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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 7, July 2011 Colorization of gray level images by using optimization Hossein Ghayoumi Zadeh Hojat Jafari Alireza Malvandi Javad Haddadnia Department of Electrical Engineering Department of Electrical Engineering Department of Electrical Engineering Department of Electrical Engineering Sabzevar Tarbiat Moallem University Sabzevar Tarbiat Moallem University Sabzevar Tarbiat Moallem University Sabzevar Tarbiat Moallem University Sabzevar, Khorasan Razavi, Iran Sabzevar, Khorasan Razavi, Iran Sabzevar, Khorasan Razavi, Iran Sabzevar, Khorasan Razavi, Iran h.ghayoumizadeh@gmail.com jafari.hojat@gmail.com ali.malvandi0@gmail.com haddadnia@sttu.ac.ir Abstract —This article discusses the colorization of gray Another well known approach to colorization [5] level images. Because of the technique applied in this assumes that small changes take place between two paper, this method can be used in colorizing medical consecutive frames; therefore, it is possible to use images. Color images achieved have good distinction optical flow to estimate dense pixel to pixel and separation. The proposed method can be used to correspondences. Chromatic information can then be separate the objects in gray images. Our method is transferred directly between the corresponding pixels. based on a simple premise: neighboring pixels in space- time that have similar intensities should have similar There are some approaches [6], [7], [8] which make colors. We formalize this premise using a quadratic cost use of the assumption that the homogeneity in the function and obtain an optimization problem that can gray-scale domain indicates homogeneity in the color be solved efficiently using standard techniques. In our domain and vice versa. This assumption provides a approach an artist only needs to annotate the image possibility to propagate color from several user- with a few color scribbles, and the indicated colors are defined seed pixels to the rest of the image. In [9], automatically propagated in both space and time to colorization is done through luminance-weighted produce a fully colorized image or sequence. chrominance blending and fast intrinsic distance computations. Shi et al.[10] color the grayscale images by segmentation and color filling method, Keywords- colorization, Equalization, gray level where an image is first segmented into regions and then the desired colors are Used to fill each region. I. INTRODUCTION Since the existing automatic image segmentation algorithms usually cannot segment the image into Colorization is the art of adding color to a meaningful regions, only color filling of each monochrome image or movie. This is done in order to segmented region cannot produce natural colorized increase the visual appeal of images such as old black results. Sykora et al. [11] suggested using and white photos, classic movies or scientific unsupervised image segmentation in cartoons illustrations. Various semi-automatic colorization colorization. However the method usually cannot get approaches have been published previously. They all ideal results for other types of images and is restricted involve some form of partial human intervention in to only cartoons.A major difficulty with colorization, order to make a mapping between the color and the however, lies in the fact that it is an expensive and intensity. Luminance keying also known as time-consuming process. For example, in order to pseudocoloring[1] is a basic colorization technique colorize a still image an artist typically begins by which utilizes a userdefined look-up table to segmenting the image into regions, and then proceeds transform each level of grayscale intensity into a to assign a color to each region. Unfortunately, specified hue, saturation and brightness, i.e a global automatic segmentation algorithms often fail to color vector is assigned to each grayscale value. correctly identify fuzzy or complex region boundaries, Welsh et al.[2] proposed techniques where rather than such as the boundary between a subject's hair and her choosing colors from a palette to color individual face. Thus, the artist is often left with the task of components, the color is transferred from a source manually delineating complicated boundaries between color image to a target grayscale image by matching regions. Colorization of movies requires, in addition, luminance and texture information between the tracking regions across the frames of a shot. Existing images. This approach is inspired by a method of tracking algorithms typically fail to robustly track color transfer between images described in Reinhard non-rigid regions, again requiring massive user et al. [3] and image analogies by Hertzmann et al. [4]. intervention in the process. 20 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 7, July 2011 III. HISTOGRAM EQUALIZATION II. ALGORITHM This method usually increases the global contrast of The first step in colorizing the gray level images is many images, especially when the usable data of the to remove noise and perform threshold operation on image is represented by close contrast values. images so that colorization is done accurately. If the Through this adjustment, the intensities can be better primary picture is similar to fig.1, the figure histogram distributed on the histogram. This allows for areas of needs to be examined carefully presented in fig. 2. lower local contrast to gain a higher contrast. Histogram equalization accomplishes this by effectively spreading out the most frequent intensity values. The method is useful in images with backgrounds and foregrounds that are both bright or both dark. In particular, the method can lead to better views of bone structure in x-ray images, and to better detail in photographs that are over or under-exposed. A key advantage of the method is that it is a fairly straightforward technique and an invertible operator. So in theory, if the histogram equalization function is known, then the original histogram can be recovered. The calculation is not computationally intensive. A disadvantage of the method is that it is indiscriminate. It may increase the contrast of background noise, while decreasing the usable signal.Histogram equalization often produces unrealistic effects in photographs; however it is very useful for scientific Figure 1. Gray level main image to colorize images like thermal, satellite or x-ray images, often the same class of images that user would apply false- color to. Also histogram equalization can produce undesirable effects (like visible image gradient) when applied to images with low color depth. For example, if applied to 8-bit image displayed with 8-bit gray- scale palette it will further reduce color depth (number of unique shades of gray) of the image. Histogram equalization will work the best when applied to images with much higher color depth than palette size, like continuous data or 16-bit gray-scale images. To transfer the gray levels so that the histogram of the resulting image is equalized to be a constant: H[i] =constant for all i The purposes: To equally use all available gray levels ; for further histogram specification. (Fig .3) Figure 2. Histogram of the primary figure As you observe in fig.2, histogram is not even so we use equalization. 21 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 7, July 2011 1} and the continuous mapping function becomes discrete: x y = f[x] ≜ i=0 h i =Hx (5) Where h[i] is the probability for the gray level of any given pixel to be I (0≤i≤L-1): ni ni L−1 h[i]= L −1 n = and i=0 h i = 1 (6) i=0 i N Of course here h [i] is the histogram of the image and H[i] is the cumulative histogram. The resulting function y is in the range 0 ≤y ≤ 1 and it needs to be converted to the gray levels 0 ≤y≤ L-1 by either of the two ways: y = y L − 1 + 0.5 (8) Figure 3. This figure shows that for any given mapping function y − ymin y=f(x) between the input and output images y= L − 1 + 0.5 1 − ymin Where [x] is the floor, or the integer part of a real number x, and adding 0.5 is for proper rounding. Note The following holds: that while both conversions map ymax = 1 to the P(y)dy=p(x)dx (1) highest gray level L-1, the second conversion also maps ymin to 0 to stretch the gray levels of the output i.e., the number of pixels mapped from x to y is image to occupy the entire dynamic range 0≤Y<L-1. unchanged. The result is shown in fig.4. To equalize the histogram of the output image, we let p(y) be a constant. In particular, if the gray levels are assumed to be in the ranges between 0 and 1 (0≤x≤1, 0≤y≤1), then p(y) =1. Then we have: dy=p(x)dx or dy/dx=p(x) (2) i.e., the mapping function y=f(x) for histogram equalization is: x y=f X = 0 p u du = p x − p 0 = p(x) (3) Where x p x = 0 p u du , p 0 = 0 (4) Is the cumulative probability distribution of the input image, which monotonically increases . Intuitively, histogram equalization is realized by the following: Figure 4. Image equalization If p(x) is high, P(x) has a steep slope, dy will be wide, We work in YUV color space, commonly used in causing p(y) to be low to keep p(y)dy=p(x)dx ; video, where Y is the monochromatic luminance If p(x) is low, P(x) has a shallow slope; dy will be channel, which we will refer to simply as intensity, narrow, causing p(y) to be high. while U and V are the chrominance channels, encoding the color [Jack 2001]. The algorithm is given as input an intensity volume For discrete gray levels, the gray level of the input x Y(x; y; t) and outputs two color volumes U(x; y; t) takes one of the L discrete values: x∈ {0,1,2, . . , L − 22 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 7, July 2011 and V(x; y; t). To simplify notation we will use Then the pixel (x0, y0, t) is a neighbor of pixel (x1, boldface letters (e.g. r; s) to denote (x; y; t) triplets. y1, t +1) if: Thus, Y(r) is the intensity of a particular pixel. As mentioned in the introduction, we wish to impose the x0 + vx x0 , y0 + vy y0 − (x1 , y1 ) < ���� (12) constraint that two neighboring pixels r; s should have similar colors if their intensities are similar. Thus, we The tow field vx(x0),vy(y0) is calculated using a wish to minimize the difference between the color standard motion estimation algorithm [Lucas and U(r) at pixel r and the weighted average of the colors Kanade 1981]. Note that the optical flow is only used at neighboring pixels: to define the