INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)

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1 INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN (Print) ISSN (Online) Volume 3, Issue 3, October- December (2012), pp IAEME: Journal Impact Factor (2012): (Calculated by GISI) IJECET I A E M E SPECTRAL APPROACH TO IMAGE PROJECTION WITH CUBIC B-SPLINE INTERPOLATION 1. M. Nagaraju Naik, 2. P. Rajesh Kumar 1. Assoc. Prof., Mahaveer Institute of Science and Technology, Hyderabad, A P, India. nagraju_naik@yahoo.co.in 2. Assoc. Prof, A.U. College of Engineering (Autonomous), Vizag, A P, India. rajeshauce@gmail.com. ABSTRACT This paper proposes an energy spectrum interpolating method based on energy variations in an image. As the size of an image is increased, so the pixels, which comprise the image, become increasingly visible, making the image to appear soft. Super scalar representation of image sequence is limited due to image information present in low dimensional image sequence. To project an image frame sequence into high-resolution static or fractional scaling value, a scaling approach is developed based on energy spectral interpolation by combining both Fast Fourier transform and Bicubical interpolation. Keywords: Bicubical interpolation, Super Resolution, Digital image, smoothness I. INTRODUCTION Image processing is a form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or a set of characteristics or parameters related to the image. Most image-processing techniques involve treating the image as a two-dimensional signal and applying standard signal-processing techniques to it. In the area of image processing there is a need to improve the resource requirement for progressive image processing using resource optimization techniques. In earlier approaches it is observed that image sequencing can be improved by optimizing usage of available resources. The earlier proposed methods based on super resolution [1-4] were observed to be developed keeping available resources and there constrains in mind. Today s applications demand is high-resolution representation of gray scale and color [8] of image data for real time interfacing and communications. With the incorporation of developed optimization scheme as 153

2 outlined above can provide a significant improvement in coding but in current scenario these methods may get constrained. As the available resources such as bandwidth, power, coding techniques are limited to certain minimum values. To achieve high resolution representation images are to be retained for good visual quality. As resource optimizations are constrained, coding based on vector regression [6, 7, 9] techniques are stated to improve quality in image processing. To achieve higher visual quality the stated interpolation approaches were carried out in frequency representation [5, 10] using transformation techniques. Though these interpolation methods are efficient to produce a HR image from a low LR image they are not able to provide efficient visibility. So a new interpolating method is proposed in this paper based on energy evaluation of an image using FFT and interpolating by Bicubical interpolation and the paper is organized as follows. Section II gives brief information about different types of interpolation methods, Section III gives describes the proposed method and section IV gives the system architecture. The results and conclusions are drawn in Section V and Section VI respectively. II. INTERPOLATION APPROACH Interpolation is the process of estimating the values of a continuous function from discrete samples. Image processing applications of interpolation include image magnification or reduction, sub pixel image registration, to correct spatial distortions, and image decompression. There are so many interpolation techniques like linear interpolation, bilinear interpolation and Cubical interpolations. II.1 Bilinear interpolation Bilinear Interpolation determines the grey level value from the weighted average of the four closest pixels to the specified input coordinates, and assigns that value to the output coordinates. First, two linear interpolations are performed in one direction and then one more linear interpolation is performed in the perpendicular direction. For one-dimension Linear Interpolation, the number of grid points needed to evaluate the interpolation function is two. For Bilinear Interpolation (linear interpolation in two dimensions), the number of grid points needed to evaluate the interpolation function is four. For linear interpolation, the interpolation kernel is: u(s) = {0 s > 1 {1 s s < 1.. (1) Where s is the distance between the point to be interpolated and the grid point being considered. The interpolation coefficients c k = f (x k ). II.2 Bi-Cubic Interpolation Cubic Convolution Interpolation determines the grey level value from the weighted average of the 16 closest pixels to the specified input coordinates, and assigns that value to the output coordinates. The image is slightly sharper than that produced by Bilinear Interpolation, and it does not have the disjointed appearance produced by Nearest Neighbor Interpolation. First, four one-dimension cubic convolutions are performed in one direction (horizontally in this paper) and then one more one-dimension cubic convolution is performed in the perpendicular 154

