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Description
GHS: Image Stretching 101
David Payne
Since the initial release of the Generalized Hyperbolic Stretch (GHS) script, uptake of the script has been high due to the control and flexibility it provides for image stretching. Many imagers have attested to what it can do and shared excellent results that they have, at least partially, attributed to the technique. However, to many, it appears complicated and “black-boxy”; some may even be intimidated by the options. Using the analogy of a bicycle, with this presentation I hope to show what the pedals, brakes, and handlebars do so that even a neophyte can ride GHS. Thanks largely to the work of my GHSAstro colleague, GHS has recently been ported to an easy to use module/process in Pixinsight. This is transformative in its use and workflow incorporation, including the use of standard image previews that most Pixinsight users are already familiar with. The approach I take design is to make use of both the histogram and image previews to set the sliders and set up the stretch. I will first show what the histogram represents and how it should look for various types and styles of astronomical images. Adjustment of both brightness and contrast distribution can then be selected to change the image and histogram towards the desired result. I will also demonstrate how the five main GHS parameter/slider inputs each affect both the histogram and image stretch results including shortcuts for new users. I will also explain how features of the new GHS process also allow for dynamic fine adjustment of parameters to get the histogram and image just right. Again, through examples, I will show how GHS can be used seamlessly with other processes, both starless and starred image components, and both monochrome and colour images, including colour balancing and manipulation.
A
A
So
Mike's
gonna
promise
to
keep
me
out
of
trouble,
but
I
do
want
to
give
a
big
shout
out
to
Mike
for
all
all
the
work
he's
done
on
the
the
the
the
script
and
the
process
and
the
methodology,
it
really
was
a
a
a
a
chance
meeting.
Put
it
out
that
I
needed
help.
Putting
this
together,
Mike
answered
the
call
and
turns
out.
A
We
have
very
synergistic
backgrounds,
not
the
same
backgrounds,
but
the
kinds
of
that
came
together
were
both
amateurs,
though
we
don't
get
any
money
for
do
for
doing
this
and
we
offer
it
up
for
whoever
wants
it.
It
does
come
back,
come
with
a
money-back
guarantee,
though,
so
we're
going
to
talk
about
the
Pix
Insight
implementation
tonight,
but
soon
fully
function,
it'll
be
fully
functional
ghs
in
in
Cyril.
A
It
currently
is
in
its
development
release
and
I'm,
not
sure
when
the
serial
guys,
who
actually
put
it
into
Cyril,
are
going
to
release
it,
but
there
it
is.
If
you,
if
you,
if
you're,
not
a
pixie
Insight
fan
like
I,
think
most
of
us
are,
if
you
want
a
whole
bunch
of
details
or
you
want
whatever
you
want,
please
visit
ghsastro.co.uk.
A
A
A
A
And
I
hope
it
doesn't
look
like
an
assembly
line
at
that
point,
but
maybe
it
maybe
that
would
be
a
good
thing.
So
I'm
going
to
start
off
with
the
simplest
image
I
could
think
of
which
is
essentially
a
monochrome
single
brightness
pixel
in
in
an
image
and
I'm
just
going
to
make
one
little
modification
I'm
just
going
to
put
a
reference
on
the
left
hand,
side
of
this
image
and
the
reference
on
the
right
hand.
Side
of
this
image
and
I
want
to
look
at
that.
A
Now
the
the
home
system
started
off
as
a
script
only
and
it's
it's
still
there,
because
it
really
provides
a
lot
more
structure
to
using
ghs,
and
perhaps
the
process
does
there's
nothing.
You
can't
do
in
the
process
that
you
can
do,
but
it
provides
a
little
bit
more
customizable
customization
options,
but
one
of
the
things
about
scripts,
of
course,
is
before
you
do
anything
else.
You
have
to
exit
the
script
and
I
find
using
the
process.
A
Much
much
simpler
and
I
tend
to
have
it
open
a
lot
of
the
time
when
I'm
doing
my
processing?
If
for
nothing
else,
just
to
look
at
the
histogram
now
I've
opened
up
the
program
here
and
I.
Don't
know
if
it's
too
small
for
you
to
see
the
the
numbers
or
the
fonts
are
not
on
your
screen
that
you're
watching
it
I've
tried
changing
the
resolution
and
that
can
work,
but
it
causes
some
other
issues.
A
B
C
A
A
Zero
in
terms
of
brightness
and
the
maximum
brightness
that
your
monitor
or
your
eyes
or
whatever
is
limiting
it
here,
can
perceive
Now
by
normalizing
the
pixel
values
in
your
image.
This
brightness
becomes
a
one
inside
pixinsight
and
I
can
actually
see
that
by
putting
my
cursor
over
it
and
then
at
the
bottom,
it
tells
me
it's
a
one
and
at
the
other
side
it
tells
me
it's
a
zero
now.
The
reason
why
this
is
not
a
limitation
of
your
eyes.
A
My
histogram
to
the
right-
and
this
happens
whenever
you
brighten
something
that's
what
happens
on
the
histogram
it
moves
the
the
histogram
over
to
the
right.
I
can
move
it
almost
all
the
way
up
to
absolute
brightness,
and
you
can
see
it's
moved
further
to
the
right
and
then
once
I
make
it
total
brightness.
A
You
can't
tell
the
difference
between
it
and
the
reference
on
the
left
and
the
pick.
The
histogram
is
actually
a
spike.
That's
over
to
the
right.
All
the
other
pixel
quantities
in
in
there
are
are
zero,
so
you
don't
see
them
and
the
opposite.
When
you
make
something
darker,
it
moves
to
the
left,
but
I'm
going
to
go
back
and
say
that
now,
so
that's
how
the
histogram
kind
of
works
with
brightness
and
I'm
going
to
talk
a
little
bit
about
contrast.
A
A
You
can
see
my
histogram.
We
write,
yellow
line
that
histogram
forms
two
bars
separated
one
for
the
left
on
the
darker
side
and
one
for
the
on
the
right
for
the
lighter
side.
So
I've
actually
created
this.
This
contrast
by
brightening
one
side
of
that
block
and
darkening
the
other
side
of
the
block
and
I'm
starting
to
see
some
contrast
in
that
image.
