Calibration and rectification for reflection stereo

This paper presents a calibration and rectification method for single-camera range estimation using a single complex image with a transparent plate or a double-sided half-mirror plate, which are collectively called a reflection stereo. The range to an object is obtainable by finding the correspondence on a constraint line in the complex image, which consists of a surface and a rear-surface reflected image in the transparent plate, or also includes a transmitted and internal reflected image through a double-sided half-mirror plate. The range estimation requires extrinsic parameters of the reflection stereo that include the shape and position of the plate and its refraction index. The proposed method assumes that the plate is non-parallel but planar for a local region around the point of interest in the complex image. The method estimates the extrinsic parameters from a set of displacements in the complex images. Experiments using real images demonstrate the effectiveness of the proposed calibration and rectification method along with fine range estimation results.