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Use Fx to:</p> 162 163<ul> 164 <li>create canvases, gradients, mathematical colormaps</li> 165 <li>move color values between images and channels</li> 166 <li>translate, flip, mirror, rotate, scale, shear and generally distort images</li> 167 <li>merge or composite multiple images together</li> 168 <li>convolve or merge neighboring pixels together</li> 169 <li>generate image metrics or 'fingerprints'</li> 170</ul> 171 172<p>The expression can be simple:</p> 173 174<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> 175<p>Here, we convert a black to a navy blue image:</p> 176 177<p class="image"> 178 <a href="/images/black.png"><img src="/images/black.png" width="64" height="64" alt="black" /></a> 179 <img style="margin-top:22px; margin-bottom:22px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 180 <a href="/images/navy.png"><img src="/images/navy.png" width="64" height="64" alt="navy" /></a> 181</p> 182 183<p>Or the expression can be complex:</p> 184 185<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert rose.jpg \ <br/> 186 -fx "(1.0/(1.0+exp(10.0*(0.5-u)))-0.006693)*1.0092503" \ <br/> 187 rose-sigmoidal.png</span></p> 188<p>This expression results in a high contrast version of the image:</p> 189 190<p class="image"> 191 <a href="/images/rose.jpg"><img src="/images/rose.jpg" width="70" height="46" alt="rose" /></a> 192 <img style="margin-top:13px; margin-bottom:13px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 193 <a href="/images/rose-sigmoidal.png"><img src="/images/rose-sigmoidal.png" width="70" height="46" alt="rose-sigmoidal" /></a> 194</p> 195 196<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> 197 198<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert -size 70x70 xc: \ <br/> 199 -fx "Xi=i-w/2; Yj=j-h/2; 1.2*(0.5-hypot(Xi,Yj)/70.0)+0.5" \ <br/> 200 radial-gradient.png</span></p> 201<p>The command above returns this image:</p> 202 203<p class="image"> 204 <a href="/images/radial-gradient.png"><img src="/images/radial-gradient.png" width="70" height="70" alt="radial-gradient" /></a> 205</p> 206<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> 207 208<p>The next section discusses the Fx expression language.</p> 209 210</div> 211 212<h2><a name="anatomy"></a>The Anatomy of an Fx Expression</h2> 213<div class="doc-section"> 214 215<h3>The Fx Expression Language</h3> 216<div class="doc-section"> 217 218<p>The formal Fx expression language is defined here:</p> 219 220<dl class="doc"> 221 <dt class="doc"> numbers:</dt> 222 <dd> integer, floating point, or scientfic notation (+/- required, e.g. 3.81469e-06)</dd> 223 <dt class="doc"> constants: </dt> 224 <dd> e, Epsilon, QuantumRange, QuantumScale, Opaque, Pi, Transparent</dd> 225 <dt class="doc"> Fx operators (in order of precedence): </dt> 226 <dd> ^ (power), *, /, % (modulo), +, -, 227 <<, >>, <, <=, >, >=, ==, !=, 228 & (bitwise AND), | (bitwise OR), 229 && (logical AND), || (logical OR), 230 ~ (logical NOT), ?: (ternary conditional)</dd> 231 <dt class="doc"> math functions: </dt> 232 <dd> abs(), acos(), airy(), alt(), asin(), atan(), atan2(), ceil(), cos(), cosh(), debug(), exp(), floor(), 233 hypot(), int(), j0(), j1(), jinc(), ln(), log(), logtwo(), max(), min(), mod(), pow(), rand(), round(), 234 sign(), sin(), sinc(), sinh(), sqrt(), tan(), tanh()</dd> 235 <dt class="doc"> channel functions: </dt> 236 <dd> channel(r,g,b,a), channel(c,m,y,k,a)</dd> 237 <dt class="doc"> color names:</dt> 238 <dd> red, cyan, black, etc.