ImageMagick: Legacy | The FX Special Effects Image Operator (original) (raw)

FX Special Effects Image Operator

The FX Special Effects Image Operator • The Anatomy of an FX Expression

Use the FX special effects image operator to apply a mathematical expression to an image or image channels. The FX expression language provides a powerful and flexible way to manipulate images, allowing you to perform a wide range of operations and transformations on your images. Use FX to:

The expression can be simple:

convert -size 64x64 canvas:black -channel blue -fx "1/2" fx_navy.png

Here, we convert a black to a navy blue image:

Or the expression can be complex:

convert rose:
-fx "(1.0/(1.0+exp(10.0*(0.5-u)))-0.006693)*1.0092503"
rose-sigmoidal.png

This expression results in a high contrast version of the source image:

The expression can include variable assignments. Assignments, in most cases, reduce the complexity of an expression and permit some operations that might not be possible any other way. For example, lets create a radial gradient:

convert -size 70x70 canvas:
-fx "Xi=i-w/2; Yj=j-h/2; 1.2*(0.5-hypot(Xi,Yj)/70.0)+0.5"
radial-gradient.png

The command above returns this image:

radial-gradient

This FX expression adds random noise to an image:

convert photo.jpg -fx 'iso=32; rone=rand(); rtwo=rand();
myn=sqrt(-2ln(rone))cos(2Pirtwo); myntwo=sqrt(-2ln(rtwo))
cos(2Pirone); pnoise=sqrt(p)mynsqrt(iso)*
channel(4.28,3.86,6.68,0)/255; max(0,p+pnoise)' noisy.png

This FX script utilizes a loop to create a Julia set:

convert -size 400x400 xc:black -colorspace gray -fx "
Xi=2.4i/w-1.2;
Yj=2.4j/h-1.2;
for (pixel=0.0, (hypot(Xi,Yj) < 2.0) && (pixel < 1.0),
delta=Xi^2-Yj^2;
Yj=2.0XiYj+0.2;
Xi=delta+0.4;
pixel+=0.00390625
);
pixel == 1.0 ? 0.0 : pixel"
( -size 1x1 xc:white xc:red xc:orange xc:yellow xc:green1 xc:cyan xc:blue
xc:blueviolet xc:white -reverse +append -filter Cubic -resize 1024x1! )
-clut -rotate -90 julia-set.png

Julia Fractals

This FX script prints the first 10 prime numbers:

convert xc: -channel gray -fx "
for (prime=2, prime < 30, composite=0;
for (nn=2, nn < (prime/2+1), if ((prime % nn) == 0, composite++, ); nn++);
if (composite <= 0, debug(prime), ); prime++)" null:

See Using FX, The Special Effects Image Operator for more examples.

The next section discusses the FX expression language.

The Anatomy of an FX Expression

The FX Expression Language

The formal FX expression language is defined here:

numbers:

integer, floating point, scientific notation (+/- required, e.g. 3.81469e-06), International System number postfixes (.e.g KB, Mib, GB, etc.)

constants:

E (Euler's number), Epsilon, Opaque, Phi (golden ratio), Pi, QuantumRange, QuantumScale, Transparent

FX operators (in order of precedence):

^ (power), unary -, *, /, % (modulo), +, -, <<, >>, <, <=, >, >=, +=, -=, *=, /=, %=, <<=, >>=, &=, |=, ++, --, ==, !=, & (bitwise AND), | (bitwise OR), && (logical AND), || (logical OR), ~ (logical NOT), ?: (ternary conditional)

array:

an image offers array storage (e.g. p[-1,-1].r) bounded by its width and height. An image sequence represents multiple arrays (e.g. u.p[0,0].r, v.p[0,0].r). Storage is limited to Quantum values, e.g. [0..65535] for Q16 builds and floating point for HDRI-enabled builds.

math functions:

abs(), acos(), acosh(), airy(), alt(), asin(), asinh(), atan(), atanh(), atan2(), ceil(), clamp(), cos(), cosh(), debug(), drc(), erf(), exp(), floor(), gauss(), gcd(), hypot(), int(), isnan(), j0(), j1(), jinc(), ln(), log(), logtwo(), max(), min(), mod(), not(), pow(), rand(), round(), sign(), sin(), sinc(), sinh(), sqrt(), squish(), tan(), tanh(), trunc()

channel functions:

channel(r,g,b,a), channel(c,m,y,k,a)

color names:

red, cyan, black, etc.

color functions:

srgb(), srgba(), rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla(), etc.

color hex values:

#ccc, #cbfed0, #b9e1cc00, etc.

