1Pamscale User Manual(0) Pamscale User Manual(0)
2
6 pamscale - scale a Netpbm image
7
9 pamscale
10 [
11 scale_factor
12 |
13 {-xyfit | -xyfill | -xysize} cols rows
14 |
15 -reduce reduction_factor
16 |
17 [-xsize=cols | -width=cols | -xscale=factor]
18 [-ysize=rows | -height=rows | -yscale=factor]
19 |
20 -pixels n
21 ]
22 [
23 [-verbose]
24 [
25 -nomix
26 |
27 -filter=functionName [-window=functionName]
28 ]
29 [-linear]
30 }
31 [pnmfile]
32 Minimum unique abbreviation of option is acceptable. You may use dou‐
35 ble hyphens instead of single hyphen to denote options. You may use
36 white space in place of the equals sign to separate an option name from
37 its value.
38
41 This program is part of Netpbm(1).
42 pamscale scales a Netpbm image by a specified factor, or scales indi‐
44 vidually horizontally and vertically by specified factors.
45 You can either enlarge (scale factor > 1) or reduce (scale factor < 1).
47 The Scale Factors
50 The options -width, -height, -xsize, -ysize, -xscale, -yscale, -xyfit,
51 -xyfill, -reduce, and -pixels control the amount of scaling. For back‐
52 ward compatibility, there is also -xysize and the scale_factor argu‐
53 ment, but you shouldn't use those.
54 -width and -height specify the width and height in pixels you want the
56 resulting image to be. See below for rules when you specify one and
57 not the other.
58 -xsize and -ysize are synonyms for -width and -height, respectively.
60 -xscale and -yscale tell the factor by which you want the width and
62 height of the image to change from source to result (e.g. -xscale 2
63 means you want to double the width; -xscale .5 means you want to halve
64 it). See below for rules when you specify one and not the other.
65 When you specify an absolute size or scale factor for both dimensions,
67 pamscale scales each dimension independently without consideration of
68 the aspect ratio.
69 If you specify one dimension as a pixel size and don't specify the
71 other dimension, pamscale scales the unspecified dimension to preserve
72 the aspect ratio.
73 If you specify one dimension as a scale factor and don't specify the
75 other dimension, pamscale leaves the unspecified dimension unchanged
76 from the input.
77 If you specify the scale_factor parameter instead of dimension options,
79 that is the scale factor for both dimensions. It is equivalent to
80 -xscale=scale_factor -yscale=scale_factor.
81 Specifying the -reduce reduction_factor option is equivalent to speci‐
83 fying the scale_factor parameter, where scale_factor is the reciprocal
84 of reduction_factor.
85 -xyfit specifies a bounding box. pamscale scales the input image to
87 the largest size that fits within the box, while preserving its aspect
88 ratio. -xysize is a synonym for this. Before Netpbm 10.20 (January
89 2004), -xyfit did not exist, but -xysize did.
90 -xyfill is similar, but pamscale scales the input image to the smallest
92 size that completely fills the box, while preserving its aspect ratio.
93 This option has existed since Netpbm 10.20 (January 2004).
94 -pixels specifies a maximum total number of output pixels. pamscale
96 scales the image down to that number of pixels. If the input image is
97 already no more than that many pixels, pamscale just copies it as out‐
98 put; pamscale does not scale up with -pixels.
99 If you enlarge by a factor of 3 or more, you should probably add a
101 pnmsmooth step; otherwise, you can see the original pixels in the
102 resulting image.
103 Usage Notes
107 A useful application of pamscale is to blur an image. Scale it down
108 (without -nomix) to discard some information, then scale it back up
109 using pamstretch.
110 Or scale it back up with pamscale and create a 'pixelized' image, which
112 is sort of a computer-age version of blurring.
113 Transparency
117 pamscale understands transparency and properly mixes pixels considering
118 the pixels' transparency.
119 Proper mixing does not mean just mixing the transparency value and the
121 color component values separately. In a PAM image, a pixel which is
122 not opaque represents a color that contains light of the foreground
123 color indicated explicitly in the PAM and light of a background color
124 to be named later. But the numerical scale of a color component sample
125 in a PAM is as if the pixel is opaque. So a pixel that is supposed to
126 contain half-strength red light for the foreground plus some light from
127 the background has a red color sample that says full red and a trans‐
128 parency sample that says 50% opaque. In order to mix pixels, you have
129 to first convert the color sample values to numbers that represent
130 amount of light directly (i.e. multiply by the opaqueness) and after
131 mixing, convert back (divide by the opaqueness).
132 Input And Output Image Types
135 pamscale produces output of the same type (and tuple type if the type
136 is PAM) as the input, except if the input is PBM. In that case, the
137 output is PGM with maxval 255. The purpose of this is to allow mean‐
138 ingful pixel mixing. Note that there is no equivalent exception when
139 the input is PAM. If the PAM input tuple type is BLACKANDWHITE, the
140 PAM output tuple type is also BLACKANDWHITE, and you get no meaningful
141 pixel mixing.
142 If you want PBM output with PBM input, use pamditherbw to convert pam‐
144 scale's output to PBM. Also consider pbmreduce.
145 pamscale's function is essentially undefined for PAM input images that
147 are not of tuple type RGB, GRAYSCALE, BLACKANDWHITE, or the _ALPHA
148 variations of those. (By standard Netpbm backward compatibility, this
149 includes PBM, PGM, and PPM images).
150 You might think it would have an obvious effect on other tuple types,
152 but remember that the aforementioned tuple types have gamma-adjusted
153 sample values, and pamscale uses that fact in its calculations. And it
154 treats a transparency plane different from any other plane.
155 pamscale does not simply reject unrecognized tuple types because
157 there's a possibility that just by coincidence you can get useful func‐
158 tion out of it with some other tuple type and the right combination of
159 options (consider -linear in particular).
160 Methods Of Scaling
164 There are numerous ways to scale an image. pamscale implements a bunch
165 of them; you select among them with invocation options.
166 Pixel Mixing
168 Pamscale's default method is pixel mixing. To understand this, imagine
170 the source image as composed of square tiles. Each tile is a pixel and
171 has uniform color. The tiles are all the same size. Now take a trans‐
172 parent sheet the size of the target image, marked with a square grid of
173 tiles the same size. Stretch or compress the source image to the size
174 of the sheet and lay the sheet over the source.
175 Each cell in the overlay grid stands for a pixel of the target image.
177 For example, if you are scaling a 100x200 image up by 1.5, the source
178 image is 100 x 200 tiles, and the transparent sheet is marked off in
179 150 x 300 cells.
180 Each cell covers parts of multiple tiles. To make the target image,
182 just color in each cell with the color which is the average of the col‐
183 ors the cell covers -- weighted by the amount of that color it covers.
184 A cell in our example might cover 4/9 of a blue tile, 2/9 of a red
185 tile, 2/9 of a green tile, and 1/9 of a white tile. So the target
186 pixel would be somewhat unsaturated blue.
187 When you are scaling up or down by an integer, the results are simple.
189 When scaling up, pixels get duplicated. When scaling down, pixels get
190 thrown away. In either case, the colors in the target image are a sub‐
191 set of those in the source image.
192 When the scale factor is weirder than that, the target image can have
194 colors that didn't exist in the original. For example, a red pixel
195 next to a white pixel in the source might become a red pixel, a pink
196 pixel, and a white pixel in the target.
197 This method tends to replicate what the human eye does as it moves
199 closer to or further away from an image. It also tends to replicate
200 what the human eye sees, when far enough away to make the pixelization
201 disappear, if an image is not made of pixels and simply stretches or
202 shrinks.
203 Discrete Sampling
205 Discrete sampling is basically the same thing as pixel mixing except
207 that, in the model described above, instead of averaging the colors of
208 the tiles the cell covers, you pick the one color that covers the most
209 area.
210 The result you see is that when you enlarge an image, pixels get dupli‐
212 cated and when you reduce an image, some pixels get discarded.
213 The advantage of this is that you end up with an image made from the
215 same color palette as the original. Sometimes that's important.
216 The disadvantage is that it distorts the picture. If you scale up by
218 1.5 horizontally, for example, the even numbered input pixels are dou‐
219 bled in the output and the odd numbered ones are copied singly. If you
220 have a bunch of one pixel wide lines in the source, you may find that
221 some of them stretch to 2 pixels, others remain 1 pixel when you
222 enlarge. When you reduce, you may find that some of the lines disap‐
223 pear completely.
