Interpolation table with logarithmically distributed entries

Abstract

A system and method for correcting pixel intensities for output on a video display is disclosed. In one embodiment, the method includes the operation of generating an interpolation table having a plurality of interpolation segment endpoints spaced over a transfer function correction curve. The plurality of interpolation segment end points are distributed logarithmically over the transfer function correction curve to increase a number of correction points along a curved portion of the transfer function correction curve without substantially increasing a total number of correction points over the entire curve. Correction values for a graphic display can be determined by interpolating between the logarithmically distributed interpolation segment endpoints.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

Additional features and advantages of the invention will be apparent from the detailed description which follows, taken in conjunction with the accompanying drawings, which together illustrate, by way of example, features of the invention; and, wherein:

FIG. 1 is a diagram of RGB color space defined by a Cartesian cube;

FIG. 2 is a diagram of a typical gamma curve for a cathode ray tube and the inverse gamma correction curve;

FIG. 3 is a diagram of a transfer function correction curve showing straight line approximations;

FIG. 4 is flow chart depicting a method for correcting pixel intensities for output on a video display in accordance with an embodiment of the present invention;

FIG. 5 is a diagram of a transfer function correction curve divided into a plurality of logarithmically distributed levels in accordance with an embodiment of the present invention;

FIG. 6 is a diagram of a transfer function correction curve having plurality of interpolation segment endpoints 604 distributed logarithmically along the curve in accordance with an embodiment of the present invention; and

FIG. 7 a is an illustration of an implementation of a system for correcting pixel intensities for output on a video display that involves logarithmically distributing interpolation table endpoints along a transfer function correction curve in accordance with an embodiment of the present invention.

FIG. 7 b is a continuation of the illustration in FIG. 7a.

Reference will now be made to the exemplary embodiments illustrated, and specific language will be used herein to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENT(S)

In one embodiment of the present invention, an interpolation table can be implemented in place of a lookup table. Instead of storing a correction value for each pixel intensity, as is done in a lookup table, a correction curve can be divided into a series of segments 508, as shown in the transfer function correction curve 504 in FIG. 5. An interpolation table includes a plurality of interpolation segment endpoints. Each of the interpolation table entries can be identified as an endpoint (or starting point) for a segment along the curve.

Depending on the desired resolution, each curve segment 508 can represent correction values for tens or hundreds of pixel intensities. A second input can include a proportion value. The proportion value can represent a distance through the segment. The proportion value can then be used to estimate a location along the segment curve between the two interpolation table entries (endpoints). The use of an interpolation table substantially reduces the number of stored entries used to obtain a substantially accurate representation of a curve.

However, both the shape of the curve and the resolution of the intensity step size can limit the accuracy of an interpolation table. As an exponential curve approaches an asymptotical limit, the amount of curvature can significantly increase. The increased curvature can reduce the accuracy of an interpolation table for straight line approximations near the increased curvature. Reducing the size of the straight line approximation (increasing the number of interpolation segments) can increase the accuracy. However, zooming in on an asymptotic type curve to display the curve in greater detail can emphasize the amount of curvature as the curve gets ever closer to its asymptotical limit.

For example, a transfer function correction curve 304 is shown in FIG. 3. Straight line approximations 308 having a length of 0.001 are also shown. As the curve approaches zero, the amount of curvature, or slope, of the line approaches infinity. Zooming in on the curve only increases the amount of curvature or slope. As can be seen, the last straight line approximation 312 has a significant discrepancy from the actual curve.

Additionally, adding enough interpolation segment endpoints in a table to provide reasonably accurate straight line approximations near an asymptote or other large curvatures having a large amount of slope can be a waste of memory for approximations of straighter areas of the curve having a smaller amount of slope, as seen on the right side of FIG. 3. In one embodiment, the present invention provides a solution to this problem by distributing the interpolation segment endpoints along the curve logarithmically. Logarithmic distribution of interpolation endpoints allows an interpolation table to be used instead of the vastly larger lookup tables, while minimizing error near asymptotes and other highly curved areas and reducing the number of points used in less curved portions of the overall correction curve.

