Backward Diffusion Methods for Digital Halftoning

We examine using discrete backward diffusion to produce digital halftones. The noise introduced by the discrete approximation to backwards diffusion forces the intensity away from uniform values, so that rounding each pixel to black or white can produce a pleasing halftone. We formulate our method by considering the Human Visual System norm and approximating the inverse of the blurring operator. We also investigate several possible mobility functions for use in a nonlinear backward diffusion equation for higher quality results

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

Nonlinear Diffusion and Image Contour Enhancement

The theory of degenerate parabolic equations of the forms $$u_t=(\Phi(u_x))_{x} \quad {\rm and} \quad v_{t}=(\Phi(v))_{xx}$$ is used to analyze the process of contour enhancement in image processing, based on the evolution model of Sethian and Malladi. The problem is studied in the framework of nonlinear diffusion equations. It turns out that the standard initial-value problem solved in this theory does not fit the present application since it it does not produce image concentration. Due to the degenerate character of the diffusivity at high gradient values, a new free boundary problem with singular boundary data can be introduced, and it can be solved by means of a non-trivial problem transformation. The asymptotic convergence to a sharp contour is established and rates calculated.Comment: 29 pages, includes 6 figure

Multi Stage based Time Series Analysis of User Activity on Touch Sensitive Surfaces in Highly Noise Susceptible Environments

This article proposes a multistage framework for time series analysis of user activity on touch sensitive surfaces in noisy environments. Here multiple methods are put together in multi stage framework; including moving average, moving median, linear regression, kernel density estimation, partial differential equations and Kalman filter. The proposed three stage filter consisting of partial differential equation based denoising, Kalman filter and moving average method provides ~25% better noise reduction than other methods according to Mean Squared Error (MSE) criterion in highly noise susceptible environments. Apart from synthetic data, we also obtained real world data like hand writing, finger/stylus drags etc. on touch screens in the presence of high noise such as unauthorized charger noise or display noise and validated our algorithms. Furthermore, the proposed algorithm performs qualitatively better than the existing solutions for touch panels of the high end hand held devices available in the consumer electronics market qualitatively.Comment: 9 pages (including 9 figures and 3 tables); International Journal of Computer Applications (published

Left-Invariant Diffusion on the Motion Group in terms of the Irreducible Representations of SO(3)

In this work we study the formulation of convection/diffusion equations on the 3D motion group SE(3) in terms of the irreducible representations of SO(3). Therefore, the left-invariant vector-fields on SE(3) are expressed as linear operators, that are differential forms in the translation coordinate and algebraic in the rotation. In the context of 3D image processing this approach avoids the explicit discretization of SO(3) or $S_2$, respectively. This is particular important for SO(3), where a direct discretization is infeasible due to the enormous memory consumption. We show two applications of the framework: one in the context of diffusion-weighted magnetic resonance imaging and one in the context of object detection

A fourth-order PDE denoising model with an adaptive relaxation method

In this paper, an adaptive relaxation method and a discontinuity treatment of edges are proposed to improve the digital image denoising process by using the fourth-order partial differential equation (known as the YK model) first proposed by You and Kaveh. Since the YK model would generate some speckles into the denoised image, a relaxation method is incorporated into the model to reduce the formation of isolated speckles. An additional improvement is employed to handle the discontinuity on the edges of the image. In order to stop the iteration automatically, a control of the iteration is integrated into the denoising process. Numerical results demonstrate that such modifications not only make the denoised image look more natural, but also achieve a higher value of PSNR

A PDE-based Mathematical Method in Image Processing: Digital-Discrete Method for Perona-Malik Equation

In this study, we propose a new and effective algorithm for image processing. The method based on the combination of digital topology, partial differential equations and finite difference scheme is called the digital-discrete method. We try to solve the Perona-Malik equation using the digital-discrete method. We use the MATLAB package program when analyzing images. The analyzes we make on the images show how the algorithm is useful, effective and open to development

Properties of higher order nonlinear diffusion filtering

This paper provides a mathematical analysis of higher order variational methods and nonlinear diffusion filtering for image denoising. Besides the average grey value, it is shown that higher order diffusion filters preserve higher moments of the initial data. While a maximum-minimum principle in general does not hold for higher order filters, we derive stability in the 2-norm in the continuous and discrete setting. Considering the filters in terms of forward and backward diffusion, one can explain how not only the preservation, but also the enhancement of certain features in the given data is possible. Numerical results show the improved denoising capabilities of higher order filtering compared to the classical methods