Now
one
thing
your
eyes
might
tell
you.
A
So
what
I'm
doing
is
directing
one
but
I'm
actually
by
providing
contrast,
I'm
actually
pushing
the
the
histogram
apart
and
if
you
notice
on,
according
to
my
reference
as
I'm,
pushing
them
apart,
they're,
actually
getting
closer
to
the
left
hand,
side
and
the
right
hand
side.
So
I
start
reducing
the
contrast
on
this
side
and
then,
if
I
go
a
lot
further,
you
can
see
that
now
the
contrast
is
getting
very
low
here
and
it's
getting
very
low
there
and
here's
the
maximum
contrast
I
can
put
into
the
image
it's
absolute
dark
on
the
left.
A
Absolute
dark
on
the
right.
There's
no
contrast
between
the
reference-
and
this
is
all
just
to
illustrate
that
while
we
can
take
any
pixel
in
any
image
and
brighten
it
all
the
way
from
zero
to
one.
The
maximum
contrast
we
can
put
in
the
image
is
a
number
one.
We
can't
we
can
split
the
number
one
we
can
put
it
wherever
we
want,
but
but
ultimately
you're
limited
in
what
contrast
you
can,
which
is
a
bit
different
than
you
say.
Well,
I've
seen
lots
of
Sliders.
That
say
add
contrast.
A
A
A
A
After
the
stretch
for
this
straight
straight
line,
it
shows
that
for
any
input,
I
can
think
of
along
this
brightness
curve.
It'll
give
me
the
exact
same
brightness
back
out.
For
that
reason,
this
is
called
the
identity
stretch
and
is
a
straight
line
that
goes
from
the
lower
left
corner
to
the
upper
left
corner.
A
A
There
are
five
parameters
and
I
just
want
to
focus
on
the
top
parameter
here
now
in
the
in
the
script,
you
see
it's
called
stretch
factor
it
could
have
been
called
stretch,
amount
and
Mike
and
I
went
debating
what
we
should
call
these
things,
but
really
I
call
it
big
big
D
Big
D
for
for
Daddy,
because
it's
the
daddy
of
all
the
the
other
parameters
now
I'm
not
trying
to
be
sexist.
Here.
A
The
D
actually
comes
from
a
different
formulation
of
these
equations,
so
I
couldn't
make
it
mummy,
but
but
just
think
of
it
as
capital,
D
and
I'll
be
referring
to
it.
So
to
perform
a
stretch
on
this
pixel
I
start
to
move.
It
starts
at
zero
and
whenever
it's
zero
I'll
get
this
when
Big
B
for
big
big
D
for
daddy
is
zero.
I
always
get
this
identity.
A
Transform.
As
I
increase
d
you'll,
see
I
start
to
stretch
that
pixel.
What
I'm
doing
is
brightening
it
and,
as
we
just
learned,
I'm
moving
it
to
the
right,
but
what
happens
with
this
transform?
Well
I
can't
I
don't
want
to
move
the
zero
zero
point,
because
that's
I
can't
make
it
lower,
because
I
can't
make
it
darker
than
zero
and
I.
Don't
want
to
raise
that
zero
point,
because
I
don't
want
to
lose
I
start
losing
the
maximum
contrast.
A
I
have
available
to
me
at
the
same
time:
I
don't
I
can't
raise
the
brightest
pixels
I
can't
rate
their
brightness
anymore
and
I
don't
want
to
lower
it
for
the
same
reason,
because
I'll
start
to
lose
the
contrast.
So
for
any
stretch,
you'll
see,
ghs
do
they'll,
always
start
at
that
lower
left
hand
corner
and
end
up
on
the
right.
A
So
the
only
way
I
can
make
a
pixel
brighter
than
this
line
is
to
make
the
stretch
bendy,
and
that
makes
it
non-linear
and
hence
the
the
name
non-linear
so
I
can
do
that
nonlinear
stretch
so
now,
I
take
I
can
show
my
original
pixel
value
and
I
can
place
that
pixel.
Let's
say
we
want
to
place
it
right.
There.
A
So
now
I've
brightened
it
up.
If
you
see
the
original
image,
my
my
stretched
image
looks
below
I
can
see
that
pixel
fine.
Now
so,
I
took
my
value
from
my
pixel
right
up
to
the
red
up
to
where
the
red
line
exists.
It
it
says
it's
at
0.25
and
at
0.25,
that's
where
my
new
pixel
wise.
So
that's
how
you
read
this
in
terms
of
brightness,
if
you
want
to
say
how
much
did
I
brighten
the
pixel?
A
Well,
that's
given
by
the
distance
between
my
red
line
and
my
original
identity
line,
the
further
the
right
I
go.
It
will
make
the
pixels
brighter,
but
it
can't
make
it
it's
limited
to
how
bright
it
can
make
it
because
it
has
to
make
this
turn
and
end
up
in
the
right
corner.
It
looks
flat
out
here,
but
it
really
isn't.
It's
really
just
hugging
this
and
can't
reach
one
until
it
actually
makes
it
up
here,
if
you
think
of
it
as
a
hill.
A
A
A
A
And
make
11
bands
in
total,
but
bands
that
are
0.1
difference,
in
contrast
between
each
other,
so
that
histogram
shows
here
I'm
going
to
X
I'm
going
to
just
hide
this
for
a
second.
So
what
I'm
going
to
describe
here
is
the
transform
in
terms
of
contrast
levels.
Now
you
can
imagine
any
two
pixels
that
are
pretty
close
to
one
another
at
this
end
of
the
scale
they're
going
to
be
result
in
much
bigger
difference
in
the
brightness
coming
out
of
this
transform
two
pixels
beside
each
other.
A
So
if
you
look
at
the
steepness
of
this
slope
or
the
the
the
the
amount
of
incline
or
the
right
rise
over
run
of
this
slope,
that's
how
it's
redistributing
the
contrast.
Now
it
has
to
end
up
at
1
1..
So
it
has
it.
As
it
travels
from
left
to
right.
You
can
see
it
increasingly
changes
its
pointing
back
to
one
so
in
here.
