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Use Fx to:</p> 158 159<ul> 160 <li>create canvases, gradients, mathematical colormaps</li> 161 <li>move color values between images and channels</li> 162 <li>translate, flip, mirror, rotate, scale, shear and generally distort images</li> 163 <li>merge or composite multiple images together</li> 164 <li>convolve or merge neighboring pixels together</li> 165 <li>generate image metrics or 'fingerprints'</li> 166</ul> 167 168<p>The expression can be simple:</p> 169 170<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert -size 64x64 xc:black -channel blue -fx "1/2" fx_navy.png</span></p> 171<p>Here, we convert a black to a navy blue image:</p> 172 173<p class="image"> 174 <a href="/images/black.png"><img src="/images/black.png" width="64" height="64" alt="black" /></a> 175 <img style="margin-top:22px; margin-bottom:22px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 176 <a href="/images/navy.png"><img src="/images/navy.png" width="64" height="64" alt="navy" /></a> 177</p> 178 179<p>Or the expression can be complex:</p> 180 181<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert rose.jpg \ <br/> 182 -fx "(1.0/(1.0+exp(10.0*(0.5-u)))-0.006693)*1.0092503" \ <br/> 183 rose-sigmoidal.png</span></p> 184<p>This expression results in a high contrast version of the image:</p> 185 186<p class="image"> 187 <a href="/images/rose.jpg"><img src="/images/rose.jpg" width="70" height="46" alt="rose" /></a> 188 <img style="margin-top:13px; margin-bottom:13px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 189 <a href="/images/rose-sigmoidal.png"><img src="/images/rose-sigmoidal.png" width="70" height="46" alt="rose-sigmoidal" /></a> 190</p> 191 192<p>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:</p> 193 194<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert -size 70x70 xc: \ <br/> 195 -fx "Xi=i-w/2; Yj=j-h/2; 1.2*(0.5-hypot(Xi,Yj)/70.0)+0.5" \ <br/> 196 radial-gradient.png</span></p> 197<p>The command above returns this image:</p> 198 199<p class="image"> 200 <a href="/images/radial-gradient.png"><img src="/images/radial-gradient.png" width="70" height="70" alt="radial-gradient" /></a> 201</p> 202<p>See <a href="http://www.imagemagick.org/Usage/transform/index.html#fx">Using FX, The Special Effects Image Operator</a> for more examples.</p> 203 204<p>The next section discusses the Fx expression language.</p> 205 206</div> 207 208<h2><a name="anatomy"></a>The Anatomy of an Fx Expression</h2> 209<div class="doc-section"> 210 211<h3>The Fx Expression Language</h3> 212<div class="doc-section"> 213 214<p>The formal Fx expression language is defined here:</p> 215 216<dl class="doc"> 217 <dt class="doc"> numbers:</dt> 218 <dd> integer, floating point, or scientfic notation (+/- required, e.g. 3.81469e-06)</dd> 219 <dt class="doc"> constants: </dt> 220 <dd> e, Epsilon, QuantumRange, QuantumScale, Opaque, Pi, Transparent</dd> 221 <dt class="doc"> Fx operators (in order of precedence): </dt> 222 <dd> ^ (power), *, /, % (modulo), +, -, 223 <<, >>, <, <=, >, >=, ==, !=, 224 & (bitwise AND), | (bitwise OR), 225 && (logical AND), || (logical OR), 226 ~ (logical NOT), ?: (ternary conditional)</dd> 227 <dt class="doc"> math functions: </dt> 228 <dd> abs(), acos(), alt(), asin(), atan(), atan2(), ceil(), cos(), cosh(), debug(), exp(), floor(), 229 hypot(), int(), ln(), log(), logtwo(), max(), min(), mod(), pow(), rand(), round(), 230 sign(), sin(), sinh(), sqrt(), tan(), tanh()</dd> 231 <dt class="doc"> channel functions: </dt> 232 <dd> channel(r,g,b,a), channel(c,m,y,k,a)</dd> 233 <dt class="doc"> color names:</dt> 234 <dd> red, cyan, black, etc.</dd> 235 <dt class="doc"> color functions:</dt> 236 <dd> rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</dd> 237 <dt class="doc"> color hex values:</dt> 238 <dd> #ccc, #cbfed0, #b9e1cc00</dd> 239 <dt class="doc"> symbols:</dt> 240 <dd style="white-space:pre"> 241 s = current image in sequence 242 t = scene number of current image in sequence 243 u = first image in sequence 244 v = second image in sequence 245 n = number of images in sequence 246 247 i = column offset 248 j = row offset 249 p = pixel to use (absolute or relative to current pixel) 250 251 w = width of this image 252 h = height of this image 253 z = channel depth 254 255 r = red value (from RGBA), of a specific or current pixel 256 g = green '' 257 b = blue '' 258 a = alpha '' 259 o = opacity '' 260 261 c = cyan value of CMYK color of pixel 262 y = yellow '' 263 m = magenta '' 264 k = black '' 265 266 intensity = pixel intensity 267 268 hue = pixel hue 269 saturation = pixel saturation 270 lightness = pixel lightness 271 luminance = pixel luminance 272 273 page.width = page width 274 page.height = page height 275 page.x = page x offset 276 page.y = page y offset 277 278 resolution.x = x resolution 279 resolution.y = y resolution 280 281 depth = image depth 282 minima = image minima 283 maxima = image maxima 284 mean = image mean 285 standard_deviation = image standard deviation 286 kurtosis = image kurtosis 287 skewness = image skewness 288 (add a channel specifier to compute a statistic for that channel, e.g. depth.r) 289 </dd> 290</dl> 291 292</div> 293 294<h3>The Fx Expression</h3> 295<div class="doc-section"> 296 297<p>An Fx expression may include any combination of the following:</p> 298<ul> 299<li> <em>x</em> <kbd>^</kbd> <em>y</em>: exponentiation (<em>x<sup>y</sup></em>)</li> 300<li> <kbd>(</kbd> ... <kbd>)</kbd>: grouping</li> 301<li> <em>x</em> <kbd>*</kbd> <em>y</em>: multiplication (the asterisk <kbd>*</kbd> is optional, for example, <kbd>2u</kbd> or <kbd>2(x+y)</kbd> are acceptable)</li> 302<li> <em>x</em> <kbd>/</kbd> <em>y</em>: division</li> 303<li> <em>x</em> <kbd>%</kbd> <em>y</em>: modulo</li> 304<li> <em>x</em> <kbd>+</kbd> <em>y</em>: addition</li> 305<li> <em>x</em> <kbd>-</kbd> <em>y</em>: subtraction</li> 306<li> <em>x</em> <kbd><<</kbd> <em>y</em>: left shift</li> 307<li> <em>x</em> <kbd>>></kbd> <em>y</em>: right shift</li> 308<li> <em>x</em> <kbd><</kbd> <em>y</em>: boolean relation, return value 1.0 if <em>x</em> < <em>y</em>, otherwise 0.0</li> 309<li> <em>x</em> <kbd><=</kbd> <em>y</em>: boolean relation, return value 1.0 if <em>x</em> <= <em>y</em>, otherwise 0.0</li> 310<li> <em>x</em> <kbd>></kbd> <em>y</em>: boolean relation, return value 1.0 if <em>x</em> > <em>y</em>, otherwise 0.0</li> 311<li> <em>x</em> <kbd>>=</kbd> <em>y</em>: boolean relation, return value 1.0 if <em>x</em> >= <em>y</em>, otherwise 0.0</li> 312<li> <em>x</em> <kbd>==</kbd> <em>y</em>: boolean relation, return value 1.0 if <em>x </em>==<em> y</em>, otherwise 0.0</li> 313<li> <em>x</em> <kbd>!=</kbd> <em>y</em>: boolean relation, return value 1.0 if <em>x </em>!=<em> y</em>, otherwise 0.0</li> 314<li> <em>x</em> <kbd>&</kbd> <em>y</em>: binary AND</li> 315<li> <em>x</em> <kbd>|</kbd> <em>y</em>: binary OR</li> 316<li> <em>x</em> <kbd>&&</kbd> <em>y</em>: logical AND connective, return value 1.0 if <em>x</em> > 0 and <em>y</em> > 0, otherwise 0.0</li> 317<li> <em>x</em> <kbd>||</kbd> <em>y</em>: logical OR connective (inclusive), return value 1.0 if <em>x</em> > 0 or <em>y</em> > 0 (or both), otherwise 0.0</li> 318<li> <kbd>~</kbd><em>x</em>: logical NOT operator, return value 1.0 if <em>not</em> <em>x</em> > 0, otherwise 0.0</li> 319<li> <kbd>+</kbd><em>x</em>: unary plus, return 1.0*value</li> 320<li> <kbd>-</kbd><em>x</em>: unary minus, return -1.0*value</li> 321<li> <em>x</em> <kbd>?