224 You select discrete sampling with pamscale's -nomix option.
226 Actually, -nomix doesn't do exactly what I described above. It does
228 the scaling in two passes - first horizontal, then vertical. This can
229 produce slightly different results.
230 There is one common case in which one often finds it burdensome to have
232 pamscale make up colors that weren't there originally: Where one is
233 working with an image format such as GIF that has a limited number of
234 possible colors per image. If you take a GIF with 256 colors, convert
235 it to PPM, scale by .625, and convert back to GIF, you will probably
236 find that the reduced image has way more than 256 colors, and therefore
237 cannot be converted to GIF. One way to solve this problem is to do the
238 reduction with discrete sampling instead of pixel mixing. Probably a
239 better way is to do the pixel mixing, but then color quantize the
240 result with pnmquant before converting to GIF.
241 When the scale factor is an integer (which means you're scaling up),
243 discrete sampling and pixel mixing are identical -- output pixels are
244 always just N copies of the input pixels. In this case, though, con‐
245 sider using pamstretch instead of pamscale to get the added pixels
246 interpolated instead of just copied and thereby get a smoother enlarge‐
247 ment.
248 pamscale's discrete sampling is faster than pixel mixing, but pamen‐
250 large is faster still. pamenlarge works only on integer enlargements.
251 discrete sampling (-nomix) was new in Netpbm 9.24 (January 2002).
253 Resampling
256 Resampling assumes that the source image is a discrete sampling of some
258 original continuous image. That is, it assumes there is some non-pix‐
259 elized original image and each pixel of the source image is simply the
260 color of that image at a particular point. Those points, naturally,
261 are the intersections of a square grid.
262 The idea of resampling is just to compute that original image, then
264 sample it at a different frequency (a grid of a different scale).
265 The problem, of course, is that sampling necessarily throws away the
267 information you need to rebuild the original image. So we have to make
268 a bunch of assumptions about the makeup of the original image.
269 You tell pamscale to use the resampling method by specifying the -fil‐
271 ter option. The value of this option is the name of a function, from
272 the set listed below.
273 To explain resampling, we are going to talk about a simple one dimen‐
275 sional scaling -- scaling a single row of grayscale pixels horizon‐
276 tally. If you can understand that, you can easily understand how to do
277 a whole image: Scale each of the rows of the image, then scale each of
278 the resulting columns. And scale each of the color component planes
279 separately.
280 As a first step in resampling, pamscale converts the source image,
282 which is a set of discrete pixel values, into a continuous step func‐
283 tion. A step function is a function whose graph is a staircase-y
284 thing.
285 Now, we convolve the step function with a proper scaling of the filter
287 function that you identified with -filter. If you don't know what the
288 mathematical concept of convolution (convolving) is, you are officially
289 lost. You cannot understand this explanation. The result of this con‐
290 volution is the imaginary original continuous image we've been talking
291 about.
292 Finally, we make target pixels by picking values from that function.
294 To understand what is going on, we use Fourier analysis:
296 The idea is that the only difference between our step function and the
298 original continuous function (remember that we constructed the step
299 function from the source image, which is itself a sampling of the orig‐
300 inal continuous function) is that the step function has a bunch of high
301 frequency Fourier components added. If we could chop out all the
302 higher frequency components of the step function, and know that they're
303 all higher than any frequency in the original function, we'd have the
304 original function back.
305 The resampling method assumes that the original function was sampled at
307 a high enough frequency to form a perfect sampling. A perfect sampling
308 is one from which you can recover exactly the original continuous func‐
309 tion. The Nyquist theorem says that as long as your sample rate is at
310 least twice the highest frequency in your original function, the sam‐
311 pling is perfect. So we assume that the image is a sampling of some‐
312 thing whose highest frequency is half the sample rate (pixel resolu‐
313 tion) or less. Given that, our filtering does in fact recover the
314 original continuous image from the samples (pixels).
315 To chop out all the components above a certain frequency, we just mul‐
317 tiply the Fourier transform of the step function by a rectangle func‐
318 tion.