In one embodiment, a method for correcting pixel intensities for output on a video display is depicted in the flow chart in FIG. 4. The method includes the operation of generating an interpolation table having a plurality of interpolation segment endpoints spaced over a transfer function correction curve, as shown in block 410. The number of interpolation segment endpoints in the interpolation table is related to the desired accuracy of the approximations made between the endpoints.

An additional operation provides distributing the plurality of interpolation segment end points logarithmically over the correction transfer function curve to enable a higher resolution on a first portion of the correction transfer function curve having a greater amount of slope relative to a second portion of the correction transfer function curve having a smaller amount of slope, as shown in block 420. The resolution on the first portion can be exponentially higher than the resolution on the second portion of the curve due to the logarithmic distribution of the interpolation segment endpoints.

Another operation includes determining correction values for a graphic display by interpolating between the logarithmically distributed interpolation segment endpoints, as shown in block 430. As previously stated, an additional input value can include a proportion value that can represent a distance through the segment. The proportion value can then be used to estimate a location along the segment curve between the two interpolation table entries (endpoints). In one embodiment, an interpolation table can include two different types of entries, the interpolation segment endpoints representing locations along the correction curve and segment offset values associated with each of the segment endpoints. The segment offset values can represent a distance between two interpolation segment endpoints. The proportion value can then be multiplied by the segment offset value to provide a relative offset that is a substantially accurate interpolation between two segment endpoints for a specific pixel intensity value.

The interpolation segment endpoints can be logarithmically distributed along the correction curve using a variety of mathematical or graphical techniques. In one embodiment, a desired correction curve similar to those shown in FIGS. 2 and 3, can be divided into 2^N levels, wherein N is the number of bits of accuracy of a pixel intensity value. For example, a system may employ sixteen bit accuracy for a gray scale to allow for 2¹⁶, or 65, 536 different shades of gray. A color system may use sixteen bit accuracy for each of the RGB colors, allowing for 65,536 different shades each of red, green, and blue to be displayed. The desired level of pixel intensity accuracy can be dependent on a number of factors such as desired number of colors, size of color gamut, resolution of the display, and so forth. Having an increased pixel intensity accuracy enables the display to have a substantially continuous variation in intensity and/or color across the display. The substantially continuous variation limits perceived boundaries between similar areas and reduces anomalies such as banding.

For a sixteen bit system, the correction curve can be divided into 65,536 pixel correction values, with each correction value representing a correction for pixel intensity. The curve can then be divided into a predetermined number of evenly spaced interpolation segments. For example, the curve can be divided into 16 segments, though any number of segments may be used, depending on the desired accuracy. Each segment endpoint is assigned a value that is proportional or equal to an x axis value of a pixel correction value on the correction curve.

The correction curve representing 2^N pixel correction values can then be divided into 2^p additional segments, where p is an integer. In one example embodiment, p can be set equal to 1 to divide the correction curve in half. The number of segments in the half of the curve having the greater amount of curvature (greater amount of slope) can be increased by 2^p times, or 2 times in this example to provide for 16 segments. The 16 segment half of the correction curve can then be divided again and the number of segments in the half with the greatest amount of slope can again be multiplied by 2^p times. The division of the curve into 2^p pieces and multiplication of the segments by 2^p can be repeated until a desired level of accuracy is provided on the maximally curved section of the correction curve. In other words, the curve can be divided in this manner until the desired resolution is reached in the maximally curved section of the correction curve.

Following is an example interpolation table of a correction curve divided into seven levels with each level divided evenly into eight segments, with the final level having 16 segments. The hexadecimal values in this example are the values for the correction curve along the x axis (in hexadecimal) for the pixel correction value. The y axis value along the curve could then be determined based on the interpolated x axis value. The (decimal) number of pixel correction values between each segment is shown in the column on the right.

