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ccbord.c CCBORDA and CCBORD creation and destruction CCBORDA *ccbaCreate() void *ccbaDestroy() CCBORD *ccbCreate() void *ccbDestroy() CCBORDA addition l_int32 ccbaAddCcb() static l_int32 ccbaExtendArray() CCBORDA accessors l_int32 ccbaGetCount() l_int32 ccbaGetCcb() Top-level border-finding routines CCBORDA *pixGetAllCCBorders() CCBORD *pixGetCCBorders() PTAA *pixGetOuterBordersPtaa() PTA *pixGetOuterBorderPta() Lower-level border location routines l_int32 pixGetOuterBorder() l_int32 pixGetHoleBorder() l_int32 findNextBorderPixel() void locateOutsideSeedPixel() Border conversions l_int32 ccbaGenerateGlobalLocs() l_int32 ccbaGenerateStepChains() l_int32 ccbaStepChainsToPixCoords() l_int32 ccbaGenerateSPGlobalLocs() Conversion to single path l_int32 ccbaGenerateSinglePath() PTA *getCutPathForHole() Border and full image rendering PIX *ccbaDisplayBorder() PIX *ccbaDisplaySPBorder() PIX *ccbaDisplayImage1() PIX *ccbaDisplayImage2() Serialize for I/O l_int32 ccbaWrite() l_int32 ccbaWriteStream() l_int32 ccbaRead() l_int32 ccbaReadStream() SVG output l_int32 ccbaWriteSVG() char *ccbaWriteSVGString() Border finding is tricky because components can have holes, which also need to be traced out. The outer border can be connected with all the hole borders, so that there is a single border for each component. [Alternatively, the connecting paths can be eliminated if you're willing to have a set of borders for each component (an exterior border and some number of interior ones), with "line to" operations tracing out each border and "move to" operations going from one border to the next.] Here's the plan. We get the pix for each connected component, and trace its exterior border. We then find the holes (if any) in the pix, and separately trace out their borders, all using the same border-following rule that has ON pixels on the right side of the path. [For svg, we may want to turn each set of borders for a c.c. into a closed path. This can be done by tunnelling through the component from the outer border to each of the holes, going in and coming out along the same path so the connection will be invisible in any rendering (display or print) from the outline. The result is a closed path, where the outside border is traversed cw and each hole is traversed ccw. The svg renderer is assumed to handle these closed borders properly.] Each border is a closed path that is traversed in such a way that the stuff inside the c.c. is on the right side of the traveller. The border of a singly-connected component is thus traversed cw, and the border of the holes inside a c.c. are traversed ccw. Suppose we have a list of all the borders of each c.c., both the cw and ccw traversals. How do we reconstruct the image? Reconstruction: Method 1. Topological method using connected components. We have closed borders composed of cw border pixels for the exterior of c.c. and ccw border pixels for the interior (holes) in the c.c. (a) Initialize the destination to be OFF. Then, in any order: (b) Fill the components within and including the cw borders, and sequentially XOR them onto the destination. (c) Fill the components within but not including the ccw borders and sequentially XOR them onto the destination. The components that are XOR'd together can be generated as follows: (a) For each closed cw path, use pixFillClosedBorders(): (1) Turn on the path pixels in a subimage that minimally supports the border. (2) Do a 4-connected fill from a seed of 1 pixel width on the border, using the inverted image in (1) as a filling mask. (3) Invert the fill result: this gives the component including the exterior cw path, with all holes filled. (b) For each closed ccw path (hole): (1) Turn on the path pixels in a subimage that minimally supports the path. (2) Find a seed pixel on the inside of this path. (3) Do a 4-connected fill from this seed pixel, using the inverted image of the path in (1) as a filling mask. ------------------------------------------------------ Method 2. A variant of Method 1. Topological. In Method 1, we treat the exterior border differently from the interior (hole) borders. Here, all borders in a c.c. are treated equally: (1) Start with a pix with a 1 pixel OFF boundary enclosing all the border pixels of the c.c. This is the filling mask. (2) Make a seed image of the same size as follows: for each border, put one seed pixel OUTSIDE the border (where OUTSIDE is determined by the inside/outside convention for borders). (3) Seedfill into the seed image, filling in the regions determined by the filling mask. The fills are clipped by the border pixels. (4) Inverting this, we get the c.c. properly filled, with the holes empty! (5) Rasterop using XOR the filled c.c. (but not the 1 pixel boundary) into the full dest image. Method 2 is about 1.2x faster than Method 1 on text images, and about 2x faster on complex images (e.g., with halftones). ------------------------------------------------------ Method 3. The traditional way to fill components delineated by boundaries is through scan line conversion. It's a bit tricky, and I have not yet tried to implement it. ------------------------------------------------------ Method 4. [Nota Bene: this method probably doesn't work, and won't be implemented. If I get a more traditional scan line conversion algorithm working, I'll erase these notes.] Render all border pixels on a destination image, which will be the final result after scan conversion. Assign a value 1 to pixels on cw paths, 2 to pixels on ccw paths, and 3 to pixels that are on both paths. Each of the paths is an 8-connected component. Now scan across each raster line. The attempt is to make rules for each scan line that are independent of neighboring scanlines. Here are a set of rules for writing ON pixels on a destination raster image: (a) The rasterizer will be in one of two states: ON and OFF. (b) Start each line in the OFF state. In the OFF state, skip pixels until you hit a path of any type. Turn the path pixel ON. (c) If the state is ON, each pixel you encounter will be turned on, until and including hitting a path pixel. (d) When you hit a path pixel, if the path does NOT cut through the line, so that there is not an 8-cc path pixel (of any type) both above and below, the state is unchanged (it stays either ON or OFF). (e) If the path does cut through, but with a possible change of pixel type, then we decide whether or not to toggle the state based on the values of the path pixel and the path pixels above and below: (1) if a 1 path cuts through, toggle; (1) if a 2 path cuts through, toggle; (3) if a 3 path cuts through, do not toggle; (4) if on one side a 3 touches both a 1 and a 2, use the 2 (5) if a 3 has any 1 neighbors, toggle; else if it has no 1 neighbors, do not toggle; (6) if a 2 has any neighbors that are 1 or 3, do not toggle (7) if a 1 has neighbors 1 and x (x = 2 or 3), toggle To visualize how these rules work, consider the following component with border pixels labeled according to the scheme above. We also show the values of the interior pixels (w=OFF, b=ON), but these of course must be inferred properly from the rules above: 3 3 w 3 1 1 1 1 2 1 1 b 2 b 1 1 b 1 3 w 2 1 3 b 1 1 b 2 b 1 3 w 3 1 1 1 3 w 3 1 b 2 b 1 1 2 w 2 1 1 b 2 w 2 b 1 1 2 w 2 1 1 2 b 1 1 b 1 1 Even if this works, which is unlikely, it will certainly be slow because decisions have to be made on a pixel-by-pixel basis when encountering borders.
CCBORD * ccbCreate ( PIX *pixs )
ccbCreate() Input: pixs (<optional>) Return: ccb or null on error
void ccbDestroy ( CCBORD **pccb )
ccbDestroy() Input: &ccb (<to be nulled>) Return: void
l_int32 ccbaAddCcb ( CCBORDA *ccba, CCBORD *ccb )
ccbaAddCcb() Input: ccba ccb (to be added by insertion) Return: 0 if OK; 1 on error
CCBORDA * ccbaCreate ( PIX *pixs, l_int32 n )
ccbaCreate() Input: pixs (binary image; can be null) n (initial number of ptrs) Return: ccba, or null on error
void ccbaDestroy ( CCBORDA **pccba )
ccbaDestroy() Input: &ccba (<to be nulled>) Return: void
PIX * ccbaDisplayBorder ( CCBORDA *ccba )
ccbaDisplayBorder() Input: ccba Return: pix of border pixels, or null on error Notes: (1) Uses global ptaa, which gives each border pixel in global coordinates, and must be computed in advance by calling ccbaGenerateGlobalLocs().