symbols:

u: first image in list

v: second image in list

s: current image in list (for %[fx:] otherwise = u)

t: index of current image (s) in list

n: number of images in list

i: column offset

j: row offset

p: pixel to use (absolute or relative to current pixel)

w: width of this image

h: height of this image

z: channel depth

r: red value (from RGBA), of a specific or current pixel

g: green

b: blue

a: alpha

o: opacity

c: cyan value of CMYK color of pixel

y: yellow

m: magenta

k: black

intensity: pixel intensity

hue: pixel hue

saturation: pixel saturation

lightness: pixel lightness

luma: pixel luma

page.width: page width

page.height: page height

page.x: page x offset

page.y: page y offset

printsize.x: x printsize

printsize.y: y printsize

resolution.x: x resolution

resolution.y: y resolution

depth: image depth

extent: image extent

minima: image minima

maxima: image maxima

mean: image mean

standard_deviation: image standard deviation

kurtosis: image kurtosis

skewness: image skewness (add a channel specifier to compute a statistic for that channel, e.g. depth.r)

iterators:

do(), for(), while()

image attributes:

image.depth, image.kurtosis, image.maxima, image.mean, image.median, image.minima, image.resolution.x, image.resolution.y, image.skewness, image.standard_deviation

The FX Expression

An FX expression may include any combination of the following:

x ^ y

exponentiation (xy)

( ... )

grouping

x * y

multiplication

x / y

division

x % y

modulo

x + y

addition

x - y

subtraction

x << y

left shift

x >> y

right shift

x < y

boolean relation, return value 1.0 if x < y, otherwise 0.0

x <= y

boolean relation, return value 1.0 if x <= y, otherwise 0.0

x > y

boolean relation, return value 1.0 if x > y, otherwise 0.0

x >= y

boolean relation, return value 1.0 if x >= y, otherwise 0.0

x == y

boolean relation, return value 1.0 if x == y, otherwise 0.0

x != y

boolean relation, return value 1.0 if x != y, otherwise 0.0

x & y

binary AND

x | y

binary OR

x && y

logical AND connective, return value 1.0 if x > 0 and y > 0, otherwise 0.0

x || y

logical OR connective (inclusive), return value 1.0 if x > 0 or y > 0 (or both), otherwise 0.0

~x

logical NOT operator, return value 1.0 if not x > 0, otherwise 0.0

+x

unary plus, return 1.0*value

-x

unary minus, return -1.0*value

x ? y : z

ternary conditional expression, return value y if x != 0, otherwise z; only one ternary conditional permitted per statement

x = y

assignment; single character variables are reserved, instead use 2 or more characters, letter combinations only (e.g. Xi not X1)

x ; y

statement separator

phi

constant (1.618034...)

pi

constant (3.14159265359...)

e

constant (2.71828...)

QuantumRange

constant maximum pixel value (255 for Q8, 65535 for Q16)

QuantumScale

constant 1.0/QuantumRange

intensity

pixel intensity whose value respects the -intensity option.

hue

pixel hue

saturation

pixel saturation

lightness

pixel lightness; equivalent to 0.5*max(red,green,blue) + 0.5*min(red,green,blue)

luminance

pixel luminance; equivalent to 0.212656*red + 0.715158*green + 0.072186*blue

red, green, blue, etc.

color names

#ccc, #cbfed0, #b9e1cc00, etc.

color hex values

rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()

color functions

s, t, u, v, n, i, j, w, h, z, r, g, b, a, o, c, y, m, k

symbols

abs(x)

absolute value function

acos(x)

arc cosine function

acosh(x)

inverse hyperbolic cosine function

airy(x)

Airy function (max=1, min=0); airy(x)=[jinc(x)]2=[2*j1(pi*x)/(pi*x)]2

alt(x)

sign alternation function (return 1.0 if int(x) is even, -1.0 if int(x) is odd)

asin(x)

arc sine function

asinh(x)

inverse hyperbolic sine function

atan(x)

arc tangent function

atanh(x)

inverse hyperbolic tangent function

atan2(y,x)

arc tangent function of two variables

ceil(x)

smallest integral value not less than argument

channel(r,g,b,a)

select numeric argument based on current channel

channel(c,m,y,k,a)

select numeric argument based on current channel

clamp(x)

clamp value

cos(x)

cosine function

cosh(x)

hyperbolic cosine function

debug(x)

print x (useful for debugging your expression)

do(condition test, statements)

iterate while the condition is not equal to 0

drc(x,y)

dynamic range compression (knee curve); drc(x,y)=(x)/(y*(x-1)+1); -1<y<1

erf(x)

error function

exp(x)

natural exponential function (ex)

floor(x)

largest integral value not greater than argument

for(initialization, condition test, expression)

iterate while the condition is not equal to 0

gauss(x)

gaussian function; gauss(x)=exp(-x*x/2)/sqrt(2*pi)

gcd(x,y)

greatest common denominator

hypot(x,y)

the square root of x2+y2

if(condition test, nonzero-expression, zero-expression)

interpret expression depending on condition

int(x)

greatest integer function (return greatest integer less than or equal to x)

isnan(x)

return 1.0 if x is NAN, 0.0 otherwise

j0(x)

Bessel functions of x of the first kind of order 0

j1(x)

