ShapefromShadingByHorn资源-CSDN文库

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4.1

INTRODUCTION

4.1.1

Shading

as

a

Monocular

Depth

Cue

An

image

of

a

smooth

object

known

to

have

a

uniform

surface

will

exhibit

gradations

of

reflected

light

intensity

which

can

be

used

to

determine

its

shape.

This

is

not

obvious

since

at

each

point

in

the

image

we

know

only

the

reflectivity

at

the

corresponding

object

point.

For

some

points

(called

singular

points

here)

the

reflectivity

does

uniquely

determine

the

local

normal,

but

for

almost

all

points

it

does

not.

Consequently,

the

shape

of

the

surface

cannot

be

found

by

local

operations

alone.

For

many

surfaces

the

fraction

of

the

incident

light

which

is

scattered

in

a

given

direction

is

a

smooth

function

of

the

angles

involved.

It

is

convenient

to

think

of

the

situation

as

depending

on

the

three

angles

shown

in

Fig.

4.1:

the

incident

angle

between

the

local

normal

and

the

incident

ray,

the

emittance

angle

between

the

local

normal

and

the

emitted

ray,

and

the

phase

angle

between

the

incident

and

the

emitted

rays.

115

Obtaining

Shape

from

Shading

Information

119

locally.

One

can

solve

inside

each

region

bounded

by

these

various

edges,

but

some

global

or

external

knowledge

is

needed

to

match

up

the

regions.

In

the

case

of

an

angular

edge

on

an

object

one

can

integrate

up

to

the

edge

and

then

use

the

known

location

of

the

edge

as

an

initial

curve

for

another

region.

A

very

similar

situation

obtains

when

one

bridges

a

shadow.

Since

one

edge

of

the

shadow

and

the

position

of

the

light

source

is

known,

we

can

trace

along

the

rays

grazing

the

edge

until

the

corresponding

image

points

fall

on

an

illuminated

region.

Since

we

know

the

path

of

each

ray,

we

can

calculate

the

coordinates

of

the

point

where

it

impinges

on

the

object

by

triangulation.

The

edge

of

the

shadow

(which

need

not

be

on

the

same

object)

can

then

serve

as

an

initial

curve

from

which

to

continue

the

solution.

4.1.2

Applications

A

number

of

interesting

applications

of

this

method

can

be

mentioned.

The

first

of

these

concerns

the

scanning

electron

microscope

which

produces

images

which

are

particularly

easy

to

interpret

because

the

intensity

recorded

is

a

function

of

the

slope

of

the

object

at

that

point

and

is

thus

a

form

of

shading.

In

optical

and

transmission

electron

microscopes,

intensities

depend

instead

on

thickness

and

optical

or

electron

density.

The

geometry

of

the

scanning

electron

microscope

allows

several

simplifications

in

the

algorithm

for

determining

shape

from

shading.

Because

of

the

random

access

capability

of

the

microscope

beam,

it

should

be

easy

and

useful

to

combine

it

with

a

small

computer

to

obtain

three-dimensional

information

directly.

Another

interesting

demonstration

lies

in

the

determination

of

lunar

topography.

Here

the

special

reflectivity

function

of

the

material

in

the

maria

of

the

moon

allows

a

very

great

simplification

of

the

equations

used

in

the

shape-from-shading

algorithm.

The

equations

in

fact

reduce

to

one

integral

which

must

be

evaluated

along

each

of

a

family

of

predetermined

straight

lines

in

the

image.

So

far

we

have

assumed

that

the

surface

is

uniform

in

its

photometric

properties.

Any

nonuniformity

will

cause

this

algorithm

to

determine

an

incorrect

shape.

This

is

one

of

the

uses

of

facial

makeup,

because

by

darkening

certain

slopes

those

slopes

can

be

made

to

appear

steeper.

In

some

cases

surface-markings

can

be

detected

if

they

lead

to

discontinuities

of

the

calculated

shape.

Judging

by

our

wide

use

of

monocular

pictures

(photographs

or

even

paintings

and

woodcuts)

of

people

and

other

smooth

objects,

humans

are

good

at

interpreting

shading

information.

The

shortcomings

of

our

method

which

are

related

to

the

shading

information

available

can

be

expected

to

be

found

in

human

visual

perception

too.

It

will

of

course

be

difficult

to

decide

whether

the

visual

system

actually

determines

the

shape

quantitatively

or

whether

it

uses

the

shading

information

in

a

very

qualitative

way

only.

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