Digital Image Processing Chapter 6: Color Image Processing ( )

Transcription

1 Digital Image Processing Chapter 6: Color Image Processing ( )

2 6.4 Basics of Full-Color Image Processing Full-color images are handled for a variety of image processing tasks. Full-color image processing approaches fall into two major categories. In the first category, we process each component image individually and then form a composite processed color image from the individually processed components. In the second category, we work with color pixels directly. Because full-color images have at least three components, color pixels are vectors. C= [ CR CG CB ] ] = G [ R (6.4-1) B [ CR(x,y) ] [ R(x,y) ] C(x,y)= CG(x,y) = G(x,y) (6.4-2) CB(x,y) B(x,y)

3 6.4 Basics of Full-Color Image Processing In order for per-color-component and vector-based processing to be equivalent, two conditions have to be satisfied: First, the process has to be applicable to both vectors and scalars. Second, the operation on each component of a vector must be independent of the other components. As an illustration, Fig shows neighborhood spatial processing of gray-scale and full-color images.

4 Formulation As with the intensity transformation techniques of Chapter3, we model color transformation using the expression g x, y = T[f x, y ] where f(x, y) is a color input image, g x, y is the transformed or processed color output image, and T is an operator on f over a spatial neighborhood of (x, y). We will restrict attention in this section to color transformations of the form S i = T i r 1, r 2,, r n, i = 1, 2,, n where, for notational simplicity, r i and s i are variables denoting the color components of f x, y and g x, y ant any point (x, y), n is the number of color components, and {T 1, T 2,, T n } is a set of transformation of color mapping functions that operate on r i to produce s i.

5 FIGURE 6.30 A full-color image and its various color-space components. (Original image courtesy of MedData Interactive). 5

6 In Fig 6.30 The first row of the figure shows a high resolution color image The second row of the figure contains the components of the initial CMYK scan. Black represents 0 and white represents 1 in each CMYK color component When the CMYK image is converted to RGB, as shown in the third row of the figure, the strawberries are seen to contain a large amount of red and very little green and blue The last row of the figure shows the HIS components of the full color image computed using Eqs.(6.2-2) through (6.2-4). 6

7 Suppose that we wish to modify the intensity of the full color image in Fig using g x, y = kf(x, y) (6.5-3) Where 0<k<1. In the HIS color space, this can be done with the simple transformation s 3 = k r 3 (6.5-4) Where s 1 = r 1 and s 2 = r 2. Only HIS intensity component r 3 is modified. In the RGB color space, three components must be transformed : s i = kr i i = 1,2,3 (6.5-5) The CMY space requires a similar set of linear transformations: s i = kr i + 1 k I = 1, 2, 3 (6.5-6) 7

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9 Color Complements The hues directly opposite one another on the color circle are called complements

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11 6.5.3 Color slicing One of the simplest ways to slice a color image is to map the colors outside some range of interest to a nonprominent neutral color. If the colors of interest are enclosed by a cube (or hypercube for n > 3) of width W and centered at a prototypical (e.q.,average) color with components, the necessary set of transformations is If a sphere is used to specify the colors of interest, Eq.(6.5-7) becomes

12 6.5.3 Color slicing Equations (6.5-7) and (6.5-8) can be used to separate the edible part of the strawberries in Fig. 6.31(a) from the background cups, bowl, coffee, and table. Figures 6.34(a) and (b) show the results of applying both transformation.

13 and Xw, Yw, and Zw are reference white tristimulus values-typically the white of a perfectly reflecting diffuser under CIE standard D65 illumination Tone and Corrections The model of choice for many color management system (CMS) is the CIE L*a*b*model, also called CIELAB (CIE[1978],Robertson[1977]). The L*a*b*color components are given by the following equation: Where

14 6.5.4 Tone and Corrections

15 6.5.4 Tone and Corrections Figure 6.35 shows typical transformations used for correcting three common tonal imbalances-flat, Light, and dark images. The S-shaped curve in the first row of the figure is ideal for boosting contrast[see Fig.3.2(a)]. Its midpoint is anchored so that highlight and shadow areas can be lightened and darkened, respectively. The transformations in the second and third rows of the figure correct light and dark images and are reminiscent of the power-law transformations in Fig. 3.6.

16 6.5.4 Tone and Corrections

17 6.5.4 Tone and Corrections Figure 6.36 shows the transformations used to correct simple CMYK Output imbalances. Note that the transformations depicted are the functions required for correcting the images; the inverse of these Functions were used to generate the associated color imbalances. Together, the images are analogous to a color ring-around print of a darkroom environment and are useful as a reference tool for identifying color printing problems. Note, for example, that too much red can be due to excessive magenta or too little cyan.

18 6.5.5 Histogram Processing Figure.6.37(a) shows a color image of a caster stand cruets and shakers whose intensity component spans entire(normalized) range of possible values,[0,1] Figure.6.37(b) shows the intensity histogram of the n as well as the intensity transformation used to equali intensity component Figure.6.37(c) histogram equalizing the intensity com without altering the hue and saturation Figure.6.37(d) shows the result of correcting this par increasing the image`s saturation component, subse histogram equalization, using the transformation in F

19 6.6.1 Color Image Smoothing c x, y = 1 K s,t S xy c s, t c x, y = 1 K 1 K 1 K s,t S xy R s, t s,t S xy G s, t s,t S xy B s, t Consider the RGB color image in Fig.6.38(a). Its red, green, and blue component images are shown in Figs.6.38(b) through (d). Figures 6.39(a) through (c) show the HIS components of the image

20 6.6.1 Color Image Smoothing In Section 6.2, we noted that an important advantage of the HSI color model is the it decouples intensity and color information. This makes it suitable for many gray-scale processing techniques and suggests that it might be more efficient to smooth only the intensity component of the HIS representation in Fig.6.39.