PIX * ccbaDisplayImage1 ( CCBORDA *ccba )
ccbaDisplayImage1() Input: ccborda Return: pix of image, or null on error Notes: (1) Uses local ptaa, which gives each border pixel in local coordinates, so the actual pixel positions must be computed using all offsets. (2) For the holes, use coordinates relative to the c.c. (3) This is slower than Method 2. (4) This uses topological properties (Method 1) to do scan conversion to raster This algorithm deserves some commentary. I first tried the following: - outer borders: 4-fill from outside, stopping at the border, using pixFillClosedBorders() - inner borders: 4-fill from outside, stopping again at the border, XOR with the border, and invert to get the hole. This did not work, because if you have a hole border that looks like: x x x x x x x x x x x x x x x o x x x x x x x x x if you 4-fill from the outside, the pixel 'o' will not be filled! XORing with the border leaves it OFF. Inverting then gives a single bad ON pixel that is not actually part of the hole. So what you must do instead is 4-fill the holes from inside. You can do this from a seedfill, using a pix with the hole border as the filling mask. But you need to start with a pixel inside the hole. How is this determined? The best way is from the contour. We have a right-hand shoulder rule for inside (i.e., the filled region). Take the first 2 pixels of the hole border, and compute dx and dy (second coord minus first coord: dx = sx - fx, dy = sy - fy). There are 8 possibilities, depending on the values of dx and dy (which can each be -1, 0, and +1, but not both 0). These 8 cases can be broken into 4; see the simple algorithm below. Once you have an interior seed pixel, you fill from the seed, clipping with the hole border pix by filling into its invert. You then successively XOR these interior filled components, in any order.
PIX * ccbaDisplayImage2 ( CCBORDA *ccba )
ccbaDisplayImage2() Input: ccborda Return: pix of image, or null on error Notes: (1) Uses local chain ptaa, which gives each border pixel in local coordinates, so the actual pixel positions must be computed using all offsets. (2) Treats exterior and hole borders on equivalent footing, and does all calculations on a pix that spans the c.c. with a 1 pixel added boundary. (3) This uses topological properties (Method 2) to do scan conversion to raster (4) The algorithm is described at the top of this file (Method 2). It is preferred to Method 1 because it is between 1.2x and 2x faster than Method 1.
PIX * ccbaDisplaySPBorder ( CCBORDA *ccba )
ccbaDisplaySPBorder() Input: ccba Return: pix of border pixels, or null on error Notes: (1) Uses spglobal pta, which gives each border pixel in global coordinates, one path per c.c., and must be computed in advance by calling ccbaGenerateSPGlobalLocs().
l_int32 ccbaGenerateGlobalLocs ( CCBORDA *ccba )
ccbaGenerateGlobalLocs() Input: ccba (with local chain ptaa of borders computed) Return: 0 if OK, 1 on error Action: this uses the pixel locs in the local ptaa, which are all relative to each c.c., to find the global pixel locations, and stores them in the global ptaa.
l_int32 ccbaGenerateSPGlobalLocs ( CCBORDA *ccba, l_int32 ptsflag )
ccbaGenerateSPGlobalLocs() Input: ccba ptsflag (CCB_SAVE_ALL_PTS or CCB_SAVE_TURNING_PTS) Return: 0 if OK, 1 on error Notes: (1) This calculates the splocal rep if not yet made. (2) It uses the local pixel values in splocal, the single path pta, which are all relative to each c.c., to find the corresponding global pixel locations, and stores them in the spglobal pta. (3) This lists only the turning points: it both makes a valid svg file and is typically about half the size when all border points are listed.
l_int32 ccbaGenerateSinglePath ( CCBORDA *ccba )
ccbaGenerateSinglePath() Input: ccba Return: 0 if OK, 1 on error Notes: (1) Generates a single border in local pixel coordinates. For each c.c., if there is just an outer border, copy it. If there are also hole borders, for each hole border, determine the smallest horizontal or vertical distance from the border to the outside of the c.c., and find a path through the c.c. for this cut. We do this in a way that guarantees a pixel from the hole border is the starting point of the path, and we must verify that the path intersects the outer border (if it intersects it, then it ends on it). One can imagine pathological cases, but they may not occur in images of text characters and un-textured line graphics. (2) Once it is verified that the path through the c.c. intersects both the hole and outer borders, we generate the full single path for all borders in the c.c. Starting at the start point on the outer border, when we hit a line on a cut, we take the cut, do the hold border, and return on the cut to the outer border. We compose a pta of the outer border pts that are on cut paths, and for every point on the outer border (as we go around), we check against this pta. When we find a matching point in the pta, we do its cut path and hole border. The single path is saved in the ccb.
