boxaGetWhiteblocks()
Input: boxas (typically, a set of bounding boxes of fg components)
box (initial region; typically including all boxes in boxas;
if null, it computes the region to include all boxes
in boxas)
sortflag (L_SORT_BY_WIDTH, L_SORT_BY_HEIGHT,
L_SORT_BY_MIN_DIMENSION, L_SORT_BY_MAX_DIMENSION,
L_SORT_BY_PERIMETER, L_SORT_BY_AREA)
maxboxes (maximum number of output whitespace boxes; e.g., 100)
maxoverlap (maximum fractional overlap of a box by any
of the larger boxes; e.g., 0.2)
maxperim (maximum half-perimeter, in pixels, for which
pivot is selected by proximity to box centroid;
e.g., 200)
fract (fraction of box diagonal that is an acceptable
distance from the box centroid to select the pivot;
e.g., 0.2)
maxpops (maximum number of pops from the heap; use 0 as default)
Return: boxa (of sorted whitespace boxes), or null on error
Notes: (1) This uses the elegant Breuel algorithm, found in "Two
Geometric Algorithms for Layout Analysis", 2002, url: "citeseer.ist.psu.edu/breuel02two.html". It starts with the bounding boxes (b.b.) of the connected components (c.c.) in a region, along with the rectangle representing that region. It repeatedly divides the rectangle into four maximal rectangles that exclude a pivot rectangle, sorting them in a priority queue according to one of the six sort flags. It returns a boxa of the "largest" set that have no intersection with boxes from the input boxas. (2) If box == NULL, the initial region is the minimal region that includes the origin and every box in boxas. (3) maxboxes is the maximum number of whitespace boxes that will be returned. The actual number will depend on the image and the values chosen for maxoverlap and maxpops. In many cases, the actual number will be 'maxboxes'. (4) maxoverlap allows pruning of whitespace boxes depending on the overlap. To avoid all pruning, use maxoverlap = 1.0. To select only boxes that have no overlap with each other (maximal pruning), choose maxoverlap = 0.0. Otherwise, no box can have more than the 'maxoverlap' fraction of its area overlapped by any larger (in the sense of the sortflag) box. (5) Choose maxperim (actually, maximum half-perimeter) to represent a c.c. that is small enough so that you don't care about the white space that could be inside of it. For all such c.c., the pivot for 'quadfurcation' of a rectangle is selected as having a reasonable proximity to the rectangle centroid. (6) Use fract in the range [0.0 ... 1.0]. Set fract = 0.0 to choose the small box nearest the centroid as the pivot. If you choose fract > 0.0, it is suggested that you call boxaPermuteRandom() first, to permute the boxes (see usage below). This should reduce the search time for each of the pivot boxes. (7) Choose maxpops to be the maximum number of rectangles that are popped from the heap. This is an indirect way to limit the execution time. Use 0 for default (a fairly large number). At any time, you can expect the heap to contain about 2.5 times as many boxes as have been popped off. (8) The output result is a sorted set of overlapping boxes, constrained by 'maxboxes', 'maxoverlap' and 'maxpops'. (9) The main defect of the method is that it abstracts out the actual components, retaining only the b.b. for analysis. Consider a component with a large b.b. If this is chosen as a pivot, all white space inside is immediately taken out of consideration. Furthermore, even if it is never chosen as a pivot, as the partitioning continues, at no time will any of the whitespace inside this component be part of a rectangle with zero overlapping boxes. Thus, the interiors of all boxes are necessarily excluded from the union of the returned whitespace boxes. (10) USAGE: One way to accommodate to this weakness is to remove such large b.b. before starting the computation. For example, if 'box' is an input image region containing 'boxa' b.b. of c.c.:
// Faster pivot choosing
boxaPermuteRandom(boxa, boxa);
// Remove anything either large width or height
boxat = boxaSelectBySize(boxa, maxwidth, maxheight,
L_SELECT_IF_BOTH, L_SELECT_IF_LT,
NULL);
boxad = boxaGetWhiteblocks(boxat, box, type, maxboxes,
maxoverlap, maxperim, fract,
maxpops);
The result will be rectangular regions of "white space" that extend into (and often through) the excluded components. (11) As a simple example, suppose you wish to find the columns on a page. First exclude large c.c. that may block the columns, and then call:
boxad = boxaGetWhiteblocks(boxa, box, L_SORT_BY_HEIGHT,
20, 0.15, 200, 0.2, 2000);
to get the 20 tallest boxes with no more than 0.15 overlap between a box and any of the taller ones, and avoiding the use of any c.c. with a b.b. half perimeter greater than 200 as a pivot.
1.8.15