Common Image Processing Tools

Image Thresholding

The simplest method of segmenting a gray-scale image is to threshold it. By selecting a certain value, and setting all pixel values below it to one (white), and all pixel values above it to zero (black), we get a binary image. From the histogram we see that the pixel values of the characters are usually below 80. We'll first try to threshold the image with a low value to minimize the background noise: [figure X5] is thresholded with value 65. The writing is unreadable. Using a larger value, 80, suggested by the histogram [figure X4], we have [figure X6]. The writing is quite readable, with some of the background still left. Parts of the last character are missing, so we'll try yet another threshold value, 100, and end up with [figure X7]. Here, the last character is easier to identify, but the first characters are beginning to disappeaar into the background.

If the background could be separated from the writing with a certain grey scale value, image thresholding would be the only method needed for processing the images. Of all our digitized images, none of them could perfectly be segmented using thresholding; there were always parts of characters missing, or background blurred the characters. But for a properly chosen threshold value, the writing was quite readable.

The best threshold value changes from an image to another. It is also dependent of location, because some parts of the text are darker or lighter than others. So, the larger the image, the harder it is to choose a globally acceptable threshold value. A good estimate can easily be found by examining histograms (or single pixel values) of areas inside characters and choosing an upper boundary appropriately. The best value can be quickly found manually, because the process is very quick. Because the writing does not show up in a global histogram, it is hard to find a way for automatic selection of a good threshold value. One could estimate a ratio between the number of character pixels and background pixels in an average image, and use it to select a cutoff point, for the first approximation.

Figure 32: Sample image, thresholded at 65.

Figure 33: Sample image, thresholded at 80.

Figure 34: Sample image, thresholded at 100.

Histogram Modification

One of the best ways to improve contrast without loosing much information and too many grey levels is to use histogram- modification. This technique re-maps the original grey levels to anothers according to a mapping function. One can re-map the grey levels very quickly by a statistically optimal algorithm (equalization) or manually. Many image processing programs, like Adobe Photoshop ©, have very easy to use tools available for this. If the mapping function is monotonically increasing, the order of pixel values is preserved, and the process is purely contrast-modifying. The automatic histogram equalization method stretches the grey levels of a given image so that it is as equally possible for any given pixel to be of any gray scale value; i.e. the number of pixels belonging to any grey level is equal.

The histogram mapping function is typically presented as a curve, original greyscale values on x-axis and their mapped values on y-axis. The grey levels at the area of interest, in this case the grey levels of characters, can be dynamically separated from other areas by applying a steep mapping curve to that area. The method is very good in enhancing contrast. Figures [X8] show the test figure [X5] optimally equalized [X8a], and the new, stretched histogram [X8b]. A manually adjusted version can be seen in [figure X10a] with resulting histogram [X10c].

Figure 35a: Sample image, histogram equalized.

Figure 35b: Histogram of sample image after equalization (compare to pic. X3).

Figure 36a: Sample image, manually equalized.

Figure 36b: Histogram of sample image after manual histogram modification.

Edge Detection

Edge detection algorithms search for rapid changes of pixel values. These operators are typically different kinds of first or second order derivatives. Results of several differential operators can bee seen in figures [37] (horizontal derivative), [38] (vertical derivative), [39] (sum of horizontal and vertical derivatives) and [40] (the square environment derivative). These images are histogram-equalized, because resulting values of these operators are typically very low, and the images therefore very dark. The edges of the characters are visible, but unluckily the background noise is too. The cyclic error of the scanner's 4th bit that causes peaks every 16 grey levels might show up when applying these algorithms.

Figure 37: Horizontal derivative of the sample image (histogram equalized).

Figure 38: Vertical derivative of the sample image (histogram equalized).

Figure 39: Sum of X-and Y-derivatives of the sample image (histogram equalized).

Figure 40: Square-environment derivative of the sample image (histogram equalized).

Noise Reduction

Noise in a grayscale image is usually understood as single pixels or very small areas containing very different grayscale values from their environment. Averaging is probably the most basic noise reduction method. One can choose, say, a 5x5 pixel matrix, calculate the average of all the 25 pixels, and set the value of the middle pixel to that [figure X]. The averaged image is blurry, and, especially, sharp edges are lost. One can modify the algorithm by setting a threshold to it, so that the value of the middle pixel is changed only when its value is very different from the average, or use the average with weighting factor. The shape of the matrix can also be varied from square to, say, hexagonal, or a cross.

