ImageMagick: The Fx Special Effects Image Operator

The Fx Special Effects Image Operator

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 xc:black -channel blue -fx "1/2" fx_navy.png

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

-- or complex:

    convert rose.jpg -fx "(1.0/(1.0+exp(10.0*(0.5-u)))-0.0066928509)*1.0092503" rose-sigmoidal.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 permits some operations that might not be possible any other way. For example, lets create a radial gradient with statements:

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

These statements return this image:

See Using FX, The Special Effects Image Operator for more examples on how to apply a mathematical expression to an image or image channels.

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 in this table:

  constants: QuantumRange, QuantumScale, Opaque, Transparent, e, Pi
  Fx operators (in order of precedence):
     ^ (power), *, /, % (modulo), +, -, <<, >>, <, <=, >, >=, ==, !=, & (bitwise AND),
     | (bitwise OR), && (logical AND), || (logical OR), ~ (logical NOT), ?: (ternary conditional)
  math functions:
     abs(), acos(), asin(), alt(), atan(), atan2(), ceil(), cos(), debug(), exp(), floor(), hypot(), int(),
     log(), log2(), ln(), mod(), pow(), rand(), round(), sign(), sin(), sqrt(), tan()
  color names: red, cyan, black, etc.
  color functions: rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()
  color hex values: #ccc, #cbfed0, #b9e1cc00
  symbols:
     s = current image in sequence
     t = scene number of current image in sequence
     u = first image in sequence
     v = second image in sequence
     n = number of images in sequence
     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
     luminance = pixel luminance
     image.resolution.x = x resolution
     image.resolution.y = y resolution
     image.depth = image depth
     image.minima = image minima
     image.maxima = image maxima
     image.mean = image mean
     image.standard_deviation = image standard deviation

The Fx Expression

The Fx expressions includes any combination of the following:

x ^ y: exponentiation (x^y)
( ... ): grouping
x * y: multiplication (the asterisk * is optional, for example, 2u or 2(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
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 0.2126*red + 0.7152*green + 0.0722*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
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
atan(x): arc tangent function
atan2(y,x): arc tangent function of two variables
ceil(x): smallest integral value not less than argument
cos(x): cosine function
debug(x): print x (useful for debugging your expression)
exp(x): natural exponential function (e^x)
floor(x): largest integral value not greater than argument
hypot(x,y): the square root of x²+y²
int(x): greatest integer function (return greatest integer less than or equal to x)
ln(x): natural logarithm function
log(x): logarithm base 10
max(x, y): maximum of x and y
min(x, y): minimum of x and y
mod(x, y): floating-point remainder function
pow(x,y): power function (x^y)
rand(): value uniformly distributed over the interval [0.0, 1.0) with a 2 to the 128th-1 period
sign(x): return -1.0 if x is less than 0.0 otherwise 1.0
sin(x): sine function
sqrt(x): square root function
tan(x): tangent function

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 built-ins do not throw errors and have no effect; e.g. r=3.0; r returns the pixel red color value, not 3.0

Source Image

The default image for p, r, g, b, a, etc. is s which refers to the current image being looked at in %[fx: ] and %[pixel: ] escapes. The -fx image s defaults to the first (zeroth) image u. The index of s is given by t.

The symbol u refers to the first (zeroth) image in the current image sequence, v the second image. Refer to a particular image in a sequence by appending its index to any image reference (usually u). A negative index counts from the end. For example, u[2] is the third image the sequence, u[-1] is the last image, and u[t] is s.

Here we reduce the intensity of the red channel by 50%:

  convert image.png -channel red -fx "u/2.0" image.jpg

Accessing Pixels

All color values are in 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 a image can be specified with a pixel index represented by p. For example,

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

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

  p{12,34}.b   blue pixel value at the 12th column and 34th row of the image

The other symbols specify the value you wish to retrieve.

Integer pixel references retrieve the color of the pixel referred to, whereas non-integer references return a blended color according to the current -interpolate setting.

A pixel outside the boundary of the image has 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, suppose you want 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 once for each pixel in the first image (u) in the sequence for each channel. The computed value is placed in a copy (clone) of that first image. This new image replaces all images in the current image sequence. As such in the previous example, the updated alpha.png replaces both the original alpha.png and beta.png images, before being saved as gamma.png.

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

The value escape %[fx: ] is evaluated once only for each image in the current image sequence, with s and t specifying which image is being referred to i and j is set to zero and the current channel is set to red (-channel is ignored).

The color escape %[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 (named color or hex color value). The symbols i and j are set to zero and s and t define the current image.