319 We could find the Fourier transform of the step function, multiply it
321 by a rectangle function, and then Fourier transform the result back,
322 but there's an easier way. Mathematicians tell us that multiplying in
323 the frequency domain is equivalent to convolving in the time domain.
324 That means multiplying the Fourier transform of F by a rectangle func‐
325 tion R is the same as convolving F with the Fourier transform of R.
326 It's a lot better to take the Fourier transform of R, and build it into
327 pamscale than to have pamscale take the Fourier transform of the input
328 image dynamically.
329 That leaves only one question: What is the Fourier transform of a rec‐
331 tangle function? Answer: sinc. Recall from math that sinc is defined
332 as sinc(x) = sin(PI*x)/PI*x.
333 Hence, when you specify -filter=sinc, you are effectively passing the
335 step function of the source image through a low pass frequency filter
336 and recovering a good approximation of the original continuous image.
337 Refiltering
339 There's another twist: If you simply sample the reconstructed original
341 continuous image at the new sample rate, and that new sample rate isn't
342 at least twice the highest frequency in the original continuous image,
343 you won't get a perfect sampling. In fact, you'll get something with
344 ugly aliasing in it. Note that this can't be a problem when you're
345 scaling up (increasing the sample rate), because the fact that the old
346 sample rate was above the Nyquist level means so is the new one. But
347 when scaling down, it's a problem. Obviously, you have to give up
348 image quality when scaling down, but aliasing is not the best way to do
349 it. It's better just to remove high frequency components from the
350 original continuous image before sampling, and then get a perfect sam‐
351 pling of that.
352 Therefore, pamscale filters out frequencies above half the new sample
354 rate before picking the new samples.
355 Approximations
357 Unfortunately, pamscale doesn't do the convolution precisely. Instead
359 of evaluating the filter function at every point, it samples it --
360 assumes that it doesn't change any more often than the step function
361 does. pamscale could actually do the true integration fairly easily.
362 Since the filter functions are built into the program, the integrals of
363 them could be too. Maybe someday it will.
364 There is one more complication with the Fourier analysis. sinc has
366 nonzero values on out to infinity and minus infinity. That makes it
367 hard to compute a convolution with it. So instead, there are filter
368 functions that approximate sinc but are nonzero only within a manage‐
369 able range. To get those, you multiply the sinc function by a window
370 function, which you select with the -window option. The same holds for
371 other filter functions that go on forever like sinc. By default, for a
372 filter that needs a window function, the window function is the Black‐
373 man function.
374 Filter Functions Besides Sinc
376 The math described above works only with sinc as the filter function.
378 pamscale offers many other filter functions, though. Some of these
379 approximate sinc and are faster to compute. For most of them, I have
380 no idea of the mathematical explanation for them, but people do find
381 they give pleasing results. They may not be based on resampling at
382 all, but just exploit the convolution that is coincidentally part of a
383 resampling calculation.
384 For some filter functions, you can tell just by looking at the convolu‐
386 tion how they vary the resampling process from the perfect one based on
387 sinc:
388 The impulse filter assumes that the original continuous image is in
390 fact a step function -- the very one we computed as the first step in
391 the resampling. This is mathematically equivalent to the discrete sam‐
392 pling method.
393 The box (rectangle) filter assumes the original image is a piecewise
395 linear function. Its graph just looks like straight lines connecting
396 the pixel values. This is mathematically equivalent to the pixel mix‐
397 ing method (but mixing brightness, not light intensity, so like pam‐
398 scale -linear) when scaling down, and interpolation (ala pamstretch)
399 when scaling up.
400 Gamma
402 pamscale assumes the underlying continuous function is a function of
404 brightness (as opposed to light intensity), and therefore does all this
405 math using the gamma-adjusted numbers found in a PNM or PAM image. The
406 -linear option is not available with resampling (it causes pamscale to
407 fail), because it wouldn't be useful enough to justify the implementa‐
408 tion effort.
409 Resampling (-filter) was new in Netpbm 10.20 (January 2004).
411 The filter functions
413 Here is a list of the function names you can specify for the -filter
415 option. For most of them, you're on your own to figure out just what
416 the function is and what kind of scaling it does. These are common
417 functions from mathematics.
418 point The graph of this is a single point at X=0, Y=1.