This
level
is
the
same
slope
as
my
identity
line.
A
So
I'm
going
to
be
adding
contrast,
it's
a
much
larger
slope
than
my
identity
line,
so
I'm
going
to
be
adding
a
lot
more
more
contrast
here
somewhere
in
the
middle.
It's
about
the
same.
So
the
contrast
that's
going
to
be
put
in
the
image
at
this
level
is
going
to
be
about
the
same
as
the
identity
line.
I
had
no
changing
contrast
and
then
up
at
the
high
end,
I'm
going
to
be
changing
contrast
very
little
and
much
taking
it
away
from
my
original
image.
A
Put
it
together
a
banded
image,
I'm
going
to
try
and
put
this
at
the
top
and
bring
this
down
below
that's
more
representative
what
you
might
find
in
the
grayscale
of
a
of
an
astral
image.
So
what
we
have
is
a
lot
of.
We
have
very
dark
pixels
and
most
of
our
pixels
are
are
very
dark
and
we
have
some
very
bright
pixels.
We
have
brighter
pixels.
These
would
be
more
like
the
stars
in
our
image
and
what
I
want
to
do
is
stretch
this
image.
A
You
can
see
a
lot
of
contrast
in
in
the
brights
and
very
little
contrast
down
here
in
the
darks,
and
so
this
is
the
opposite
of
what
we
were
doing.
So,
let's
hope
that
this
gives
us
a
better
image,
better
view
into
our
astral
image,
so
I'm
going
to
take
the
preview
and
start
adding
our
Big
D
big
D
for
Daddy
parameter
by
sliding
it
to
the
right.
A
A
So
really
what
I
would
like
to
do
for
this
particular
image
is
I
want
to
change
the
change.
The
degree
of
stretching
that
I'm
taking
up
here
and
change
it
to
and
stretch
this
a
little
more
and
stretch
this
a
little
less
I
want
to
leave
some
more
contrast
up
here
and
add
a
little
contrast
down
here
now.
A
Looking
at
the
shape
of
the
curve
I'm
going
to
put
a
fairly
decent
stretch
here,
Now
by
changing
B,
it
starts
initially
at
zero
by
sliding
it
to
the
right
you
can
see
it
changes
the
parameters
that
go
into
the
general
hyperbolic
equations
and
you
can
see
it.
It
actually
does
exactly
what
I
was
talking
about,
so
it
actually
leave
some
contrast
in
the
upper
end.
Maybe
I
should
make
that
bigger
start
off
with
a
little
bit
higher
stretch.
A
It
will
be
for
baby,
and
you
can
see
now
as
I
go
on
the
right
hand,
side
I've
reached
a
point
where
I
can
still
see
contrast
on
the
right
hand,
side
and
I
can
actually
get
a
fair,
decent
amount
of
contrast
on
the
left
hand,
side
along
our
way,
going
from
0
to
15
on
B,
we
passed
a
couple
of
significant
points.
Now
one
is
when
B
is
equal
to
one.
A
A
B
A
A
Now,
as
I,
add
B
to
this
I'm,
going
to
add
a
little
bit
more
D.
First,
you
can
see
what
happens
in
the
image.
I'm
brightening
the
whole
image,
I'm,
adding
a
whole
bunch
of
contrast
down
here.
Taking
it
away
from
up
here,
then,
as
I
add
B,
I'm
continuing
to
add
contrast
right
at
the
zero
point,
I'm
sort
of
taking
it
away
up.
This
is
hard
to
say
see
because
this
is
a
linear
image,
but
you
can
see
what
happens
to
the
shape
of.
A
What
happens
to
the
shape
of
the
histogram
now
we'll
be
revisiting
this
in
a
few
minutes?
But
that's
that's
enough
of
theory.
For
now,
I
want
to
Let's.
Oh
I
need
to
show
you
one
more
parameter
before
we
go
so
one
thing
I
found
limiting
about
the
stretch
functions
is
they
were
all
focusing
on
putting
the.
A
A
What
you
do
is
the
equivalent
of
moving
this
third
input
all
the
way
to
the
right,
and
what
happens
then
is
the
stretch
becomes
a
compression.
If
you
will,
the
whole
image
is
darkened
and
what
I've
done
is
taken.
The
point
of
Maximum
steepness,
the
most
the
point
of
Maximum
contrast,
add
and
I've
changed
it
from
zero
point
and
I
change
it
to
the
one
point.
A
A
A
So
it
almost
appears
like
a
blurry
line
in
the
middle
and
in
fact,
I
can
really
refine
that
line
by
putting
a
whole
bunch
of
contrast
right
in
the
middle
and,
of
course,
I
can
move
that
back
and
forth
to
wherever
I
want
in
the
image,
and
you
so
I'd
say
well.
Why
would
I
want
to
do
that
so
I'm
going
to
show
you
a
quick
example
of
why
I
want
to
do
that?
Oh,
let
me
lower
this
back
again.
A
B
A
So
this
is
good
for
gentle
stretches
over
the
entire
image,
but
it
is
focused
at
my
SP
point,
because
when
I
put
it
in
the
middle,
it
creates
even
more
of
a
v.
But
if
I
put
D
here,
you
can
see
now
it's
creating
a
a
real
Spike
down
where
I'm
adding
the
contrast,
as
those
pixels
are
pushed
to
one
side
of
the
other.
A
A
Let's
say
we
come
across
an
image
that
looks
like
this
and
you'll
see
this.
This
is
an
exaggerated
case,
of
course,
but
you'll
see
this.
Sometimes
when
you
stretch
an
image,
you'll
see
that
there's
a
whole
area
in
your
image,
where
there's
not
a
lot
of
contrast,
there's
not
a
lot
going
on
and
it's
humdrom
and
boring,
and
you
know
all
the
contrast
is
at
the
far
ends
of
the
of
the
image,
and
so
you
want
to
add
some
contrast
right
in
the
middle
of
the
image.
A
Well,
I
can
find
out
where
that
is
by
clicking
on
the
image
and
it'll.