</dd> 239 <dt class="doc"> color functions:</dt> 240 <dd> rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</dd> 241 <dt class="doc"> color hex values:</dt> 242 <dd> #ccc, #cbfed0, #b9e1cc00</dd> 243 <dt class="doc"> symbols:</dt> 244 <dd style="white-space:pre"> 245 s = current image in sequence 246 t = scene number of current image in sequence 247 u = first image in sequence 248 v = second image in sequence 249 n = number of images in sequence 250 251 i = column offset 252 j = row offset 253 p = pixel to use (absolute or relative to current pixel) 254 255 w = width of this image 256 h = height of this image 257 z = channel depth 258 259 r = red value (from RGBA), of a specific or current pixel 260 g = green '' 261 b = blue '' 262 a = alpha '' 263 o = opacity '' 264 265 c = cyan value of CMYK color of pixel 266 y = yellow '' 267 m = magenta '' 268 k = black '' 269 270 intensity = pixel intensity 271 272 hue = pixel hue 273 saturation = pixel saturation 274 lightness = pixel lightness 275 luminance = pixel luminance 276 277 page.width = page width 278 page.height = page height 279 page.x = page x offset 280 page.y = page y offset 281 282 resolution.x = x resolution 283 resolution.y = y resolution 284 285 depth = image depth 286 minima = image minima 287 maxima = image maxima 288 mean = image mean 289 standard_deviation = image standard deviation 290 kurtosis = image kurtosis 291 skewness = image skewness 292 (add a channel specifier to compute a statistic for that channel, e.g. depth.r) 293 </dd> 294</dl> 295 296</div> 297 298<h3>The Fx Expression</h3> 299<div class="doc-section"> 300 301<p>An Fx expression may include any combination of the following:</p> 302<ul> 303<li> <em>x</em> <kbd>^</kbd> <em>y</em>: exponentiation (<em>x<sup>y</sup></em>)</li> 304<li> <kbd>(</kbd> ... <kbd>)</kbd>: grouping</li> 305<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> 306<li> <em>x</em> <kbd>/</kbd> <em>y</em>: division</li> 307<li> <em>x</em> <kbd>%</kbd> <em>y</em>: modulo</li> 308<li> <em>x</em> <kbd>+</kbd> <em>y</em>: addition</li> 309<li> <em>x</em> <kbd>-</kbd> <em>y</em>: subtraction</li> 310<li> <em>x</em> <kbd><<</kbd> <em>y</em>: left shift</li> 311<li> <em>x</em> <kbd>>></kbd> <em>y</em>: right shift</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>: 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>: binary AND</li> 319<li> <em>x</em> <kbd>|</kbd> <em>y</em>: binary OR</li> 320<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> 321<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> 322<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> 323<li> <kbd>+</kbd><em>x</em>: unary plus, return 1.0*value</li> 324<li> <kbd>-</kbd><em>x</em>: unary minus, return -1.0*value</li> 325<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> 326<li> <em>x</em> <kbd>=</kbd> <em>y</em>: assignment; assignment variables are restricted to letter combinations only (e.g. Xi not X1)</li> 327<li> <em>x</em> <kbd>;</kbd> <em>y</em>: statement separator </li> 328<li> <kbd>pi</kbd>: constant (3.141659...)</li> 329<li> <kbd>e</kbd>: constant (2.71828...)</li> 330<li> <kbd>QuantumRange</kbd>: constant maximum pixel value (255 for Q8, 65535 for Q16)</li> 331<li> <kbd>QuantumScale</kbd>: constant 1.0/<kbd>QuantumRange</kbd></li> 332<li> <kbd>intensity</kbd>: pixel intensity; equivalent to 0.299*red+0.587*green+0.114*blue</li> 333<li> <kbd>hue</kbd>: pixel hue</li> 334<li> <kbd>saturation</kbd>: pixel saturation</li> 335<li> <kbd>lightness</kbd>: pixel lightness; equivalent to 0.5*max(red,green,blue) + 0.5*min(red,green,blue)</li> 336<li> <kbd>luminance</kbd>: pixel luminance; equivalent to 0.2126*red + 0.7152*green + 0.0722*blue</li> 337<li> <kbd>red, green, blue</kbd>, etc.: color