Projective rectification of image triplets

Abstract

This paper describes a method for image rectification of a trinocular setup. The rectification method used is an extension of a recent approach based on the fundamental matrix to generate the correcting homographies in the case of a stereo pair. The extended method uses the fact that the triplet of images can be treated as two pairs and that homographies are projections of the different images planes onto new planes. Rectification thus becomes a matter of deciding which plane will be the common one and what transformation or homography is to be applied to each image.

Automated thermal 3D reconstruction based on a robot equipped with uncalibrated infrared stereovision cameras

“…The minimization of Eqs. (32) and (40) was performed by a BFGS algorithm [57] with the initial guess vector composed of the initial intrinsic and baseline parameters and the initial parameters of the hand-eye transformation which are tabulated in Table 3.…”

“…Evolution of the mean value of ∊ r K , the relative error of intrinsic parameters of camera c, and ∊ t a , the relative error of translation parameter versus the standard deviation of noise for fits to Eqs. (32) and (40).…”

“…(5). The distortions are then corrected by applying symmetrical [26,27] or independent [28][29][30][31][32]…”

“…Evolution of the mean value of the error of hand-eye translation parameters, ∊ a t X (high figure) and hand-eye rotation parameters, ∊ a R X , (low figure) versus the noise parameter ν for fits to Eqs. (32) and (40). Thus, the matched points on each of the pairs of images are the inputs to calculate the pair of rectification homographies of the stereovision bench which minimize the projective deformations according to the method described in Section 2.…”

“…This set of quadruplets is used in the self-calibration and reconstruction step presented in Section 3 and to solve Eq. (32). Solving this problem provides the calibration parameters ′ K K T , , , the hand-eye parameters X and two sets Q Q…”