Show
me
exactly
where
that
point
is
in
my
histogram,
and
indeed
it's
where
that
bump
is
in
the
history
what's
going
on
here,
it's
where
that
bump
is
in
the
histogram
and
whenever
you
see
a
histogram
and
you
see
a
bump
on
it,
you
can
tell
pixel
brightnesses
are
gathering
there
and
that's
where
you
want
to
add
some
contrast.
So
what
I
want
to
do
there
in
this
case
is
I
want
to
make
SP
at
that
point.
A
A
If
I
look
at
what's
happening
in
my
preview
of
that
image,
you
can
see
I'm
putting
a
lot
of
the
contrast
back
in
and
I
can
play
with
b
a
little
bit
and
now
really
get
it
quite
quite
level
across
the
edges.
I
can
apply
that
and
you
can
see
now
I've
restored
the
contrast
pretty
close
to
what
it
was
originally.
A
C
C
A
A
Well,
it's
actually
I
have
to
zoom
into
the
histogram
and
there's
a
quick
Zoom
that
goes
250
times
and
I
can
see
that
my
histogram
is
far
on
the
left
of
the
entire
histogram
range.
So
I've
zoomed
in
on
the
far
left
hand,
side
and
I
can
see
where
it
is.
So
if
I
were
just
to
do
a
histogram
transfer
stretch,
I
would
have
to
set
bead
1
to
be
equivalent.
I
would
start
increasing
my
stretch
factor
and
what
I'd
start
to
see
is
the
histogram
shift
to
the
right
now.
A
I
have
the
ability
to
show
what
the
original
histogram,
as
well
as
the
one
that
I'm
changing,
looks
like
on
The
View.
So
as
I'm
adding
my
stretch,
you
can
see
I'm
starting
to
shift
the
histogram
to
the
right
and
and
I'm
actually
putting
contrast
in
the
histogram
as
well.
You
can
see
it
start
to
spread
apart.
A
A
A
A
Normally
the
histograms
show
up
just
like
a
normal
view
of
a
histogram
and
I'd
liken
this
to
looking
at
like
a
cityscape
from
a
distance,
but
I
prefer
using
the
log
View,
which
is
more
like
going
downtown
in
the
city
and
looking
up
and
around
the
buildings.
I,
don't
just
see.
The
skyscrapers
I
now
see
the
small
buildings
because
it
exaggerates
those
bins
that
have
few
pixels
in
them
and
and
sort
of
de-exaggerates,
the
the
very
full
bins
that
resulted
in
spikes.
A
A
If
we,
like
that
view
more
but
I'm
going
to
start
adding
at
my
plus
15,
my
plus
15
B
for
baby
and
I'm,
going
to
start
adding
my
D
and
again
I
see
the
histograms
start
to
move
to
the
right
now
it
doesn't
appear
that
I'm
actually
making
this
apart
as
much
as
I
did
before
so
I'll.
Just
keep
stretching
this
to
the
right
and
zoom
back
out
and
parking
it
well
I'll
bring
the
preview
up.
A
So
you
can
see
it
actually
come
into
view
as
I'm
doing
the
stretch
and
park
it
at
the
same
place
right
there.
Now
you
say:
oh
well,
that's
not
better!
Why
am
I
doing
this?
Why
am
I
am
I
doing
this
I've
increased
the
background,
brightness
quite
a
bit
from
from
my
original
Stretch
and
furthermore,
you
know
it
hasn't,
really
does
not
making
everything
Pop
there's
a
lack
of
contrast
in
the
image,
albeit
it
has
done
a
better
job
on
my
stars.
A
You'll
see
that
I
ended
up.
Adding
contrast
where
this
is
steepest.
I
ended
up,
adding
it
mainly
behind
my
histogram
Peak
right.
That's
not
where
I
really
wanted
I
want
that
maximum
contrast
in
my
histogram
Peak,
so
I
can
click
on
this
histogram
Peak
find
out
pretty
much
where
it
is.
It
tells
me
a
number
it's
a
very,
very
small
number,
because
I'm
zoomed
in
and
I'm
still
far
to
the
left
and
I
can
make
that
my
SP
number,
so
I
can
make
SP
by
moving
SP
here.
I
can
make
this
transform.
A
Put
the
maximum
contrast
right
where
my
histogram
Peak
was
now
SP
stands
for
symmetry
Point
here,
but
the
p
means
that
it's
a
point
on
here
in
symmetry,
because
you
can
see
that
the
stretch
is
actually
symmetrical
about
that
SP
point
but
the,
but
the
point
I
really
want
to
make
is
now
I've
put
it.
If
I
bring
this
back
and
I
bring
this
back
I've
put
as
I
increase
the
slide.
A
I
can
park
that
histogram
wherever
I
like
I,
can
do
it
a
little
more
and
a
little
less
you'll
see
at
some
point,
I
start
to
divide
the
image
into
two
because
I'm
actually
adding
so
much
contrast
that
I'm
splitting
this
you
don't
want
to
do
that
because
it
looks,
looks
awful
I
call
that
bifurcating
the
the
histogram.
You
don't
want
to
do
that.
So
maybe
you
want
to
leave
it.
B
A
So
already
you
can
see
I've
done,
I
think
a
better
job
of
stretching
this
image,
and
especially
in
terms
of
the
stars,
but
the
next
step
I
want
to
do
was.
That
was
a
very
rough
placement
of
my
SP
Factor.
So,
thanks
to
Mike,
he's
put
this
adjustment
slider
in
the
bottom
and
what
I
can
do
is
it
comes
selected
with
SP
I
can
there's
a
little
box
here
to
use
highest
sensitivity.
A
You
always
want
to
use
highest
sensitivity
when
you're
using
a
linear
image
and
I
can
actually
lower
slightly
lower
and
slightly
raise
that
SP
level.
So
here's
where
I
I've
lowered
it.
So
it's
behind
my
histogram
and
as
I
increase
it
you
can
see.
The
first
thing
that
happens
is
my
background,
where
there's
nothing
going
on,
starts
getting
darker
and
then,
as
I
continue
to
raise
it.
I
start
losing
some
of
my
dim
stuff,
but
my
bright
stuff
starts
to
pop
out
more
so
this
might
become
a
matter
of
personal
taste.
