40 research outputs found
Image Demosaicking with Contour Stencils
No full textDemosaicking (or demosaicing) is the problem of interpolating full color information on an image where only one color component is known at each pixel. Most demosaicking methods involve some kind of estimation of the underlying image structure, for example, choosing adaptively between interpolating in the horizontal or vertical direction. This article discusses the implementation details of the method introduced in Getreuer, “Color Demosaicing with Contour Stencils,” 2011. Mosaicked contour stencils first estimate the image contour orientations directly from the mosaicked data. The mosaicked contour stencils are then used to guide a simple demosaicking method based on graph regularization
A Survey of Gaussian Convolution Algorithms
No full textGaussian convolution is a common operation and building block for algorithms in signal and image processing. Consequently, its efficient computation is important, and many fast approximations have been proposed. In this survey, we discuss approximate Gaussian convolution based on finite impulse response filters, DFT and DCT based convolution, box filters, and several recursive filters. Since boundary handling is sometimes overlooked in the original works, we pay particular attention to develop it here. We perform numerical experiments to compare the speed and quality of the algorithms
Total Variation Inpainting using Split Bregman
No full textGiven an image where a specified region is unknown, image inpainting or image completion is the problem of inferring the image content in this region. Traditional retouching or inpainting is the practice of restoring aged artwork, where damaged or missing portions are repainted based on the surrounding content to approximate the original appearance. In the context of digital images, inpainting is used to restore regions of an image that are corrupted by noise or where the data is missing. Inpainting is also used to solve disocclusion, to estimate the scene behind an obscuring foreground object. A popular use of digital inpainting is object removal, for example, to remove a trashcan that disrupts a scene of otherwise natural beauty.
Inpainting is an interpolation problem, filling the unknown region with a condition to agree with the known image on the boundary. A classical solution for such an interpolation is to solve Laplace's equation. However, Laplace's equation is usually unsatisfactory for images since it is overly smooth. It cannot recover a step edge passing through the region.
Total variation (TV) regularization is an effective inpainting technique which is capable of recovering sharp edges under some conditions (these conditions will be explained). The use of TV regularization was originally developed for image denoising by Rudin, Osher, and Fatemi and then applied to inpainting by Chan and Shen. TV-regularized inpainting does not create texture, the method is limited to inpainting the geometric structure
Malvar-He-Cutler Linear Image Demosaicking
No full textImage demosaicking (or demosaicing) is the interpolation problem of estimating complete color information for an image that has been captured through a color filter array (CFA), particularly on the Bayer pattern. In this paper we review a simple linear method using 5 x 5 filters, proposed by Malvar, He, and Cutler in 2004, that shows surprisingly good results
Total Variation Deconvolution using Split Bregman
No full textDeblurring is the inverse problem of restoring an image that has been blurred and possibly corrupted with noise. Deconvolution refers to the case where the blur to be removed is linear and shift-invariant so it may be expressed as a convolution of the image with a point spread function. Convolution corresponds in the Fourier domain to multiplication, and deconvolution is essentially Fourier division. The challenge is that since the multipliers are often small for high frequencies, direct division is unstable and plagued by noise present in the input image. Effective deconvolution requires a balance between frequency recovery and noise suppression.
Total variation (TV) regularization is a successful technique for achieving this balance in deblurring problems. It was originally developed for image denoising by Rudin, Osher, and Fatemi and then applied to deconvolution by Rudin and Osher. In this article, we discuss TV-regularized deconvolution with Gaussian noise and its efficient solution using the split Bregman algorithm of Goldstein and Osher. We show a straightforward extension for Laplace or Poisson noise and develop empirical estimates for the optimal value of the regularization parameter λ
Zhang-Wu Directional LMMSE Image Demosaicking
No full textMost digital cameras capture samples through a color filter array. At every pixel location, the camera observes one of either the red, green, or blue component. Demosaicking (or demosaicing) is the problem of using this incomplete information to estimate all three color components at every pixel. Zhang and Wu proposed an effective solution to this problem in “Color Demosaicking via Directional Linear Minimum Mean-Square-Error Estimation”
Rudin-Osher-Fatemi Total Variation Denoising using Split Bregman
No full textDenoising is the problem of removing noise from an image. The most commonly studied case is with additive white Gaussian noise (AWGN), where the observed noisy image f is related to the underlying true image u by f=u+η and η is at each point in space independently and identically distributed as a zero-mean Gaussian random variable.
Total variation (TV) regularization is a technique that was originally developed for AWGN image denoising by Rudin, Osher, and Fatemi. The TV regularization technique has since been applied to a multitude of other imaging problems, see for example Chan and Shen's book. We focus here on the split Bregman algorithm of Goldstein and Osher for TV-regularized denoising
Linear Methods for Image Interpolation
No full textWe discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation
