Apply Special Effects to an Image with an Fx Expression
Use the Fx special effects image operator to apply a mathematical expression to an image or image channels. Use Fx to:
 create canvases, gradients, mathematical colormaps
 move color values between images and channels
 translate, flip, mirror, rotate, scale, shear and generally distort images
 merge or composite multiple images together
 convolve or merge neighboring pixels together
 generate image metrics or 'fingerprints'
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.jpg \
fx "(1.0/(1.0+exp(10.0*(0.5u)))0.006693)*1.0092503" \
rosesigmoidal.png
This expression results in a high contrast version of the 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=iw/2; Yj=jh/2; 1.2*(0.5hypot(Xi,Yj)/70.0)+0.5" \
radialgradient.png
The command above returns this image:
This FX expression adds random noise to an image:
$ convert photo.jpg fx 'iso=32; rone=rand(); rtwo=rand(); \
myn=sqrt(2*ln(rone))*cos(2*Pi*rtwo); myntwo=sqrt(2*ln(rtwo))* \
cos(2*Pi*rone); pnoise=sqrt(p)*myn*sqrt(iso)* \
channel(4.28,3.86,6.68,0)/255; max(0,p+pnoise)' noisy.png
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, scientfic notation (+/ required, e.g. 3.81469e06), International System number postfixes (.e.g KB, Mib, GB, etc.)
 constants:
 E (Euler's number), Epsilon, QuantumRange, QuantumScale, Opaque, Phi (golden ratio), Pi, Transparent
 Fx operators (in order of precedence):
 ^ (power), unary , *, /, % (modulo), +, , <<, >>, <, <=, >, >=, ==, !=, & (bitwise AND),  (bitwise OR), && (logical AND),  (logical OR), ~ (logical NOT), ?: (ternary conditional)
 math functions:
 abs(), acos(), acosh(), airy(), alt(), asin(), asinh(), atan(), atanh(), atan2(), ceil(), cos(), cosh(), debug(), drc(), 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 resolution.x = x resolution resolution.y = y resolution depth = image depth 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:
 while()
The Fx Expression
An Fx expression may include any combination of the following:
 x
^
y: exponentiation (x^{y}) 
(
...)
: grouping  x
*
y: multiplication (the asterisk*
is optional, for example,2u
or2(x+y)
are acceptable)  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; assignment variables are restricted to letter combinations only (e.g. Xi not X1)  x
;
y: statement separator 
phi
: constant (1.618034...) 
pi
: constant (3.141659...) 
e
: constant (2.71828...) 
QuantumRange
: constant maximum pixel value (255 for Q8, 65535 for Q16) 
QuantumScale
: constant 1.0/QuantumRange

intensity
: pixel intensity; equivalent to 0.299*red+0.587*green+0.114*blue 
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 
cos(
x)
: cosine function 
cosh(
x)
: hyperbolic cosine function 
debug(
x)
: print x (useful for debugging your expression) 
drc(
x,y)
: dynamic range compression (knee curve); drc(x,y)=(x)/(y*(x1)+1); 1<y<1 
exp(
x)
: natural exponential function (e^{x}) 
floor(
x)
: largest integral value not greater than argument 
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 x^{2}+y^{2} 
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)
: floatingpoint remainder function 
not(
x)
: return 1.0 if x is zero, 0.0 otherwise 
pow(
x,y)
: power function (x^{y}) 
rand()
: value uniformly distributed over the interval [0.0, 1.0) with a 2 to the 128th1 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,expression)
: interate while the condition is not equal to 0
The expression semantics include these rules:
 symbols are case insensitive
 only one ternary conditional (e.g. x ? y : z) per statement
 statements are assignments or the final expression to return
 an assignment starts a statement, it is not an operator
 assignments to builtins do not throw an exception and have no effect; e.g.
r=3.0; r
returns the pixel red color value, not 3.0  Unary operators have a lower priority than binary operators, that is, the unary minus (negation) has lower precedence than exponentiation, so 3^2 is interpreted as (3^2) = 9. Use parentheses to clarify your intent (e.g. (3)^2 = 9).
 Similarly, care must be exercised when using the slash ('/') symbol. The string of characters 1/2x is interpreted as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x). Again, the use of parentheses helps clarify the meaning and should be used whenever there is any chance of misinterpretation.
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 3image 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 equivelent 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 red channel; nothing in the green or blue channels will change. It is instructive to ponder why the result is not symmetric.
$ convert channel red 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 noninteger 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 virtualpixel 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 valueescape %[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 rgb \
format 'Red channel of NW corner of image #%[fx:t] is %[fx: s]' info:Red channel of NW corner of image #0 is 0.453758
Red channel of NW corner of image #1 is 0.184588
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 virtualpixel Gray distort SRT '%[fx:360.0*t/n]' \
set delay '%[fx:t == 0 ? 240 : 10]' loop 0 rose.gif
The colorescape %[pixel: ]
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.