3 direction (vertically in this paper). This means that to implement a two-dimension cubic convolution, a one-dimension cubic convolution is all that is needed. For one-dimension Cubic Convolution Interpolation, the number of grid points needed to evaluate the interpolation function is four, two grid points on either side of the point under consideration. For Bicubic Interpolation (cubic convolution interpolation in two dimensions), the number of grid points needed to evaluate the interpolation function is 16, two grid points on either side of the point under consideration for both horizontal and vertical directions. Though these interpolation methods are efficient to produce a HR image from a low LR image they are not able to provide efficient visibility. So a new interpolating method is proposed in this paper based on energy evaluation of an image using FFT and interpolating by Bicubical interpolation, and is discussed in next section. III. PROPOSED METHOD This method is accomplished in two steps. First the image interpolation is done by Bicubical interpolation and second the projection is done using Fast Fourier transform. III.1 Image Coding The following figure describes the image conversion from LR to HR. On the left hand side four low-resolution images are shown Motion estimation is used to estimate the pixel positions of the three images with respect to the 1 st image. Once this information is calculated accurately, it is possible to project this information on a desired high-resolution grid. Figure 1 Conversion of low-resolution images to high-resolution images Any Super-resolution algorithm is to estimate the motion between given LR frames. A good ME is a hard prerequisite for SR. In this paper the motion is restricted to shifts and rotation, so a very simple (though accurate) approach is enough for image registration. Rotate the individual images at all the angles and correlate them with the first image. The angle that gives the maximum correlation is the angle of rotation between them. The angle can be calculated as follows. Angle (i) = max index (correlation (I 1 (θ), Ii (θ))) (2) Where I 1 (θ) is the pixel intensity of the reference pixel and Ii(θ) is the intensity of the i th pixel. It turned out that though the first method is computationally expensive, but gives more precise results, so it was used in this project. III.2 Shift Calculation Once rotation angle is known between different images, shift calculation can be performed. Before calculating the shift, all the images are rotated with respect to the first image. For determining the amount of shift in any pixel of an image, 155

4 Fi(u T ) = e j2πu s. F 1 (u T ) (3) This is obtained by applying Fourier Transform of a reference pixel matrix. The shift angle s from the above relation can be calculated as: s = [angle (Fi(u T )/ F 1 (u T ))]/2π (4) And in matrix form, s= [ x y] T (5) Where, U(x, y) is the pixel coordinate, x is the variation of current x-position from reference x- position, y is the variation of current y-position from reference y-position, Fi (u T ) is the transform of transposed i th pixel, F 1 (u T ) is the transform of transposed reference pixel, s is the shift angle respectively. In the next step the projection of pixel values is going to be done and called as iterative back projection. III.3 Iterative Back Projection The iterative back-projection (IBP) technique [6] can accomplish the HR image interpolation and de-blurring simultaneously. Its underlying idea is that the reconstructed HR image from the degraded LR image should produce the same observed LR image if passing it through the same blurring and down sampling process. The iterative back-projection (IBP) technique can minimize the reconstruction error by iteratively back projecting the reconstruction error into the reconstructed image. Taking into account several considerations, a method that was fairly simple and straightforward - Fourier algorithm (P-G Algorithm) is proposed. III.3.1 Fourier Projection This method assumes two things: Some of the pixel values in the high-resolution grid are known. The high frequency components in the high-resolution image are zero. It works by projecting HR grid data on the two sets described above. The steps are: Form a high resolution grid. Set the known pixels values from the low-resolution images (after converting their pixel position to the ref frame of first low-resolution image). The position on the HR grid is calculated by rounding the magnified pixel positions to nearest integer locations. Set the high-frequency components to zero in the frequency domain. Force the known pixel values in spatial domain. Iterate. 156

5 Figure 2 Flow Chart for P-G Algorithm By making the high-frequency equal to zero, this method tries to interpolate the unknown values and so correct the aliasing for low-frequency components. Also, by forcing the known values, it does predict some of the high-frequency values. The set of images walks through the actual working of this algorithm. Initially, the HR grid is filled with known pixel values and makes the unknown pixel values to be zero. In the next step, the higher frequencies can be made zero in the frequency domain. This effectively is low-pass filtering the image. The unknown pixels now have got some value, and the known values have gone down in amplitude, due to low-pass filtering. The magnitude of known pixels can be increased by forcing them to what they should be. This again creates some high-frequency components by iteratively doing this again and again, correcting the lowfrequency values (by guessing the values for unknown pixels) and finding some the highfrequency components by forcing the known values is achieved. By juggling between the two data sets, i.e. forcing the high frequency to zero and forcing the known values, we have estimated the value of unknown pixels. Thus a super resolute image is produced and the model of the system related to this paper is shown below. IV. SYSTEM MODEL The Architecture of Proposed Method is shown below, here frame generator takes low resolution image sequences as input and converts it into static frames. These static frames converted into grey level in the pre-processing step. Next these grey level frames converted into frequency domain using FFT transformation to compare we are using Cubic-B-Spline method. The transformed data to than interpolated (spectral projection/spectral resolution) using FFT and Cubic-B-Spline. The projected data is aligned over a predefined grid format to obtain high resolution image. This image sequence is compared with original data to extract Mean Error. 157