</kbd> <em>y</em> : <em>z</em>: ternary conditional expression, return value <em>y</em> if <em>x</em> != 0, otherwise <em>z</em>; only one ternary conditional permitted per statement</li> 322<li> <em>x</em> <kbd>=</kbd> <em>y</em>: assignment; assignment variables are restricted to letter combinations only (e.g. Xi not X1)</li> 323<li> <em>x</em> <kbd>;</kbd> <em>y</em>: statement separator </li> 324<li> <kbd>pi</kbd>: constant (3.141659...)</li> 325<li> <kbd>e</kbd>: constant (2.71828...)</li> 326<li> <kbd>QuantumRange</kbd>: constant maximum pixel value (255 for Q8, 65535 for Q16)</li> 327<li> <kbd>QuantumScale</kbd>: constant 1.0/<kbd>QuantumRange</kbd></li> 328<li> <kbd>intensity</kbd>: pixel intensity; equivalent to 0.299*red+0.587*green+0.114*blue</li> 329<li> <kbd>hue</kbd>: pixel hue</li> 330<li> <kbd>saturation</kbd>: pixel saturation</li> 331<li> <kbd>lightness</kbd>: pixel lightness; equivalent to 0.5*max(red,green,blue) + 0.5*min(red,green,blue)</li> 332<li> <kbd>luminance</kbd>: pixel luminance; equivalent to 0.2126*red + 0.7152*green + 0.0722*blue</li> 333<li> <kbd>red, green, blue</kbd>, etc.: color names</li> 334<li> <kbd>#ccc, #cbfed0, #b9e1cc00</kbd>, etc.: color hex values</li> 335<li> <kbd>rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</kbd>: color functions</li> 336<li> <kbd>s, t, u, v, n, i, j, w, h, z, r, g, b, a, o, c, y, m, k</kbd>: symbols</li> 337<li> <kbd>abs(</kbd><em>x</em><kbd>)</kbd>: absolute value function</li> 338<li> <kbd>acos(</kbd><em>x</em><kbd>)</kbd>: arc cosine function</li> 339<li> <kbd>alt(</kbd><em>x</em><kbd>)</kbd>: sign alternation function (return 1.0 if <kbd>int(</kbd><em>x</em><kbd>)</kbd> is even, -1.0 if <kbd>int(</kbd><em>x</em><kbd>)</kbd> is odd)</li> 340<li> <kbd>asin(</kbd><em>x</em><kbd>)</kbd>: arc sine function</li> 341<li> <kbd>atan(</kbd><em>x</em><kbd>)</kbd>: arc tangent function</li> 342<li> <kbd>atan2(</kbd><em>y</em>,<em>x</em><kbd>)</kbd>: arc tangent function of two variables</li> 343<li> <kbd>ceil(</kbd><em>x</em><kbd>)</kbd>: smallest integral value not less than argument</li> 344<li> <kbd>channel(</kbd><em>r</em>,<em>g</em>,<em>b</em>,<em>a</em><kbd>)</kbd>: select numeric argument based on current channel</li> 345<li> <kbd>channel(</kbd><em>c</em>,<em>m</em>,<em>y</em>,<em>k</em>,<em>a</em><kbd>)</kbd>: select numeric argument based on current channel</li> 346<li> <kbd>cos(</kbd><em>x</em><kbd>)</kbd>: cosine function</li> 347<li> <kbd>cosh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic cosine function</li> 348<li> <kbd>debug(</kbd><em>x</em><kbd>)</kbd>: print <em>x</em> (useful for debugging your expression)</li> 349<li> <kbd>exp(</kbd><em>x</em><kbd>)</kbd>: natural exponential function (<em>e<sup>x</sup></em>)</li> 350<li> <kbd>floor(</kbd><em>x</em><kbd>)</kbd>: largest integral value not greater than argument</li> 351<li> <kbd>hypot(</kbd><em>x</em>,<em>y</em><kbd>)</kbd>: the square root of x<sup>2</sup>+y<sup>2</sup></li> 352<li> <kbd>int(</kbd><em>x</em><kbd>)</kbd>: greatest integer function (return greatest integer less than or equal to <em>x</em>)</li> 353<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>: natural logarithm function</li> 354<li> <kbd>log(</kbd><em>x</em><kbd>)</kbd>: logarithm base 10</li> 355<li> <kbd>logtwo(</kbd><em>x</em><kbd>)</kbd>: logarithm base 2</li> 356<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>: natural logarithm</li> 357<li> <kbd>max(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: maximum of <em>x</em> and <em>y</em></li> 358<li> <kbd>min(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: minimum of <em>x</em> and <em>y</em></li> 359<li> <kbd>mod(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: floating-point remainder function</li> 360<li> <kbd>pow(</kbd><em>x</em>,<em>y</em><kbd>)</kbd>: power function (<em>x<sup>y</sup></em>)</li> 361<li> <kbd>rand()</kbd>: value uniformly distributed over the interval [0.0, 1.0) with a 2 to the 128th-1 period</li> 362<li> <kbd>round()</kbd>: round to integral value, regardless of rounding direction</li> 363<li> <kbd>sign(</kbd><em>x</em><kbd>)</kbd>: return -1.0 if <em>x</em> is less than 0.0 otherwise 1.0</li> 364<li> <kbd>sin(</kbd><em>x</em><kbd>)</kbd>: sine function</li> 365<li> <kbd>sinh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic sine function</li> 366<li> <kbd>sqrt(</kbd><em>x</em><kbd>)</kbd>: square root function</li> 367<li> <kbd>tan(</kbd><em>x</em><kbd>)</kbd>: tangent function</li> 368<li> <kbd>tanh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic tangent function</li> 369</ul> 370 371<p>The expression semantics include these rules:</p> 372 373<ul> 374<li>symbols are case insensitive</li> 375<li>only one ternary conditional (e.g. x ? y : z) per statement</li> 376<li>statements are assignments or the final expression to return</li> 377<li>an assignment starts a statement, it is not an operator</li> 378<li>assignments to built-ins do not throw an exception and have no effect; e.g. <kbd>r=3.0; r</kbd> returns the pixel red color value, not 3.0</li> 379</ul> 380 381</div> 382 383<h3>Source Images</h3> 384<div class="doc-section"> 385 386<p>The symbols <kbd>u</kbd> and <kbd>v</kbd> 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 <kbd>u</kbd>), with a zero index for the beginning of the sequence. A negative index counts from the end. For example, <kbd>u[0]</kbd> is the first image in the sequence, <kbd>u[2]</kbd> is the third, <kbd>u[-1]</kbd> is the last image, and <kbd>u[t]</kbd> is the current image. The current image can also be referenced by <kbd>s</kbd>. If the sequence number exceeds the length of the sequence, the count is wrapped. Thus in a 3-image sequence, <kbd>u[-1]</kbd>, <kbd>u[2]</kbd>, and <kbd>u[5]</kbd> all refer to the same (third) image.</p> 387 388<p>As an example, we form an image by averaging the first image and third images:</p> 389 390<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert image1.jpg image2.jpg image3.jpg -fx "(u+u[2])/2.0" image.jpg</span></p> 391<p>By default, the image to which <kbd>p</kbd>, <kbd>r</kbd>, <kbd>g</kbd>, <kbd>b</kbd>, <kbd>a</kbd>, etc., are applied is the first image <kbd>u</kbd> in the image list, which may also be referenced using <kbd>s</kbd>. </p> 392 393<p>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, any other images being used only for their data. As an illustrative example, comsider the following, and note that the setting <a href="/www/command-line-options.html#channel">-channel red</a> instructs <a href="/www/command-line-options.html#fx">-fx</a> 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.</p> 394 395<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert -channel red logo: -flop logo: -resize "20%" -fx "(u+v)/2" image.jpg</span></p> 396<div class="image"> 397<p> 398 <a href="/images/logo-sm-flop.png"><img src="/images/logo-sm-flop.png" width="128" height="96" alt="logo-sm-flop.png" /></a> 399 <a href="/images/logo-sm.png"><img src="/images/logo-sm.png" width="128" height="96" alt="logo-sm.png" /></a> 400<img style="margin-top:38px; margin-bottom:38px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 401 <a href="/images/logo-sm-fx.png"><img src="/images/logo-sm-fx.png" width="128" height="96" alt="logo-sm-fx.png" /></a> 402</p> 403</div> 404 405 406</div> 407 408<h3>Accessing Pixels</h3> 409<div class="doc-section"> 410 411<p>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).</p> 412 413<p>The pixels are processed one at a time, but a different pixel of an image can be specified using a pixel index represented by <kbd>p</kbd>. For example,</p> 414 415<pre class="text"> 416 p[-1].g green value of pixel to the immediate left of the current pixel 417 p[-1,-1].r red value of the pixel diagonally left and up from current pixel 418</pre> 419 420<p>To specify an absolute position, use braces, rather than brackets.