Screened Poisson Equation for Image Contrast Enhancement

Abstract

In this work we propose a discussion and detailed implementation of a very simple gradient domain method that tries to eliminate the effect of nonuniform illumination and at the same time preserves the images details. This model, which to the best of our knowledge has not been explored in spite of its simplicity, acts as a high pass filter. We show that with a single contrast parameter (which keeps the same value in most experiments), the model delivers state of the art results. They compare favorably to results obtained with more complex algorithms. Our algorithm is designed for all kinds of images, but with the special specification of making minimal image detail alteration thanks to a first order fidelity term, instead of the usual zero order term. Experiments on non-uniform medical images and on hazy images illustrate significant perception gain. Source Code The source code and the online demo are accessible at the IPOL web page of this article 1. In this link an ANSI C source code is available for download which produces the same results as the demo. Compilation and usage instructions are included in a README.txt file. The online demo allows one to try Screened Poisson Equation on any uploaded image choosing the tradeoff parameter λ and the level of saturation of the simplest color balance s. By default the values of λ and s are 0.0001 and 0.1 respectively.

Poisson Image Editing

“…Secondly, as the solution of the Poisson equation will have a different dynamic range (compared to the original input image), a normalization strategy must be chosen in order to remap the resulting image to the display range (typically in [0 255]). To that end, the simplest color balance [17,21] proved to be a good normalization method as it can handle a few outliers that may be introduced due to the residual irrotational components of the guidance field. The simplest color balance algorithm simply stretches as much as it can, the values of the three channels Red, Green, Blue (R, G, B), so that they occupy the maximal possible range by applying an affine transform ax + b to each channel.…”

“…For those regions in which f (x) = T the derivative of the mapping function h is not defined, however this does not represent a problem as long as the set {x ∈ R / f (x) = T } is of measure zero. Figure 16 shows the result obtained by integrating the set of amplified gradient (result of Poisson equation with guidance vector v = α(x, y)∇I ) and the result of directly remapping the intensity values of the image according to equation (21). In order to display and compare the output images, both results were rescaled to the interval [0 255] using the simplest color balance algorithm.…”

“…This method is very similar to one of the applications presented in Pérez et al work [24] as Texture flattening, in which only the gradients at edge locations are kept before integrating with the Poisson solver. Finally, in a related work by Morel et al [21] a functional containing a first order term and a zero order term was used with the aim of removing the effect of nonuniform illumination while preserving the fine details of the image. The proposed approach is similar to the one presented by Bhat et al in [7], the main difference lies in the data (zero order) term, while Bhat et al adjust the solution to an input image, Morel et al adjust the solution to be close to it's own mean value.…”

Impact of Dehazing on Underwater Marker Detection for Augmented Reality

“…The SP presented in Morel et al (2014) represents an approach of image enhancement. It uses the Screened Poisson equation in the Fourier domain to remove uneven illumination in the image.…”

“…One of the approaches in image enhancement techniques is to remove uneven illumination and preform color balancing. A contrast enhancement method of Morel et al (2014) uses Screened Poisson Equation as a high-pass filter to remove uneven illumination while preserving details of the image, and includes a simple color balancing method to equalize colors of the result. Some enhancement methods are based on modeling mechanisms of the human visual system.…”