Projective Rectification with Minimal Geometric Distortion
P. Hsien-Huang, Chih-Cheng Che · 2007
Scene Reconstruction, Pose Estimation and Tracking 222pair of identical cameras placed side-by-side and pointed in the same direction, known as a rectilinear stereo rig, the epipolar lines will coincide with scan lines (x-axis) of the images.Given this ideal epipolar geometry, the correspondent points will lie on the same scan line in the two images.However, for an arbitrary placement of cameras, the epipolar lines are skew and the 1-D search will still be time consuming.Whether the imagery is used for stereo vision or stereoscopic video, we would like the image pair to be taken from an ideal epipolar-geometry.When the epipolar geometry is not in ideal form, the image pairs can be warped to make correspondent points lie on the same scan lines.This process is known as image rectification, and can be accomplished by applying a 2D projective transforms, or homographies, to each image.The homography is a linear one to one transformation of the projective plane, which is represented by a × 3 3 non-singular matrix.The rectified images can then be treated as obtained by a rectilinear stereo rig and the correspondence problem is greatly simplified.Since most stereo algorithms assume input images having ideal epipolar geometry, image rectification is usually a pre-requisite operation for stereoscopic related applications.The idea of rectification has long been used in photogrammetry (Slama, 1980).The techniques originally used were optical-based, but now are replaced by software methods that model the geometry of optical projection.The software-based photogrammetric approaches, similar to most of the computer vision ones, assume the knowledge of projection matrices or cameras parameters (Ayache & Hanse, 1988)(Ayache & Lustman, 1991) (Fusiello, et al., 2000)These methods require camera parameters to compute a pair of homographies for transformations.The necessity of camera calibration is one of their disadvantages.In contrast to these traditional approaches, several researchers have developed techniques called projective rectification to rectify images directly without using camera parameters.They utilized the epipolar geometry of the acquired images and various criteria to compute the homographies.Robert et al. (Robert, 1997) attempted to find the transform that best preserves orthogonality around image centers.Hartley (Hartley, 1999) proposed using minimization of the differences between matching points for the solution of homographies.He also gave a detailed theoretical presentation of the projective rectification.Loop and Zhang (Loop & Zhang, 1999) suggested decomposing each homography into projective and affine components.They then found the projective component that minimizes a defined projective distortion criterion.Gluckman and Nayar (Gluckman & Nayar, 2001) recently presented a stereo rectification method, which takes geometric distortion into account and tries to minimize the effects of resampling.Pollefeys (Pollefeys et al., 1999) proposed a simple and efficient algorithm for general two view stereo image.The other available approaches include (Papadimitriou and Dennis, 1996) which considers only the special case of partially aligned cameras, and (Al-Shalfan et al., 2000) which requires the estimation of the epipolar geometry.Although these proposed methods provided many possibilities for projective rectification, they all solve the problem indirectly.That is, they must explicitly estimate the fundamental matrix before rectification.Since the solution of fundamental matrix has its own uncertainty (Zhang, 1998) this indirect approach might obtain unpredictable rectifying results.Isgrò and Trucco (Isgrò & Trucco, 1999) adopted a different procedure and obtained homographies directly without first computing the fundamental matrix.However, in order How to referenceIn order to correctly reference this scholarly work, feel free to