Color Image Reconstruction Using A New R'G'I Model 1

Problem statement: A new color model for digital image was discussed; this model can be used to separate low and high frequencies in the image without loosing any information from the image. Approach: A comparative study between different color models (RGB, HSI) applied to a very large microscopic image analysis and the proposed model was presented. Such analysis of different color models is needed in order to carry out a successful detection and therefore a classification of different Regions of Interest (ROIs) within the image. Results: This, in turn, allows both distinguishing possible ROIs and retrieving their proper color for further ROI analysis. This analysis was not commonly done in many biomedical applications that deal with color images. Other important aspects were the computational cost of the different processing algorithms according to the color model. The proposed model took these aspects into consideration and the experimental results showed the advantages of proposed model compared with HSI model by decreasing the computational time for various image-processing operations. Conclusion: The proposed model can be used in different application such as separating low and high frequencies from the image.


INTRODUCTION
Color models: Digital image, or bitmap, is a structure representing a rectangular grid of pixels, or points of colors, on a computer monitor. The color of each pixel defined in the RGB color space where each pixel defined by three bytes-one byte each for red, green and blue.
Digital image processing methods include various operations such as: • Tone processing: Brightening, lightening, contrast stretching ( Fig. 1) • Image enhancement in spatial domain (histogram processing, gamma correction, image filtration in spatial domain and other methods) Color models provide a standard way to specify a particular color, by defining a 3D coordinate system and a subspace that contains all constructible colors within a particular model. Any color that can be specified using a model will correspond to a single point within the subspace it defines. Each color model is oriented towards either specific hardware (RGB, CMY, YIQ), or image processing applications (HSI) [1][2][3] . The RGB model: In the RGB model, an image consists of three independent image planes, one in each of the primary colors: red, green and blue. Specifying particular colors is by specifying the amount of each of the primary components present. Figure 1 shows the geometry of the RGB color model for specifying colors using a Cartesian coordinate system. The grayscale spectrum, i.e., those colors made from equal amounts of each primary, lies on the line joining the black and white vertices [4][5][6] .  This is an adaptive model, i.e., the colors present in the light add to form new colors and is appropriate for the mixing of colored light for example.
The RGB model is used for color monitors and most video cameras.
The HSI model: As mentioned above, color may be specified by the three quantities hue, saturation and intensity. This is the HSI model and the entire space of colors that may be specified in this way is shown in Fig. 3.
The HSI model showing the HSI solid on the left and the HSI triangle on the right, formed by taking a horizontal slice through the HSI solid at a particular intensity. Hue is measured from red and saturation is given by distance from the axis. Colors on the surface of the solid are fully saturated, i.e., pure colors and the grayscale spectrum is on the axis of the solid. For these colors, hue is undefined.
Conversion between the RGB model and the HSI model is quite complicated. The intensity is given by where the quantities R, G and B are the amounts of the red, green and blue components, normalized to the range [0, 1]. The intensity is therefore just the average of the red, green and blue components. The saturation is given by [5][6][7][8][9] : for the GB sector ( ) Where the min(R,G,B) term is really just indicating the amount of white present. If any of R, G or B is zero, there is no white and we have a pure color [1] . For color images, standard image processing methods possible to provide according to the algorithm (Fig. 4).
The proposed color model for digital image processing: The proposed color model includes the following Stages of digital image processing: Image processing using only the intensity I.
Apply the method proposed in [10] to separate low and high frequencies in the black and white image. Inverse transforms:    Now this model can be applied to the proposed method in [10] and can be implemented in following way: • Read the color image • Perform direct transoms • Separate low and high frequencies in the black and white image using the method proposed in [10] • Return back the black and white frequencies to color frequencies using inverse transforms

MATERIALS AND METHODS
The proposed model was implemented using mat lab.
More than 500 color images were treated using HSI model. For each color model we find the total time needed to perform each of the following tasks: • Direct conversion (transform) • Inverse conversion • Inverse conversion with gamut correction • Brightness with gamut correction • Contrast stretching with gamut correction • Histogram equalization with gamut correction • Histogram equalization without gamut correction The same tasks for each color image were treated using the proposed R'G'I model and for each task the acceleration was calculated.

RESULTS
The proposed model was implemented using deferent color images with deferent type of image processing operations (Brightening, contrast stretching and image equalization).
The implementation results were compared with other results obtained by using other existing models. Table 1 contains the experimental results and shows the enhancements, which can be achieved using the proposed model.  Fig. 6: Speed up using proposed color model Figure 6 shows the speedup using the proposed model.

DISCUSSION
Direct and inverse conversions using the proposed model were tested using different images. The proposed conversion was tested using an original color image to get the gray image and without applying any processing we got the color image using inverse conversion, the experimental results showed that the correlation between the original image and the obtained color image was always equal one, which means full matching between the original image and the obtained one.
The HSI and R'G'I models were applied and the experimental results show that the proposed model has always a speed-up greater than 1 in different steps of processing such as: Direct conversion, inverse conversion and image stretching and image equalization.
The proposed model was implanted using a lot of color images and the obtained results shows that this medal can replace the HSI model because of its efficiency.

CONCLUSION
A new color model for digital image processing was proposed, the experimental results show the efficiency of using this model comparing with other existing models performing deferent types of image processing operations.
The acceleration factor was computed for the proposed method and HSI method, the obtained results show that the acceleration (speedup) ranges from 1.29 (when performing image equalization) to 4.5 (when performing inverse transforms).