422 box The graph of this is a rectangle sitting on the X axis and cen‐
425 tered on the Y axis with height 1 and base 1.
426 triangle
429 The graph of this is an isosceles triangle sitting on the X axis
430 and centered on the Y axis with height 1 and base 2.
431 quadratic
434 cubic
436 catrom
438 mitchell
440 gauss
442 sinc
444 bessel
446 hanning
448 hamming
450 blackman
452 kaiser
454 normal
456 hermite
458 lanczos
460 Not documented
461 Linear vs Gamma-adjusted
466 The pixel mixing scaling method described above involves intensities of
467 pixels (more precisely, it involves individual intensities of primary
468 color components of pixels). But the PNM and PNM-equivalent PAM image
469 formats represent intensities with gamma-adjusted numbers that are not
470 linearly proportional to intensity. So pamscale, by default, performs
471 a calculation on each sample read from its input and each sample writ‐
472 ten to its output to convert between these gamma-adjusted numbers and
473 internal intensity-proportional numbers.
474 Sometimes you are not working with true PNM or PAM images, but rather a
476 variation in which the sample values are in fact directly proportional
477 to intensity. If so, use the -linear option to tell pamscale this.
478 pamscale then will skip the conversions.
479 The conversion takes time. In one experiment, it increased by a factor
481 of 10 the time required to reduce an image. And the difference between
482 intensity-proportional values and gamma-adjusted values may be small
483 enough that you would barely see a difference in the result if you just
484 pretended that the gamma-adjusted values were in fact intensity-propor‐
485 tional. So just to save time, at the expense of some image quality,
486 you can specify -linear even when you have true PPM input and expect
487 true PPM output.
488 For the first 13 years of Netpbm's life, until Netpbm 10.20 (January
490 2004), pamscale's predecessor pnmscale always treated the PPM samples
491 as intensity-proportional even though they were not, and drew few com‐
492 plaints. So using -linear as a lie is a reasonable thing to do if
493 speed is important to you. But if speed is important, you also should
494 consider the -nomix option and pnmscalefixed.
495 Another technique to consider is to convert your PNM image to the lin‐
497 ear variation with pnmgamma, run pamscale on it and other transforma‐
498 tions that like linear PNM, and then convert it back to true PNM with
499 pnmgamma -ungamma. pnmgamma is often faster than pamscale in doing the
500 conversion.
501 With -nomix, -linear has no effect. That's because pamscale does not
503 concern itself with the meaning of the sample values in this method;
504 pamscale just copies numbers from its input to its output.
505 Precision
509 pamscale uses floating point arithmetic internally. There is a speed
510 cost associated with this. For some images, you can get the acceptable
511 results (in fact, sometimes identical results) faster with pnmscale‐
512 fixed, which uses fixed point arithmetic. pnmscalefixed may, however,
513 distort your image a little. See the pnmscalefixed user manual for a
514 complete discussion of the difference.
515
518 pnmscalefixed(1), pamstretch(1), pamditherbw(1), pbmreduce(1), pbmp‐
519 scale(1), pamenlarge(1), pnmsmooth(1), pamcut(1), pnmgamma(1), pnm‐
520 scale(1), pnm(1), pam(1)
521
524 pamscale was new in Netpbm 10.20 (January 2004). It was adapted from,
525 and obsoleted, pnmscale. pamscale's primary difference from pnmscale
526 is that it handles the PAM format and uses the "pam" facilities of the
527 Netpbm programming library. But it also added the resampling class of
528 scaling method. Furthermore, it properly does its pixel mixing arith‐
529 metic (by default) using intensity-proportional values instead of the
530 gamma-adjusted values the pnmscale uses. To get the old pnmscale
531 arithmetic, you can specify the -linear option.
532 The intensity proportional stuff came out of suggestions by Adam M
534 Costello in January 2004.
535 The resampling algorithms are mostly taken from code contributed by
537 Michael Reinelt in December 2003.
538 The version of pnmscale from which pamscale was derived, itself evolved
540 out of the original Pbmplus version of pnmscale by Jef Poskanzer (1989,
541 1991). But none of that original code remains.
542netpbm documentation 18 February 2005 Pamscale User Manual(0)