大分工業高等専門学校紀要

第 52 号(平成 27 年 11 月)

GENERATION OF STONE-STRIPE-LIKE COLOR IMAGESBY BILATERAL MINIMUM AND MAXIMUM FILTERSFOR NON-PHOTOREALISTIC RENDERING

Toru HIRAOKA
Dept. of Information Eng., National Institute of Technology, Oita College

In the past, a number of non-photorealistic rendering methods that generate stone-stripe-like images
from gray-scale photographic images have been proposed. In this paper, the conventional method isextended to a non-photorealistic rendering technique that generates stone-stripe-like color images fromcolor photographic images. In order to validate the effectiveness of the proposed method, examination isconducted using several color photographic images, and the attractiveness of the stone-stripe-like color
images generated by the proposed method is evaluated visually.
Key Words : non-photorealistic rendering, bilateral minimum and maximum filters, stone stripe

1. INTORODUCTION
Among the various image processing techniquescurrently in use1)-4), non-photorealistic rendering(NPR) is a field of computer graphics in whichphotographed images are processed and converted
to images that resemble paintings, illustrations, orsketches. Such NPR-converted images arefrequently seen in our daily lives in television
programming, magazines, and web pages.
Among the available NPR techniques, this paper
focuses in particular on a method of generatingstone-stripe-like5) color images. Images of this typeimitate the striped patterns that appear when naturalrock like malachite or Laguna Agate is cut, asshown in Figure 1. Since striped layers appear along
the contour lines of such photographic images asstone-striped patterns, the resulting image allows theviewer to imagine, to some extent, what the original
image was like. Moreover, stone-stripe-like images
show concentric stone-striped patterns generated at
locations other than the contour-line portions of theimages (Figure 1, right). The conventional method,which generates stone-stripe-like images throughiterative processing employing bilateral minimum
and bilateral maximum filters6), has previously been
applied to gray-scale photographic images.
This paper proposes an extended method thatcan be used to apply the conventional method tocolor photographic images. Using this technique, thestone-stripe-like color images show multiple

Fig.1 Examples of stone-striped patterns.

naturally colorful and overlapping stone-striped
patterns that have their contour-line portions wellpreserved, and which are considerably more
attractive than gray-scale stone-stripe-like images.
In order to validate the effectiveness of the proposed
method, examination is conducted with several
color images, and attractiveness of the color images
generated by the proposed method is evaluatedvisually.

2. METHOD
Red, green, and blue pixel values in 256
gradations (integer values from 0 to 255) of a color
image of I  J pixels are defined as f R ,i , j , f G ,i , j ,j  1,2, , J ) , respectively.
f B,i , j (i  1,2, , I ;First, the mean f i , j of red, green, and blue
pixel
valuesisdetermined
as―37―

大分工業高等専門学校紀要

第 52 号(平成 27 年 11 月)( f R,i , j  f G,i , j  f B,i , j ) / 3 , and then, after applying thebilateral minimum and bilateral maximum filters,
the pixel values of the image f min,i , j and f max ,i,j arerespectively determined by Equations (1) and (2).
ww

 e

f i  k , j  l   ( k 2 l 2 )  ( f i , j  f i  k , j  l ) 2

f min,i , j  k  wl w w w

 ew

 e

3. EXPERIMENTS

f i  k , j  l   ( k 2 l 2 )  ( f i , j  f i  k , j  l ) 2

f max,i , j  k  wl w w w

 e

f i  k , j l

f i  k , j  l   ( k 2 l 2 )  ( f i , j  f i  k , j  l ) 2(2)k   wl   w

In these equations,  ,  , and  are positive
constants, and w is the window size. Withf min,i , j  f max,i , j as d i , j , and the minima and maxima
within d i , j as d min and d max respectively, f i , j is
updated using Equation (3).
fi , j  255

(4)

(1)

k   wl   wwf  d min fi , j  2551  i , j d max  d min 

The image generated in this way is called a modified
stone-stripe-like color image.

f i  k , j lf i  k , j  l   ( k 2 l 2 )  ( f i , j  f i  k , j  l ) 2

the generated and original images are adopted.

fi , j  d min
d max  d min(3)Gaussian noise is applied selectively to the red,green, and blue pixels of a color image if f i , j isless than S (sites where variation in luminancevalue of image is small). Following, f R ,i , j , f G ,i , j ,and f B ,i , j respectively represents the red, green,
and blue pixel values of color images augmented
with Gaussian noise. Gaussian noise is applied inorder to produce stone-striped patterns even at sites
where variation in luminance value of image issmall. The reason for extracting sites with small
luminance variations by employing the mean of red,green, and blue pixel values rather than therespective red, green, and blue of the color image is
as follows. Since contour-line portions are different
for red, green, and blue, extraction of the mean
reduce the possibility of disruption to thecontour-line portions when stone-striped patterns aregenerated.
Next, f i , j is changed respectively tof R ,i , j , f G ,i , j , and f B ,i , j in Equations (1) and (2), andthen derive f R, min,i , j , f R, max,i , j , fG , min,i , j , fG , max,i , j ,f B , min,i , j , and f B , max,i , j . d R ,i , j , d G ,i , j , and d B ,i , j wererespectively derived from f R, max,i , j  f R, min,i , j ,f G , max, i , j  f G , min,i , j , and f B, max,i , j  f B, min,i , j . Finally,f R ,i , j , f G ,i , j , and f B ,i , j are updated with Equation(3). By repeating this iterative calculation T times,
the stone-stripe-like color image is generated.
Furthermore, to improve the reproducibility of
the colors in the stone-stripe-like color image at thetime of the conversions of red, green, and blue using
Equation (4) in place of Equation (3), the smaller
sum of the absolute pixel value differences betweenThe proposed method is applied to six color
images, each 512  512 pixels with 256 color levels,
as shown in Figure 2. The following examinations
are based on Reference 5), using the values   0.1 ,  0.1 ,   0.001 , w  5 , S  1 , and T  5 . The
standard deviation for Gaussian noise is 20.
First, the stone-stripe-like color images
generated according to the proposed method areshown in Figure 3.As we can be seen in this figure,stone-striped patterns are generated as striped layers
along the contour lines of the photographs, while
concentric stone-striped patterns are generated atother places in the images. Furthermore, the―38―

Fig.2 Input color images.

大分工業高等専門学校紀要

第 52 号(平成 27 年 11 月)

Fig.3 Stone-stripe-like color images.

Fig.4 Modified stone-stripe-like color images.

stone-stripe-like color images appear colorful sincepatterns are naturally overlapping.
As a final examination, we compare
stone-stripe-like image generated from a gray-scale
image (Figure 5) and stone-stripe-like color images
at the upper right of Figure 3 and Figure 4. Weconclude that colorizing stone-stripe-like images
could improve image attractiveness.
Fig.5 Stone-stripe-like image.

4. CONCLUSION
In this paper, a NPR method that generated
stone-stripe-like color images from color
photographic images was proposed. In order tovalidate the effectiveness of the proposed method,
examination was conducted with several color
images and the attractiveness of the color images
generated by the proposed method was evaluatedvisually. We found that the color images generatedby the proposed method had natural overlapping
multiple stone-striped patterns, were colorful, andhad their contour-line regions preserved. In future

work, we intend to study the changes in thegenerated stone-stripe-like color images by varying
the parameter values.
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(Received September 30, 2015)―40――38―