Image rectification

Abstract: Plenoptic cameras are gaining attention for their unique light gathering and post-capture processing capabilities. We describe a decoding, calibration and rectification procedure for lenselet-based plenoptic cameras appropriate for a range of computer vision applications. We derive a novel physically based 4D intrinsic matrix relating each recorded pixel to its corresponding ray in 3D space. We further propose a radial distortion model and a practical objective function based on ray reprojection. Our 15-parameter camera model is of much lower dimensionality than camera array models, and more closely represents the physics of lenselet-based cameras. Results include calibration of a commercially available camera using three calibration grid sizes over five datasets. Typical RMS ray reprojection errors are 0.0628, 0.105 and 0.363 mm for 3.61, 7.22 and 35.1 mm calibration grids, respectively. Rectification examples include calibration targets and real-world imagery.

Abstract: This paper gives a new method for image rectification, the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of “matched epipolar projections”. These are projections in which the epipolar lines run parallel with the x-axis and consequently, disparities between the images are in the x-direction only. The method is based on an examination of the fundamental matrix of Longuet-Higgins which describes the epipolar geometry of the image pair. The approach taken is consistent with that advocated by Faugeras (1992) of avoiding camera calibration. The paper uses methods of projective geometry to determine a pair of 2D projective transformations to be applied to the two images in order to match the epipolar lines. The advantages include the simplicity of the 2D projective transformation which allows very fast resampling as well as subsequent simplification in the identification of matched points and scene reconstruction.

Abstract: Image rectification is the process of applying a pair of 2D projective transforms, or homographies, to a pair of images whose epipolar geometry is known so that epipolar lines in the original images map to horizontally aligned lines in the transformed images. We propose a novel technique for image rectification based on geometrically well defined criteria such that image distortion due to rectification is minimized. This is achieved by decomposing each homography into a specialized projective transform, a similarity transform, followed by a shearing transform. The effect of image distortion at each stage is carefully considered.

Abstract: We describe the geometry constraints and algorithmic implementation for metric rectification of planes. The rectification allows metric properties, such as angles and length ratios, to be measured on the world plane from a perspective image. The novel contributions are: first, that in a stratified context the various forms of providing metric information, which include a known angle, two equal though unknown angles, and a known length ratio; can all be represented as circular constraints on the parameters of an affine transformation of the plane-this provides a simple and uniform framework for integrating constraints; second, direct rectification from right angles in the plane; third, it is shown that metric rectification enables calibration of the internal camera parameters; fourth, vanishing points are estimated using a Maximum Likelihood estimator; fifth, an algorithm for automatic rectification. Examples are given for a number of images, and applications demonstrated for texture map acquisition and metric measurements.