</p> 421 422<pre class="text"> 423 p{0,0}.r red value of the pixel in the upper left corner of the image 424 p{12,34}.b blue pixel value at column number 12, row 34 of the image 425</pre> 426 427<p>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 <a href="/www/command-line-options.html#interpolate">-interpolate</a> setting.</p> 428 429<p>A position outside the boundary of the image retrieves a value dictated by the <a href="/www/command-line-options.html#virtual-pixel">-virtual-pixel</a> option setting.</p> 430 431</div> 432 433<h3>Apply an Expression to Select Image Channels</h3> 434<div class="doc-section"> 435 436<p>Use the <a href="/www/command-line-options.html#channel">-channel</a> 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 <kbd>alpha.png</kbd> with the average of the green channels from the images <kbd>alpha.png</kbd> and <kbd>beta.png</kbd>, use:</p> 437 438<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert alpha.png beta.png -channel red -fx "(u.g+v.g)/2" gamma.png</span></p> 439</div> 440 441<h3>Results</h3> 442<div class="doc-section"> 443 444<p>The <a href="/www/command-line-options.html#fx">-fx</a> operator evaluates the given expression for each channel (set by <a href="/www/command-line-options.html#channel">-channel</a>) of each pixel in the first image (<kbd>u</kbd>) 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 <kbd>alpha.png</kbd> replaces both of the original images, <kbd>alpha.png</kbd> and <kbd>beta.png</kbd>, before being saved as <kbd>gamma.png</kbd>.</p> 445 446<p>The current image <kbd>s</kbd> is set to the first image in the sequence (<kbd>u</kbd>), and <kbd>t</kbd> to its index, 0. The symbols <kbd>i</kbd> and <kbd>j</kbd> reference the current pixel being processed.</p> 447 448 449<p>For use with <a href="/www/command-line-options.html#format_identify_">-format</a>, the value-escape <kbd>%[fx: ]</kbd> is evaluated just once for each image in the current image sequence. As each image in the sequence is being evaluated, <kbd>s</kbd> and <kbd>t</kbd> successively refer to the current image and its index, while <kbd>i</kbd> and <kbd>j</kbd> are set to zero, and the current channel set to red (<a href="/www/command-line-options.html#channel">-channel</a> is ignored). An example:</p> 450 451<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert xc:'rgb(25%,50%,75%)' rose: -colorspace rgb \ <br/> 452 -format 'Red channel of NW corner of image # %[fx:t] is %[fx: s]' info:</span><span class='crtout'>Red channel of NW corner of image # 0 is 0.250004 <br/> 453 Red channel of NW corner of image # 1 is 0.188235</span></p> 454<p>The color-escape <kbd>%[pixel: ]</kbd> is evaluated once per image and per color channel in that image (<a href="/www/command-line-options.html#channel">-channel</a> is ignored), The values generated are then converted into a color string (a named color or hex color value). The symbols <kbd>i</kbd> and <kbd>j</kbd> are set to zero, and <kbd>s</kbd> and <kbd>t</kbd> refer to each successively current image and index.</p> 455 456</div> 457</div> 458 459</div> 460 461<div id="linkbar"> 462 <!-- <span id="linkbar-west"> </span> --> 463 <span id="linkbar-center"> 464 <a href="http://www.imagemagick.org/discourse-server/">Discourse Server</a> • 465 <a href="/www/mailing-list.html">Mailing Lists</a> • 466 <a href="http://www.imagemagick.org/MagickStudio/scripts/MagickStudio.cgi">Studio</a> 467 </span> 468 <span id="linkbar-east"> </span> 469 </div> 470 <div class="footer"> 471 <span id="footer-west">© 1999-2009 ImageMagick Studio LLC</span> 472 <span id="footer-east"> <a href="http://www.imagemagick.org/script/contact.php">Contact the Wizards</a></span> 473 </div> 474 <div style="clear: both; margin: 0; width: 100%; "></div> 475</body> 476</html> 477