names</li> 338<li> <kbd>#ccc, #cbfed0, #b9e1cc00</kbd>, etc.: color hex values</li> 339<li> <kbd>rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</kbd>: color functions</li> 340<li> <kbd>s, t, u, v, n, i, j, w, h, z, r, g, b, a, o, c, y, m, k</kbd>: symbols</li> 341<li> <kbd>abs(</kbd><em>x</em><kbd>)</kbd>: absolute value function</li> 342<li> <kbd>acos(</kbd><em>x</em><kbd>)</kbd>: arc cosine function</li> 343<li> <kbd>airy(</kbd><em>x</em><kbd>)</kbd>: return the Airy function Ai(<em>x</em>)</li> 344<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> 345<li> <kbd>asin(</kbd><em>x</em><kbd>)</kbd>: arc sine function</li> 346<li> <kbd>atan(</kbd><em>x</em><kbd>)</kbd>: arc tangent function</li> 347<li> <kbd>atan2(</kbd><em>y</em>,<em>x</em><kbd>)</kbd>: arc tangent function of two variables</li> 348<li> <kbd>ceil(</kbd><em>x</em><kbd>)</kbd>: smallest integral value not less than argument</li> 349<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> 350<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> 351<li> <kbd>cos(</kbd><em>x</em><kbd>)</kbd>: cosine function</li> 352<li> <kbd>cosh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic cosine function</li> 353<li> <kbd>debug(</kbd><em>x</em><kbd>)</kbd>: print <em>x</em> (useful for debugging your expression)</li> 354<li> <kbd>exp(</kbd><em>x</em><kbd>)</kbd>: natural exponential function (<em>e<sup>x</sup></em>)</li> 355<li> <kbd>floor(</kbd><em>x</em><kbd>)</kbd>: largest integral value not greater than argument</li> 356<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> 357<li> <kbd>int(</kbd><em>x</em><kbd>)</kbd>: greatest integer function (return greatest integer less than or equal to <em>x</em>)</li> 358<li> <kbd>j0(</kbd><em>x</em><kbd>)</kbd>: Bessel functions of <em>x</em> of the first kind of orders 0</li> 359<li> <kbd>j1(</kbd><em>x</em><kbd>)</kbd>: Bessel functions of <em>x</em> of the first kind of orders 1</li> 360<li> <kbd>jinc(</kbd><em>x</em><kbd>)</kbd>: jinc function</li> 361<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>: natural logarithm function</li> 362<li> <kbd>log(</kbd><em>x</em><kbd>)</kbd>: logarithm base 10</li> 363<li> <kbd>logtwo(</kbd><em>x</em><kbd>)</kbd>: logarithm base 2</li> 364<li> <kbd>ln(</kbd><em>x</em><kbd>)</kbd>: natural logarithm</li> 365<li> <kbd>max(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: maximum of <em>x</em> and <em>y</em></li> 366<li> <kbd>min(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: minimum of <em>x</em> and <em>y</em></li> 367<li> <kbd>mod(</kbd><em>x</em>, <em>y</em><kbd>)</kbd>: floating-point remainder function</li> 368<li> <kbd>pow(</kbd><em>x</em>,<em>y</em><kbd>)</kbd>: power function (<em>x<sup>y</sup></em>)</li> 369<li> <kbd>rand()</kbd>: value uniformly distributed over the interval [0.0, 1.0) with a 2 to the 128th-1 period</li> 370<li> <kbd>round()</kbd>: round to integral value, regardless of rounding direction</li> 371<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> 372<li> <kbd>sin(</kbd><em>x</em><kbd>)</kbd>: sine function</li> 373<li> <kbd>sinc(</kbd><em>x</em><kbd>)</kbd>: sinc function</li> 374<li> <kbd>sinh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic sine function</li> 375<li> <kbd>sqrt(</kbd><em>x</em><kbd>)</kbd>: square root function</li> 376<li> <kbd>tan(</kbd><em>x</em><kbd>)</kbd>: tangent function</li> 377<li> <kbd>tanh(</kbd><em>x</em><kbd>)</kbd>: hyperbolic tangent function</li> 378</ul> 379 380<p>The expression semantics include these rules:</p> 381 382<ul> 383<li>symbols are case insensitive</li> 384<li>only one ternary conditional (e.g. x ? y : z) per statement</li> 