0000	0040	0080	00C0	0100	0140	0180	01C0	Level	Δ 64
								7
0200	0240	0280	02C0	0300	0340	0380	03C0	Level	Δ 64
								7
0400	0480	0500	0580	0600	0680	0700	0780	Level	Δ 128
								6
0800	0900	0A00	0B00	0C00	0D00	0E00	0F00	Level	Δ 256
								5
1000	1200	1400	1600	1800	1A00	1C00	1E00	Level	Δ 512
								4
2000	2400	2800	2C00	3000	3400	3800	3C00	Level	Δ 1024
								3
4000	4800	5000	5800	6000	6800	7000	7800	Level	Δ 2048
								2
8000	9000	A000	B000	C000	D000	E000	F000	Level	Δ 4096
								1

Thus, the eight interpolation points in Level 1 of this example each have 4096 pixel correction values between the interpolation segment endpoints. There are 2048 pixel correction values between each interpolation segment endpoint in Level 2, 1024 pixel correction values between endpoints in Level 3, and so forth, until Level 7, which represents the portion of the correction curve with the greatest amount of curvature. Level 7 includes 16 interpolation segment endpoints with only 64 pixel correction values between each endpoint.

FIG. 5 shows a correction curve divided into 7 levels as previously described. Level 1, encompassing the right half of the curve having the least amount of slope, includes half of the 65,536 pixel correction values. With eight interpolation segment endpoints within Level 1, there are 4096 pixel correction values between each segment endpoint. The next level contains half of the previous level, and so forth, until Level 7, which includes 16 interpolation segment endpoints divided among 1024 pixel correction values, or 64 values between each segment endpoint. It should be noted that Level 7, having a portion of the correction curve with the greatest amount of slope, has an exponentially greater amount of resolution than Level 1. Specifically, Level 7 has 64 values per segment endpoint while Level 1, having a portion of the correction curve with the smallest amount of slope, has 4096 pixel correction values between each segment endpoint. In other words, Level 7 has 26 times greater resolution than Level 1.

A correction value for any of the 65,536 pixel intensities can be determined using the interpolation table. For example, a correction value for pixel intensity 27,000 (hexadecimal 6,978) can be determined by interpolating in Level 2 between the 7000 segment endpoint and the 6800 segment endpoint. It can also be determined that pixel intensity 27,000 is 1,672 pixel intensities below the 7000 segment and 376 pixel intensities above the 6800 segment. This knowledge can be used to determine an offset value of the segment that will be interpolated to enable more accurate interpolation between the two segments to better determine a correction value using the interpolation table. This will be discussed more fully below.

FIG. 6 shows a normalized plot of a transfer function correction curve 602 having a plurality of interpolation segment endpoints 604 distributed logarithmically along the curve. As previously discussed, the interpolation segment endpoints are evenly distributed among each of the seven logarithmically distributed levels, with each of the seven levels having half the width of the previous level. Of course, this is only one method for logarithmically distributing the interpolation segment endpoints. Other methods include logarithmically distributing each endpoint within each of the seven segments (instead of evenly distributing the endpoints within the levels), and logarithmically distributing the endpoints over the entire curve without breaking the curve into a plurality of levels. However, dividing the curve into levels provides certain advantages to implementing the interpolation in hardware and/or software, as will be discussed more fully below.

In one embodiment, a procedure has been devised for processing a pixel intensity input value to determine between which interpolation segment endpoints on a transfer function correction curve the pixel correction value is located and a proportion value that can be used to calculate the output value by interpolating between the endpoints. The process can be divided into five steps, as follows:

• • 1) Determine the interpolation table level;
  • 2) Shift the input value a level specific amount to determine the Level Offset and Proportion;
  • 3) Determine the Level Base as a function of the interpolation table level from step 1;
  • 4) Determine the interpolation segment address as a function of the Level Base from step 3 and the level offset from step 2; and
  • 5) Complete the Interpolation.

The first step is to determine which level of the interpolation table is being used. For example, it must be determined in which of the seven levels of the curve shown in FIG. 5 that the pixel intensity will be located. This can be done in several different ways which include, but are not limited to: 1) using a table lookup, 2) counting leading non-significant zero bits, and 3) comparing input values to level boundary values (i.e. the values 0400, 0800, 1000, 2000, 4000, 8000 from the table above).

