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IMAGE INTERPOLATION USING CLASSIFICATION AND STITCHING

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IMAGE INTERPOLATION USING CLASSIFICATION AND STITCHINGNickolaus Mueller, Truong Q. NguyenUniversity of California - San DiegoDepartment of Electrical and Computer Engineering9500 Gilman Drive, MC 0407, La Jolla, CA 92093-0407ABSTRACTImage interpolation is a well-studied signal processing appli-cation that continues to receive substantial attention from theresearch community. It has been recognized that taking intoaccount the presence of edges in an image can significantlyimprove the resulting interpolated image. Many techniquesmodify the interpolation method in the presence of edges toavoid common artifacts such as blurring, blocking and ring-ing. We propose to improve upon this idea by fusing thebest features of several interpolation methods. This can bedone using a novel region classification algorithm to deter-mine which method is best suited to a particular region. Fromthis information, we can use image mosaic techniques to fusethe m ethods into a result that contains both sharp edges anddetailed textures.Index Terms— image interpolation, mosaicing, m ultires-olution transforms, block matching, image denoising1. INTRODUCTIONThe goal of image interpolation is to produce a higher resolu-tion version of a given image. Several potential applicationsexist for image interpolation, such as enhancing the resolutionof an image taken by a low-quality camera on a cell phoneor displaying video from a low resolution source on a highdefinition television. Basic techniques, such as bilinear andbicubic interpolation, accomplish this at a low cost, but theysacrifice quality o f the final image by assuming that the un-derlying “true image” is piecewise polynomial.In recent literature, several algorith ms imp r ove the sub-jective quality of an interpolated image by taking into accountedge regions of an image during interpolation. The methodsemployed by these algorithms ran ge from explicitly avoidinginterpolation across edges [1, 2] to probabilistic formulationsthat involve calculating an optimal Wiener filter [3].We propose that a single interpolation method is inade-quate for producing the highest possible quality of resolutionenhancement. We view an image as consisting of smoothareas, edges and texture regions, and we use different inter-polation methods to enhance these regions. Using a regionclassification scheme in conjunction with an image stitchingalgorithm , we are able to seamlessly blend the results to cre-ate a high quality interpolation result.2. IMAGE INTERPOLATIONFor our purposes, we consider the simplified problem of usingtwo interpolation methods to create the final image. An inter-polation method based on the wavelet and contourlet trans-forms is used to generate the regions determined to containhigh levels of texture as determined by the region classifica-tion algorithm. For the regions that are classified as eitheredges or smooth regions, an interpolation method based on a3-D block-matching denoising technique is used.2.1. Contourlet-Based InterpolationThe interpolation method proposed in [4] increases the res-olution of a low resolution image by assuming that the lowresolution image is obtained from the low-pass output of aknown wavelet filter. An initial estimate of the image is thenformed by zero-padding the high-pass wavelet coefficientsand inverting the wavelet transform. The algorithm then it-erates between two constraints to achieve the final high reso-lution image. Using the new contourlet transform proposed in[5], hard thresholding of the transform coefficients enforces asparsity constraint while preserving edges and texture regionsof the image. The second constraint is then met by enforcingthe assumption that the low-pass output should be equal to theoriginal low resolution ima ge.Let C and C−1be the forward and inverse contourlettransforms, respectively. Given an image ˆx and a thresholdparameter T , the sparsity constraint of the high resolution im-age is obtained by˜x = C−1DTCˆx,where DTis a m atrix that performs hard-thresholding on co-efficients based on the parameter T .Given a low resolution image xL,letˆx0be the initial highresolution estimate obtained by zero-padding the high-passwavelet coefficients. Let W and W−1be the forward and in-verse wavelet transforms, respectively, and let P be the diag-onal matrix of 1’s and 0’s that preserves the low-pass wavelet901978-1-4244-1764-3/08/$25.00 ©2008 IEEE ICIP 2008Authorized licensed use limited to: Univ of Calif San Diego. Downloaded on February 23, 2009 at 16:41 from IEEE Xplore. Restrictions apply.coefficients and zeros out the high-pass subbands. The matrixcorresponding to preservation of the high-pass coefficients isthen given by P⊥= I − P where I is the identity matrix.Then for any image y, the second constraint is met byˆy = W−1(P⊥Wy+ PWˆx0).2.2. 3-D Block Matching Interpolation2.2.1. AlgorithmThe contourlet-based interpolation technique is capable ofproducing sharp edges, but ringing artifacts are often presentin these regions. We seek a method of interpolating an im-age that will not produce these artifacts near object edges.The main tool that we use to achieve this is the 3-D blockmatching denoising technique used in [6]. The idea behind3-D block matching denoising is to collect similar 2-D imag efragments into a 3-D array, apply a 3-D wavelet transform,and then use ha rd thresholding on the resulting coefficients.Applying a 3-D transform to similar 2-D fragments improvessparsity and therefore a better d enoising result is achieved.Our proposed interpolation using the 3 -D block matchingalgorithm is a slight modification on the contourlet interpola-tion method. We use the same constraint on the low resolutionimage as found in the contourlet interpolation method. Thekey difference is that now we use the 3-D block matching al-gorithm to denoise the result. The procedure of enforcing thisnew sparsity constraint followed by enforcement of the con-straint on the low pass wavelet coefficients is then iterated toproduce the final image.2.2.2. MotivationOur motivation for use of the 3-D block matching algorithmfor preserv ing sharp edg e s is as f ollows. Consider the simplerproblem of denoising a noisy one-dimensional step edge us-ing a two-dimensional discrete wavelet tranform. Let f be anideal step function o n [0, 1],f(ti)=0 i =1,...,Δai=Δ+1,...,nwhere ti= i/n and i =1,...,n. The known samplesare corrupted by white Gaussian noise (WGN), expressed asy(i)=f(ti)+σ i,


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