We present a method for the automatic estimation of two-parameter radial distortion models, considering polynomial as well as division models. The method first detects the longest distorted lines within the image by applying the Hough transform enriched with a radial distortion parameter. From these lines, the first distortion parameter is estimated, then we initialize the second distortion parameter to zero and the two-parameter model is embedded into an iterative nonlinear optimization process to improve the estimation. This optimization aims at reducing the distance from the edge points to the lines, adjusting two distortion parameters as well as the coordinates of the center of distortion. Furthermore, this allows detecting more points belonging to the distorted lines, so that the Hough transform is iteratively repeated to extract a better set of lines until no improvement is achieved. We present some experiments on real images with significant distortion to show the ability of the proposed approach to automatically correct this type of distortion as well as a comparison between the polynomial and division models. Source CodeThe source code, the code documentation, and the online demo are accessible at the IPOL web page of this article 1 In this page, an implementation is available for download. Compilation and usage instructions are included in the README.txt file of the archive.

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In this paper, we study lens distortion for still images considering two well-known distortion models: the twoparameter polynomial model and the two-parameter division model. We study the invertibility of these models and we mathematically characterize the conditions for the distortion parameters under which the distortion model defines a one-to-one transformation. This ensures that the inverse transformation is well-defined and the distortion-free image can be properly computed, which provides robustness to the distortion models. A new automatic method to correct the radial distortion is proposed and a comparative analysis for this method is extensively performed using the polynomial and the division models. With the aim of obtaining an accurate estimation of the model, we propose an optimization scheme which iteratively improves the parameters to achieve a better matching between the distorted lines and the edge points.The proposed method estimates twoparameter radial distortion models by detecting the longest distorted lines within the image. This is done by applying the Hough transform extended with a radial distortion parameter. Next, a two-parameter model is estimated using an iterative non-linear optimization scheme. This scheme aims at minimizing the distance from the edge points to their associated lines by adjusting the two distortion parameters as well as the coordinates of the center of distortion. We present some experiments on real images with significant distortion to show the ability of the proposed approach to correct the radial distortion. A visual and quantitative comparison between both automatic two-parameter model estimations indicates that the division model is more efficient for those images showing strong distortion.

In this paper we present an image quantization model based on a reaction-diffusion partial differential equation. The quantized image is given by the asymptotic state of this equation.Existence and uniqueness of the solution are proved in the framework of viscosity solutions. We introduce an L?? stable algorithm in order to compute numerically the solution of the equation, and some experimental results are shown. A new energy functional based on the classical Lloyd method is used to compute the quantizer codewords.