385<li>statements are assignments or the final expression to return</li> 386<li>an assignment starts a statement, it is not an operator</li> 387<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> 388</ul> 389 390</div> 391 392<h3>Source Images</h3> 393<div class="doc-section"> 394 395<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> 396 397<p>As an example, we form an image by averaging the first image and third images:</p> 398 399<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> 400<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> 401 402<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, other images are used only for their data. As an illustrative example, consider 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> 403 404<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> 405<div class="image"> 406<p> 407 <a href="/images/logo-sm-flop.png"><img src="/images/logo-sm-flop.png" width="128" height="96" alt="logo-sm-flop.png" /></a> 408 <a href="/images/logo-sm.png"><img src="/images/logo-sm.png" width="128" height="96" alt="logo-sm.png" /></a> 409<img style="margin-top:38px; margin-bottom:38px;" src="/images/right.gif" width="20" height="20" alt="==>" /> 410 <a href="/images/logo-sm-fx.png"><img src="/images/logo-sm-fx.png" width="128" height="96" alt="logo-sm-fx.png" /></a> 411</p> 412</div> 413 414 415</div> 416 417<h3>Accessing Pixels</h3> 418<div class="doc-section"> 419 420<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> 421 422<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> 423 424<pre class="text"> 425 p[-1].g green value of pixel to the immediate left of the current pixel 426 p[-1,-1].r red value of the pixel diagonally left and up from current pixel 427</pre> 428 429<p>To specify an absolute position, use braces, rather than brackets.</p> 430 431<pre class="text"> 432 p{0,0}.r red value of the pixel in the upper left corner of the image 433 p{12,34}.b blue pixel value at column number 12, row 34 of the image 434</pre> 435 436<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> 437 438<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> 439 440</div> 441 442<h3>Apply an Expression to Select Image Channels</h3> 443<div class="doc-section"> 444 445<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> 446 447<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> 448</div> 449 450<h3>Results</h3> 451<div class="doc-section"> 452 453<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> 454 455<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> 456 457 458<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> 459 460<p class='crt'><span class="crtprompt"> $magick> </span><span class='crtin'>convert xc:'rgb(25%,50%,75%)' rose: -colorspace rgb \ <br/> 461 -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/> 462 Red channel of NW corner of image # 1 is 0.188235</span></p> 463<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> 464 465</div> 466</div> 467 468</div> 469 470<div id="linkbar"> 471 <!-- <span id="linkbar-west"> </span> --> 472 <span id="linkbar-center"> 473 <a href="http://www.imagemagick.org/discourse-server/">Discourse Server</a> • 474 <a href="http://studio.webbyland.com/ImageMagick/MagickStudio/scripts/MagickStudio.cgi">Studio</a> 475 </span> 476 <span id="linkbar-east"> </span> 477 </div> 478 <div class="footer"> 479 <span id="footer-west">© 1999-2010 ImageMagick Studio LLC</span> 480 <span id="footer-east"> <a href="http://www.imagemagick.org/script/contact.php">Contact the Wizards</a></span> 481 </div> 482 <div style="clear: both; margin: 0; width: 100%; "></div> 483</body> 484</html> 485