What
do
you
want?
A
A
A
Module
but
I
do
want
to
review
one
thing
and
before
I
go
on
to
the
last
two
parameters,
which
are
basically
two
versions
of
the
same
parameter
who
you'll
see
in
a
second
before
that
I
want
to
go
on
some
ground
rules,
and
these
were
Ground
rules.
I
call
them
ground
rules,
because
this
is
what
we
wanted.
A
Mike
and
I
want
a
ghs
to
do
when
we've
already
talked
about
one
is
we
wanted
any
stretch
that
we
are
doing
to
run
from
zero
zero
to
one
one,
I.E
start
in
the
lower
left
corner
and
end
in
the
right
corner,
so
that
meant
no
clipping
is
going
to
take
place.
So
you
can,
you
can
do
ghs
in
this
manner
all
day
long.
You
won't
clip
anything.
A
We
wanted
the
pixels
always
to
get.
We
wanted
to
transform
the
stretch
always
to
get
higher
from
left
to
right,
and
this
is
a
rule
of
of
conformal
mapping
in
math.
Really
I
want
I,
don't
want
to
destroy
the
Integrity
of
my
data,
so
if
I
were
to
line
up
all
the
pixels
say
in
terms
of
brightness
and
then
did
a
transform
on
them.
Well,
that
lineup
wouldn't
change
the
rank
ordering
of
brightness
of
the
pixels
won't
change,
no
matter
what
stretch
I
I
do
this.
A
This
again
is
no
artifacts,
no
noise,
you
can't
overwork
the
stretch
and
it
is
actually
completely
invertible.
I
can
actually
go
backwards
and
I'll
show
you
this
in
a
in
a
little
bit.
I
can
go
backwards
at
any
time.
It's
an
analytical
equation.
I
can
get
any
arbitrary
position,
Precision,
there's
no
Newton
iterations,
there's,
there's
no
step
loops
and
no
masking
all
these
things
can
give
give
you
artifacts,
and
it
also
provides
for
an
instantaneous
preview
so
that
you
can
see
what
you're
going
to
get
before.
You
actually
apply
the
function.
A
There
are
no
jumps
or
bumps
in
the
transform
it's
smooth,
and
not
only
is
the
brightness
smooth,
but
the
contrast
is
added
smoothly
too,
and
that
means
no
artifacts
and
pixel.
Brightness
is
the
only
input
that
this
transform
is
taking
the
original
pixel
brightness.
It
doesn't
know
where
the
pixel
came
from
on
the
image
it
doesn't
know.
If
it's
part
of
a
star
it
doesn't
know
if
it's
part
of
a
nebula,
it
doesn't
know
anything
about
this
pixel
other
than
the
brightness
going
in.
A
So
there's
no
interpretation
going
on,
and
this
is
a
beauty,
but
it's
also
a
constraint
somehow.
So,
following
all
these
rules,
there's
only
the
ghs
process
in
pixinsight
for
post-processing
the
histogram
transform
with
the
middle
slider
only
and
the
arc
shine
transform
that
if
you
don't
use
it
on
a
color
image,
those
are
the
only
three
processes
that
can
can
make
this
claim.
Your
data
is
completely
contains
its
scientific
Integrity.
A
By
doing
this
sort
of
stretch,
not
the
other
processes
are
bad
I
use
them
all
the
time,
they're
great,
but
they're
Jedi
enhancements.
If
you
will,
they
are
playing
games
with
your
mind
or
they're
playing
games
with
the
pixels
to
make
the
image
look
better,
but
in
doing
them
you
are
adding
noise
or
artifacts
that
you
have
to
watch
and
you
actually
removing
the
scientific
Integrity
of
the
of
the
data.
A
A
A
Is
here
that's
the
point
where
I'm
adding
the
most
contrast,
but
as
you
can
see
in
relation
to
the
identity
line,
that's
actually
dimming
that
particular
pixel.
So
the
bottom
of
the
valley,
I
created,
is
actually
shifted
to
the
left
somewhat,
but
I
am
creating
a
a
fairly
broad
values,
fairly
strong
stretch
on
a
linear
image
and
I
am
that's
what
I'm
doing
to
the
histogram.
A
A
It's
labeled
here
as
protect
Shadows,
but
what
it
does
it
starts
off
at
zero
and
as
I
move
it
to
the
right
very
slowly
at
first,
but
then
it
sort
of
gathers
steam
as
I
move
it
further
to
the
right
it
actually
linearly.
Linearizes
makes
this
a
straight
line
to
the
left
of
LP,
and
it
adds
contrast.
You
can
see
it's
raising
up
a
bit,
it's
getting
steeper!
So
it's
and
in
contrast
back
on
this
left
hand
side
well:
where
is
it
taking
it
from?
Because
our
total
contrast
is
the
same?
A
A
A
Max
Point
SP
the
point
of
Maximum
contrast
where
this
is
steepest
actually
coincides
where
it
crosses
the
identity
curve.
What
that
means
is
the
bottom
of
my
Valley
is
right
below
my
point
of
maximum
contrast
addition,
so
there's
no
overall,
brightening
or
or
or
darkening
of
the
this
point
I
should
have
kept
the
the
preview
opening,
as
I
was
doing
that
so
I'll
just
back
off
to
see
how
this
is
changing
the
preview
so
I'm
going
to
back
off
here's
with
no
LP
as
I
move
it
to
the
right
it
starts.
A
Where
my
transform
sorry,
my
stretch
crosses
the
identity
line,
the
same
point
as
SP.
Now,
that's
somewhere
I'm
guessing
here
on
my
preview,
but
I
can
turn
the
preview
on
and
off
and
I
can
see.
That
point
is
right
here.
Remember,
I
form
quite
a
bit
of
a
line
when
I
had
a
bit
of
a
line
when
I
add
a
bunch
of
contrast,
but
you
can
see
its
brightness
is
not
changing
when
I
turn
the
preview
on
and
off.
A
All
my
stretch
is
taking
place
up
here,
there's
a
little
bit
of
Valley
still
being
formed
to
the
left
of
SP,
but
most
of
the
stretch
is
taken
to
the
right
of
SP.