21 6.6.1 Color Image Smoothing The smoothed color image is shown in Fig.6.40(b). Note that it is similar to Fig.6.40(a), but, as you can see from the difference image in Fig.6.40(c), the two smoothed images are not identical. This is because in Fig.6.40(a) the color of each pixel is the average color of the pixels in the neighborhood. On the other hand, by smoothing only the intensity component image in Fig.6.40(b), the hue and saturation of each pixel was not affected and, therefore, the pixel colors did not change.

22 6.6.2 Color Image Sharpening 2 c x, y = 2 R x, y 2 G x, y 2 B x, y Figure.6.41(a) was obtained using Eq.(3.6-7) and the mask in Fig.3.37(c) to compute the Laplacians of the RGB component images in Fig These results were combined to produce the sharpened full-color result. Figure6.41(b) shows a similarly sharpener image based the HIS components in Fig This result was generated by combining Laplacian of the intensity component with the unchanged hue and saturation components. The difference between the RGB and HIS sharpened images is shown in Fig.6.41(c).

23 6.7.1 Segmentation in HIS Color Space Suppose that it is of interest to segment the reddish region in the lower left of the image in Fig.6.42(a). Figures 6.42(b) through (d) are its HIS component images. Note by comparing Figs.6.42(a) and (b) that the region in which we are interested has relatively high values of hue, indicating that the colors are on the blue-magenta side of red(see Fig.6.13). Figure6.42(e) shows a binary mask generated by thresholding the saturation image with a threshold equal to 10% of the maximum value in that image. Any pixel value greater than the threshold was set to 1(white). All others were set to 0(black). Figure 6.42(f) is the product of the mask with the hue image, and Fig.6.42(g) is the histogram of the product image. The result of thresholding the product image with threshold value of 0.9 resulted in the binary image shown in Fig.6.42(h)

24 6.7.2 Segmentation in RGB Vector Space D z, α = z α = z α T z α 1 2 =[(z R a R ) 2 + (z R a R ) 2 + (z R a R ) 2 ] 1 2 D z, α = [ z α T C 1 z α ] 1 2

25 6.7.2 Segmentation in RGB Vector Space Fig.6.44(a) Original image with colors of interest shown enclosed by a rectangle. Fig.6.44(b) Result of segmentation in RGB vector space.

26 6.7.3 Color Edge Detection Fig.6.45 (a)-(c) R, G, and B component images and (d) resulting RGB color image. Fig.6.45 (e)-(g) R, G, and B component images and (h) resulting RGB color image.

27 6.7.3 Color Edge Detection u = R x r + G x g + B x b, v = R y r + G y g + B g xx = u u = u T u = R x g yy = v v = v T v = R g xy = u v = u T v = R θ x, y = 1 2 tan 1 b y 2 G 2 B x x 2 G 2 B y y y R + G G + B B x y x y x y 2g xy g xx g yy F θ x, y = 1 2 (g xx + g yy ) + (g xx g yy ) cos 2θ(x, y) + 2g xy sin 2θ(x, y) 1 2

28 6.7.3 Color Edge Detection Figure 6.46(b) is the gradient of the image in Fig.6.46(a), obtained using the vector method just discussed. Figure 6.46(c) shows the image obtained by computing the gradient of each RGB component image and forming a composite gradient image by adding the corresponding values of the three component images at each coordinate (x, y). The edge detail of the vector gradient image is more complete than the detail in the individual-plane gradient image in Fig.6.46(c); for example, see the detail around the subject`s right eye. The image in Fig.6.46(d) shows the difference between the two gradient images at each point(x, y).

29 6.7.3 Color Edge Detection Fig.6.47 shows the three component gradient images, which, when added and scaled, were used to obtain Fig.6.46(c).

30 6.8 Noise in Color Images Fig.6.48(a) through (c) show the three color planes of an RGB image corrupted by Gaussian noise, and Fig.6.48(d) is the composite RGB image.

31 6.8 Noise in Color Images Fig.6.49(a) through (c) show the result of converting the RGB image in Fig.6.48(d) to HSI.

32 6.8 Noise in Color Images Fig6.50(a) shows an RGB image whose green image is corrupted by salt-andpepper noise, in which the probability of either salt or pepper is The HIS component images in Figs.6.50(b) through (d) show clearly how the noise spread from the green RGB channel to all the HSI images. Of course, this is not unexpected because computation of the HSI components makes use of all RGB components, as shown in Section 6.2.3

33 6.9 Color Image Compression Fig.6.51(a) shows a 24-bit RGB full-color image of an iris in which 8 bits each are used to represent the red, green, and blue components. Fig.6.51(b) was reconstructed from a compressed version of the image in (a) and is, in fact, a compressed and subsequently decompressed approximation of it. Fig.6.51(b) is a recently introduced standard that is described in detail in Section Note that the reconstructed approximation image is slightly blurred.