The second step is to process the input value in order to determine the proportion and level offset needed to complete the interpolation. This can be accomplished by shifting the input value left a level specific amount. In one embodiment, this can be accomplished by shifting a binary input value by an amount equal to the level (determined in step 1)−1 bits. So a pixel intensity that is determined to be in Level 4 of the curve would have its input value shifted to the left by 4−1 bits, or 3 bits. This operation does not discard any significant bits and it aligns the remaining significant bits so they can be divided into two fields referred to as the level offset field and the proportion field.

In the example embodiment above, the initial number space was divided into 16 interpolation segment endpoints, or 2⁴ segments. The four high bits can be used as the level offset value while the remaining lower order bits can be the proportion value. The proportion value, with a radix point assumed to be left of its high order bit, is one of the values that can be used to determine the interpolation amount.

The third step is to determine the Level Base value. Note that in the example above the interpolation table was divided into seven levels. An index to the interpolation table can be calculated as the level base plus the level offset, or (((Total number of Levels−Selected Level)*8)+level offset). As such, the Level Base is represented by the equation ((Total number of Levels−Selected Level)*8). Since the level base resolves to a constant value proportional to one of the number of levels, the Level Base value can be implemented by using the Level (the signal from step 1) to select the appropriate constant.

The fourth step is to determine the interpolation table segment entry by adding the Level Offset from step two and the Level Base from step 3.

The fifth step is to complete the interpolation by multiplying the proportion from step two by the segment offset value and then adding the result to the segment base value to form the output value. The segment offset and segment base values for this step are retrieved from the interpolation table based on the segment entry determined in step four.

FIGS. 7 a and 7b are a diagram of one possible implementation of a system for correcting pixel intensities for output on a video display that involves logarithmically distributing interpolation table endpoints along a transfer function correction curve. The diagram is divided into 5 blocks over FIGS. 7a and 7b.

In block 1 in FIG. 7a, an input value can be received. The input value can be configured to enable a pixel correction value to be determined along the transfer function correction curve for any of 2ⁿ pixel intensities. The input value can be a 16 bit value in this example, though any resolution sufficient to obtain desired results interpolating along the transfer function curve can be used. In one example embodiment, the input value can be 5,615 in decimal or 15ef in hex (15efh). Translated to binary, this value is 0001 0101 1110 1111. Bits 15-13 are zero and bit 12 is a one. Translating the logic shown in block 1, it can be seen that Level 4 will be true and all other levels will be false.

As previously stated in step two above, the input value is shifted to the left by an amount equal to the level−1 bits, or 4−1=3 bits. This gives a value of 1010 1111 0111 1000. In block 2 in FIG. 7a the input value is then separated into a level offset value comprising bits 12-15 and a proportion value comprising bits 0-11. The 12 bit proportion value is then shifted to the left and padded by 4 zeros to form a proportion value of 1111 0111 1000 000 (0f780h) and a Level Offset value of 1010 (0ah).

In block 3, as shown in FIG. 7b, it is known that Level 4 has been selected. The Level 4 signal is again used to select one of seven constants which represent the value which would be computed by the equation ((Total number of Levels−Selected Level)*8). In this example, there are 7 total levels and level 4 has been selected, so the output is 24 decimal, or 18 hex. Therefore, Level Base becomes 18h when Level 4 is true.

In block 4, as shown in FIG. 7b the Level Offset value (0ah) from block 2 in FIG. 7a is then added to the Level Base value (18h) to produce the interpolation table address of 22 hex or 34 decimal.