My
Valley
is
now
to
the
right
of
SP,
because
now
I'm
brightening
the
whole
image,
but
if
I
turn
the
preview
on
and
off,
you
see,
I
actually
haven't
changed
any
of
the
pixels
from
my
LP
Point.
Here
all
the
way
to
the
left.
They
remained
unchanged.
This
is
kind
of
Handy.
A
A
A
A
E
Yeah,
just
it's
a
great
presentation
and
you
know
I
I,
want
to
say
that
what
I
got
from
it
was
first
of
all,
I'm
sort
of
intuitively
I
did
a
lot
of
the
same
sort
of
things,
just
learning
it
by
doing.
But
what
I
felt
was
interesting
was
that
what
your
program
does,
which
you
can't
do
in
anything
else
in
pics
Insight,
it's
kind
of
like
what
we
used
to
say
in
Photoshop,
putting
an
S
curve
into
that
histogram.
E
E
Because
you
can
visualize
that
that
that
small,
linear
histogram,
you
then
can
put
the
Symmetry
Point
into
it
and
then
to
enhance
the
contrast
and
there's
no
other
way
of
doing
that
and
picks
and
picks
Insight.
So
I
thought
that
was
the
way
I
understood
intuitively.
What
was
going
on
so
I
think
that's
a
great
thing.
E
A
Yeah
I,
probably
I,
primarily
use
the
log,
View
and
and
I
will
address
that
in
a
few
minutes.
I'm
going
to
show
you
a
bunch
of
examples
and
become
a
parent
I'll
actually
show
you
the
character
of
the
log
view
histogram
that
you
should
perhaps
aim
for
in
your
stretches
and
then
you're
in
your
refinements,
great.
E
So
one
of
the
things
I've
been
doing
with
ghs
is
to
do
noise
Exterminator
on
the
linear
image
before
I
hit
it
with
GS
ghs,
because
otherwise
what
you're
going
to
do
is
you're
going
to
stretch
the
noise
so
I
just
I.
Just
that's
just
my
comment,
but
if
you
have
any
comments
about
that,
I
think
that's
a
reasonable
strategy,
because
your
histogram
is
tighter
to
start
with.
A
A
A
You
know
it
doesn't
have
a
big
that
the
resolution
to
the
pixel
brightnesses
but
as
they
tell
me
in
black
and
white
photography,
we
want
black
and
white
pictures.
We
don't
want
gray
and
white
pictures
and
really
they
add
a
lot
of
contrast,
and
this
is
for
mood
effects.
But,
let's
say
I'm
not
interested
in
mood
effects
in
this
image,
maybe
I'm
more
interested
in.
What's
there
maybe
I'm
from
another
planet,
because
you
know
being
a
human
and
seeing
scenes
like
this,
we
can
fill
in
a
lot
of
details
in
our
mind.
A
A
I
usually
do
that
you
don't
have
to
do
that,
but
it
really
makes
the
stretch
focused
and
I
can
well
I
want
to
move
SP
all
the
way
to
the
right,
because
I
want
the
maximum
contrast
to
be
added
on
the
far
right
hand,
side.
So
I
can
do
that
by
clicking
on
SP
it'll.
Send
it
to
one
or
I
can
move
the
slider
over
there.
So,
let's
add
some
stretch
to
this
image
and
let's
put
the
preview
on
which
I
keep
forgetting
to
do
well.
A
A
I
can
see,
there's,
maybe
some
clouds,
maybe
I've
zoomed
in
a
little
bit
too
much,
but
I
can
see
some
clouds
below
the
position
of
the
sun
and
above
this
is
kind
of
squaring
it
off.
So
I've
learned
something
about
that
by
by
applying
this
kind
of
stretch
to
an
image.
Now
this
is
actually
the
shape
of
this
curve
is
actually
handy.
If
you
happen
to
have
some
saturated
stars
and
you're
overstretching
the
Stars.
This
is
a
good
way
to
recover
some
contrast
in
your
brightest
points,
but
I
can
apply
that
to
my
image.
A
C
A
C
E
C
A
E
E
Okay,
that's
why
he
did
it
always
dodging
and
burning
and
whatnot
he
used
to
do
with
with
film
and
I
thought.
That
was
a
interesting
because
in
a
sense,
that's
what
you're
aiming
for
with
that
logarithmic
scale
or
you're
trying
to
get
those
you're
trying
to
get
that
histogram
sort
of
evened
out,
because
anyway,
that's
that's.
What
Ansel
would
have
said.
A
Well,
yeah
I,
don't
know
the
details
of
that,
but
what
I
do
see
is
this
make
your
black
and
white
images,
black
and
white,
not
gray
and
white?
If
you
do
so,
if
you,
if
you
start
adding
a
whole
bunch
of
contrast
on
the
edges
where
it
is
black
and
it
is
white
and
you
start
making
the
whole
image
gray
by
redistributing
the
the
that
contrast
in
that
way,
you
will.
A
Yeah,
but
if
you,
if
you
look
in,
say
Lightroom
what
what
it
says
is
it
has
five
sliders
right
at
the
top.
The
first
one
is
exposure
and
I
look
at
exposure.
I,
don't
know
what
transform
it's
doing,
but
I
think
it's
doing
a
stretch
with
SP
at
zero.
It's
doing
a
gentle
stretch,
one
with
like
a
negative
B
being
applied,
and
it's
brightening
the
whole
image
Without
Really
drastically
changing
the
contrast
anywhere.
A
The
next
slider
down,
I,
think
is
highlights
which
is
putting
contrast,
sort
of
around
0.75
and
then
there's
a
low
light,
so
putting
at
at
0.25
say
and
then
there's
a
whites
and
a
blacks
and
I.
Think
whites
is
putting
contrast,
really
high,
not
quite
at
one
but
and
blacks
is
putting
it
in
the
very
darks,
and
so
they
end
up
with
you
know:
five
slider
six
Sliders
in
total
doing
what
I'm
trying
to
do
with
the
SP
slider
and
because
the
histogram
transformed
and
the
the
ghs
transform.