l_int32 ccbaGenerateStepChains ( CCBORDA *ccba )
ccbaGenerateStepChains() Input: ccba (with local chain ptaa of borders computed) Return: 0 if OK, 1 on error Notes: (1) This uses the pixel locs in the local ptaa, which are all relative to each c.c., to find the step directions for successive pixels in the chain, and stores them in the step numaa. (2) To get the step direction, use 1 2 3 0 P 4 7 6 5 where P is the previous pixel at (px, py). The step direction is the number (from 0 through 7) for each relative location of the current pixel at (cx, cy). It is easily found by indexing into a 2-d 3x3 array (dirtab).
CCBORD * ccbaGetCcb ( CCBORDA *ccba, l_int32 index )
ccbaGetCcb() Input: ccba Return: ccb, or null on error
l_int32 ccbaGetCount ( CCBORDA *ccba )
ccbaGetCount() Input: ccba Return: count, with 0 on error
CCBORDA * ccbaRead ( const char *filename )
ccbaRead() Input: filename Return: ccba, or null on error
CCBORDA * ccbaReadStream ( FILE *fp )
ccbaReadStream() Input: stream Return: ccba, or null on error Format: ccba: %7d cc\n (num. c.c.) (ascii) (17B) pix width (4B) pix height (4B) [for i = 1, ncc] ulx (4B) uly (4B) w (4B) -- not req'd for reconstruction h (4B) -- not req'd for reconstruction number of borders (4B) [for j = 1, nb] startx (4B) starty (4B) [for k = 1, nb] 2 steps (1B) end in z8 or 88 (1B)
l_int32 ccbaStepChainsToPixCoords ( CCBORDA *ccba, l_int32 coordtype )
ccbaStepChainsToPixCoords() Input: ccba (with step chains numaa of borders) coordtype (CCB_GLOBAL_COORDS or CCB_LOCAL_COORDS) Return: 0 if OK, 1 on error Notes: (1) This uses the step chain data in each ccb to determine the pixel locations, either global or local, and stores them in the appropriate ptaa, either global or local. For the latter, the pixel locations are relative to the c.c.
l_int32 ccbaWrite ( const char *filename, CCBORDA *ccba )
ccbaWrite() Input: filename ccba Return: 0 if OK, 1 on error
l_int32 ccbaWriteSVG ( const char *filename, CCBORDA *ccba )
ccbaWriteSVG() Input: filename ccba Return: 0 if OK, 1 on error
char * ccbaWriteSVGString ( const char *filename, CCBORDA *ccba )
ccbaWriteSVGString() Input: filename ccba Return: string in svg-formatted, that can be written to file, or null on error.
l_int32 ccbaWriteStream ( FILE *fp, CCBORDA *ccba )
ccbaWriteStream() Input: stream ccba Return: 0 if OK; 1 on error Format: ccba: %7d cc\n (num. c.c.) (ascii) (18B) pix width (4B) pix height (4B) [for i = 1, ncc] ulx (4B) uly (4B) w (4B) -- not req'd for reconstruction h (4B) -- not req'd for reconstruction number of borders (4B) [for j = 1, nb] startx (4B) starty (4B) [for k = 1, nb] 2 steps (1B) end in z8 or 88 (1B)
l_int32 findNextBorderPixel ( l_int32 w, l_int32 h, l_uint32 *data, l_int32 wpl, l_int32 px, l_int32 py, l_int32 *pqpos, l_int32 *pnpx, l_int32 *pnpy )
findNextBorderPixel() Input: w, h, data, wpl (px, py), (current P) &qpos (input current Q; <return> new Q) (&npx, &npy) (<return> new P) Return: 0 if next pixel found; 1 otherwise Notes: (1) qpos increases clockwise from 0 to 7, with 0 at location with Q to left of P: Q P (2) this is a low-level function that does not check input parameters. All calling functions should check them.