In block 5, as shown in FIG. 7b, the interpolation table address is used to locate an entry in the interpolation table 704 having logarithmically distributed entries. For example, as previously shown in the table above, and in FIG. 6, the interpolation table can include logarithmically distributed entries representing the interpolation segment endpoints. As in the previously presented example, with 6 levels having 8 segments each, and a seventh level having 16 segments, the table can include 64 entries, with each entry representing a logarithmically distributed segment endpoint, referred to as the Segment Base. Each of the entries can have 16 bits of precision in this example. The actual level of precision can vary from 8 bits to 64 bits, depending on a number of factors as previously discussed. A second section in the interpolation table can include a Segment Offset value, representing a width of each segment base, or the distance between two segment endpoints. The second section can comprise 64 Segment Offset values, with each segment offset value having 16 bits of precision. The Segment Offset values can have the same precision as the Segment base values or a different level of precision. The segment base and associated segment offset values can be accessed using the interpolation table address determined in block 4.

For example, entry 34 in the interpolation lookup table, determined in block 4, may have a Segment Offset value of 2d0h and a Segment Base value of 7b4eh. Interpolation continues by computing the Interpolation Offset value as the Proportion value (0f780h) times the Segment Offset value (2d0h). The result is a 32 bit number. The 16 most significant bits can be selected, in this embodiment, as the Interpolation Offset value of 0000 0010 1011 1000, or 2b8h. The interpolation offset value (2b8h) can then be added to the Segment Base (7b4eh) to produce the resulting interpolation output value of 7e06h (32,262 decimal) on the transfer function correction curve. The pixel correction value can then be applied to the pixel intensity to produce a desired intensity on a display.

The implementation of a system for correcting pixel intensities shown in FIGS. 7a and 7b represents a viable system having sufficient speed that it can be used for real time correction of high resolution video signals. The system is also simple enough that it can be implemented cost effectively in a complex video display device.

For example, a grating light valve (GLV) type display can be used to achieve a video display having a tremendous level of resolution of 32 megapixels or more. The GLV produces images using thousands of ribbons, with each ribbon representing a row in a display. A high end GLV display may include over 4,000 ribbons. Each ribbon can require a separate transfer function to correct for nonlinearities specific to that ribbon in the display system. A transfer function correction system, as shown in FIGS. 7a and 7b, can be implemented in a cost effective manner for each of the ribbons in a GLV. The system(s) and method(s) disclosed enable compensation for nonlinearities in pixel intensity for display devices having relatively high intensity step size resolution. The system can be implemented in any type of display that requires near-real-time correction for non-linear displays used to display high resolution images having high resolution color displays, such as 30, 36, 48 bit or even greater resolution color images.

While the forgoing examples are illustrative of the principles of the present invention in one or more particular applications, it will be apparent to those of ordinary skill in the art that numerous modifications in form, usage and details of implementation can be made without the exercise of inventive faculty, and without departing from the principles and concepts of the invention. Accordingly, it is not intended that the invention be limited, except as by the claims set forth below.

Claims

1. A method for correcting pixel intensities for output on a video display, comprising: generating an interpolation table having a plurality of interpolation segment endpoints spaced over a transfer function correction curve;distributing the plurality of interpolation segment end points logarithmically over the correction transfer function curve to enable a higher resolution on a first portion of the correction transfer function curve having a greater amount of slope relative to a second portion of the correction transfer function curve having a smaller amount of slope; anddetermining correction values for a graphic display by interpolating between the logarithmically distributed interpolation segment endpoints.

2. A method as in claim 1, wherein generating an interpolation table further comprises generating an interpolation table having a plurality of interpolation segment endpoints spaced over a transfer function correction curve, wherein the correction transfer function curve comprises 2n pixel intensity correction values, wherein n is a number of bits of precision of a pixel intensity value.

3. A method as in claim 2, further comprising defining a transfer function correction curve having 2n pixel intensity correction values, wherein n is greater than 8.

4. A method as in claim 2, further comprising dividing the transfer function correction curve into 2p levels, where p is an integer.

5. A method as in claim 4, further comprising increasing a number of interpolation segment end points in each new level by 2p times.

6. A method as in claim 5, further comprising dividing each new level into 2p levels and increasing the number of interpolation segment end points in each new level by 2p times until a desired number of interpolation segment end points are distributed along the transfer function correction curve.

