Spectral approach to image projection with cubic
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    Spectral approach to image projection with cubic Spectral approach to image projection with cubic Document Transcript

    • International Journal of Electronics and JOURNAL OF ELECTRONICS AND ISSN 0976 – INTERNATIONAL Communication Engineering & Technology (IJECET), 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)ISSN 0976 – 6464(Print)ISSN 0976 – 6472(Online)Volume 3, Issue 3, October- December (2012), pp. 153-161 IJECET© IAEME: www.iaeme.com/ijecet.aspJournal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEMEwww.jifactor.com 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
    • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEoutlined above can provide a significant improvement in coding but in current scenario thesemethods may get constrained. As the available resources such as bandwidth, power, codingtechniques are limited to certain minimum values. To achieve high resolution representationimages 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 imageprocessing. To achieve higher visual quality the stated interpolation approaches were carried outin frequency representation [5, 10] using transformation techniques.Though these interpolation methods are efficient to produce a HR image from a low LR imagethey are not able to provide efficient visibility. So a new interpolating method is proposed in thispaper based on energy evaluation of an image using FFT and interpolating by Bicubicalinterpolation and the paper is organized as follows. Section II gives brief information aboutdifferent types of interpolation methods, Section III gives describes the proposed method andsection IV gives the system architecture. The results and conclusions are drawn in Section V andSection VI respectively.II. INTERPOLATION APPROACHInterpolation is the process of estimating the values of a continuous function from discretesamples. Image processing applications of interpolation include image magnification orreduction, sub pixel image registration, to correct spatial distortions, and image decompression.There are so many interpolation techniques like linear interpolation, bilinear interpolation andCubical interpolations.II.1 Bilinear interpolationBilinear Interpolation determines the grey level value from the weighted average of the fourclosest 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 linearinterpolation is performed in the perpendicular direction. For one-dimension LinearInterpolation, the number of grid points needed to evaluate the interpolation function is two. ForBilinear Interpolation (linear interpolation in two dimensions), the number of grid points neededto 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 coefficientsck = f (xk). II.2 Bi-Cubic InterpolationCubic Convolution Interpolation determines the grey level value from the weighted average ofthe 16 closest pixels to the specified input coordinates, and assigns that value to the outputcoordinates. The image is slightly sharper than that produced by Bilinear Interpolation, and itdoes not have the disjointed appearance produced by Nearest Neighbor Interpolation.First, four one-dimension cubic convolutions are performed in one direction (horizontally in thispaper) and then one more one-dimension cubic convolution is performed in the perpendicular 154
    • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEdirection (vertically in this paper). This means that to implement a two-dimension cubicconvolution, a one-dimension cubic convolution is all that is needed.For one-dimension Cubic Convolution Interpolation, the number of grid points needed toevaluate the interpolation function is four, two grid points on either side of the point underconsideration. For Bicubic Interpolation (cubic convolution interpolation in two dimensions), thenumber of grid points needed to evaluate the interpolation function is 16, two grid points oneither 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 imagethey are not able to provide efficient visibility. So a new interpolating method is proposed in thispaper based on energy evaluation of an image using FFT and interpolating by Bicubicalinterpolation, and is discussed in next section.III. PROPOSED METHODThis method is accomplished in two steps. First the image interpolation is done by Bicubicalinterpolation and second the projection is done using Fast Fourier transform.III.1 Image CodingThe following figure describes the image conversion from LR to HR. On the left hand side fourlow-resolution images are shown Motion estimation is used to estimate the pixel positions of the stthree images with respect to the 1 image. Once this information is calculated accurately, it ispossible to project this information on a desired high-resolution grid. Figure 1 Conversion of low-resolution images to high-resolution imagesAny Super-resolution algorithm is to estimate the motion between given LR frames. A good MEis a hard prerequisite for SR. In this paper the motion is restricted to shifts and rotation, so a verysimple (though accurate) approach is enough for image registration. Rotate the individual imagesat all the angles and correlate them with the first image. The angle that gives the maximumcorrelation is the angle of rotation between them. The angle can be calculated as follows . Angle (i) = max index (correlation (I1(θ), Ii (θ))) ………(2)Where I1(θ) is the pixel intensity of the reference pixel and Ii(θ) is the intensity of the ith pixel. Itturned out that though the first method is computationally expensive, but gives more preciseresults, so it was used in this project.III.2 Shift CalculationOnce 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. Fordetermining the amount of shift in any pixel of an image, 155
    • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME Fi(uT) = ej2πu∆s. F1 (uT) ______(3)This is obtained by applying Fourier Transform of a reference pixel matrix. The shift angle ∆sfrom the above relation can be calculated as: ∆s = [angle (Fi(uT)/ F1(uT))]/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 (uT) is thetransform of transposed ith pixel, F1 (uT) is the transform of transposed reference pixel, ∆s is theshift angle respectively.In the next step the projection of pixel values is going to be done and called as iterative backprojection.III.3 Iterative Back ProjectionThe iterative back-projection (IBP) technique [6] can accomplish the HR image interpolation andde-blurring simultaneously. Its underlying idea is that the reconstructed HR image from thedegraded LR image should produce the same observed LR image if passing it through the sameblurring and down sampling process. The iterative back-projection (IBP) technique can minimizethe reconstruction error by iteratively back projecting the reconstruction error into thereconstructed image. Taking into account several considerations, a method that was fairly simpleand straightforward - Fourier algorithm (P-G Algorithm) is proposed.III.3.1 Fourier ProjectionThis 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
    • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME Figure 2 Flow Chart for P-G AlgorithmBy making the high-frequency equal to zero, this method tries to interpolate the unknown valuesand so correct the aliasing for low-frequency components. Also, by forcing the known values, itdoes predict some of the high-frequency values. The set of images walks through the actualworking of this algorithm. Initially, the HR grid is filled with known pixel values and makes theunknown pixel values to be zero.In the next step, the higher frequencies can be made zero in the frequency domain. Thiseffectively is low-pass filtering the image. The unknown pixels now have got some value, andthe known values have gone down in amplitude, due to low-pass filtering. The magnitude ofknown pixels can be increased by forcing them to what they should be. This again creates somehigh-frequency components by iteratively doing this again and again, correcting the low-frequency values (by guessing the values for unknown pixels) and finding some the high-frequency components by forcing the known values is achieved. By juggling between the twodata sets, i.e. forcing the high frequency to zero and forcing the known values, we have estimatedthe value of unknown pixels.Thus a super resolute image is produced and the model of the system related to this paper isshown below.IV. SYSTEM MODELThe Architecture of Proposed Method is shown below, here frame generator takes low resolutionimage sequences as input and converts it into static frames. These static frames converted intogrey level in the pre-processing step. Next these grey level frames converted into frequencydomain using FFT transformation to compare we are using Cubic-B-Spline method. Thetransformed data to than interpolated (spectral projection/spectral resolution) using FFT andCubic-B-Spline. The projected data is aligned over a predefined grid format to obtain highresolution image. This image sequence is compared with original data to extract Mean Error. 157
    • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME Figure 3 Architecture of proposed methodThe concept of resolution projection of image stream is developed using spectral and frequencyinterpolations and evaluated for computational time and retrieval accuracy.IV.1 Operational Description1) Input Interface: The developed system is processed over a very low image sequencerepresented in low dimensional projection. To evaluate the performance of suggested scalingsystem, a low dimensional, colored image streams are read and transformed into frame sequenceusing input interface unit. The processed frame sequence is then passed to a pre-processing unitfor the equalization of input frame sequence for further processing.1) Pre-Processing: This unit extracts the gray pixel intensity of the continuous frame sequenceand pass to the transformation unit for further processing. The gray pixel intensity are extractedfrom the input information segregated colored information.2) Transformation Unit: This unit transforms the given input information into power spectraldistribution using Fourier transformation. It is observed in conventional architectures that theenergy distribution of the original