Planar Metric Rectification via planar circles

INVESTIGATORS

Dr. Yisong Chen et al.

 

KEYWORDS:

Projective geometry, Planar homography, Scene recovery, Circular points, Absolute conic, Polynomial equations, Curve fitting.

 

BRIEF DESCRIPTION

Where shall we start? Well...

       

From the first image, can you tell the width-height ratio of the mosaic?

From the second image, can you tell the diameters of the inner and the outer circles if you know that the strip width is 45 cm?

From the third image, can you tell the sizes and the shapes of all geometric elements?

The goal of our work is to remove the projective distortion in the perspective image of a world plane and make Euclidean measures on the plane possible. The classic approach is to recover the homography parameters with the help of several known points. More advanced stratified or unstratified rectification requires the vanishing line to be identified and several additional geometric information to be known.     

Our work provides another attractive solution to this problem. The advantage of our work is that all kinds of length and shape measurement on the world plane can be conveniently done from the image plane without explicitly recovering the homography parameters, provided several circles can be identified on the image plane. The key idea here is that circles are used to identify the image of the circular points. Vanishing line identification might help in our work but is NOT necessary in many cases because in theory two circles can provide adequate information for rectification. Computation of the vanishing line is just a by-product of our approach.

Following are several rectified fronto-parallel view images. Note that in our work it is not necessary to explicitly rectify the image to make Euclidean measurements. We give these images just for comparison. 

       

 

FUNDING AGENCY

N/A

 

PUBLICATIONS

  1. Yisong Chen and Horace H. S. Ip, Planar Metric Rectification by Algebraically Estimating the Image of the Absolute Conic, In Proc. ICPR'2004, August 23-26, Cambridge, UK, Vol. 4, pp. 88-91..

  2. Horace H. S. Ip and Yisong Chen, Planar Rectification by Solving the Intersection of two circles under 2D homography, Pattern Recognition, in press.