7. A method as in claim 1, wherein distributing the plurality of interpolation segment end points further comprises distributing the plurality of interpolation segment endpoints evenly in each of a plurality of logarithmically distributed levels, wherein each level represents a portion of the transfer function correction curve.

8. A method as in claim 1, wherein interpolating between the segments further comprises interpolating between the segments based on an offset value and a proportion value.

9. A method as in claim 8, wherein the step of generating an interpolation table further comprises generating an interpolation table comprised of a plurality of logarithmically distributed interpolation segment endpoints and a plurality of segment offset values corresponding to each interpolation segment endpoint.

10. A method as in claim 1, wherein determining correction values for a graphic display further comprises determining correction values for a plurality of colors in a graphic display by interpolating between the logarithmically distributed interpolation segment endpoints for each of the plurality of colors.

11. A method as in claim 10, further comprising determining transfer function correction values for a plurality of colors, wherein the colors are selected from the group consisting of red, green, blue, cyan, magenta, yellow, and black.

12. A method as in claim 1, wherein distributing the plurality of interpolation segment end points logarithmically further comprises distributing the plurality of interpolation segment end points logarithmically over the correction transfer function curve to enable an exponentially higher resolution on a first portion of the correction transfer function curve having a greater amount of slope relative to a second portion of the correction transfer function curve having a smaller amount of slope.

13. A system for correcting pixel intensities for output on a video display, comprising a computer memory device configured to store an interpolation table with logarithmically distributed entries;an input value configured to represent a pixel intensity on the video display;wherein the input value includes a level value that represents a selected level of a correction transfer function curve;wherein the input value further includes a level offset value that represents a segment of the level of the correction transfer function curve;wherein the input value further includes a proportion value configured to represent a proportional distance along the segment;a computer processing device configured to access the interpolation table in the computer memory device and access one or more inputs within the interpolation table based on a table address of the interpolation table to determine a specific segment base value and a segment offset value;the computer processing device further configured to multiply the proportion value by the segment offset value to determine an interpolation offset value; andthe computer processing device further configured to add the interpolation offset value with the segment base value to determine an output value, wherein the output value represents a corrected pixel intensity value.

14. A means for correcting pixel intensities for output on a video display, comprising: a means for generating an interpolation table having a plurality of interpolation segment endpoints spaced over the input values;a means for distributing the plurality of interpolation segment end points logarithmically to enable an exponentially higher resolution in a portion of the interpolation table related to a first portion of a correction transfer function curve having a greater amount of slope relative to a second portion of the correction transfer function curve having a smaller amount of slope; anda means for determining correction values for a graphic display by interpolating between the logarithmically distributed interpolation segment endpoints.

15. A method for correcting pixel intensities for output on a video display using an interpolation table, comprising: dividing the interpolation table into a plurality of table levels, wherein each succeeding table level is 1/2p times a size of a preceding table level;separating each table level into a plurality of segments comprising interpolation segment endpoints;interpolating between the interpolation segment endpoints to determine a pixel intensity correction value for a predetermined pixel intensity level.

16. A method as in claim 15, wherein interpolating between the interpolation segment endpoints further comprises determining which of the table levels is represented in an input value.

17. A method as in claim 16, wherein interpolating between the interpolation segment endpoints further comprises shifting the input value a level specific amount to determine a level offset value and a proportion value.

18. A method as in claim 17, wherein interpolating between the interpolation segment endpoints further comprises calculating a level base value as a function of the table level.

19. A method as in claim 18, wherein interpolating between the interpolation segment endpoints further comprises determining an interpolation segment address of the interpolation table, wherein the address is a function of the level base value and the level offset value.

20. A method as in claim 19, wherein interpolating between the interpolation segment endpoints further comprises accessing the address to retrieve a segment base value and a segment offset value.

21. A method as in claim 20, wherein interpolating between the interpolation segment endpoints further comprises calculating a pixel intensity output value by multiplying the proportion value by the segment offset value to form an interpolation offset value and adding the interpolation offset value to the segment base value to form the pixel intensity output value.