Image::Leptonica::Func::seedfill
version 0.04
seedfill.c
seedfill.c Binary seedfill (source: Luc Vincent) PIX *pixSeedfillBinary() PIX *pixSeedfillBinaryRestricted() Applications of binary seedfill to find and fill holes, remove c.c. touching the border and fill bg from border: PIX *pixHolesByFilling() PIX *pixFillClosedBorders() PIX *pixExtractBorderConnComps() PIX *pixRemoveBorderConnComps() PIX *pixFillBgFromBorder() Hole-filling of components to bounding rectangle PIX *pixFillHolesToBoundingRect() Gray seedfill (source: Luc Vincent:fast-hybrid-grayscale-reconstruction) l_int32 pixSeedfillGray() l_int32 pixSeedfillGrayInv() Gray seedfill (source: Luc Vincent: sequential-reconstruction algorithm) l_int32 pixSeedfillGraySimple() l_int32 pixSeedfillGrayInvSimple() Gray seedfill variations PIX *pixSeedfillGrayBasin() Distance function (source: Luc Vincent) PIX *pixDistanceFunction() Seed spread (based on distance function) PIX *pixSeedspread() Local extrema: l_int32 pixLocalExtrema() static l_int32 pixQualifyLocalMinima() l_int32 pixSelectedLocalExtrema() PIX *pixFindEqualValues() Selection of minima in mask of connected components PTA *pixSelectMinInConnComp() Removal of seeded connected components from a mask PIX *pixRemoveSeededComponents() ITERATIVE RASTER-ORDER SEEDFILL The basic method in the Vincent seedfill (aka reconstruction) algorithm is simple. We describe here the situation for binary seedfill. Pixels are sampled in raster order in the seed image. If they are 4-connected to ON pixels either directly above or to the left, and are not masked out by the mask image, they are turned on (or remain on). (Ditto for 8-connected, except you need to check 3 pixels on the previous line as well as the pixel to the left on the current line. This is extra computational work for relatively little gain, so it is preferable in most situations to use the 4-connected version.) The algorithm proceeds from UR to LL of the image, and then reverses and sweeps up from LL to UR. These double sweeps are iterated until there is no change. At this point, the seed has entirely filled the region it is allowed to, as delimited by the mask image. The grayscale seedfill is a straightforward generalization of the binary seedfill, and is described in seedfillLowGray(). For some applications, the filled seed will later be OR'd with the negative of the mask. This is used, for example, when you flood fill into a 4-connected region of OFF pixels and you want the result after those pixels are turned ON. Note carefully that the mask we use delineates which pixels are allowed to be ON as the seed is filled. We will call this a "filling mask". As the seed expands, it is repeatedly ANDed with the filling mask: s & fm. The process can equivalently be formulated using the inverse of the filling mask, which we will call a "blocking mask": bm = ~fm. As the seed expands, the blocking mask is repeatedly used to prevent the seed from expanding into the blocking mask. This is done by set subtracting the blocking mask from the expanded seed: s - bm. Set subtraction of the blocking mask is equivalent to ANDing with the inverse of the blocking mask: s & (~bm). But from the inverse relation between blocking and filling masks, this is equal to s & fm, which proves the equivalence. For efficiency, the pixels can be taken in larger units for processing, but still in raster order. It is natural to take them in 32-bit words. The outline of the work to be done for 4-cc (not including special cases for boundary words, such as the first line or the last word in each line) is as follows. Let the filling mask be m. The seed is to fill "under" the mask; i.e., limited by an AND with the mask. Let the current word be w, the word in the line above be wa, and the previous word in the current line be wp. Let t be a temporary word that is used in computation. Note that masking is performed by w & m. (If we had instead used a "blocking" mask, we would perform masking by the set subtraction operation, w - m, which is defined to be w & ~m.) The entire operation can be implemented with shifts, logical operations and tests. For each word in the seed image there are two steps. The first step is to OR the word with the word above and with the rightmost pixel in wp (call it "x"). Because wp is shifted one pixel to its right, "x" is ORed to the leftmost pixel of w. We then clip to the ON pixels in the mask. The result is t <-- (w | wa | x000... ) & m We've now finished taking data from above and to the left. The second step is to allow filling to propagate horizontally in t, always making sure that it is properly masked at each step. So if filling can be done (i.e., t is neither all 0s nor all 1s), iteratively take: t <-- (t | (t >> 1) | (t << 1)) & m until t stops changing. Then write t back into w. Finally, the boundary conditions require we note that in doing the above steps: (a) The words in the first row have no wa (b) The first word in each row has no wp in that row (c) The last word in each row must be masked so that pixels don't propagate beyond the right edge of the actual image. (This is easily accomplished by setting the out-of-bound pixels in m to OFF.)