A better way to reduce noise is by using order-based statistical filters such as the median filter. These filters, or algorithms, arrange the grayscale values of a chosen area in increasing order, and set one of these values to the current pixel value. Basic median filter chooses the middle value. These filters can be biased to select some other value or the pixels involved can be weighted. Figure [X] shows the test image median-filtered with a 5x5 matrix.

Figure 41: Sample image, averaged with 5x5 matrix.

Figure 42: Sample image, median filtered with 5x5 matrix.

Deviation Method

Suppose that the writing on a papyrus covers the structural features of the carbonized papyrus surface, and that the writing is nearly equally colored with less disturbances than the background. In that case, we could distinguish the writing with a filter that detects the deviation or variance of a chosen area. The deviation inside a character shuld be small, and large outside. Also, the edges of the characters would be enhanced, because there the deviation would be quite large. [Figure X] shows the deviation of the sample image using an 7x7 matrix. The edges are enhanced, but the deviation inside and outside the characters seems to be equally small, so that it cannot really be used to distinguish the writing from the background. The enhancement of the edges, howewer, is good. The variance (7x7 pixels) is shown in [figure 43].

Figure 43: Deviation of sample image

Figure 44: Variance of sample image

Papyrus Structure Elimination

The papyrus sheet is made from horizontal and vertical papyrus stripes. These stripes, and the cell structure, can be seen in any piece of papyrus, and also in our carbonized fragments. Vertical and horizontal lines can be detected, for example, by comparing a line to the average of its left-and right-hand square environments and searching for a large difference. If the width of these lines vary much, simple line detectors are not so efficient. We tried to reduce the vertical structure by calculating the averages of pixel values of each vertical line, and then subtracting these averages from the original image. Many of the disturbing lines were removed, and the original figure wasn't otherwise altered too much [figure X] (the slope of vertical lines was estimated and accounted for). The removal of the structure is indeed very discreet; all small details remain, and it may even be difficult to spot the differences to the original picture. As a test, we asked several people to spot the differences between the original and the image from which vertical structure was eliminated; none of them found the differences. This means, on the one hand, that the removal didn't alter too much the pictures, but on the other, that the readability was not so much improved. Most of the visible background structure is local, so that the removal of averaged lines really removes only the longest and straightest ones.

The papyrus background structure is not always purely vertical and horizontal. In our sample picture, for example, the vertical lines are tilted about 6 ° (one pixel to the right every 10 pixels). A simple algorithm for detecting the direction of axes could compare successive lines, testing them by shifting the previous line horizontally by -1, 0, or 1 pixels, and choosing the shift as the one wich causes least difference to the current line (in least square error sense, for example). The average slope would be the average of all the shifts. Some rules should be applied to the process to prevent it from too strong deviations. One could apply momentum, for example, to keep the changes of the shifts small. There is also other ways to find the major axes of a picture, like correlation.

The problems with this kind of structure elimination are related to the way the averages are calculated, and to the structure itself. If characters or large parts of them are tilted along the structural lines, they may affect the calculation of the average and be also reduced from the pictures. Also, some of the structural lines are not continuous, and can be short compared to the size of the characters, so that they cannot effectively be reduced using this algorithm.

Figure 45: The original sample image.

Figure 46: Sample image, vertical structure eliminated.

Figure 47: Sample image, horizontal structure eliminated.

Figure 48: Sample image, horizontal and vertical structures eliminated (in this order).

FFT Filters

Fourier transformation allows us to handle the pictures in frequency domain insteadt of spatial domain. The simplest Fourier filters are low-pass and high-pass filters, which filter out high or low frequencies (rapid changes in pixel values or average values). A notch filter cancels only certain frequencies. The effect of a low- pass filter is blurring, noise-reducting. The high-pass filter cancels the overall grey values, emphasizing edges and noise. Proper filters in frequency domain could reduce the vertical and horizontal lines and enhance edges of characters. The drawback of filters using Fourier transformations is the need for very complex and slow calculations. Further experiments are encouraged.

Miscellaneous Viewing

There are many different simple viewing tools along with these filters. Many new views to the images can be found by histogram (or color map) manipulation. The grey level map can be reversed to turn the pictures to their negatives, it can be rotated, pseudo-coloured, or multiplied. Every method may give some new information, so that one should not count any of them out.

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Antti Nurminen, 34044T,
laplacian (F(x,y)=dx ²+dy²), [figure X] - sobel.