Abstract In this paper we develop a theory of non-parametric self-calibration. Recently, schemes have been devised for non-parametric laboratory calibration, but not for self-calibration.
We allow an arbitrary warp to model the intrinsic map-ping, with the only restriction that the camera is central and that the intrinsic mapping has a well-defined non-singular matrix derivative at a finite number of points under study.We give a number of theoretical results, both for in-finitesimal motion and finite motion, for a finite number of observations and when observing motion over a dense im-age, for rotation and translation. 22815
Our main result is that through observing the flow in-
duced by three instantaneous rotations at a finite number
of points of the distorted image, we can perform projective
reconstruction of those image points on the undistorted im-
age. We present some results with synthetic and real data.
1. Introduction
Classical calibration of the intrinsic parameters of a cam-
era is done by identifying the image points corresponding
to known points on a calibration object. Self-calibration on
the other hand is performed by identifying correspondences
while observing an unknown static scene undergoing an un-
known but rigid motion. In both classical calibration and
self-calibration, the internals of the camera are assumed to
follow some model with a fairly limited number of param-
eters. Recently, methods have been developed that perform
calibration without assuming a parametric model for the
camera intrinsics. This is done by calibrating each image
ray separately while observing a known object undergoing
known or unknown motion.
The topic of this paper is to develop a theory of self-
calibration without requiring a parametric form for the in-
trinsics of the camera. We focus on the case of flow induced by three infinitesimal rotations and observed at a finite num-
ber of locations in the distorted image. Our main result is
in short that it is possible to perform projective reconstruc-
tion of the observed locations. The main result is relatively
easy to state precisely, so we state it here as a preview of the
theory. The following is essentially a restatement of Theo-
rem 4:
Theorem 1 If we observe the flow vectors a x , b x and
c x at the points x of the distorted image, induced by three
instantaneous rotations, we obtain a projective reconstruc-
tion of the undistorted image points y by setting If the scene is distant enough relative to the camera ge-
ometry and motion, the camera can always be modeled as
central and the motion approximated by a rotation. Some
insects rotate their heads intensively, and although we do
not claim that they perform self-calibration in the manner
suggested by our theory, we find self-calibration with few
or no assumptions on the camera an exciting prospect. In
principle, one could then over time cope with any aberra-
tions present, and in theory solve for ’everything’ including
an unknown scene and unknown camera.
To provide some context to our main result, we also sum-
marize theory arising from various assumptions, including
infinitesimal and finite rotations and translations, and mo-
tion observed in a finite number of locations as well as
over the complete dense image sphere. With two flow-fields
from a purely rotating camera, it is possible in theory to re-
cover the intrinsics of the camera without a priori assuming
a parametric form. Moreover, starting from a smooth but
otherwise arbitrary intrinsic mapping, two flow-fields from
a purely translating camera determine the intrinsic mapping
up to a projective transformation of the image plane. Fur-
ther, non-parametric self-calibration is in theory possible 非参数自校准英文文献和中文翻译:http://www.751com.cn/fanyi/lunwen_15596.html