Virtual Restoration of Antique Books and Photographs (Digital Imaging) Part 5

Word Descriptors

For a given image, we compute the number of points in the scatter plot that fall on each of four triangles A, B, C, and D that subdivide the basic μρ triangle; the four regions correspond to high-contrast/medium-luminance, low-contrast/low-luminance, medium-contrast/medium-luminance and low-contrast/high-luminance, respectively. Variety seems to be a characteristic of good-quality images and we expect such images to have the four regions well represented. Based on the resulting percentages of occupancy, we derive a four-letter word descriptor of the image as follows. Using the percentages, in a decreasing fashion we order the names of the corresponding regions A, B, C, and D; a descriptor of the image is obtained. There are 4!=24 possibilities for the descriptor; nevertheless, some are rather unlikely. As an example, and in order to have an initial reference, based on a small image set of 35 images we computed the min, max, average, and median values of the percentages corresponding to each region A, B, C, and D. The results are summarized in Table 10.2.

We further elaborate on the definition of the word descriptor. By using lowercase or uppercase letters, for each region, respectively, depending on whether or not the percentage is below the corresponding median (observe the third column in Table 10.3), a more sophisticated descriptor result. Nevertheless, it requires the use of a reference data base.

Table 10.3 gives statistics regarding a subset of four images that were subjectively classified as good and in Table 10.4 the four images classified as bad. The corresponding descriptors are CdAb, CBdA, BCdA, and Bdca, for the good images, and Dacb, Da’b’c’ (primed letters indicate absence of points), ACdb, and CdbA, for the bad images.

Under gamma correction, the image Pisa underwent a change in word descriptor from Dacb to DCab; its quality improved by a decrement of the luminance and an increment of the texture contents. The image description changed from BcdA to Bdca; it became less dark and got more detail as well. Texture1 (ACdb) has higher contrast than Texture2 (CdbA); in each case, local contrast occurs above certain minimal, positive levels, also regions B and D (light and dark regions) are underrepresented; this in opposition to good-quality images which often include regions that are nearly constant (Figure 10.22).

TABLE 10.3

Statistics corresponding to four images considered of good quality.

TABLE 10.4

Statistics corresponding to four images considered of bad quality.

Texture images tend to have a strong C region as well. Globally, texture images tend to have an intermediate luminance and a medium to large contrast. The effects of i.i.d. noise on luminance-contrast plots can be studied theoretically with some distribution analysis. The joint distribution of the max and the min of a sample of n data from an underlying population with probability density function / and cumulative distribution function F is given by [14]

For an underlying uniform distribution U[0,1], with F(t)=t and f(t)=1, the joint density becomes,which has a maximum at (min, max) = (a, b) = (0, 1) and expectationthus,    translating    the

result to the (midrange, range) plane, the largest likelihood will correspond to the point (0.5, 1) and the cloud of points will have a center of mass atA strong A region may be an indication of noise or fine textures in the image. Image regions containing white noise will normally have an intermediate luminance, of a value depending on their mean value, and a contrast that will depend on the strength and distribution of the noise: impulsive noise (with a heavy tailed distribution) will have a larger contrast than uniform noise; higher range values are probable for larger windows. Textured regions having a scale-dependent behavior depend more on the size of the window. For faded images, the distribution of the points in the μρ-triangle is highly concentrated near the point (1,0), an indication of an image with overall high intensity and low contrast. Gamma correction causes a migration of the points, according to a certain flow, that makes the scatter plot more uniformly distributed on the one hand and also makes the overall average luminance near 0.5, on the other; images with good coverage of the μρ-triangle and global average luminance near 0.5 look well, in general. Dark images tend to live in the B region while light images tend to live in the D region. We argue that luminance-contrast plots give important information regarding image quality, in the sense that visual quality requires variety in the combination of local contrast and local intensity in the image. In particular, images that live only in the B and D regions only are to be considered of poor quality. Figure 10.23 shows a case of a light (faded) image.

Broadly, we conclude that the letters A and C should be at the end of the descriptor, otherwise the image is likely to have excessive detail. The regions B and D should be balanced; in fact, at least 20% of the points should fall on each of the regions B and D, otherwise the image is too light or too dark; also, a 5% minimum on the A and C regions is highly desired. At least two upper-case letters should be present: this will depend on the underlying data set used. In addition, the absence of points in any of the regions is an indicator of lack of variety and of bad image quality.

FIGURE 10.23

Original image “Pisa” (size 512 x 512 pixels) and μρ-plot.

Conclusions

Some comments on image quality, as far as these types of images are concerned, have been added. It is important to observe that the field we have addressed is far from mature; few authors study it, and many algorithms and techniques are borrowed from similar but not identical application areas. Moreover, in general the automatic detection of damaged areas in imaged material is a difficult task, due to the superposition of the defects with the peculiar structure of the object. Also adequate models for the damage, which would permit one to build dedicated restoration algorithms, are often missing. For all these reasons, we hope that this collection of otherwise dispersed information will trigger further research and improvements.