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Use Fx to:</p> 165 166<ul> 167 <li>create canvases, gradients, mathematical colormaps</li> 168 <li>move color values between images and channels</li> 169 <li>translate, flip, mirror, rotate, scale, shear and generally distort images</li> 170 <li>merge or composite multiple images together</li> 171 <li>convolve or merge neighboring pixels together</li> 172 <li>generate image metrics or 'fingerprints'</li> 173</ul> 174 175<p>The expression can be simple:</p> 176 177<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> 178<p>Here, we convert a black to a navy blue image:</p> 179 180<p class="image"> 181 <a href="/images/black.png"><img src="/images/black.png" width="64" height="64" alt="black" /></a> 182 <img style="margin-top:22px; margin-bottom:22px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 183 <a href="/images/navy.png"><img src="/images/navy.png" width="64" height="64" alt="navy" /></a> 184</p> 185 186<p>Or the expression can be complex:</p> 187 188<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert rose.jpg \ <br/> 189 -fx "(1.0/(1.0+exp(10.0*(0.5-u)))-0.006693)*1.0092503" \ <br/> 190 rose-sigmoidal.png</span></p> 191<p>This expression results in a high contrast version of the image:</p> 192 193<p class="image"> 194 <a href="/images/rose.jpg"><img src="/images/rose.jpg" width="70" height="46" alt="rose" /></a> 195 <img style="margin-top:13px; margin-bottom:13px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 196 <a href="/images/rose-sigmoidal.png"><img src="/images/rose-sigmoidal.png" width="70" height="46" alt="rose-sigmoidal" /></a> 197</p> 198 199<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> 200 201<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert -size 70x70 xc: \ <br/> 202 -fx "Xi=i-w/2; Yj=j-h/2; 1.2*(0.5-hypot(Xi,Yj)/70.0)+0.5" \ <br/> 203 radial-gradient.png</span></p> 204<p>The command above returns this image:</p> 205 206<p class="image"> 207 <a href="/images/radial-gradient.png"><img src="/images/radial-gradient.png" width="70" height="70" alt="radial-gradient" /></a> 208</p> 209<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> 210 211<p>The next section discusses the Fx expression language.</p> 212 213</div> 214 215<h2><a name="anatomy"></a>The Anatomy of an Fx Expression</h2> 216<div class="doc-section"> 217 218<h3>The Fx Expression Language</h3> 219<div class="doc-section"> 220 221<p>The formal Fx expression language is defined here:</p> 222 223<dl class="doc"> 224 <dt class="doc"> numbers:</dt> 225 <dd> integer, floating point, or scientfic notation (+/- required, e.g. 3.81469e-06)</dd> 226 <dt class="doc"> constants: </dt> 227 <dd> e, Epsilon, QuantumRange, QuantumScale, Opaque, Pi, Transparent</dd> 228 <dt class="doc"> Fx operators (in order of precedence): </dt> 229 <dd> ^ (power), *, /, % (modulo), +, -, 230 <<, >>, <, <=, >, >=, ==, !=, 231 & (bitwise AND), | (bitwise OR), 232 && (logical AND), || (logical OR), 233 ~ (logical NOT), ?: (ternary conditional)</dd> 234 <dt class="doc"> math functions: </dt> 235 <dd> abs(), acos(), alt(), asin(), atan(), atan2(), ceil(), cos(), cosh(), debug(), exp(), floor(), 236 hypot(), int(), ln(), log(), logtwo(), max(), min(), mod(), pow(), rand(), round(), 237 sign(), sin(), sinh(), sqrt(), tan(), tanh()</dd> 238 <dt class="doc"> channel functions: </dt> 239 <dd> channel(r,g,b,a), channel(c,m,y,k,a)</dd> 240 <dt class="doc"> color names:</dt> 241 <dd> red, cyan, black, etc.</dd> 242 <dt class="doc"> color functions:</dt> 243 <dd> rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</dd> 244 <dt class="doc"> color hex values:</dt> 245 <dd> #ccc, #cbfed0, #b9e1cc00</dd> 246 <dt class="doc"> symbols:</dt> 247 <dd style="white-space:pre"> 248 s = current image in sequence 249 t = scene number of current image in sequence 250 u = first image in sequence 251 v = second image in sequence 252 n = number of images in sequence 253 254 i = column offset 255 j = row offset 256 p = pixel to use (absolute or relative to current pixel) 257 258 w = width of this image 259 h = height of this image 260 z = channel depth 261 262 r = red value (from RGBA), of a specific or current pixel 263 g = green '' 264 b = blue '' 265 a = alpha '' 266 o = opacity '' 267 268 c = cyan value of CMYK color of pixel 269 y = yellow '' 270 m = magenta '' 271 k = black '' 272 273 intensity = pixel intensity 274 275 hue = pixel hue 276 saturation = pixel saturation 277 lightness = pixel lightness 278 luminance = pixel luminance 279 280 page.width = page width 281 page.height = page height 282 page.x = page x offset 283 page.y = page y offset 284 285 resolution.x = x resolution 286 resolution.y = y resolution 287 288 depth = image depth 289 minima = image minima 