6 Figure 3 Architecture of proposed method The concept of resolution projection of image stream is developed using spectral and frequency interpolations and evaluated for computational time and retrieval accuracy. IV.1 Operational Description 1) Input Interface: The developed system is processed over a very low image sequence represented in low dimensional projection. To evaluate the performance of suggested scaling system, a low dimensional, colored image streams are read and transformed into frame sequence using input interface unit. The processed frame sequence is then passed to a pre-processing unit for the equalization of input frame sequence for further processing. 1) Pre-Processing: This unit extracts the gray pixel intensity of the continuous frame sequence and pass to the transformation unit for further processing. The gray pixel intensity are extracted from the input information segregated colored information. 2) Transformation Unit: This unit transforms the given input information into power spectral distribution using Fourier transformation. It is observed in conventional architectures that the energy distribution of the original data could be used as interpolating information to represent high quality images. But it is observed that spectral distributions need not be sufficient for accurate interpolation, as the frequency resolution for spectrum energy coefficients may vary distinctly. To achieve better representation Cubic-B-Spline method is incorporated for such requirement. 3) Interpolation: Once the spectral resolutions were obtained, the pixel is to project on a higher grid level depending upon the scale value. Scaling of the image is achieved by interpolating the pixel information based on energy distribution of the given image sequence. To achieve better interpolation rather than energy resolution, spectral resolution could provide highresolution accuracy developed using Cubic-B-Spline approach. The interpolated information is then projected on a grid projection to represent the given low dimensional image sequence into high-resolution image sequence. The results related to functional description of system architecture are shown below. V. RESULTS & OBSERVATIONS For the evaluation of the suggested method a simulation implementation is carried out for a sequence of video frames. A real time video sample 158

7 Figure 4 Original image sequence considered The original frame sequence is taken for processing of the image coding system. The original frame sequence is taken at a very low resolution with pixel representation of 150x250 size frame. These 5 frame sequences are passed to the developed system for pre processing. Figure 5 Scaled image sequences at 1:2.5 ratio using Fourier approach The interpolation is carried out for the spectral distributed image coefficients obtained after Fourier transformation. The interpolation is made for the spectral distributed data as shown above. Figure 6 Scaled image sequences at 1:2.5 ratio using cubical-b-spline approach The observation clearly illustrates the accuracy in retrieval in terms of visual quality as compared to the conventional Fourier based coding technique P roc essing tim e plot Fourier interpolation C u b ic -b -s p lin e in t e rp o la tio n Computation time(sec) O bservation Figure 7 Computation time taken for the two methods 159

8 The system developed is also evaluated for the computation time taken for the computation and projection of the frame sequence for interpolation. The total time taken for reading, processing and projecting is considered for the processing system and the conclusions are drawn below. VI. CONCLUSIONS The energy spectral resolution projecting is carried out using Fourier transform techniques, where a low dimensional image sequence is projected to a high grid based on energy distribution. To improve resolution accuracy, a frequency based projection scheme is developed. To realize the frequency spectral resolution Cubic-B-Spline method is used. It is observed that the resolution accuracy with respect to visual quality, mean error and computational time is comparatively improved compared to conventional Fourier based interpolation technique. For the evaluation of the suggested approach, the system is tested over various low dimensions of image sequence and scaled over fixed and fractional scaling value. Due to the higher visual quality the system find applications in various real time applications such as Television processing, Image conferencing, Internet image processing, Tele medicine etc. VII. REFERENCES [1] S. P. Kim, N. K. Bose, and H. M. Valenzuela, Recursive reconstruction of high resolution image from noisy undersampled multiframes, IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp , June [2] S. Farsiu, M. D. Robinson, M. Elad, and P. Milanfar, Fast and robust multiframe super resolution, IEEE Trans. Image Processing, vol. 13, pp , Oct [3] X. Li and M. T. Orchard, New edge-directed interpolation, IEEE Trans. Image Proc., vol. 10, pp , Oct [4] H. A. Aly and E. Dubois, Specification of the observation model for regularized image upsampling, IEEE Trans. Image Processing, vol. 14, pp , May [5] R. S. Prendergast and T. Q. Nguyen, Spectral modelling and Fourier domain recovery of high-resolution images from jointly undersampled image sets, under review for IEEE Trans. Image Proc., submitted Dec. 18, [6] K. S. Ni and T. Q. Nguyen, Image superresolution using support vector regression, IEEE Trans. Image Proc., vol. 16, pp , June [7] S. C. Park, M. K. Park, and M. G. Kang, Super-resolution image reconstruction: a technical overview, IEEE Signal Processing Mag., vol. 20, pp , May [8] B. Narayanan, R. C. Hardie, K. E. Barner, and M. Shao, A computationally efficient superresolution algorithm for image processing using partition filters, IEEE Trans. on Circ. Syst. For Image Technology, vol. 17, no. 5, pp , May [9] S. Farsiu, M. Elad, and P. Milanfar, Image-to-image dynamic superresolution for grayscale and color sequences, EURASIP Journal of Applied Signal Processing, Special Issue on Superresolution Imaging, vol. 2006, pp. 1 15, [10] R. C. Hardie, A fast image super-resolution algorithm using an adaptive Wiener filter, IEEE Trans. Image Proc., vol. 16, no. 12, pp , Dec

9 M. Nagaraju Naik received his B.Tech from S.V.University, Thirupati, A. P., India in Masters Degree in Digital Systems and Computer Electronics from JNTU Anantapur A.P., India in He is pursuing Ph.D in Andhra University College of Engineering (Autonomous). His interest area Video Processing, Image Processing and Signal Processing Dr. P. Rajesh Kumar, Associate Professor Department of ECE, Andhra University Vizag. A.P., India. Received his Ph.D degree in 2007 on Radar Signal Processing.He is presently engaed in research in Image Processing. His interest area Signal Processing, Radar Signaling, Image Processing. 161