generate inverse discrete cosine transform (IDCT) coefficients in block 1 10 by taking an IDCT of the blocks of filtered DCT coefficients, then saving selected portions of the inverted blocks, i.e. the saved region, corresponding to the pixels which have been filtered. Use of a pruned scaled IDCT eliminates redundant terms introduced by the overlapping procedure and correspondingly reduces the computational resources required for derivation of a filtered image data matrix. The details concerning the operation and application of the pruned scaled IDCT are incoφorated herein by reference as described in U. S. Patent Application No. 08/441,383 filed May 15, 1995 by Hajjahmad and Wober. The saved IDCT coefficients are then sent to a display or other output device for reproduction of the original image which has been filtered. However as earlier noted, the reproduced image could possibly exhibit blocking artifacts due to the independent application in the variant Wiener filtering method of various filters to the many blocks of the segmented image.

As will be explained in more detail to follow, the above problem concerning blocking artifacts is overcome according to the inventive stitching method by calculating, then adding a true pixel correction value to each pixel in the image so that the transition between adjacent overlapped blocks of image data will be smooth. Stitching is applied to each block of filtered image data in the image and generally includes the steps of:

(i) choosing measurement points within a given block, so that the measurement points reside in areas overlapped by adjacent blocks and are situated in between pixels which have been saved in the saved region and pixels which have been discarded during filtering;

(ii) determining measurement point values at each measurement point by pixel measurement or approximation from neighboring pixels, as necessary;

(iii) calculating measurement point correction values which will be non¬ zero when the measurement points are situated between pixels;

(iv) calculating true pixel correction values for pixels situated in the saved region by inteφolating between the measurement point correction values; and

(v) modifying pixel values within the saved region in accordance with the true pixel correction values, respectively.

The stitching routine 125 begins in step 112 where measurement points are chosen according to the amount of overlap desired. In the current example a horizontal overlapping coefficient of k_h = 4 is used for 8 point blocks as shown in Figures 3, 4 A and 4B. The blocks have been previously filtered, saving the central four pixels and discarding a two pixel wide perimeter for each block. An ideal measurement point would fall between the saved and discarded pixels. Since pixels 6, 7, 8 and 9 are saved in block 1 and pixels 4, 5, 10 and 1 1 are discarded, ideal measurement points m₀=5.5 and mι=9.5 are chosen as shown in Figure 3.

Actually, the measurement points are defined as preselected points within a block where measurement point correction values will be determined. In rare cases, the measurement point may be chosen to fall on a pixel, whereupon measurement point values can be directly measured. More typically, however, the measurement points are chosen to fall between pixels so that the measurement point values are determined by approximation from neighboring pixels using any known approximation method (such as bilinear inteφolation of neighboring pixel values).

At each measurement point mo and m/ two calculations are made in step 1 14 - one calculation for each block overlapping each measurement point. Block 0 overlaps block 1 at points 4, 5, 6, 7 and block 2 overlaps block 1 at 8, 9, 10, 1 1. Corresponding to measurement point mo is mo_a in block 0 and mob in block 1. Corresponding to measurement point mi is m_ia in block 1 and m\b in block 2. The measurement points for the stitching method must be chosen to be conterminous between adjacent blocks. In the present case, measurement point m is located at 5.5 for both blocks 0 and 1 and measurement point m is located at 9.5 for both blocks 1 and 2. Each calculation of a measurement point value can generally be made by either direct measurement, if the measurement point is chosen on a pixel, or by inteφolation or other known estimation techniques if the measurement point is chosen to fall between pixels. In this case, since measurement point m has been chosen between pixels at 5.5, then the measurement point value mo_a corresponding to block 0 along line Lo can be determined by inteφolation from neighboring pixels, such as pixels 5 and 6 in block 0. The measurement point value mo_b corresponding to block 1 along line L₀ is similarly determined by inteφolating values of pixels 5 and 6 in block 1. In a like fashion along line Li, a measurement point value mι_α is determined corresponding to block 1 , and a measurement point value m_7f, is determined corresponding to block 2. Similar calculations occur for each block ofthe image.

