DESIGN AND VERIFICATION OF NEWTON RAPSON REGRESSION (NRR) BASED IMAGE INTERPOLATION METHODS

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1 DESIGN AND VERIFICATION OF NEWTON RAPSON REGRESSION (NRR) BASED IMAGE INTERPOLATION METHODS 1 Shubhra Pal, 2 Neeta Nathani 1 MTech Scholar, 2 Assistant Professor 1,2 GGCT, Jabalpur Abstract: The proposed work proposes a unique edge-adaptive image interpolation method using an edge-directed smoothness filter Many image interpolation techniques are already been developed and designed we are proposing a new method is been used for edge-adaptive image interpolation which uses Newton forward difference This difference provides very good grouping of pixels ones we consider target pixel for interpolation Proposed approach estimates the enlarged image from the original image based on an observation model The estimated image is constrained to have many edge-directed smooth pixels which are measured by using the edge-directed smoothness filter Simulation results for the work is developed using MATLAB and produces images with higher visual quality, higher PSNRs and faster computational times than the conventional methods Keywords: PSNR(Peak Signal to Noise Ratio), MSE( Mean Square Error), PEE(Percentage Edge Error) HSV( Hue Saturation and Value), MF( Magnification Factor), NN(Nearest Nabors) I-INTRODUCTION Digital Image is a discrete representation of its continuous counterpart perceived through our eyes, a camera or any such devices Its representation and processing in computer requires storing it in digital format Sampling the image for computer storage often degrades its visual representation in a variety of display units So the image needs further processing to suit our demands Image interpolation is one such image processing task to find the values of the pixels of the image which are not originally present in the image It finds application in medical image processing like X-ray imaging, representation of multimedia content in web, satellite images processing for weather forecasting, industrial inspection for defective manufactured parts which requires image resizing, high resolution In this technological endeavour several interpolation techniques have been developed ranging from very simple to highly complex techniques Image interpolation becomes the pre-processing step for other image processing tasks like image registrations, image rotation Image registration needs interpolation to accurately register the image at sub-pixel level II-METHODOLOGY Proposed method is an Interpolation technique based on Newton forward difference As Newton forward difference method is popular for knowing the unknown from the known set of value but using that method on image is our concern Grouping of pixels around the target pixel based on forward difference, and then interpolation using the difference is the basis of the method For any given finite set of data points, there is only one polynomial, of least possible degree, that passes through all of them Thus, it is more appropriate to speak of "the Newton form of the interpolation polynomial" rather than of "the Newton interpolation polynomial" Like the Lagrange form, it is merely another way to write the same polynomial Figure above is the Grouping of pixels for forth order interpolation, process explain bekow Step-1: find 1 st unknown pixel from known 8 pixels as shown above green is unknown and orange are known Step-2: find 2 nd unknown pixel from known 8 pixels as shown above green is unknown and orange are known here the pixel which was computed in step1 is known now Step-3: find 3 rd to 7 th unknown pixel from known 8 pixels as shown above green is unknown and orange are known IJRTI International Journal for Research Trends and Innovation (wwwijrtiorg) 50

2 Step-4 compute the vertical unknown pixel value from the known pixel here the pink was unknown and orange was the original and green was computed using horizontal interpolation Step-5 Compute the vertical unknown pixel value from the known pixel as step4 and for the full image IJRTI International Journal for Research Trends and Innovation (wwwijrtiorg) 51

3 Image Capture Any RGB image which need to interpolate Histogram Equalisation Equalized Image HSV Stretching Equalized and Enhance colour Image Horizontal Interpolation Vertical Interpolation Horizontally interpolated Image Vertically Interpolated Image Winner Image Filter Final high resolution Image Figure-1 block of Proposed Interpolation technique Proposed block diagram is shown above, the flow of the proposed algorithm as follow:- Step 1: capture or choose any image in any YUY or RGB format, image should be a low resolution image which we require to interpolation Step 2: perform histogram equalization for equalized distribution of colour quantity Step 3: perform HSV (Hue, Saturation amd Value) stretching is for enhancing the quality of image, MAX is the maximal value in R, G, B of all the pixels in the image, and MIN is the minimal one H= { Undefine G B if MAX = Min 60X + 0 if MAX = R and G B 60X G B if MAX = R and G < B B R 60X X R G if MAX = 0 S={ 1 MIN otherwise MAX V=MAX if MAX = G if MAX = B Step 5: Perform horizontal interpolation as explain above it will produce a horizontally interpolated image IJRTI International Journal for Research Trends and Innovation (wwwijrtiorg) 52

