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Use Fx to:</p> 161 162<ul> 163 <li>create canvases, gradients, mathematical colormaps</li> 164 <li>move color values between images and channels</li> 165 <li>translate, flip, mirror, rotate, scale, shear and generally distort images</li> 166 <li>merge or composite multiple images together</li> 167 <li>convolve or merge neighboring pixels together</li> 168 <li>generate image metrics or 'fingerprints'</li> 169</ul> 170 171<p>The expression can be simple:</p> 172 173<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> 174<p>Here, we convert a black to a navy blue image:</p> 175 176<p class="image"> 177 <a href="/images/black.png"><img src="/images/black.png" width="64" height="64" alt="black" /></a> 178 <img style="margin-top:22px; margin-bottom:22px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 179 <a href="/images/navy.png"><img src="/images/navy.png" width="64" height="64" alt="navy" /></a> 180</p> 181 182<p>Or the expression can be complex:</p> 183 184<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert rose.jpg \ <br/> 185 -fx "(1.0/(1.0+exp(10.0*(0.5-u)))-0.006693)*1.0092503" \ <br/> 186 rose-sigmoidal.png</span></p> 187<p>This expression results in a high contrast version of the image:</p> 188 189<p class="image"> 190 <a href="/images/rose.jpg"><img src="/images/rose.jpg" width="70" height="46" alt="rose" /></a> 191 <img style="margin-top:13px; margin-bottom:13px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 192 <a href="/images/rose-sigmoidal.png"><img src="/images/rose-sigmoidal.png" width="70" height="46" alt="rose-sigmoidal" /></a> 193</p> 194 195<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> 196 197<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert -size 70x70 xc: \ <br/> 198 -fx "Xi=i-w/2; Yj=j-h/2; 1.2*(0.5-hypot(Xi,Yj)/70.0)+0.5" \ <br/> 199 radial-gradient.png</span></p> 200<p>The command above returns this image:</p> 201 202<p class="image"> 203 <a href="/images/radial-gradient.png"><img src="/images/radial-gradient.png" width="70" height="70" alt="radial-gradient" /></a> 204</p> 205<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> 206 207<p>The next section discusses the Fx expression language.</p> 208 209</div> 210 211<h2><a name="anatomy"></a>The Anatomy of an Fx Expression</h2> 212<div class="doc-section"> 213 214<h3>The Fx Expression Language</h3> 215<div class="doc-section"> 216 217<p>The formal Fx expression language is defined here:</p> 218 219<dl class="doc"> 220 <dt class="doc"> numbers:</dt> 221 <dd> integer, floating point, or scientfic notation (+/- required, e.g. 3.81469e-06)</dd> 222 <dt class="doc"> constants: </dt> 223 <dd> e, Epsilon, QuantumRange, QuantumScale, Opaque, Pi, Transparent</dd> 224 <dt class="doc"> Fx operators (in order of precedence): </dt> 225 <dd> ^ (power), *, /, % (modulo), +, -, 226 <<, >>, <, <=, >, >=, ==, !=, 227 & (bitwise AND), | (bitwise OR), 228 && (logical AND), || (logical OR), 229 ~ (logical NOT), ?: (ternary conditional)</dd> 230 <dt class="doc"> math functions: </dt> 231 <dd> abs(), acos(), alt(), asin(), atan(), atan2(), ceil(), cos(), cosh(), debug(), exp(), floor(), 232 hypot(), int(), ln(), log(), logtwo(), max(), min(), mod(), pow(), rand(), round(), 233 sign(), sin(), sinh(), sqrt(), tan(), tanh()</dd> 234 <dt class="doc"> channel functions: </dt> 235 <dd> channel(r,g,b,a), channel(c,m,y,k,a)</dd> 236 <dt class="doc"> color names:</dt> 237 <dd> red, cyan, black, etc.</dd> 238 <dt class="doc"> color functions:</dt> 239 <dd> rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</dd> 240 <dt class="doc"> color hex values:</dt> 241 <dd> #ccc, #cbfed0, #b9e1cc00</dd> 242 <dt class="doc"> symbols:</dt> 243 <dd style="white-space:pre"> 244 s = current image in sequence 245 t = scene number of current image in sequence 246 u = first image in sequence 247 v = second image in sequence 248 n = number of images in sequence 249 250 i = column offset 251 j = row offset 252 p = pixel to use (absolute or relative to current pixel) 253 254 w = width of this image 255 h = height of this image 256 z = channel depth 257 258 r = red value (from RGBA), of a specific or current pixel 259 g = green '' 260 b = blue '' 261 a = alpha '' 262 o = opacity '' 263 264 c = cyan value of CMYK color of pixel 265 y = yellow '' 266 m = magenta '' 267 k = black '' 268 269 intensity = pixel intensity 270 271 hue = pixel hue 272 saturation = pixel saturation 273 lightness = pixel lightness 274 luminance = pixel luminance 275 276 page.width = page width 277 page.height = page height 278 page.x = page x offset 279 page.y = page y offset 280 281 resolution.x = x resolution 282 resolution.y = y resolution 283 284 depth = image depth 285 minima = image minima 286 maxima = image maxima 287 mean = image mean 288 standard_deviation = image standard deviation 289 kurtosis = image kurtosis 290 skewness = image skewness 291 (add a channel specifier to compute a statistic for that channel, e.g. depth.r) 292 </dd> 293</dl> 294 295</div> 296 297<h3>The Fx Expression</h3> 298<div class="doc-section"> 299 300<p>An Fx expression may include any combination of the following:</p> 301<ul> 302<li> <em>x</em> <kbd>^</kbd> <em>y</em>: exponentiation (<em>x<sup>y</sup></em>)</li> 303<li> <kbd>(</kbd> ... <kbd>)</kbd>: grouping</li> 304<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> 305<li> <em>x</em> <kbd>/</kbd> <em>y</em>: division</li> 306<li> <em>x</em> <kbd>%</kbd> <em>y</em>: modulo</li> 307<li> <em>x</em> <kbd>+</kbd> <em>y</em>: addition</li> 308<li> <em>x</em> <kbd>-</kbd> <em>y</em>: subtraction</li> 309<li> <em>x</em> <kbd><<</kbd> <em>y</em>: left shift</li> 310<li> <em>x</em> <kbd>>></kbd> <em>y</em>: right shift</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>: boolean relation, return value 1.0 if <em>x</em> >= <em>y</em>, otherwise 0.0</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>: binary AND</li> 318<li> <em>x</em> <kbd>|</kbd> <em>y</em>: binary OR</li> 319<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> 320<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> 321<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> 322<li> <kbd>+</kbd><em>x</em>: unary plus, return 1.0*value</li> 323<li> <kbd>-</kbd><em>x</em>: unary minus, return -1.0*value</li> 324<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> 325<li> <em>x</em> <kbd>=</kbd> <em>y</em>: assignment; assignment variables are restricted to letter combinations only (e.g. Xi not X1)</li> 326<li> <em>x</em> <kbd>;</kbd> <em>y</em>: statement separator </li> 327<li> <kbd>pi</kbd>: constant (3.141659...)</li> 328<li> <kbd>e</kbd>: constant (2.71828...)</li> 329<li> <kbd>QuantumRange</kbd>: constant maximum pixel value (255 for Q8, 65535 for Q16)</li> 330<li> <kbd>QuantumScale</kbd>: constant 1.0/<kbd>QuantumRange</kbd></li> 331<li> <kbd>intensity</kbd>: pixel intensity; equivalent to 0.299*red+0.587*green+0.114*blue</li> 332<li> <kbd>hue</kbd>: pixel hue</li> 333<li> <kbd>saturation</kbd>: pixel saturation</li> 334<li> <kbd>lightness</kbd>: pixel lightness; equivalent to 0.5*max(red,green,blue) + 0.5*min(red,green,blue)</li> 335<li> <kbd>luminance</kbd>: pixel luminance; equivalent to 0.2126*red + 0.7152*green + 0.0722*blue</li> 336<li> <kbd>red, green, blue</kbd>, etc.: color names</li> 337<li> <kbd>#ccc, #cbfed0, #b9e1cc00</kbd>, etc.: color hex values</li> 338<li> <kbd>rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</kbd>: color functions</li> 339<li> <kbd>s, t, u, v, n, i, j, w, h, z, r, g, b, a, o, c, y, m, k</kbd>: symbols</li> 340<li> <kbd>abs(</kbd><em>x</em><kbd>)</kbd>: absolute value function</li> 341<li> <kbd>acos(</kbd><em>x</em><kbd>)</kbd>: arc cosine function</li> 342<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> 343<li> <kbd>asin(</kbd><em>x</em><kbd>)</kbd>: arc sine function</li> 344<li> <kbd>atan(</kbd><em>x</em><kbd>)</kbd>: arc tangent function</li> 345<li> <kbd>atan2(</kbd><em>y</em>,<em>x</em><kbd>)</kbd>: arc tangent function of two variables</li> 346<li> <kbd>ceil(</kbd><em>x</em><kbd>)</kbd>: smallest integral value not less than argument</li> 347<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> 348<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> 349<li> <kbd>cos(</kbd><em>x</em><kbd>)</kbd>: cosine function</li> 350<li> <kbd>cosh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic cosine function</li> 351<li> <kbd>debug(</kbd><em>x</em><kbd>)</kbd>: print <em>x</em> (useful for debugging your expression)</li> 352<li> <kbd>exp(</kbd><em>x</em><kbd>)</kbd>: natural exponential function (<em>e<sup>x</sup></em>)</li> 353<li> <kbd>floor(</kbd><em>x</em><kbd>)</kbd>: largest integral value not greater than argument</li> 354<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> 355<li> <kbd>int(</kbd><em>x</em><kbd>)</kbd>: greatest integer function (return greatest integer less than or equal to <em>x</em>)</li> 356<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>: natural logarithm function</li> 357<li> <kbd>log(</kbd><em>x</em><kbd>)</kbd>: logarithm base 10</li> 358<li> <kbd>logtwo(</kbd><em>x</em><kbd>)</kbd>: logarithm base 2</li> 359<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>: natural logarithm</li> 360<li> <kbd>max(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: maximum of <em>x</em> and <em>y</em></li> 