The accumulation of measurement point values throughout the image can be arranged in corresponding arrays \ m_α\ and I /M for this one-dimensional example where the array of mean values

\m..\ + \m_h

M (1)

where \

_a) and b\

_b) are next calculated in step 1 16 for each measurement point mo, mi and stored in arrays so that I δ(mo

_a) I = I M I - 1 mo

_a I and I δ(mø,) I = I Mo I - 1 mo

_b I ■ When processing block 1 , δ(mo

_a) represents the measurement point correction value associated with block 0 at mo; and δ(

_b) represents the measurement point correction value associated with block 1 at mo (see Figures 4A and 4B). Similarly, δ(m

_/a) represents the measurement point correction value associated with block 1 at m , and represents the measurement point correction value associated with block 2 at my. Note that in order to produce symmetrical correction values from each block, (mι

_a) and h(mι

_h) relating to a particular measurement point have equal magnitude and opposite signs. In the same manner as described above for block 0, the measurement point correction values b(m

_0b) and δ(m

_/fl) associated with block 1 , are shown in Figure 4B at measurement points m = 5.5 and m/ = 9.5, respectively.

If two measurement point values of adjacent blocks along a same line (e.g. mι_a and mn, along Lj as shown in Figure 4A) are identical or very close in value, then no discontinuity is evident between the blocks and it is easy to show that the corresponding measurement point correction values δ(m_a) and δ(/w/j) will be zero or very close to zero. Logically, if the two measurement point values are disparate, it is likely that a block discontinuity exists between the two adjacent blocks (in this case block 0 and block 1), resulting in the absolute value of one or both ofthe measurement point correction values (m_a) , δ(/Wi) being substantially greater than zero.

Once the measurement point correction values δ(m_&,), δ\^m _b), δ(m_/a) and are determined during processing, then a second set of correction values, termed the true pixel correction values, can be determined from inteφolation of the measurement point correction values for each pixel location in the saved region, i.e. pixel locations 6, 7, 8 and 9. The true pixel correction values are designated as σ(/) and are calculated in step 1 18, / being an integer ranging from 6 to 9. In the preferred method, the true pixel correction values σ( ) are calculated for the pixels in the saved region (in this case, for i = 6, 7, 8 and 9), and the other pixels within the block are discarded. However, true pixel correction values at every pixel in a block can be calculated if desired. In Figure 4B the true pixel correction values σ(z^'), for pixels located within the saved region of block 1 , are estimated by inteφolation from the surrounding measurement point correction values δ(mo_b) and δ(/wy_a). Any known inteφolation method can be applied. Once the true pixel correction values σ(z^') have been determined for each pixel of interest, then the true pixel correction values σ(z^') are added in step 120 to the respective IDCT coefficients which have been determined and saved in step 110. In other words, the true pixel correction values σ(z^') for ι ^' = 6 to 9 are added, respectively, to pixel locations 6, 7, 8 and 9 in step 120 to provide adjusted pixel values which will provide a smooth transition between adjacent blocks in the image, thus emancipating the image of blocking artifacts, without compromising the integrity ofthe image. When this procedure is carried out on every block ofthe image, the resulting output from step 120 is a final set of pixels which represents the filtered image free from blocking artifacts.

It should be noted that the above described steps of the stitching method are equally applicable to processing correction values in the frequency domain. Figure 1 B is identical to Figure IA except that in Figure IB the stitching routine is applied in the DCT domain, and the IDCT step 124 converts the results back into the spatial domain.

The above-described one-dimensional application of stitching can also be readily extended towards removing blocking artifacts in multiple dimensions. The following example of a preferred stitching method is applied to the 16x16 pixel image segment that is shown in Figure 5. The one-dimensional image segment (block 1 as shown in Figure 4 and described in the above example) is replaced with the two- dimensional image segment block 1 1 shown in Figure 5. The saved region of pixels {6, 7, 8, 9} in the one-dimensional example is replaced in the two-dimensional example with a saved region where both x and y are evaluated at integer pixel values of {6, 7, 8, 9}.

