Disparity from Monogenic Phase

Disparity estimation is a fundamental problem of computer vision. Besides other approaches, disparity estimation from phase information is a quite wide-spread technique. In the present paper, we have considered the influence of the involved quadrature filters and we have replaced them with filters based on the monogenic signal. The implemented algorithm makes use of a scale-pyramid and applies channel encoding for the representation and fusion of the estimated data. The performed experiments show a significant improvement of the results. 1 Disparity Estimation In this paper we introduce a new method for estimating the disparity between two images. Disparity typically occurs in a stereo camera setting. Due to the depth in space, the image plane position of an object point differs in the left and the right image. Knowing this displacement, it is possible to determine the depth of the object point and therefore its 3D position if the camera has been calibrated beforehand. Neglecting the problems of calibration and back-projection into 3D space, we solely focus on the problem of estimating the disparity. 1.1 Geometric Settings The geometric setting of a stereo system is sketched in Fig. 1. This figure shows a simplified stereo configuration of two identical cameras with parallel optical axes and with a distance between the optical centers of ∣∣ol − or∣∣. The image planes are at a distance of z0 from their optical centers and the object is located at a depth of z. Shifting the left optical center onto the right one yields the configuration in the right part of Fig. 1. The two projections of the house are shifted copies of each other with distance d, the disparity. From a simple geometric consideration it can be concluded that ∣∣ol − or∣∣ /z = d/z0, and hence z = z0 ∣∣ol − or∣∣ /d. For a general camera configuration, the geometric setting is much more complicated. However, the depth increases always with decreasing disparity (see e.g. [1], page 211, and [2], page 87) and the relationship between disparity and depth can be computed using the calibrated matrices of the two cameras. The detailed analysis of these relationships is out of the scope of this paper. ? This work has been supported by DFG Grant FE 583/1-1. z 0 d ep th z disparity |ol − or| |ol − or| left image plane image plane right