PIX * pixDistanceFunction ( PIX *pixs, l_int32 connectivity, l_int32 outdepth, l_int32 boundcond )
pixDistanceFunction() Input: pixs (1 bpp source) connectivity (4 or 8) outdepth (8 or 16 bits for pixd) boundcond (L_BOUNDARY_BG, L_BOUNDARY_FG) Return: pixd, or null on error Notes: (1) This computes the distance of each pixel from the nearest background pixel. All bg pixels therefore have a distance of 0, and the fg pixel distances increase linearly from 1 at the boundary. It can also be used to compute the distance of each pixel from the nearest fg pixel, by inverting the input image before calling this function. Then all fg pixels have a distance 0 and the bg pixel distances increase linearly from 1 at the boundary. (2) The algorithm, described in Leptonica on the page on seed filling and connected components, is due to Luc Vincent. In brief, we generate an 8 or 16 bpp image, initialized with the fg pixels of the input pix set to 1 and the 1-boundary pixels (i.e., the boundary pixels of width 1 on the four sides set as either: * L_BOUNDARY_BG: 0 * L_BOUNDARY_FG: max where max = 0xff for 8 bpp and 0xffff for 16 bpp. Then do raster/anti-raster sweeps over all pixels interior to the 1-boundary, where the value of each new pixel is taken to be 1 more than the minimum of the previously-seen connected pixels (using either 4 or 8 connectivity). Finally, set the 1-boundary pixels using the mirrored method; this removes the max values there. (3) Using L_BOUNDARY_BG clamps the distance to 0 at the boundary. Using L_BOUNDARY_FG allows the distance at the image boundary to "float". (4) For 4-connected, one could initialize only the left and top 1-boundary pixels, and go all the way to the right and bottom; then coming back reset left and top. But we instead use a method that works for both 4- and 8-connected.
PIX * pixExtractBorderConnComps ( PIX *pixs, l_int32 connectivity )
pixExtractBorderConnComps() Input: pixs (1 bpp) filling connectivity (4 or 8) Return: pixd (all pixels in the src that are in connected components touching the border), or null on error
PIX * pixFillBgFromBorder ( PIX *pixs, l_int32 connectivity )
pixFillBgFromBorder() Input: pixs (1 bpp) filling connectivity (4 or 8) Return: pixd (with the background c.c. touching the border filled to foreground), or null on error Notes: (1) This fills all bg components touching the border to fg. It is the photometric inverse of pixRemoveBorderConnComps(). (2) Invert the result to get the "holes" left after this fill. This can be done multiple times, extracting holes within holes after each pair of fillings. Specifically, this code peels away n successive embeddings of components: pix1 = <initial image> for (i = 0; i < 2 * n; i++) { pix2 = pixFillBgFromBorder(pix1, 8); pixInvert(pix2, pix2); pixDestroy(&pix1); pix1 = pix2; }
PIX * pixFillClosedBorders ( PIX *pixs, l_int32 connectivity )
pixFillClosedBorders() Input: pixs (1 bpp) filling connectivity (4 or 8) Return: pixd (all topologically outer closed borders are filled as connected comonents), or null on error Notes: (1) Start with 1-pixel black border on otherwise white pixd (2) Subtract input pixs to remove border pixels that were also on the closed border (3) Use the inverted pixs as the filling mask to fill in all the pixels from the outer border to the closed border on pixs (4) Invert the result to get the filled component, including the input border (5) If the borders are 4-c.c., use 8-c.c. filling, and v.v. (6) Closed borders within c.c. that represent holes, etc., are filled.
PIX * pixFillHolesToBoundingRect ( PIX *pixs, l_int32 minsize, l_float32 maxhfract, l_float32 minfgfract )
pixFillHolesToBoundingRect() Input: pixs (1 bpp) minsize (min number of pixels in the hole) maxhfract (max hole area as fraction of fg pixels in the cc) minfgfract (min fg area as fraction of bounding rectangle) Return: pixd (pixs, with some holes possibly filled and some c.c. possibly expanded to their bounding rects), or null on error Notes: (1) This does not fill holes that are smaller in area than 'minsize'. (2) This does not fill holes with an area larger than 'maxhfract' times the fg area of the c.c. (3) This does not expand the fg of the c.c. to bounding rect if the fg area is less than 'minfgfract' times the area of the bounding rect. (4) The decisions are made as follows: - Decide if we are filling the holes; if so, when using the fg area, include the filled holes. - Decide based on the fg area if we are filling to a bounding rect. If so, do it. If not, fill the holes if the condition is satisfied. (5) The choice of minsize depends on the resolution. (6) For solidifying image mask regions on printed materials, which tend to be rectangular, values for maxhfract and minfgfract around 0.5 are reasonable.
PIX * pixFindEqualValues ( PIX *pixs1, PIX *pixs2 )
pixFindEqualValues() Input: pixs1 (8 bpp) pixs2 (8 bpp) Return: pixd (1 bpp mask), or null on error Notes: (1) The two images are aligned at the UL corner, and the returned image has ON pixels where the pixels in pixs1 and pixs2 have equal values.
PIX * pixHolesByFilling ( PIX *pixs, l_int32 connectivity )
pixHolesByFilling() Input: pixs (1 bpp) connectivity (4 or 8) Return: pixd (inverted image of all holes), or null on error Action: (1) Start with 1-pixel black border on otherwise white pixd (2) Use the inverted pixs as the filling mask to fill in all the pixels from the border to the pixs foreground (3) OR the result with pixs to have an image with all ON pixels except for the holes. (4) Invert the result to get the holes as foreground Notes: (1) To get 4-c.c. holes of the 8-c.c. as foreground, use 4-connected filling; to get 8-c.c. holes of the 4-c.c. as foreground, use 8-connected filling.
l_int32 pixLocalExtrema ( PIX *pixs, l_int32 maxmin, l_int32 minmax, PIX **ppixmin, PIX **ppixmax )
pixLocalExtrema() Input: pixs (8 bpp) maxmin (max allowed for the min in a 3x3 neighborhood; use 0 for default which is to have no upper bound) minmax (min allowed for the max in a 3x3 neighborhood; use 0 for default which is to have no lower bound) &ppixmin (<optional return> mask of local minima) &ppixmax (<optional return> mask of local maxima) Return: 0 if OK, 1 on error Notes: (1) This gives the actual local minima and maxima. A local minimum is a pixel whose surrounding pixels all have values at least as large, and likewise for a local maximum. For the local minima, @maxmin is the upper bound for the value of pixs. Likewise, for the local maxima, @minmax is the lower bound for the value of pixs. (2) The minima are found by starting with the erosion-and-equality approach of pixSelectedLocalExtrema(). This is followed by a qualification step, where each c.c. in the resulting minimum mask is extracted, the pixels bordering it are located, and they are queried. If all of those pixels are larger than the value of that minimum, it is a true minimum and its c.c. is saved; otherwise the c.c. is rejected. Note that if a bordering pixel has the same value as the minimum, it must then have a neighbor that is smaller, so the component is not a true minimum. (3) The maxima are found by inverting the image and looking for the minima there. (4) The generated masks can be used as markers for further operations.