Block 1 1 will be overlapped during the filtering process of step 108 (see Figure 1) in each direction by adjacent 8x8 blocks of pixels. The breakdown of all the blocks involved in the processing of block 11 is shown in Figure 6. Each one of blocks 00, 10, 20, 01, 21, 02, 12, and 22 will overlap block 11. In this example, the horizontal and vertical overlap are equal so that the horizontal overlapping coefficient k equals the vertical overlapping coefficient k_v, i.e. kh = k_v = 4. The overlap of block 00 occurs at pixels x = {4, 5, 6, 7} and y = {4, 5, 6, 7}. The overlap of block 10 occurs at pixels x = {4, 5, 6, 7, 8, 9, 10, 1 1 } and y = {4, 5, 6, 7}. The overlap of block 20 occurs at pixels x = {8, 9, 10, 1 1 } and y = {4, 5, 6, 7}. The overlap of block 01 occurs at pixels x = {4, 5, 6, 7} and y = {4, 5, 6, 7, 8, 9, 10, 1 1 }. The overlap of block 21 occurs at x = {8, 9, 10, 11 } and y = {4, 5, 6, 7, 8, 9, 10, 1 1 }. The overlap of block 02 occurs at x = {4, 5, 6, 7} and y = {8, 9, 10, 11 }. The overlap of block 12 occurs at x = {4, 5, 6, 7, 8, 9, 10, 11 } and y = {8, 9, 10, 1 1 }. The overlap of block 22 occurs at x = {8, 9, 10, 1 1 } and y = {8, 9, 10, 11 }.

Figures 7A-7C illustrate the horizontal overlapping involved in the current example whereas Figures 8A-8C illustrate the vertical overlapping. Figure 7A shows the horizontal overlapping of blocks 00, 10 and 20; Figure 7B shows the horizontal overlapping of blocks 01,1 1 and 21 ; and Figure 7C shows the horizontal overlapping of blocks 02, 12 and 22. Figure 8A shows the vertical overlapping of blocks 00, 01 and 02; Figure 8B shows the vertical overlapping of blocks 10,1 1 and 12; and Figure 8C shows the vertical overlapping of blocks 20, 21 and 22.

The complete overlapping scheme relating to block 1 1 is shown in Figure 9. Note that the pixels located in the saved region are indicated by Xs. After processing is finished for block 11, the pixels in the saved region may be modified (i.e. corrected) to prevent blocking artifacts. The modification of these pixels will be explained hereafter.

Again turning to Figure IA, the stitching method 125 begins in step 1 12 where measurement points are chosen according to the amount of overlap desired. In the current two-dimensional example, the horizontal and vertical overlap are equal so that k = k_v = 4. Of the 64 points in block 11, the central 16 points located at x = {6, 7, 8, 9} and y = {6, 7, 8, 9} will be saved. The two pixel wide perimeter of image data points will be discarded, i.e. points within block 1 1 that are not included within the saved region. As in the one-dimensional example, measurement points are chosen so that the corrections to measurement point values can be used to estimate the true pixel correction values corresponding to each pixel within the saved region. In this case (see Figure 10), measurement point mi is chosen at {Lo, L = {5.5, 5.5}; measurement point m₂ is chosen at {Li, E?} = {9.5, 5.5}; measurement point ms is chosen at {Lo, L₃}={5.5, 9.5}; and measurement point m₄ is chosen at {L/, Li) = {9.5, 9.5} .

At each measurement point m , m₂, m₃ and m₄, four measurement point values are determined - one corresponding to each overlapped block having a common measurement point. This is due to the fact that four separate pixel blocks overlap each measurement point as can be determined from Figure 9. Measurement point ; falls within the overlapped region of blocks 00, 10, 01 and 1 1 ; m₂ falls within the overlapped region of blocks 10, 20, 1 1 and 21 ; m falls within the overlapped region of blocks 01, 1 1, 02 and 12; and ni₄ falls within the overlapped region of blocks 1 1, 21, 12 and 22.

