An Iterative Optimization Algorithm for Lens Distortion Correction Using Two-Parameter Models

Abstract

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.

Automatic Distortion Rectification of Wide-Angle Images Using Outlier Refinement for Streamlining Vision Tasks

“…The consistency in the pixel information, especially regarding the stretching issue, was clearly investigated, as shown in Figure 10 below. The stretching along the edges caused the inconsistency in the case of traditional OpenCV and Santana et al [5]. Due to the refinement of outliers, the stretching was significantly reduced in the proposed method.…”

“…Although Bukhari et al [4] was able to rectify the distortions with reliable performance for nonsevere distortion cases, it suffers from longer processing times and deformed outputs in the case of heavy distortions. The Hough parametric space approaches from Aleman et al [3] and Santana et al [5] were able to rectify the wide-angle and fish-eye lens models with reasonable performance. However, the heavy dependency on hyper-parameters and disability to handle samples acquired using low-quality camera sensors under low-light conditions make it less reliable for ADAS and video surveillance applications.…”

“…Self-calibration totally depends on the scene aspects such as lines, curves, points at infinity, edge candidates, special elements, etc. Several methodologies have been proposed to get past these challenges to formulate robust self-calibration techniques [3][4][5] but they still get severely caught off with inevitable real-world scenarios such as variation in illuminations, shadow castings, different timings in the day and night, and scenes with limited scene attributes to rely on.…”

“…A few studies were formulated to explore the arithmetic approach on the line curvatures to estimate the distortions [4]. A few others exploited the scene lines to estimate the parameters with intense iterative optimizations [3,5] within parametric Hough spaces, and a few employed the semiautomatic algebraic approach of tracing line segments over the curved lines for estimating distortions [18]. The semiautomatic study proposed by Alvarez et al [18] heavily requires user-interaction in the line tracing approach, which is not appropriate for real-time usage.…”

“…The pixel-point error calculations were made using difference of distances from two pixel points in the rectified image distortion center and given GT distortion center on difference samples. The average pixel-point errors were calculated against [5,18] algorithms and the results are stated in Table 3 below. The average pixel-point error in the case of Alvarez et al [18] and Santana et al [5] appears to be higher for the examples that have higher variations in the distortion center.…”