4 Step 6: Perform vertically interpolation as explain above it will produce a desire interpolated image Step 7: Perform image filtering for having a good final image III-RESULTS The results are been tested and interpolated on many images here we are presenting standard image of Leena Figure 2: test image and its histogram Figure 3: enhance and Interpolated leena Image Figure 2 shows the original leena image and its histogram in red green and blue colours respectively histogram helps to equalize the leena image Figure3 shows the original leena image along with the enhanced leena image, proposed Interpolated leena image which is been developed at the last after all image enhancement Originally the resolution of leena image was 225x225 after the interpolation is been improved to 2022x2022 Test image name Interpolation Scale SNR MSE BER leena Table 1 Observed results for Leena Image IJRTI International Journal for Research Trends and Innovation (wwwijrtiorg) 53

5 Table 1 results observed for the cameraman image at different Interpolation scale, scale 2 means image is resolution improved to double, scale 6 means image is resolution improved to 6 times for its original, scale 10 means image is resolution improved to 10 times for its original As the scale is improving the SNR is decreasing through the MSE and BER is improving Test image Proposed Work [1] [2] [3] SNR Leena db 3231 db 3546 db 3342 db Cameraman db 2804 db Ganpati db Table 2: Comparative Results From the results shown in the table 2 above it can be clearly seen that proposed work have higher SNR as compare to [1], [2] and [3] when the test image of leena taken and for the test image of cameraman the proposed method achieve better SNR than [1], and the time delay achieve in proposed method for test image of leena is better than [1], it is to be noted that the image of leena and cameraman image are the MATLAB standard images which is been provided for accurate comparison and verification IV-CONCLUSION Proposed work has achieve better results than [1], [2] and [3] and we can conclude that after implementation of our defined approach of interpolation we will have very good and better quality of image as desired modification in it One can also conclude that the time taken for the process not higher than existing work and proposed work has achieve better SNR and MSE then existing work Inage Interpolation can be used of enhancing the image quality Proposed work has explored limits of Interpolation practice & theory Improvement of image interpolation system using approximation approach is providing a good quality image A approximation has been used to system during interpolation and in near future some other approximation method can be implemented Or may possible to develop new approximation method proposed method is using one 2 dimension interpolation row wise an column wise in near future it can be in frame of image REFERENCES [1] Delibasis, KK Kechriniotis, Dept of Comput Sci & Biomed Inf, Univ of Thessaly, Lamia, Greece A New Formula for Bivariate Hermite Interpolation on Variable Step Grids and Its Application to Image Interpolation, IEEE SIGNAL PROCESSING LETTERS, VOL 11, NO 3, MARCH 2017,pp [2] Kazu Mishiba, Taizo Suzuki and Masaaki Ikehara from Department of Electronics and Electrical Engineering, Keio University, Yokohama, Kanagawa , Japan present and publish paper title edge-adaptive image interpolation using constrained least squares in Proceedings of 2016 IEEE 17th International Conference on Image Processing at September 26-29, 2010, Hong Kong [3] Mr ShengHsien Hsieh and Mr Ching Han Chen publish paper entitle adaptive image interpolation using probalistic nural network, IEEE, 2017 [4] Xiangjun Zhang and Xiaolin Wu who are Senior Member in IEEE proposed an research apper entitle Image Interpolation by Adaptive 2-D Autoregressive in Modelling and Soft-Decision Estimation it was publish in ieee transactions on image processing in vol 17, no 6, june 2008 [5] WS Dong, L Zhang, GM Shi, and XLWu, Nonlocal back-projection for adaptive image enlargement, in ICIP 2009, 2009, pp [6] Sung C Park, Min K Park, and Moon G Kang, Superresolution image reconstruction: a technical overview, Signal Processing Magazine, IEEE, vol 20, no 3, pp 21 36, 2003 [7] Specht, DF, Probabilistic neural networks for classification, mapping, or associative memory, IEEE International Conference on Neural Networks, vol1, pp ,jul 1988 [8] Specht, DF, Enhancements to probabilistic neural networks, International Joint Conference on Neural Networks, Volume: 1, pp ,1992 IJRTI International Journal for Research Trends and Innovation (wwwijrtiorg) 54