At measurement point m , four measurement point values my_α, m_/ , _/c and m^ are determined from the intersection of my with overlapped blocks 00, 10, 01 and 11, respectively, whereby the mean value at m is represented as My. In other words,

_{Mι =} m_lπ ÷ m_{lfc +} m_{u +} m„ ₍₂₎

Similarly for measurement point m₂, the mean value ? = (m_2a + m₂b + m_2c + m _i )/4; for measurement point m₃, the mean value M₃ = (m_3a + m₃h + m_3c + m_3a)I ; and for measurement point m₄, the mean value M4 = (m_4a ⁺ ni4b + rn_4c + m_4d)/4. The four measurement point values each relate to one of the four overlapping 8x8 pixel blocks which affects that particular measurement point. Thus, for example, the mean value Mi considers the effect of blocks 00, 10, 01 and 1 1 at measurement point mι={L , I₂} (see Figures 9 and 10). Measurement point values are determined for all adjacent overlapping blocks at measurement points throughout the image.

The accumulation of measurement point values from all the blocks in the image can be arranged in corresponding arrays I m_a\ , I mj , I mj and I j where, for example, the array of mean values of all measurement points y is represented as:

_/ , I myj and I yj are the arrays of all measurement point values relating to mi and I I is the array of all the mean values. Measurement point correction values δ

_a, δ

_b, δ

_c and δa are next calculated in step 1 16 for each corresponding measurement point value m

_a, m^ m

_c, m

_<y, respectively, at each measurement point.

The four measurement point correction values at mι={L₀, L₂) are determined as

The measurement point correction values at m₂ = {Li, L ), m₃ = {L₀, L₃) and m₄ = {Li, L₃) are similarly calculated. Of course, the above measurement point correction values of equations (4) through (7) can readily be written in matrix notation as understood by those skilled in the art.

After the various measurement point correction values (i.e. the δ values) have been calculated, the true pixel correction values σ(i,j) corresponding to the pixels in the saved region of block 11 can be determined in step 3 18 by inteφolation of the known measurement point correction values of equations (4) through (7). This is illustrated in Figure 1 1 for block 11 where δi, δ , δ , and δ are evaluated as previously described at measurement points mi, m₂, m₃ and m₄, respectively, and the true pixel correction values σ(i,j) are evaluated for each pixel location in the saved region, i.e. at / = {6, 7, 8, 9} and j = {6, 7, 8, 9}. The true pixel correction values for each pixel in the saved region (marked by Xs) of block 11 , are evaluated in a like manner as earlier described for the one-dimensional example. These true pixel correction values o(i,j) are, respectively, added in step 120 to the IDCT coefficients of pixels in the saved region so that the processed image can be viewed or otherwise displayed without any blocking artifacts.

As earlier mentioned, the inventive stitching method for removing or at least minimizing blocking artifacts in a filtered image can occur in either the spatial or the frequency domain. Specifically, the inputs and the outputs for processing can reside in either the spatial or frequency domain. For instance, a spatial domain input can result in either a spatial or frequency domain output, and a frequency domain input can also result in either a spatial or frequency domain output.

The size ofthe blocks, the amount of overlap between adjacent blocks, and the indexing of pixels within the blocks can all be varied to conform with acceptable design and application requirements. For instance, the four selected locations of measurement points for the above two-dimensional example can be universally translated to apply to any 8x8 block in the image where mi = { 1.5, 1.5}, m₂ = {5.5, 1.5}, m ^~ { 1.5, 5.5}, and m₄ = {5.5, 5.5}, given x and y evaluated at integer values from 0 to 7 for each block.

One workable system for implementing the above stitching method is a general puφose computer 310 as shown in Figure 12A. Selected parts of the computer 310, necessary for programming the stitching method into the computer, are shown in Figure 12B to include: means for determining measurement point values 300; means for determining mean values 302; means for determining measurement point correction values 304; means for determining true pixel correction values 306; and means for adjusting true pixel values 308. The determination of measurement points can be made manually, by operator input, or automatically according to software requirements for a specific application. Each of the components shown in Figure 12B could, for instance, be resident in the central processing unit ofthe computer.

It is to be understood that the above described embodiments are merely illustrative of the present invention and represent a limited number of the possible specific embodiments that can provide applications of the principles of the invention. Numerous and varied other arrangements may be readily devised in accordance with these principles by those skilled in the art without departing from the spirit and scope ofthe invention as claimed.