361<li> <kbd>min(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: minimum of <em>x</em> and <em>y</em></li> 362<li> <kbd>mod(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: floating-point remainder function</li> 363<li> <kbd>pow(</kbd><em>x</em>,<em>y</em><kbd>)</kbd>: power function (<em>x<sup>y</sup></em>)</li> 364<li> <kbd>rand()</kbd>: value uniformly distributed over the interval [0.0, 1.0) with a 2 to the 128th-1 period</li> 365<li> <kbd>round()</kbd>: round to integral value, regardless of rounding direction</li> 366<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> 367<li> <kbd>sin(</kbd><em>x</em><kbd>)</kbd>: sine function</li> 368<li> <kbd>sinh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic sine function</li> 369<li> <kbd>sqrt(</kbd><em>x</em><kbd>)</kbd>: square root function</li> 370<li> <kbd>tan(</kbd><em>x</em><kbd>)</kbd>: tangent function</li> 371<li> <kbd>tanh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic tangent function</li> 372</ul> 373 374<p>The expression semantics include these rules:</p> 375 376<ul> 377<li>symbols are case insensitive</li> 378<li>only one ternary conditional (e.g. x ? y : z) per statement</li> 379<li>statements are assignments or the final expression to return</li> 380<li>an assignment starts a statement, it is not an operator</li> 381<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> 382</ul> 383 384</div> 385 386<h3>Source Images</h3> 387<div class="doc-section"> 388 389<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> 390 391<p>As an example, we form an image by averaging the first image and third images:</p> 392 393<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> 394<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> 395 396<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> 397 398<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> 399<div class="image"> 400<p> 401 <a href="/images/logo-sm-flop.png"><img src="/images/logo-sm-flop.png" width="128" height="96" alt="logo-sm-flop.png" /></a> 402 <a href="/images/logo-sm.png"><img src="/images/logo-sm.png" width="128" height="96" alt="logo-sm.png" /></a> 403<img style="margin-top:38px; margin-bottom:38px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 404 <a href="/images/logo-sm-fx.png"><img src="/images/logo-sm-fx.png" width="128" height="96" alt="logo-sm-fx.png" /></a> 405</p> 406</div> 407 408 409</div> 410 411<h3>Accessing Pixels</h3> 412<div class="doc-section"> 413 414<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> 415 416<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> 417 418<pre class="text"> 419 p[-1].g green value of pixel to the immediate left of the current pixel 420 p[-1,-1].r red value of the pixel diagonally left and up from current pixel 421</pre> 422 423<p>To specify an absolute position, use braces, rather than brackets.</p> 424 425<pre class="text"> 426 p{0,0}.r red value of the pixel in the upper left corner of the image 427 p{12,34}.b blue pixel value at column number 12, row 34 of the image 428</pre> 429 430<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> 431 432<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> 433 434</div> 435 436<h3>Apply an Expression to Select Image Channels</h3> 437<div class="doc-section"> 438 439<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> 440 441<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> 442</div> 443 444<h3>Results</h3> 445<div class="doc-section"> 446 447<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> 448 449<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> 450 451 452<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> 453 454<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert xc:'rgb(25%,50%,75%)' rose: -colorspace rgb \ <br/> 455 -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/> 456 Red channel of NW corner of image # 1 is 0.188235</span></p> 457<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> 458 459</div> 460</div> 461 462</div> 463 464<div id="linkbar"> 465 <!-- <span id="linkbar-west"> </span> --> 466 <span id="linkbar-center"> 467 <a href="http://www.imagemagick.org/discourse-server/">Discourse Server</a> • 468 <a href="/www/mailing-list.html">Mailing Lists</a> • 469 <a href="http://www.imagemagick.org/MagickStudio/scripts/MagickStudio.cgi">Studio</a> 470 </span> 471 <span id="linkbar-east"> </span> 472 </div> 473 <div class="footer"> 474 <span id="footer-west">© 1999-2009 ImageMagick Studio LLC</span> 475 <span id="footer-east"> <a href="http://www.imagemagick.org/script/contact.php">Contact the Wizards</a></span> 476 </div> 477 <div style="clear: both; margin: 0; width: 100%; "></div> 478</body> 479</html> 480