F
David
one
thing
that
I
noticed
like
you
make
this
analogy
between
well
in
Photoshop.
It's
called
Shadow
highlight
so
it's
very
very
similar
to
what
you're
doing
here.
But
the
thing
I
found
with
Shadow
highlight
is
that
you
can
very
quickly
introduce
posteriorization
where
you
shift
the
colors
and
they
don't
make
sense
anymore.
I,
don't
notice
you
doing
that
here,
you
see
either
you're
just
methodically
going
through
to
prevent
that
or
there's
something
where
you're
preventing
it
from
going
overboard
in
one
area
versus
another
yeah.
F
A
E
C
A
F
A
A
Don't
now,
if
you
get
the
initial
stretch,
really
bad,
you
can
you
can
undo
it,
but
it
takes
probably
a
lot
more
time
than
going
back.
You
undo
everything
you've
done,
but
usually
it
takes
a
lot
less
time
is
trying
a
different
set
of
parameters
for
your
initial
stretch,
because
that's
the
most
violent
stretch
that
you're
actually
going
to
do
now.
Hopefully
you
know
what
I'm
going
to
skip
this.
D
B
E
Yes,
it
seems
to
me
that
if
you
make
the
first,
if
you,
if
you
don't
overdo
the
first
stretch,
you
can
come
back
and
stretch
it
a
little
bit
more,
whereas
if
you
overdo
it
to
start
with,
then
you've
made
a
Tre.
Then
you've
made
a
a
gone
a
little
bit
too
far
and
you
may
pay
the
price
later,
so
you
can
always
stretch
it
more,
but
you
can't
take
the
stretch
away
well,.
F
A
A
C
A
A
So
when
I
zoom
in
on
the
left
hand,
side
here
are
my
three-
this
is
a
log
view.
You
can
see
there's
data
everywhere,
but
here
they
are
in
the
standard
view
so
I.
Obviously
this
isn't
color
balanced
Green
is
actually
hydrogen
Alpha
and
it's
dominating
this
image.
So
I
really
want
these
to
line
up,
and
there
was
there's
a
there's,
a
good
video
on
how
to
do
this
on
our
website.
A
But
essentially,
let's
say
I
want
to
pick
the
the
green
as
to
where
the
hydrogen
Alpha,
where
I
want
to
line
up
these
other
two
colors.
So
to
line
up
the
red
I
can
click
up
out
here
right,
I
want
to
apply,
it
doesn't
really
matter.
I'll
apply
a
big
b
factor
and
I
can
stretch
this
D
and
I'm
going
to
zoom
out
a
little
bit
a
little
bit
more
I'm
going
to
apply
a
stretch
to
just
red.
A
A
To
bring
it
back
so
here
comes
back
again
and
now.
I
can
really
fine
tune
this
now
this
has
had
an
stf
with
the
colors
locked
on
it,
so
it
was
locked
on
the
basis
of
not
stretching
one
color
less.
So
this
is
actually
what
I'm
doing
to
the
color.
So
you
can
always
see
I've
stretched
the
red
and
I
see
some
stretch.
I
see
some
red
in
my
image.
A
I
can
leave
it
there,
but
I
can
now
fine
tune
that
HP
so
bring
it
down
so
that
maybe
that's
I
need
to
leave
it
a
little
bit
stronger.
I
can
fine
tune
it.
To
put
it
right
over
the
green
color
right,
I
can
take
the
blue
and
I
can
just
this
time
set
LP
I
can
apply
that
sorry
I'm
going
to
apply
that
foreign.
A
A
And
fine-tune
LP
to
put
it
right
where
I
want
it
and
there
I've
color
calibrated
that
image
now
I
can
do
it
a
little
bit.
Fancier
take
off
this
stretch.
I
can
do
it
a
little
bit
fancier,
but
then
I
start
going
into
my
standard
stretch.
Routines
now.
I
would
at
this
point,
I
would
extract
the
luminosity
and
then
stretch
the
Luminosity
separate
from
the
color,
because
all
these
fancy
Jedi
tricks,
hdmrt
and
lhe
they're,
going
to
they're
going
to
create
color
artifacts.
A
Then
I
can
do
deconvolution
on
my
starless
luminance
and
deconvolution
on
the
starless
image
is
just
a
cat's
meow,
it's
easy
to
use.
I!
Don't
have
to
worry
about
any
of
that
ringing
stuff
I,
don't
have
to
do
masking
necessarily
on
a
starless
luminous
image.
It's
just
the
best.
I
have
to
get
my
psf
function
before
I.
Remove
the
Stars
on
the
on
the
color
image.
A
I
would
normally
stretch
this
without
the
stars,
but
gives
me
a
lot
more
flexibility,
so
I'm,
probably
going
to
over
stretch
the
Stars
when
I'm
doing
this
but
I'm
going
to
pick
my
SP
I'm
back
to
an
RGB
stretch,
pick
my
SP
sent
to
SP
and
use
a
big
b
and
start
to
stretch
it
onto
the
right
zoom
out
undo
my
yes,
my
screen,
transfer
function
and
eventually
you'll
see
now
I'm
I'm
really
bifurcating
here
so
I'd
actually
do
this
in
two
steps.
I
would
go
this
far.
B
C
A
A
At
this
stage,
so
my
colors
are
kind
of
still
balanced
in
the
darks
and
but
my
green
is
dominated
so
I
might
want
to
actually
stretch
the
green
first.
As
a
second
stretch,
segment
SP
I've
got
a
bit
of
a
bump
here.
I
always
want
to
put
my
SP
on
top
of
bumps
that's
how
I
get
rid
of
bumps.
That
was
the
point
of
that
it.
That
example,
I
showed
you
earlier
and
let's
say,
I
want
to
stretch
green,
but
I
want
to
move
SP
up.
A
So
this
is
kind
of
the
shape
that
you're
generally
want
not
exactly
in
your
log
histogram.
You
want
to
go
up
to
a
peak,
maybe
across
a
bit
if
your
nebulosity
is
in
the
is
melded.
With
the
black
background
you
go
down
from
the
peak,
then
you'll
hit
an
almost
constant
flat,
Traverse
and
dropping
down
to
the
bottom.
