EXAMINATION OF LCD MODULATION UNDER HIGH SPATIAL FREQUENCY CONDITIONS
6.4 COMPARISON OF DECONVOLUTION METHOD WITH AN ITERATIVE OPTIMISATION METHOD
An alternative to processing pixels sequentially to achieve the desired displayed values is to use an iterative optimisation method. The processing power of the modern personal computer has made the repeated application of a large number o f trial solutions a viable method of solving optimisation problems. A typical example has
been the successful application of Simulated Annealing [Kir83] to problems such as the
design of computer generated holograms.
An iterative optimisation program, developed by J.Gilby of Sira Ltd., was applied to the task o f finding a suitable image for presentation to the LCD drive system. The program works on one line of the image at a time. With the unprocessed image taken as a starting point, pixels have their value incremented or decremented while the error between the desired image and that resulting from the altered values with their appropriate weights is monitored. If the change o f pixel value results in a decrease in the overall error, then that change is kept. If the change results in an increase in overall error, the change is rejected. The process is repeated such that each o f the 640 pixels in the line undergo an average o f 100 adjustments to their value. The next line is then dealt with in the same way and so on until all 480 rows have been
processed. The displayed grey levels resulting form the solution offered by the
optimisation program are shown at Fig. 6.11 (c, f & i).
A numerical examination of the mean error between desired and displayed grey levels showed the improvement achieved by using the optimised images to be similar to that using the deconvolved images. Table 6.4. While the slight additional reduction in error gained using the optimisation technique is small, the difference in processing
time is considerable. When executed on a 450 MHz Pentium III PC, the
deconvolution program processes a 640x480 pixel image in 58 seconds. The iterative
optimisation program however requires 1 hour and 11 minutes to process the same
image. This seventy fold increase in duration detracts from the marginal additional improvement of the latter technique.
However, the fact that these two considerably different approaches yield remarkably similar results gives confidence in the validity o f the deconvolution program developed for this problem.
With both described processing methods, the modified images applied to the display system have a greater abundance of steps in the grey levels of adjacent columns. The scope of this chapter has been to measure the spatial rather than temporal modulation characteristics o f the display. However, temporal fluctuations in displayed value were observed with the eye on adjacent columns of greatly differing applied grey level and it was noted that the degree of fluctuation increased with greater steps in applied grey level. With a greater abundance of large steps in the applied image there were increased fluctuations in the displayed processed images.
In view of this, for the purpose of implementing correlation filters, the processing techniques were abandoned as the displayed image varies from one instant to the next. However, the improvements achieved in the time-averaged displayed images are not without use. The deconvolution process is proposed as a useful tool for displaying images effectively where temporal fluctuations are of no consequence as
demonstrated visually in the following section. The author recognises that the
temporal modulation characteristics of display devices and their effects within optical correlation systems are extensive and are worthy of considerable investigation in there own right, possibly as the subject of a research thesis - see suggested further work in chapter 9.
6.5 A PICTORIAL DEMONSTRATION OF THE DECONVOLUTION
ALGORITHM
The algorithm was applied to drawn images containing abrupt edges (unlike those usually found in natural scenes) which were subsequently applied to the LCD. The LCD was placed between crossed polarizers on the stage of a low magnification microscope. An SLR camera was fitted to the microscope and under low level
illumination photographs of the display were taken. The low illumination levels
ensured an exposure long enough to be impervious to the temporal fluctuations in transmitted intensity.
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Fig. 6.12 (a,b,c) show the parts of the drawn image of the Trixie Turnpike character photographed through the microscope. Fig. 6.12 (c,d,e) shows the area of interest
when the unprocessed image is applied. Recall that although the polarizer and
analyser are set for intensity modulation the brightness control on the LCD interface is set to minimum - not ideal for presenting images for photographic capture - hence the low contrast in the displayed images in comparison with the originals (a,b,c). Furthermore, the original images are full colour, whereas only one VGA colour channel (the Red video component) is used to drive the LCD. The corresponding processed images are shown at Fig. 6.12 (g,h,i). Despite the low brightness setting, features barely visible in the unprocessed images have been clarified. In (g) the 'war paint' is easily visible and there is more detail in the head-hand. In (h) and (i) there is improved definition of the lips, eyes and hairline.
6 .6 SUMMARY OF DEALING WITH ADJACENT COLUMN INFLUENCE
It has been shown that when a signal is applied to the LCD drive system used in this project the value appearing on any pixel of the display does not have a one to one correspondence with that pixel on the applied image. The 'displayed' signal was seen to be heavily dependent on the signal 'applied' to its right neighbouring column. Moreover, the strength of this dependence varied according to location of that column. Irrespective of column position, the effect on crossed polarizer intensity of the remaining columns (i.e. all but the right neighbour) was less than 1.5% so only the
intended column. Go, and right neighbour, G i, were considered in the restoration
process.
Translating crossed polarizer intensity signals into displayed grey levels enabled the
weights, which represent the degree o f influence from Go and G\ columns in the
applied image, to be determined for each of the four types o f column position. Using these weights the process reconstructed the observed time-averaged displayed grey
levels to within ±16 levels, over the range of possible values for Go and G\. A
program using these weights was designed to produce an image which, when convolved by the LCD drive system displays a 25% reduction (Table 6.4) in the error
between displayed and desired image, despite clipping approximations in the algorithm.
While a more rigorous deconvolution algorithm could be employed, the margin for fiirther improvement suggested by an iterative optimisation program is so small that the additional processing invested is unlikely to return a significant error reduction profit. While the optimisation program was run from compiled code as an executable file, the Matlab deconvolution-based program was run as interpreted code. It is not inconceivable that with the continued growth in PC processing power, and by running a compiled file, real time processing o f the deconvolution algorithm might be possible.