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colorquant2.c Modified median cut color quantization High level PIX *pixMedianCutQuant() PIX *pixMedianCutQuantGeneral() PIX *pixMedianCutQuantMixed() PIX *pixFewColorsMedianCutQuantMixed() Median cut indexed histogram l_int32 *pixMedianCutHisto() Static helpers static PIXCMAP *pixcmapGenerateFromHisto() static PIX *pixQuantizeWithColormap() static void getColorIndexMedianCut() static L_BOX3D *pixGetColorRegion() static l_int32 medianCutApply() static PIXCMAP *pixcmapGenerateFromMedianCuts() static l_int32 vboxGetAverageColor() static l_int32 vboxGetCount() static l_int32 vboxGetVolume() static L_BOX3D *box3dCreate(); static L_BOX3D *box3dCopy(); Paul Heckbert published the median cut algorithm, "Color Image Quantization for Frame Buffer Display," in Proc. SIGGRAPH '82, Boston, July 1982, pp. 297-307. A copy of the paper without figures can be found on the web. Median cut starts with either the full color space or the occupied region of color space. If you're not dithering, the occupied region can be used, but with dithering, pixels can end up in any place in the color space, so you must represent the entire color space in the final colormap. Color components are quantized to typically 5 or 6 significant bits (for each of r, g and b). Call a 3D region of color space a 'vbox'. Any color in this quantized space is represented by an element of a linear histogram array, indexed by rgb value. The initial region is then divided into two regions that have roughly equal pixel occupancy (hence the name "median cut"). Subdivision continues until the requisite number of vboxes has been generated. But the devil is in the details of the subdivision process. Here are some choices that you must make: (1) Along which axis to subdivide? (2) Which box to put the bin with the median pixel? (3) How to order the boxes for subdivision? (4) How to adequately handle boxes with very small numbers of pixels? (5) How to prevent a little-represented but highly visible color from being masked out by other colors in its vbox. Taking these in order: (1) Heckbert suggests using either the largest vbox side, or the vbox side with the largest variance in pixel occupancy. We choose to divide based on the largest vbox side. (2) Suppose you've chosen a side. Then you have a histogram of pixel occupancy in 2D slices of the vbox. One of those slices includes the median pixel. Suppose there are L bins to the left (smaller index) and R bins to the right. Then this slice (or bin) should be assigned to the box containing the smaller of L and R. This both shortens the larger of the subdivided dimensions and helps a low-count color far from the subdivision boundary to better express itself. (2a) One can also ask if the boundary should be moved even farther into the longer side. This is feasable if we have a method for doing extra subdivisions on the high count vboxes. And we do (see (3)). (3) To make sure that the boxes are subdivided toward equal occupancy, use an occupancy-sorted priority queue, rather than a simple queue. (4) With a priority queue, boxes with small number of pixels won't be repeatedly subdivided. This is good. (5) Use of a priority queue allows tricks such as in (2a) to let small occupancy clusters be better expressed. In addition, rather than splitting near the median, small occupancy colors are best reproduced by cutting half-way into the longer side. However, serious problems can arise with dithering if a priority queue is used based on population alone. If the picture has large regions of nearly constant color, some vboxes can be very large and have a sizeable population (but not big enough to get to the head of the queue). If one of these large, occupied vboxes is near in color to a nearly constant color region of the image, dithering can inject pixels from the large vbox into the nearly uniform region. These pixels can be very far away in color, and the oscillations are highly visible. To prevent this, we can take either or both of these actions: (1) Subdivide a fraction (< 1.0) based on population, and do the rest of the subdivision based on the product of the vbox volume and its population. By using the product, we avoid further subdivision of nearly empty vboxes, and directly target large vboxes with significant population. (2) Threshold the excess color transferred in dithering to neighboring pixels. Doing either of these will stop the most annoying oscillations in dithering. Furthermore, by