Self

Self-calibration

of

a

rotating

camera

with

varying

intrinsic

parameters

L.

de

Agapito,

E.

Hayman

and

I.

Reid

Department

of

Engineering

Science,

Oxford

University

Parks

Road,

Oxford,

OX1

3PJ,

UK

tel:

+1865

273168

fax:

+1865

273908

[lourdes,hayman,ian]@robots.ox.ac.uk

Abstract

We

present

a

method

for

self-calibration

of

a

camera

which

is

free

to

rotate

and

change

its

intrinsic

parameters,

but

which

cannot

translate.

The

method

is

based

on

the

so-called

infinite

homography

constraint

which

leads

to

a

non-linear

minimisation

routine

to

find

the

unknown

camera

intrinsics

over

an

extended

sequence

of

images.

We

give

experimental

results

using

real

image

sequences

for

which

ground

truth

data

was

available.

1

Introduction

Camera

calibration

has

always

been

the

subject

of

research

in

the

field

of

machine

vision,

however

it

was

only

relatively

recently

that

the

possibility

of

self-calibration

of

a

camera

simply

by

observing

an

unknown

scene

was

realised

and

explored.

The

first

major

work

to

consider

the

problem

was

[3],

which

showed

that

self-calibration

was

theoretically

and

practically

feasible

for

a

camera

moving

through

an

unknown

scene

with

constant

but

unknown

intrinsics.

Since

that

time

various

methods

have

been

developed

to

deal

with

different

situations.

Table

1

summarises

the

major

contributors

to

date.

In

this

paper

we

address

one

of

the

few

cases

which

has

not

yet

been

explored,

that

of

a

stationary

camera

which

may

rotate

and

change

its

intrinsics.

This

lack

of

attention

is

somewhat

surprising

since

this

situation

is

one

which

occurs

frequently

in

a

variety

of

circumstances:

surveillance

devices

and

cameras

used

for

broadcasts

of

(for

example)

sporting

events

are

almost

invariably

fixed

in

location

but

free

to

rotate

and

zoom,

and

hand-held

camcorders

are

very

often

panned

from

a

single

viewpoint.

Note

that

although

we

address

the

case

where

the

camera

undergoes

pure

rotation

(i.e.

about

its

optic

centre),

in

practice

the

method

is

applicable

whenever

the

rotation

arm

is

very

small

relative

to

the

distance

of

the

scene.

Our

work

is

most

closely

related

to

the

works

of

Hartley

[4]

and

Pollefeys

et

al.

[10],

but

differs

from

the

former

in

that

we

consider

the

case

of

varying

rather

than

fixed

in-

trinsics,

and

from

the

latter

in

that

we

consider

pure

rotations,

a

case

not

handled

by

that

work.

The

paper

is

organised

as

follows.

We

begin

with

a

description

of

the

camera

model

(section

2),

then

derive

a

constraint

on

the

dual

of

the

image

of

the

absolute

conic,

which

forms

the

basis

of

our

approach

(section

3).

We

relate

our

work

to

[15,

10]

in

section