Bessel functions of x of the first kind of order 1

jinc(x)

jinc function (max=1, min=-0.1323); jinc(x)=2*j1(pi*x)/(pi**x)

ln(x)

natural logarithm function

log(x)

logarithm base 10

logtwo(x)

logarithm base 2

ln(x)

natural logarithm

max(x, y)

maximum of x and y

min(x, y)

minimum of x and y

mod(x, y)

floating-point remainder function

not(x)

return 1.0 if x is zero, 0.0 otherwise

pow(x,y)

power function (xy)

rand()

value uniformly distributed over the interval [0.0, 1.0) with a 2 to the 128th-1 period

round()

round to integral value, regardless of rounding direction

sign(x)

return -1.0 if x is less than 0.0 otherwise 1.0

sin(x)

sine function

sinc(x)

sinc function (max=1, min=-0.21); sinc(x)=sin(pi*x)/(pi*x)

squish(x)

squish function; squish(x)=1.0/(1.0+exp(-x))

sinh(x)

hyperbolic sine function

sqrt(x)

square root function

tan(x)

tangent function

tanh(x)

hyperbolic tangent function

trunc(x)

round to integer, towards zero

while(condition test, expression)

iterate while the condition is not equal to 0

image.depth, image.kurtosis, image.maxima, image.mean, image.minima, image.resolution.x, image.resolution.y, image.skewness, image.standard_deviation

image attributes

The expression semantics include these rules:

Source Images

The symbols u and v refer to the first and second images, respectively, in the current image sequence. Refer to a particular image in a sequence by appending its index to any image reference (usually u), with a zero index for the beginning of the sequence. A negative index counts from the end. For example, u[0] is the first image in the sequence, u[2] is the third, u[-1] is the last image, and u[t] is the current image. The current image can also be referenced by s. If the sequence number exceeds the length of the sequence, the count is wrapped. Thus in a 3-image sequence, u[-1], u[2], and u[5] all refer to the same (third) image.

As an example, we form an image by averaging the first image and third images (the second (index 1) image is ignored and just junked):

convert image1.jpg image2.jpg image3.jpg -fx "(u+u[2])/2.0" image.jpg

By default, the image to which p, r, g, b, a, etc., are applied is the current image s in the image list. This is equivalent to u except when used in an escape sequence %[fx:...].

It is important to note the special role played by the first image. This is the only image in the image sequence that is modified, other images are used only for their data. As an illustrative example, consider the following, and note that the setting -channel red instructs -fx to modify only the green channel; nothing in the red or blue channels will change. It is instructive to ponder why the result is not symmetric.

convert -channel green logo: -flop logo: -resize "20%" -fx "(u+v)/2" image.jpg

Accessing Pixels

All color values are normalized to the range of 0.0 to 1.0. The alpha channel ranges from 0.0 (fully transparent) to 1.0 (fully opaque).

The pixels are processed one at a time, but a different pixel of an image can be specified using a pixel index represented by p. For example,

p[-1].g green value of pixel to the immediate left of the current pixel p[-1,-1].r red value of the pixel diagonally left and up from current pixel

To specify an absolute position, use braces, rather than brackets.

p{0,0}.r red value of the pixel in the upper left corner of the image p{12,34}.b blue pixel value at column number 12, row 34 of the image

Integer values of the position retrieve the color of the pixel referenced, while non-integer position values return a blended color according to the current -interpolate setting.

A position outside the boundary of the image retrieves a value dictated by the -virtual-pixel option setting.

Apply an Expression to Select Image Channels

Use the -channel setting to specify the output channel of the result. If no output channel is given, the result is set over all channels except the opacity channel. For example, to replace the red channel of alpha.png with the average of the green channels from the images alpha.png and beta.png, use:

convert alpha.png beta.png -channel red -fx "(u.g+v.g)/2" gamma.png

Results

The -fx operator evaluates the given expression for each channel (set by -channel) of each pixel in the first image (u) in the sequence. The computed values are temporarily stored in a copy (clone) of that first image until all the pixels have been processed, after which this single new image replaces the list of images in the current image sequence. As such, in the previous example the updated version of alpha.png replaces both of the original images, alpha.png and beta.png, before being saved as gamma.png.

The current image s is set to the first image in the sequence (u), and t to its index, 0. The symbols i and j reference the current pixel being processed.

For use with -format, the value-escape %[fx:] is evaluated just once for each image in the current image sequence. As each image in the sequence is being evaluated, s and t successively refer to the current image and its index, while i and j are set to zero, and the current channel set to red (-channel is ignored). An example:

convert canvas:'rgb(25%,50%,75%)' rose: -colorspace gray
-format 'Red channel of NW corner of image #%[fx:t] is %[fx:s]\n' info: Red channel of NW corner of image #0 is 0.464883 Red channel of NW corner of image #1 is 0.184582

Here we use the image indexes to rotate each image differently, and use -set with the image index to set a different pause delay on the first image in the animation:

convert rose: -duplicate 29 -virtual-pixel Gray -distort SRT '%[fx:360.0*t/n]'
-set delay '%[fx:t == 0 ? 240 : 10]' -loop 0 rose.gif

The color-escape %[pixel:] or %[hex:] is evaluated once per image and per color channel in that image (-channel is ignored), The values generated are then converted into a color string (a named color or hex color value). The symbols i and j are set to zero, and s and t refer to each successively current image and index.