data could be used as interpolating information to representhigh quality images. But it is observed that spectral distributions need not be sufficient foraccurate interpolation, as the frequency resolution for spectrum energy coefficients may varydistinctly. To achieve better representation Cubic-B-Spline method is incorporated for suchrequirement.3) Interpolation: Once the spectral resolutions were obtained, the pixel is to project on ahigher grid level depending upon the scale value. Scaling of the image is achieved byinterpolating the pixel information based on energy distribution of the given image sequence. Toachieve better interpolation rather than energy resolution, spectral resolution could provide high-resolution accuracy developed using Cubic-B-Spline approach. The interpolated information isthen projected on a grid projection to represent the given low dimensional image sequence intohigh-resolution image sequence. The results related to functional description of systemarchitecture are shown below.V. RESULTS & OBSERVATIONSFor the evaluation of the suggested method a simulation implementation is carried out for asequence of video frames. A real time video sample 158
    • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME Figure 4 Original image sequence consideredThe original frame sequence is taken for processing of the image coding system. The originalframe 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 approachThe interpolation is carried out for the spectral distributed image coefficients obtained afterFourier transformation. The interpolation is made for the spectral distributed data as shownabove. Figure 6 Scaled image sequences at 1:2.5 ratio using cubical-b-spline approachThe observation clearly illustrates the accuracy in retrieval in terms of visual quality as comparedto the conventional Fourier based coding technique. P ro c e s s in g t im e p lo t 100 F o u rie r in t e rp o la t io n 90 C u b ic -b -s p lin e in t e rp o la t io n 80 70 Computation time(Sec) 60 50 40 30 20 10 0 1 2 O b s e rva t io n Figure 7 Computation time taken for the two methods 159
    • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEThe system developed is also evaluated for the computation time taken for the computation andprojection of the frame sequence for interpolation. The total time taken for reading, processingand projecting is considered for the processing system and the conclusions are drawn below.VI. CONCLUSIONSThe 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 realizethe frequency spectral resolution Cubic-B-Spline method is used. It is observed that theresolution accuracy with respect to visual quality, mean error and computational time iscomparatively improved compared to conventional Fourier based interpolation technique. Forthe evaluation of the suggested approach, the system is tested over various low dimensions ofimage sequence and scaled over fixed and fractional scaling value. Due to the higher visualquality the system find applications in various real time applications such as Televisionprocessing, 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 resolutionimage from noisy undersampled multiframes”, IEEE Trans. Acoust., Speech, Signal Processing,vol. 38, pp. 1013-1027, June 1990.[2] S. Farsiu, M. D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe superresolution”, IEEE Trans. Image Processing, vol. 13, pp. 1327-1344, Oct. 2004.[3] X. Li and M. T. Orchard, “New edge-directed interpolation”, IEEE Trans. Image Proc., vol.10, pp. 1521-1527, Oct. 2001.[4] H. A. Aly and E. Dubois, “Specification of the observation model for regularized image up-sampling,” IEEE Trans. Image Processing, vol. 14, pp. 567-576, May 2005.[5] R. S. Prendergast and T. Q. Nguyen, “Spectral modelling and Fourier domain recovery ofhigh-resolution images from jointly undersampled image sets”, under review for IEEE Trans.Image Proc., submitted Dec. 18, 2006.[6] K. S. Ni and T. Q. Nguyen,“Image superresolution using support vector regression”, IEEETrans. Image Proc., vol. 16, pp. 1596- 1610, June 2007.[7] S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technicaloverview”, IEEE Signal Processing Mag., vol. 20, pp. 21-36, May 2003.[8] B. Narayanan, R. C. Hardie, K. E. Barner, and M. Shao, “A computationally efficient super-resolution algorithm for image processing using partition filters,” IEEE Trans. on Circ. Syst. ForImage Technology, vol. 17, no. 5, pp. 621-634, May 2007.[9] S. Farsiu, M. Elad, and P. Milanfar, “Image-to-image dynamic superresolution for grayscaleand color sequences,” EURASIP Journal of Applied Signal Processing, Special Issue onSuperresolution Imaging, vol. 2006, pp. 1–15, 2006.[10] R. C. Hardie, “A fast image super-resolution algorithm using an adaptive Wiener filter,”IEEE Trans. Image Proc., vol. 16, no. 12, pp. 2953-2964, Dec. 2007. 160
    • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME M. Nagaraju Naik received his B.Tech from S.V.University, Thirupati, A. P. , India in 1999. Masters Degree in Digital Systems and Computer Electronics from JNTU Anantapur A.P., India in 2005. 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