PIX * pixRemoveBorderConnComps ( PIX *pixs, l_int32 connectivity )
pixRemoveBorderConnComps() Input: pixs (1 bpp) filling connectivity (4 or 8) Return: pixd (all pixels in the src that are not touching the border) or null on error Notes: (1) This removes all fg components touching the border.
PIX * pixRemoveSeededComponents ( PIX *pixd, PIX *pixs, PIX *pixm, l_int32 connectivity, l_int32 bordersize )
pixRemoveSeededComponents() Input: pixd (<optional>; this can be null or equal to pixm; 1 bpp) pixs (1 bpp seed) pixm (1 bpp filling mask) connectivity (4 or 8) bordersize (amount of border clearing) Return: pixd, or null on error Notes: (1) This removes each component in pixm for which there is at least one seed in pixs. If pixd == NULL, this returns the result in a new pixd. Otherwise, it is an in-place operation on pixm. In no situation is pixs altered, because we do the filling with a copy of pixs. (2) If bordersize > 0, it also clears all pixels within a distance @bordersize of the edge of pixd. This is here because pixLocalExtrema() typically finds local minima at the border. Use @bordersize >= 2 to remove these.
PIX * pixSeedfillBinary ( PIX *pixd, PIX *pixs, PIX *pixm, l_int32 connectivity )
pixSeedfillBinary() Input: pixd (<optional>; this can be null, equal to pixs, or different from pixs; 1 bpp) pixs (1 bpp seed) pixm (1 bpp filling mask) connectivity (4 or 8) Return: pixd always Notes: (1) This is for binary seedfill (aka "binary reconstruction"). (2) There are 3 cases: (a) pixd == null (make a new pixd) (b) pixd == pixs (in-place) (c) pixd != pixs (3) If you know the case, use these patterns for clarity: (a) pixd = pixSeedfillBinary(NULL, pixs, ...); (b) pixSeedfillBinary(pixs, pixs, ...); (c) pixSeedfillBinary(pixd, pixs, ...); (4) The resulting pixd contains the filled seed. For some applications you want to OR it with the inverse of the filling mask. (5) The input seed and mask images can be different sizes, but in typical use the difference, if any, would be only a few pixels in each direction. If the sizes differ, the clipping is handled by the low-level function seedfillBinaryLow().
PIX * pixSeedfillBinaryRestricted ( PIX *pixd, PIX *pixs, PIX *pixm, l_int32 connectivity, l_int32 xmax, l_int32 ymax )
pixSeedfillBinaryRestricted() Input: pixd (<optional>; this can be null, equal to pixs, or different from pixs; 1 bpp) pixs (1 bpp seed) pixm (1 bpp filling mask) connectivity (4 or 8) xmax (max distance in x direction of fill into the mask) ymax (max distance in y direction of fill into the mask) Return: pixd always Notes: (1) See usage for pixSeedfillBinary(), which has unrestricted fill. In pixSeedfillBinary(), the filling distance is unrestricted and can be larger than pixs, depending on the topology of th mask. (2) There are occasions where it is useful not to permit the fill to go more than a certain distance into the mask. @xmax specifies the maximum horizontal distance allowed in the fill; @ymax does likewise in the vertical direction. (3) Operationally, the max "distance" allowed for the fill is a linear distance from the original seed, independent of the actual mask topology. (4) Another formulation of this problem, not implemented, would use the manhattan distance from the seed, as determined by a breadth-first search starting at the seed boundaries and working outward where the mask fg allows. How this might use the constraints of separate xmax and ymax is not clear.
l_int32 pixSeedfillGray ( PIX *pixs, PIX *pixm, l_int32 connectivity )
pixSeedfillGray() Input: pixs (8 bpp seed; filled in place) pixm (8 bpp filling mask) connectivity (4 or 8) Return: 0 if OK, 1 on error Notes: (1) This is an in-place filling operation on the seed, pixs, where the clipping mask is always above or at the level of the seed as it is filled. (2) For details of the operation, see the description in seedfillGrayLow() and the code there. (3) As an example of use, see the description in pixHDome(). There, the seed is an image where each pixel is a fixed amount smaller than the corresponding mask pixel. (4) Reference paper : L. Vincent, Morphological grayscale reconstruction in image analysis: applications and efficient algorithms, IEEE Transactions on Image Processing, vol. 2, no. 2, pp. 176-201, 1993.
