Efficient extraction of metric measurements for planar scene under 2D homography with the help of planar circles

Abstract

Extraction of metric properties from perspective view is a challenging task in many machine vision applications. Most conventional approaches typically first recover the perspective transformation parameters up to a similarity transform and make measurements in the resulting rectified image. In this paper, a new approach is proposed to allow quick and reliable Euclidean measures to be made directly from a perspective view without explicitly recovering the world plane. Unlike previous planar rectification strategies, our approach makes use of planar circles to help identify the image of the absolute conic, which makes it capable of performing effective rectification under many difficult cases that are unable to be treated with other rectification approaches. This is made possible by solving the images of the circular points in closed-form from the vanishing line and the image of one arbitrary planar circle and by exploiting the invariant relationship between the circular points and the absolute conic under projective transformation. Subsequently, planar Euclidean measures can be made directly from the image plane. The practical advantages and the efficiency of this method are demonstrated by experiments on both synthetic and real scenes.