doing (1), we also improve the rendering of regions of nearly constant color, both with and without dithering. It turns out that the image quality is not sensitive to the value of the parameter in (1); values between 0.3 and 0.9 give very good results. Here's the lesson: subdivide the color space into vboxes such that (1) the most populated vboxes that can be further subdivided (i.e., that occupy more than one quantum volume in color space) all have approximately the same population, and (2) all large vboxes have no significant population. If these conditions are met, the quantization will be excellent. Once the subdivision has been made, the colormap is generated, with one color for each vbox and using the average color in the vbox. At the same time, the histogram array is converted to an inverse colormap table, storing the colormap index in every cell in the vbox. Finally, using both the colormap and the inverse colormap, a colormapped pix is quickly generated from the original rgb pix. In the present implementation, subdivided regions of colorspace that are not occupied are retained, but not further subdivided. This is required for our inverse colormap lookup table for dithering, because dithered pixels may fall into these unoccupied regions. For such empty regions, we use the center as the rgb colormap value. This variation on median cut can be referred to as "Modified Median Cut" quantization, or MMCQ. Overall, the undithered MMCQ gives comparable results to the two-pass Octcube Quantizer (OQ). Comparing the two methods on the test24.jpg painting, we see: (1) For rendering spot color (the various reds and pinks in the image), MMCQ is not as good as OQ. (2) For rendering majority color regions, MMCQ does a better job of avoiding posterization. That is, it does better dividing the color space up in the most heavily populated regions.
PIX * pixFewColorsMedianCutQuantMixed ( PIX *pixs, l_int32 ncolor, l_int32 ngray, l_int32 maxncolors, l_int32 darkthresh, l_int32 lightthresh, l_int32 diffthresh )
pixFewColorsMedianCutQuantMixed() Input: pixs (32 bpp rgb) ncolor (number of colors to be assigned to pixels with significant color) ngray (number of gray colors to be used; must be >= 2) maxncolors (maximum number of colors to be returned from pixColorsForQuantization(); use 0 for default) darkthresh (threshold near black; if the lightest component is below this, the pixel is not considered to be gray or color; use 0 for default) lightthresh (threshold near white; if the darkest component is above this, the pixel is not considered to be gray or color; use 0 for default) diffthresh (thresh for the max difference between component values; for differences below this, the pixel is considered to be gray; use 0 for default) considered gray; use 0 for default) Return: pixd (8 bpp, median cut quantized for pixels that are not gray; gray pixels are quantized separately over the full gray range); null if too many colors or on error Notes: (1) This is the "few colors" version of pixMedianCutQuantMixed(). It fails (returns NULL) if it finds more than maxncolors, but otherwise it gives the same result. (2) Recommended input parameters are: @maxncolors: 20 @darkthresh: 20 @lightthresh: 244 @diffthresh: 15 (any higher can miss colors differing slightly from gray) (3) Both ncolor and ngray should be at least equal to maxncolors. If they're not, they are automatically increased, and a warning is given. (4) If very little color content is found, the input is converted to gray and quantized in equal intervals. (5) This can be useful for quantizing orthographically generated images such as color maps, where there may be more than 256 colors because of aliasing or jpeg artifacts on text or lines, but there are a relatively small number of solid colors. (6) Example of usage: // Try to quantize, using default values for mixed med cut Pix *pixq = pixFewColorsMedianCutQuantMixed(pixs, 100, 20, 0, 0, 0, 0); if (!pixq) // too many colors; don't quantize pixq = pixClone(pixs);
l_int32 * pixMedianCutHisto ( PIX *pixs, l_int32 sigbits, l_int32 subsample )
pixMedianCutHisto() Input: pixs (32 bpp; rgb color) sigbits (valid: 5 or 6) subsample (integer > 0) Return: histo (1-d array, giving the number of pixels in each quantized region of color space), or null on error Notes: (1) Array is indexed by (3 * sigbits) bits. The array size is 2^(3 * sigbits). (2) Indexing into the array from rgb uses red sigbits as most significant and blue as least.