neighborhood of each pixel, not to propagate colors through time. Now given a set of 2 ���� ���� = ���� (���� ���� − ����∈����(����) ������������ ����(����)) (9) locations ri where the colors are specified by the user u(ri) = ui , v(ri) = vi we minimize J(U), J(V) subject to Where wrs is a weighting function that sums to one, these constraints. Since the cost functions are large when Y(r) is similar to Y(s) , and small when quadratic and the constraints are linear, this the two intensities are different. Similar weighting optimization problem yields a large, sparse system of functions are used extensively in image segmentation linear equations, which may be solved using a number algorithms (e.g. [Shi and Malik 1997; Weiss 1999]), of standard methods. Our algorithm is closely related where they are usually referred to as affinity to algorithms proposed for other tasks in image functions. We have experimented with two weighting processing. In image segmentation algorithms based functions. The simplest one is commonly used by on normalized cuts [Shi and Malik 1997], one image segmentation algorithms and is based on the attempts to find the second smallest eigenvector of the squared difference between the two intensities: matrix D -W where W is a n pixels×npixels matrix 2 ���� −���� ���� )2 /2�������� wrs∝ ���� −(���� (10) whose elements are the pair wise affinities between pixels (i.e., the r; s entry of the matrix is wrs) and D is A second weighting function is based on the a diagonal matrix whose diagonal elements are the normalized correlation between the two intensities: sum of the affinities (in our case this is always 1). The second smallest eigenvector of any symmetric matrix 1 A is a unit norm vector x that minimizes xTAx and is ������������ ∝ 1 + ���� 2 ���� ���� − �������� (���� ���� − �������� )(11) ���� orthogonal to the first eigenvector. By direct Where μr and σr are the mean and variance of the inspection, the quadratic form minimized by intensities in a window around r. normalized cuts is exactly our cost function J, that is The correlation affinity can also be derived from xT(Dj-W)x = J(x). Thus, our algorithm minimizes the assuming alocal linear relation between color and same cost function but under different constraints. In intensity [Zomet and Peleg 2002; Torralba and image denoising algorithms based on anisotropic Freeman 2003]. Formally, it assumes that the color at diffusion [Perona and Malik 1989; Tang et al. 2001] a pixel U(r) is a linear function of the intensity Y(r): one often minimizes a function similar to equation 1, but the function is applied to the image intensity as U(r) = aiY(r)+bi and the linear coefficients ai ,bi are the same for all pixels in a small neighborhood around well. r. This assumption can be justified empirically [Zomet and Peleg 2002] and intuitively it means that when the IV. EDGE REMOVING intensity is constant the color should be constant, and when the intensity is an edge the color should also be In the provided method the kind of edge removing an edge (although the values on the two sides of the is very significant. The more edge vector edge can be any two numbers). While this model adds segmentation, the more details must be presented on to the system a pair of variables per each image the image color. Because of this reason, SOBEL window, a simple elimination of the ai, bi variables algorithm is utilized. With regard to type of the edge yields an equation equivalent to equation 1 with a vector, the desired colors are put on the image (fig.5). correlation based affinity function. The notation r ∈ N(s) denotes the fact that r and s are neighboring pixels. In a single frame, we define two pixels as neighbors if their image locations are nearby. Between two successive frames, we define two pixels as neighbors if their image locations, after accounting for motion, are nearby. More formally, let vx(x, y), vy(x,y) denote the optical flow calculated at time t. 23 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 7, July 2011 Figure 8. The reduction of disturbance on the colorized image V. RESULTS Figure 5. Desired colors are drawn on RGB image. The result of colorization can be observed in fig.6. Figure 9 displays another sample of colorization on the image. Figure 9. The result from colorization on the image The histogram of RGB image color can be observed in figure 10. Figure 6. Colorized image on RGB image Looking accurately at the image, we can notice noises and disturbances on the image that should be reduced and minimized so a middle filter is used for this purpose that is a middle mask presented in figure 7 is applied for each color. (a) Figure 7. Low- pass filter, a quiet plaice The results obtained from this filter are illustrated in figure 8. (b) 24 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 7, July 2011 AUTHORS PROFILE Hossein Ghayoumi Zadeh received the B.Sc.degree in electrical engineering with honors from shahid ragae teacher training University, Tehran ,Iran, in 2008. He is now M.Sc. student in electrical and electronic engineering at Sabzevar Tarbiat Moallem University in Iran. His current research interests include computer vision, pattern recognition, image processing, artificial neural network, intelligent systems, fuzzy (c) logic and soft computing and etc. Figure 10. (a)histogram of red band.