Faculty Publications
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Item Curvature driven diffusion coupled with shock for image enhancement/reconstruction(Inderscience Publishers, 2011) Padikkal, P.; George, S.Curvature driven diffusion is widely used for image denoising and inpainting. Among the curvature driven diffusion techniques Gauss Curvature Driven Diffusion (GCDD) became a prominent image denoising method due to its capability to retain some important structures with non zero curvatures, like curved edges, corners etc. Unlike many other non-linear diffusion techniques, the curvature driven diffusion hardly has any inverse diffusion characteristics. In this work we propose to introduce a shock term along with the GCDD term to enhance the edges while smoothing-out the noise. This technique will preserve some important structures and enhance them while denoising the image. The experiments clearly demonstrates the efficiency of the method. Copyright © 2011 Inderscience Enterprises Ltd.Item Fourth-order variational model with local-constraints for denoising images with textures(2011) Padikkal, P.; George, S.A fourth-order partial differential equation-based approach with a set of local constraints is proposed in this paper, to denoise the images without losing much of the semantically important features like edges and textures. The results provided both in terms of qualitative and quantitative measures substantially endorse the capability of the method. © 2011 Inderscience Enterprises Ltd.Item Reconstruction of signals by standard Tikhonov method(2011) George, S.; Padikkal, P.In this work we propose a standard Tikhonov regularization approach for obtaining the signal f from the observed signal ye. The observed signal is distorted by an additive noise or error e. Deviating from the usual assumption on the bound onItem Shock coupled fourth-order diffusion for image enhancement(Elsevier Ltd, 2012) Padikkal, P.; George, S.In this paper a shock coupled fourth-order diffusion filter is proposed for image enhancement. This filter converges at a faster rate while preserving and enhancing edges, ramps and textures present in the images. The proposed filter diffuses with varying magnitudes in the directions normal to the level-curve and along it. The magnitude of the directional diffusion is controlled by a diffusion function, meant to provide a good response in the direction along the level-curves, than across them. The proposed filter can still preserve the planar approximation of the image, thereby avoiding the discrepancy caused due to the staircase effect, as in the second-order counterparts. The anisotropic property of the filter is thoroughly studied, analyzed and demonstrated with perspective and quantitative results. The performance of the proposed filter is compared with the state-of-the-art methods for image enhancement. The quantitative and perspective measures provided endorse the capability of the method to enhance various kinds of images. © 2012 Elsevier Ltd. All rights reserved.Item A time-dependent switching anisotropic diffusion model for denoising and deblurring images(2012) Padikkal, P.; George, S.A conditionally anisotropic diffusion based deblurring and denoising filter is introduced in this paper. This is a time-dependent curvature based model and the steady state can be attained at a faster rate, using the explicit time-marching scheme. The filter switches between isotropic and anisotropic diffusion depending on the local image features. The switching of the filter is controlled by a binary function, which returns either zero or one, based on the underlying local image gradient features. The parameters in the proposed filter can be fine-tuned to get the desired output image. The filter is applied to various kinds of input test images and the response is analyzed. The filter is found to be effective in the reconstruction of partially textured, textured, constant-intensity and color images, as is evident from the results provided. © 2011 Copyright Taylor and Francis Group, LLC.Item Fabrication of nanoporous alumina and their structural characteristics study using SEM image processing and analysis(2012) Choudhari, K.S.; Padikkal, P.; Udayashankar, N.K.Nanoporous anodic aluminum oxide (AAO) membranes were fabricated by a two-step anodization process. Quantitative structural characterization was carried out using scanning electron microscopy images of the fabricated anodized alumina. An algorithm based on mathematical morphology was developed to extract pore size distribution with average, minimum, and maximum pore diameter of the nanoporous alumina. This technique of obtaining quantitative data based on image analysis could be an efficient, unbiased, and reliable method and can be used to control the fabrication parameters of anodization process. Copyright © Taylor & Francis Group, LLC.Item Gauss curvature-driven image inpainting for image reconstruction(Taylor and Francis Ltd. michael.wagreich@univie.ac.at, 2014) Padikkal, P.; George, S.In this paper, we propose a third-order Gauss curvature-driven geometric diffusion Partial Differential Equation for inpainting and reconstructing images. In Gauss curvature-driven diffusion processes, the rate of diffusion is directly proportional to the Gauss curvature value of the level curve. Since the Gauss curvature is the product of principal curvatures, its value become zero when even one of the principal curvatures is zero. Therefore, when Gauss curvature is used as a driving function for diffusion, the evolution preserves some of the meaningful structures with nonzero mean curvature values (viz. curvy edges, corners, etc.). However, the noise features always have nonzero Gauss curvature value and hence the diffusion process effectively removes them. The inpainting property of geometric PDE based on the Gauss curvature is being used in this work for reconstructing lost or degraded information. A filter is proposed to reconstruct the original images from the observed blurred and noisy images along with inpainting the desired image domain. © 2014 Copyright The Chinese Institute of Engineers.Item Inverse free iterative methods for nonlinear ill-posed operator equations(Hindawi Publishing Corporation 410 Park Avenue, 15th Floor, 287 pmb New York NY 10022, 2014) Argyros, I.K.; George, S.; Padikkal, P.We present a new iterative method which does not involve inversion of the operators for obtaining an approximate solution for the nonlinear ill-posed operator equation F (x) = y. The proposed method is a modified form of Tikhonov gradient (TIGRA) method considered by Ramlau (2003). The regularization parameter is chosen according to the balancing principle considered by Pereverzev and Schock (2005). The error estimate is derived under a general source condition and is of optimal order. Some numerical examples involving integral equations are also given in this paper. © 2014 Ioannis K. Argyros et al.Item A Curvature-Driven Image Inpainting Approach for High-Density Impulse Noise Removal(Springer Verlag, 2014) Padikkal, P.; Bini, A.A.A PDE-based image inpainting method is proposed in this work for removing high-density impulse noise in images. In this model, the diffusion or inpainting process is driven by the difference curvature of the level curve. The proposed framework has two stages. In the first stage the noisy pixels are detected and they are piped to the second stage. In the second stage, these noisy pixels are inpainted using the information from their neighborhood. The connectivity principle is well realized and the edges and fine details are preserved well by the proposed model. The proposed method is compared (in terms of denoising capability) with the state-of-the-art impulse denoising models. The performance is quantified in terms of statistical quality measures. It is observed that the proposed method is capable of restoring images corrupted with high-density impulse noise (even up to 90 %). The experiments clearly demonstrate the effective restoration capacity of the proposed image inpainting model. © 2014 King Fahd University of Petroleum and Minerals.Item A convex regularization model for image restoration(Elsevier Ltd, 2014) Padikkal, P.Many variational formulations are introduced over the last few years to handle multiplicative data-dependent noise. Some of these models seek to minimize the Total Variation (TV) norm of the absolute gradient function subject to given constraints. Since the TV-norm (well-defined in the space of bounded variations (BVs)) minimization eventually results in the formation of piece-wise constant patches during the evolution process, the filtered output appears blocky. In this work the block effect (commonly known as staircase effect) is being handled by using a convex combination of TV and Tikhonov filters, which are defined in BV and L2 (square-integrable functions) spaces, respectively. The constraint for the minimizing functional is derived based on a maximum a posteriori (MAP) regularization approach, duly considering the noise distributions. Therefore, this model is capable of denoising speckled images, whose intensity is Gamma distributed. The results are demonstrated both in terms of visual and quantitative measures. © 2014 Elsevier Ltd. All rights reserved.