PIX * pixMedianCutQuant ( PIX *pixs, l_int32 ditherflag )
pixMedianCutQuant() Input: pixs (32 bpp; rgb color) ditherflag (1 for dither; 0 for no dither) Return: pixd (8 bit with colormap), or null on error Notes: (1) Simple interface. See pixMedianCutQuantGeneral() for use of defaulted parameters.
PIX * pixMedianCutQuantGeneral ( PIX *pixs, l_int32 ditherflag, l_int32 outdepth, l_int32 maxcolors, l_int32 sigbits, l_int32 maxsub, l_int32 checkbw )
pixMedianCutQuantGeneral() Input: pixs (32 bpp; rgb color) ditherflag (1 for dither; 0 for no dither) outdepth (output depth; valid: 0, 1, 2, 4, 8) maxcolors (between 2 and 256) sigbits (valid: 5 or 6; use 0 for default) maxsub (max subsampling, integer; use 0 for default; 1 for no subsampling) checkbw (1 to check if color content is very small, 0 to assume there is sufficient color) Return: pixd (8 bit with colormap), or null on error Notes: (1) @maxcolors must be in the range [2 ... 256]. (2) Use @outdepth = 0 to have the output depth computed as the minimum required to hold the actual colors found, given the @maxcolors constraint. (3) Use @outdepth = 1, 2, 4 or 8 to specify the output depth. In that case, @maxcolors must not exceed 2^(outdepth). (4) If there are fewer quantized colors in the image than @maxcolors, the colormap is simply generated from those colors. (5) @maxsub is the maximum allowed subsampling to be used in the computation of the color histogram and region of occupied color space. The subsampling is chosen internally for efficiency, based on the image size, but this parameter limits it. Use @maxsub = 0 for the internal default, which is the maximum allowed subsampling. Use @maxsub = 1 to prevent subsampling. In general use @maxsub >= 1 to specify the maximum subsampling to be allowed, where the actual subsampling will be the minimum of this value and the internally determined default value. (6) If the image appears gray because either most of the pixels are gray or most of the pixels are essentially black or white, the image is trivially quantized with a grayscale colormap. The reason is that median cut divides the color space into rectangular regions, and it does a very poor job if all the pixels are near the diagonal of the color space cube.
PIX * pixMedianCutQuantMixed ( PIX *pixs, l_int32 ncolor, l_int32 ngray, l_int32 darkthresh, l_int32 lightthresh, l_int32 diffthresh )
pixMedianCutQuantMixed() Input: pixs (32 bpp; rgb color) ncolor (maximum number of colors assigned to pixels with significant color) ngray (number of gray colors to be used; must be >= 2) darkthresh (threshold near black; if the lightest component is below this, the pixel is not considered to be gray or color; uses 0 for default) lightthresh (threshold near white; if the darkest component is above this, the pixel is not considered to be gray or color; use 0 for default) diffthresh (thresh for the max difference between component values; for differences below this, the pixel is considered to be gray; use 0 for default) Return: pixd (8 bpp cmapped), or null on error Notes: (1) ncolor + ngray must not exceed 255. (2) The method makes use of pixMedianCutQuantGeneral() with minimal addition. (a) Preprocess the image, setting all pixels with little color to black, and populating an auxiliary 8 bpp image with the expected colormap values corresponding to the set of quantized gray values. (b) Color quantize the altered input image to n + 1 colors. (c) Augment the colormap with the gray indices, and substitute the gray quantized values from the auxiliary image for those in the color quantized output that had been quantized as black. (3) Median cut color quantization is relatively poor for grayscale images with many colors, when compared to octcube quantization. Thus, for images with both gray and color, it is important to quantize the gray pixels by another method. Here, we are conservative in detecting color, preferring to use a few extra bits to encode colorful pixels that push them to gray. This is particularly reasonable with this function, because it handles the gray and color pixels separately, using median cut color quantization for the color pixels and equal-bin grayscale quantization for the non-color pixels.
Zakariyya Mughal <firstname.lastname@example.org>
This software is copyright (c) 2014 by Zakariyya Mughal.
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