(b) histogram of green band.(c) histogram of blue band Hojat Jafari received the B.Sc.degree in Conclusion electrical engineering with honors from The Islamic Azad University – Sabzevar Branch, Sabzevar,Iran, in 2007. He is now M.Sc. In this paper, the gray level image is converted to RGB student in electrical and electronic image by using image processing techniques combined engineering at Sabzevar Tarbiat Moallem with noise and disturbance reduction. The power of this University in Iran. His current research method is appropriately confirmed by results. interests include computer vision, pattern recognition, image processing, artificial neural network, intelligent systems and etc. REFERENCE [1] R.C.Gonzalez and R.E. Woods, Digital Image Processing Alireza Malvandi received the B.Sc.degree (second ed.), AddisonWesley Publishing, Reading, MA (1987). in electrical engineering with honors from The Islamic Azad University – Sabzevar [2] T. Welsh, M. Ashikhmin and K. Mueller, Transferring color to greyscale images, in: ACM SIGGRAPH 2002 Conference Branch ,Sabzevar ,Iran. He is now M.Sc. Proceedings (2002) pp. 277-280. student in electrical and electronic [3] E. Reinhard, M. Ashikhmin, B. Gooch and P. Shirley, Color engineering at Sabzevar Tarbiat Moallem transfer between images, IEEE Transactions on Computer University in Iran. His current research Graphics and Applications 21 (2001) (5), pp. 34-41. interests include computer vision, pattern recognition, image [4] A. Hertzmann, C.E. Jacobs, N. Oliver, B. Curless and D.H. processing, artificial neural network, intelligent systems and etc. Salesin, “Image analogies”, ACM SIGGRAPH 2001 Conference Proceedings, 327-340(2001) . [5] Z. Pan, Z. Dong and M. Zhang, A new algorithm for adding color to video or animation clips, in: Proceedings of WSCG Javad Haddadnia received his B.Sc. and International Conference in Central Europe on Computer M.Sc. degrees in electrical and electronic Graphics, Visualization and Computer Vision (2004) pp . 515-519. engineering with the first rank from [6] T. Horiuchi, Estimation of color for gray-level image by Amirkabir University of Technology, Tehran, probabilistic relaxation, in: Proceedings of IEEE Iran, in 1993 and 1995, respectively. He International Conference on Pattern Recognition (2002) pp. received his Ph.D. degree in electrical 867-870. thor’s engineering from Amirkabir University of [7] T. Horiuchi and S. Hirano, Colorization algorithm for Technology, Tehran, Iran in 2002. He joined Tarbiat Moallem grayscale image by propagating seed pixels, in: Proceedings University of Sabzevar in Iran since 2002 as an associated of IEEE International Conference on Pattern Recognition Photo professor. His research interests include neural network, digital (2003) pp. 457- 460. image processing, computer vision and medical Engineering. He [8] A. Levin, D. Lischinski and Y. Weiss, Colorization using has published several papers in these areas. He has served as a optimization, in: ACM SIGGRAPH 2004 Conference Proceedings (2004) pp. 689-694. Visiting Research Scholar at the University of Windsor, Canada during 2001- 2002. He is a member of SPIE, CIPPR, and IEICE. [9] Liron Yatziv and Guillermo Sapiro, Fast image and video colorization using chrominance blending, in: IEEE Transactions on Image Processing, Vol. 15, No. 5, May 2006, pp. 1120-1129. [10] Shi, J., Malik, J., 1997.Normalized cuts and image segmentation. In: Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 731-737. [11] Sy´kora, D., Buria´nek, J.,Zara, J., 2003. Segmentation of Black and White Cartoons, In: Proceedings of Spring Conference on Computer Graphics, pp. 245-254. 25 http://sites.google.com/site/ijcsis/ ISSN 1947-5500

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Journal of Computer Science and Information Security (IJCSIS ISSN 1947-5500) is an open access, international, peer-reviewed, scholarly journal with a focused aim of promoting and publishing original high quality research dealing with theoretical and scientific aspects in all disciplines of Computing and Information Security. The journal is published monthly, and articles are accepted for review on a continual basis. Papers that can provide both theoretical analysis, along with carefully designed computational experiments, are particularly welcome.
IJCSIS editorial board consists of several internationally recognized experts and guest editors. Wide circulation is assured because libraries and individuals, worldwide, subscribe and reference to IJCSIS. The Journal has grown rapidly to its currently level of over 1,100 articles published and indexed; with distribution to librarians, universities, research centers, researchers in computing, and computer scientists.
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Since 2009, IJCSIS is published using an open access publication model, meaning that all interested readers will be able to freely access the journal online without the need for a subscription. We wish to make IJCSIS a first-tier journal in Computer science field, with strong impact factor.
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