290 maxima = image maxima 291 mean = image mean 292 standard_deviation = image standard deviation 293 kurtosis = image kurtosis 294 skewness = image skewness 295 (add a channel specifier to compute a statistic for that channel, e.g. depth.r) 296 </dd> 297</dl> 298 299</div> 300 301<h3>The Fx Expression</h3> 302<div class="doc-section"> 303 304<p>An Fx expression may include any combination of the following:</p> 305<ul> 306<li> <em>x</em> <kbd>^</kbd> <em>y</em>: exponentiation (<em>x<sup>y</sup></em>)</li> 307<li> <kbd>(</kbd> ... <kbd>)</kbd>: grouping</li> 308<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> 309<li> <em>x</em> <kbd>/</kbd> <em>y</em>: division</li> 310<li> <em>x</em> <kbd>%</kbd> <em>y</em>: modulo</li> 311<li> <em>x</em> <kbd>+</kbd> <em>y</em>: addition</li> 312<li> <em>x</em> <kbd>-</kbd> <em>y</em>: subtraction</li> 313<li> <em>x</em> <kbd><<</kbd> <em>y</em>: left shift</li> 314<li> <em>x</em> <kbd>>></kbd> <em>y</em>: right shift</li> 315<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> 316<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> 317<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> 318<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> 319<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> 320<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> 321<li> <em>x</em> <kbd>&</kbd> <em>y</em>: binary AND</li> 322<li> <em>x</em> <kbd>|</kbd> <em>y</em>: binary OR</li> 323<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> 324<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> 325<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> 326<li> <kbd>+</kbd><em>x</em>: unary plus, return 1.0*value</li> 327<li> <kbd>-</kbd><em>x</em>: unary minus, return -1.0*value</li> 328<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> 329<li> <em>x</em> <kbd>=</kbd> <em>y</em>: assignment; assignment variables are restricted to letter combinations only (e.g. Xi not X1)</li> 330<li> <em>x</em> <kbd>;</kbd> <em>y</em>: statement separator </li> 331<li> <kbd>pi</kbd>: constant (3.141659...)</li> 332<li> <kbd>e</kbd>: constant (2.71828...)</li> 333<li> <kbd>QuantumRange</kbd>: constant maximum pixel value (255 for Q8, 65535 for Q16)</li> 334<li> <kbd>QuantumScale</kbd>: constant 1.0/<kbd>QuantumRange</kbd></li> 335<li> <kbd>intensity</kbd>: pixel intensity; equivalent to 0.299*red+0.587*green+0.114*blue</li> 336<li> <kbd>hue</kbd>: pixel hue</li> 337<li> <kbd>saturation</kbd>: pixel saturation</li> 338<li> <kbd>lightness</kbd>: pixel lightness; equivalent to 0.5*max(red,green,blue) + 0.5*min(red,green,blue)</li> 339<li> <kbd>luminance</kbd>: pixel luminance; equivalent to 0.2126*red + 0.7152*green + 0.0722*blue</li> 340<li> <kbd>red, green, blue</kbd>, etc.: color names</li> 341<li> <kbd>#ccc, #cbfed0, #b9e1cc00</kbd>, etc.: color hex values</li> 342<li> <kbd>rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</kbd>: color functions</li> 343<li> <kbd>s, t, u, v, n, i, j, w, h, z, r, g, b, a, o, c, y, m, k</kbd>: symbols</li> 344<li> <kbd>abs(</kbd><em>x</em><kbd>)</kbd>: absolute value function</li> 345<li> <kbd>acos(</kbd><em>x</em><kbd>)</kbd>: arc cosine function</li> 346<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> 347<li> <kbd>asin(</kbd><em>x</em><kbd>)</kbd>: arc sine function</li> 348<li> <kbd>atan(</kbd><em>x</em><kbd>)</kbd>: arc tangent function</li> 349<li> <kbd>atan2(</kbd><em>y</em>,<em>x</em><kbd>)</kbd>: arc tangent function of two variables</li> 350<li> <kbd>ceil(</kbd><em>x</em><kbd>)</kbd>: smallest integral value not less than argument</li> 351<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> 352<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> 353<li> <kbd>cos(</kbd><em>x</em><kbd>)</kbd>: cosine function</li> 354<li> <kbd>cosh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic cosine function</li> 355<li> <kbd>debug(</kbd><em>x</em><kbd>)</kbd>: print <em>x</em> (useful for debugging your expression)</li> 356<li> <kbd>exp(</kbd><em>x</em><kbd>)</kbd>: natural exponential function (<em>e<sup>x</sup></em>)</li> 357<li> <kbd>floor(</kbd><em>x</em><kbd>)</kbd>: largest integral value not greater than argument</li> 358<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> 359<li> <kbd>int(</kbd><em>x</em><kbd>)</kbd>: greatest integer function (return greatest integer less than or equal to <em>x</em>)</li> 360<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>: natural logarithm function</li> 361<li> <kbd>log(</kbd><em>x</em><kbd>)</kbd>: logarithm base 10</li> 362<li> <kbd>logtwo(</kbd><em>x</em><kbd>)</kbd>: logarithm base 2</li> 363<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>: natural logarithm</li> 364<li> <kbd>max(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: maximum of <em>x</em> and <em>y</em></li> 365<li> <kbd>min(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: minimum of <em>x</em> and <em>y</em></li> 366<li> <kbd>mod(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: floating-point remainder function</li> 367<li> <kbd>pow(</kbd><em>x</em>,<em>y</em><kbd>)</kbd>: power function (<em>x<sup>y</sup></em>)</li> 368<li> <kbd>rand()</kbd>: value uniformly distributed over the interval [0.0, 1.0) with a 2 to the 128th-1 period</li> 369<li> <kbd>round()</kbd>: round to integral value, regardless of rounding direction</li> 370<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> 371<li> <kbd>sin(</kbd><em>x</em><kbd>)</kbd>: sine function</li> 372<li> <kbd>sinh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic sine function</li> 373<li> <kbd>sqrt(</kbd><em>x</em><kbd>)</kbd>: square root function</li> 374<li> <kbd>tan(</kbd><em>x</em><kbd>)</kbd>: tangent function</li> 375<li> <kbd>tanh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic tangent function</li> 376</ul> 377 378<p>The expression semantics include these rules:</p> 379 380<ul> 381<li>symbols are case insensitive</li> 382<li>only one ternary conditional (e.g. x ? y : z) per statement</li> 383<li>statements are assignments or the final expression to return</li> 384<li>an assignment starts a statement, it is not an operator</li> 385<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> 386</ul> 387 388</div> 389 390<h3>Source Images</h3> 391<div class="doc-section"> 392 393<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> 394 395<p>As an example, we form an image by averaging the first image and third images:</p> 396 397<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> 398<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> 399 400<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> 401 402<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> 403<div class="image"> 404<p> 405 <a href="/images/logo-sm-flop.png"><img src="/images/logo-sm-flop.png" width="128" height="96" alt="logo-sm-flop.png" /></a> 406 <a href="/images/logo-sm.png"><img src="/images/logo-sm.png" width="128" height="96" alt="logo-sm.png" /></a> 407<img style="margin-top:38px; margin-bottom:38px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 408 <a href="/images/logo-sm-fx.png"><img src="/images/logo-sm-fx.png" width="128" height="96" alt="logo-sm-fx.png" /></a> 409</p> 410</div> 411 412 413</div> 414 415<h3>Accessing Pixels</h3> 416<div class="doc-section"> 417 418<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> 419 420<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> 421 422<pre class="text"> 423 p[-1].g green value of pixel to the immediate left of the current pixel 424 p[-1,-1].r red value of the pixel diagonally left and up from current pixel 425</pre> 426 427<p>To specify an absolute position, use braces, rather than brackets.</p> 428 429<pre class="text"> 430 p{0,0}.r red value of the pixel in the upper left corner of the image 431 p{12,34}.b blue pixel value at column number 12, row 34 of the image 432</pre> 433 434<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> 435 436<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> 437 438</div> 439 440<h3>Apply an Expression to Select Image Channels</h3> 441<div class="doc-section"> 442 443<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> 444 445<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> 446</div> 447 448<h3>Results</h3> 449<div class="doc-section"> 450 451<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> 452 453<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> 454 455 456<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> 457 458<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert xc:'rgb(25%,50%,75%)' rose: -colorspace rgb \ <br/> 459 -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/> 460 Red channel of NW corner of image # 1 is 0.188235</span></p> 461<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> 462 463</div> 464</div> 465 466</div> 467 468<div id="linkbar"> 469 <!-- <span id="linkbar-west"> </span> --> 470 <span id="linkbar-center"> 471 <a href="http://www.imagemagick.org/discourse-server/">Discourse Server</a> • 472 <a href="/www/mailing-list.html">Mailing Lists</a> • 473 <a href="http://studio.webbyland.com/ImageMagick/MagickStudio/scripts/MagickStudio.cgi">Studio</a> 474 </span> 475 <span id="linkbar-east"> </span> 476 </div> 477 <div class="footer"> 478 <span id="footer-west">© 1999-2009 ImageMagick Studio LLC</span> 479 <span id="footer-east"> <a href="http://www.imagemagick.org/script/contact.php">Contact the Wizards</a></span> 480 </div> 481 <div style="clear: both; margin: 0; width: 100%; "></div> 482</body> 483</html> 484