If
I
see
this
go
up,
I'm
loading,
the
Stars
somewhat.
If
some
of
these
features
might
be
absent,
some
might
be
present.
But
let's
say
I'm
I'm.
A
Okay
with
that,
for
my
green
and
I
can
apply
that,
but
I
want
some
more
red
in
there
in
this
image.
So
I
can
pick
a
place
for
the
red
and
separate
stretch
that
sorry
stretch
that
red
separately
from
the
green
now
I
know.
Green
is
going
to
be
the
dominant
color.
So
I
don't
really
want
to
go
past
that
green,
but
a
little
stretch
of
red.
A
Starts
to
bring
red
into
the
image
now
really,
what
am
I
doing
by
stretching
red
is
now
I'm
stretching
my
sulfur,
so
it
had
the
weakest
signal
to
noise
ratio.
So
I
might
be
increasing
the
noise
in
my
image
by
doing
that
right
actually
in
this
particular
images,
which
is
the
Christmas
tree
cluster
and
the
fox
for.
A
A
A
A
A
What
to
do
the
last
percentage
is
always
the
longest,
so
really
don't
be
afraid
to
stretch
your
individual
colors
again.
If
I
go
into
the
history
Explorer,
you
have
to
watch
your
color
balance
in
the
background
like
I've
I've,
increased
red,
but
I
can
use
the
lp
slider
to
to
make
sure
that
that
adjustment
is
made.
A
What
are
you
thinking
about
there?
We
go
now.
I
buggered
up
the
Stars
I
got
way
too
much
Magenta
in
the
stars,
but
now
I've
increased
I've
decreased
the
Green
in
the
image
I've
brought
out
some
red
areas
and
some
blue
areas.
It's
very
noisy
because
I
may
have
over
stretched
my
weak
signal
to
noise
of
my
blue
Channel
and
my
in
my
red
Channel
I.
Can
then
invert
the
image
and
make
use
of.
A
A
C
A
C
A
A
If
I
pick
any
pixels
I'll
do
clipping,
but
I
can
I
know.
I
haven't
clipped
in
this
stage,
because
I
saw
there
were
no
pixels
where
I
picked
it
so
I'm,
okay
and
when
I
do
return
the
stf
now
initially
this
is
noisy
background
and
there's
actually
nothing
in
the
background
of
interest.
But
I
can
pick
my
SP
Point
zoomed
in
right
on
my
histogram
Peak
I
generally
start
with
my
B
all
to
the
left.
I
start
my
stretch
zoom
out.
C
B
A
A
A
A
So
I
can
brighten
the
Stars
I
want
to
see
I
zoom
into
the
core
of
my
cluster
here
to
make
sure
I
can
still
resolve
the
Stars
if
I,
if
I
back
off,
B
too
much
I
start
blowing
it
out.
So
I
want
to
keep
a
good
amount
of
contrast.
I
want
that
cliff,
fairly
close
to
the
right
hand,
side
to
use
all
my
contrast,
undo
that
I
can
zoom
into
this
galaxy
2
and
see
what
that
looks
like
that
one's
got
quite
some
interesting
features,
but
the
colors
have
been
washed
out.
A
Mic
is
built
in
here
a
way
that
does
the
exact
same
thing
as
The
Arc
shine
stretch
does.
Is
it
actually
stretches
the
luminance
and
then
applies
that
luminance
stretch
to
the
individual
colors
that
way
saturation
isn't
lost
when
I,
when
I
stretch,
and
so
now,
I
get
some
vivid
colors
if
I
go
back
into
that
that
nice
Galaxy
that
I
had
I
can
really
see
some
color
detail,
as
well
as
the
detail
itself
now
this
can.
A
D
A
A
A
B
E
A
E
A
A
A
If
you
look
I,
don't
know
how
well
you
can
see
this,
but
there's
a
histogram
type
transformation
type
selection
bar
the
first
one
is
mid-tone
transfer
transfer.
So
this
is
the
same
non-linear
stretch
as
histogram
trans
transform,
except
with
B
taken
out.
So
it's
really
internally
just
setting
B
to
zero,
and
then
you
continue
on.
A
Similarly,
the
arc
sine
stretch
is
doing
the
arc
sine
stretch.
There's
no
B
in
this
one,
because
you
can't
change
B
in
Arc
shine,
they're,
both
family
members
of
the
generalized
hyperbolic
equations.
If
you
will
the
last
one
is
a
linear
stretch.
Now
this
has
been
taken
out
because
it
can
it's
too
many
parameters
on
one
screen
for
one
thing,
but
second
of
all,
it
doesn't
follow
all
those
rules
when
I'm
doing
a
linear
stretch.
A
Here,
I
can
move
the
Black
Point
and
you
can
see
when
I'm
moving
the
Black
Point.
It
no
longer
goes
from
zero
zero.
It
goes
up
here
if
I
do.
If
I
look,
what
that's
doing
to
my
image,
I'm
actually
clipping
pixels,
so
I
can't
say
that
I'm
not
hurting
the
data.
In
fact,
I'm
really
hurting
the
data
and,
if
I
actually
wasn't
hurting
the
data,
a
linear
stretch
actually
doesn't
really
look
that
great
it
does
for
for
part.
A
A
If
I
add
this
contrast
to
this
point,
it's
kind
of
wasted
contrast
right,
yeah,
right
and
I-
don't
want
to
waste
contrast
out
there,
so
I
can
by
looking
at
a
log
view.
One
thing
it
does
show
is
actually
where
that
black
point
is
because
I
don't
see
any
pixels
there
and
if
I
don't
see
them
on
the
log
view,
then
they're
not
there.
A
C
A
A
A
B
C
D
I
think
we
should
leave
some
of
these
problems
for
another
night.
Let's
do
try
to
see
if
we
could
do
something
in
the
future.
I
think
this
has
been
fascinating.
You've,
certainly
piqued
everybody's
interest,
and
you
have
taught
a
lot
of
people.
A
lot
of
things
I
sure
got
a
better
view
of
it
tonight
and
I
appreciate
that.