PIX * pixSeedfillGrayBasin ( PIX *pixb, PIX *pixm, l_int32 delta, l_int32 connectivity )
pixSeedfillGrayBasin() Input: pixb (binary mask giving seed locations) pixm (8 bpp basin-type filling mask) delta (amount of seed value above mask) connectivity (4 or 8) Return: pixd (filled seed) if OK, null on error Notes: (1) This fills from a seed within basins defined by a filling mask. The seed value(s) are greater than the corresponding filling mask value, and the result has the bottoms of the basins raised by the initial seed value. (2) The seed has value 255 except where pixb has fg (1), which are the seed 'locations'. At the seed locations, the seed value is the corresponding value of the mask pixel in pixm plus @delta. If @delta == 0, we return a copy of pixm. (3) The actual filling is done using the standard grayscale filling operation on the inverse of the mask and using the inverse of the seed image. After filling, we return the inverse of the filled seed. (4) As an example of use: pixm can describe a grayscale image of text, where the (dark) text pixels are basins of low values; pixb can identify the local minima in pixm (say, at the bottom of the basins); and delta is the amount that we wish to raise (lighten) the basins. We construct the seed (a.k.a marker) image from pixb, pixm and @delta.
l_int32 pixSeedfillGrayInv ( PIX *pixs, PIX *pixm, l_int32 connectivity )
pixSeedfillGrayInv() Input: pixs (8 bpp seed; filled in place) pixm (8 bpp filling mask) connectivity (4 or 8) Return: 0 if OK, 1 on error Notes: (1) This is an in-place filling operation on the seed, pixs, where the clipping mask is always below or at the level of the seed as it is filled. Think of filling up a basin to a particular level, given by the maximum seed value in the basin. Outside the filled region, the mask is above the filling level. (2) Contrast this with pixSeedfillGray(), where the clipping mask is always above or at the level of the fill. An example of its use is the hdome fill, where the seed is an image where each pixel is a fixed amount smaller than the corresponding mask pixel. (3) The basin fill, pixSeedfillGrayBasin(), is a special case where the seed pixel values are generated from the mask, and where the implementation uses pixSeedfillGray() by inverting both the seed and mask.
l_int32 pixSeedfillGrayInvSimple ( PIX *pixs, PIX *pixm, l_int32 connectivity )
pixSeedfillGrayInvSimple() Input: pixs (8 bpp seed; filled in place) pixm (8 bpp filling mask) connectivity (4 or 8) Return: 0 if OK, 1 on error Notes: (1) This is an in-place filling operation on the seed, pixs, where the clipping mask is always below or at the level of the seed as it is filled. Think of filling up a basin to a particular level, given by the maximum seed value in the basin. Outside the filled region, the mask is above the filling level. (2) Contrast this with pixSeedfillGraySimple(), where the clipping mask is always above or at the level of the fill. An example of its use is the hdome fill, where the seed is an image where each pixel is a fixed amount smaller than the corresponding mask pixel.
l_int32 pixSeedfillGraySimple ( PIX *pixs, PIX *pixm, l_int32 connectivity )
pixSeedfillGraySimple() Input: pixs (8 bpp seed; filled in place) pixm (8 bpp filling mask) connectivity (4 or 8) Return: 0 if OK, 1 on error Notes: (1) This is an in-place filling operation on the seed, pixs, where the clipping mask is always above or at the level of the seed as it is filled. (2) For details of the operation, see the description in seedfillGrayLowSimple() and the code there. (3) As an example of use, see the description in pixHDome(). There, the seed is an image where each pixel is a fixed amount smaller than the corresponding mask pixel. (4) Reference paper : L. Vincent, Morphological grayscale reconstruction in image analysis: applications and efficient algorithms, IEEE Transactions on Image Processing, vol. 2, no. 2, pp. 176-201, 1993.