PTA * getCutPathForHole ( PIX *pix, PTA *pta, BOX *boxinner, l_int32 *pdir, l_int32 *plen )
getCutPathForHole() Input: pix (of c.c.) pta (of outer border) boxinner (b.b. of hole path) &dir (direction (0-3), returned; only needed for debug) &len (length of path, returned) Return: pta of pts on cut path from the hole border to the outer border, including end points on both borders; or null on error Notes: (1) If we don't find a path, we return a pta with no pts in it and len = 0. (2) The goal is to get a reasonably short path between the inner and outer borders, that goes entirely within the fg of the pix. This function is cheap-and-dirty, may fail for some holes in complex topologies such as those you might find in a moderately dark scanned halftone. If it fails to find a path to any particular hole, it gives a warning, and because that hole path is not included, the hole will not be rendered.
void locateOutsideSeedPixel ( l_int32 fpx, l_int32 fpy, l_int32 spx, l_int32 spy, l_int32 *pxs, l_int32 *pys )
locateOutsideSeedPixel() Input: fpx, fpy (location of first pixel) spx, spy (location of second pixel) &xs, &xy (seed pixel to be returned) Notes: (1) the first and second pixels must be 8-adjacent, so |dx| <= 1 and |dy| <= 1 and both dx and dy cannot be 0. There are 8 possible cases. (2) the seed pixel is OUTSIDE the foreground of the c.c. (3) these rules are for the situation where the INSIDE of the c.c. is on the right as you follow the border: cw for an exterior border and ccw for a hole border.
CCBORDA * pixGetAllCCBorders ( PIX *pixs )
pixGetAllCCBorders() Input: pixs (1 bpp) Return: ccborda, or null on error
CCBORD * pixGetCCBorders ( PIX *pixs, BOX *box )
pixGetCCBorders() Input: pixs (1 bpp, one 8-connected component) box (xul, yul, width, height) in global coords Return: ccbord, or null on error Notes: (1) We are finding the exterior and interior borders of an 8-connected component. This should be used on a pix that has exactly one 8-connected component. (2) Typically, pixs is a c.c. in some larger pix. The input box gives its location in global coordinates. This box is saved, as well as the boxes for the borders of any holes within the c.c., but the latter are given in relative coords within the c.c. (3) The calculations for the exterior border are done on a pix with a 1-pixel added border, but the saved pixel coordinates are the correct (relative) ones for the input pix (without a 1-pixel border) (4) For the definition of the three tables -- xpostab, ypostab and qpostab -- see above where they are defined.
l_int32 pixGetHoleBorder ( CCBORD *ccb, PIX *pixs, BOX *box, l_int32 xs, l_int32 ys )
pixGetHoleBorder() Input: ccb (the exterior border is already made) pixs (for the connected component at hand) box (for the specific hole border, in relative coordinates to the c.c.) xs, ys (first pixel on hole border, relative to c.c.) Return: 0 if OK, 1 on error Notes: (1) we trace out hole border on pixs without addition of single pixel added border to pixs (2) therefore all coordinates are relative within the c.c. (pixs) (3) same position tables and stopping condition as for exterior borders
l_int32 pixGetOuterBorder ( CCBORD *ccb, PIX *pixs, BOX *box )
pixGetOuterBorder() Input: ccb (unfilled) pixs (for the component at hand) box (for the component, in global coords) Return: 0 if OK, 1 on error Notes: (1) the border is saved in relative coordinates within the c.c. (pixs). Because the calculation is done in pixb with added 1 pixel border, we must subtract 1 from each pixel value before storing it. (2) the stopping condition is that after the first pixel is returned to, the next pixel is the second pixel. Having these 2 pixels recur in sequence proves the path is closed, and we do not store the second pixel again.
PTA * pixGetOuterBorderPta ( PIX *pixs, BOX *box )
pixGetOuterBorderPta() Input: pixs (1 bpp, one 8-connected component) box (<optional> of pixs, in global coordinates) Return: pta (of outer border, in global coords), or null on error Notes: (1) We are finding the exterior border of a single 8-connected component. (2) If box is NULL, the outline returned is in the local coords of the input pix. Otherwise, box is assumed to give the location of the pix in global coordinates, and the returned pta will be in those global coordinates.
PTAA * pixGetOuterBordersPtaa ( PIX *pixs )
pixGetOuterBordersPtaa() Input: pixs (1 bpp) Return: ptaa (of outer borders, in global coords), or null on error
Zakariyya Mughal <firstname.lastname@example.org>
This software is copyright (c) 2014 by Zakariyya Mughal.
This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.