PIX * pixSeedspread ( PIX *pixs, l_int32 connectivity )
pixSeedspread() Input: pixs (8 bpp source) connectivity (4 or 8) Return: pixd, or null on error Notes: (1) The raster/anti-raster method for implementing this filling operation was suggested by Ray Smith. (2) This takes an arbitrary set of nonzero pixels in pixs, which can be sparse, and spreads (extrapolates) the values to fill all the pixels in pixd with the nonzero value it is closest to in pixs. This is similar (though not completely equivalent) to doing a Voronoi tiling of the image, with a tile surrounding each pixel that has a nonzero value. All pixels within a tile are then closer to its "central" pixel than to any others. Then assign the value of the "central" pixel to each pixel in the tile. (3) This is implemented by computing a distance function in parallel with the fill. The distance function uses free boundary conditions (assumed maxval outside), and it controls the propagation of the pixels in pixd away from the nonzero (seed) values. This is done in 2 traversals (raster/antiraster). In the raster direction, whenever the distance function is nonzero, the spread pixel takes on the value of its predecessor that has the minimum distance value. In the antiraster direction, whenever the distance function is nonzero and its value is replaced by a smaller value, the spread pixel takes the value of the predecessor with the minimum distance value. (4) At boundaries where a pixel is equidistant from two nearest nonzero (seed) pixels, the decision of which value to use is arbitrary (greedy in search for minimum distance). This can give rise to strange-looking results, particularly for 4-connectivity where the L1 distance is computed from steps in N,S,E and W directions (no diagonals).
l_int32 pixSelectMinInConnComp ( PIX *pixs, PIX *pixm, PTA **ppta, NUMA **pnav )
pixSelectMinInConnComp() Input: pixs (8 bpp) pixm (1 bpp) &pta (<return> pta of min pixel locations) &nav (<optional return> numa of minima values) Return: 0 if OK, 1 on error. Notes: (1) For each 8 connected component in pixm, this finds a pixel in pixs that has the lowest value, and saves it in a Pta. If several pixels in pixs have the same minimum value, it picks the first one found. (2) For a mask pixm of true local minima, all pixels in each connected component have the same value in pixs, so it is fastest to select one of them using a special seedfill operation. Not yet implemented.
l_int32 pixSelectedLocalExtrema ( PIX *pixs, l_int32 mindist, PIX **ppixmin, PIX **ppixmax )
pixSelectedLocalExtrema() Input: pixs (8 bpp) mindist (-1 for keeping all pixels; >= 0 specifies distance) &ppixmin (<return> mask of local minima) &ppixmax (<return> mask of local maxima) Return: 0 if OK, 1 on error Notes: (1) This selects those local 3x3 minima that are at least a specified distance from the nearest local 3x3 maxima, and v.v. for the selected set of local 3x3 maxima. The local 3x3 minima is the set of pixels whose value equals the value after a 3x3 brick erosion, and the local 3x3 maxima is the set of pixels whose value equals the value after a 3x3 brick dilation. (2) mindist is the minimum distance allowed between local 3x3 minima and local 3x3 maxima, in an 8-connected sense. mindist == 1 keeps all pixels found in step 1. mindist == 0 removes all pixels from each mask that are both a local 3x3 minimum and a local 3x3 maximum. mindist == 1 removes any local 3x3 minimum pixel that touches a local 3x3 maximum pixel, and likewise for the local maxima. To make the decision, visualize each local 3x3 minimum pixel as being surrounded by a square of size (2 * mindist + 1) on each side, such that no local 3x3 maximum pixel is within that square; and v.v. (3) The generated masks can be used as markers for further operations.
Zakariyya Mughal <zmughal@cpan.org>
This software is copyright (c) 2014 by Zakariyya Mughal.
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cpanm
cpanm Image::Leptonica
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