Filling by quadrants or octants

Abstract Filling by quadrants or by octants is shown to be executable in time proportional to the lenght of the border multiplied by n, the logarithm of the diameter of the image. The underlying data structure is the linear quadtree in two dimensions or the linear octtree in three dimensions. The input is the border to be filled while the output is the linear quad or octtree representing the filled region(s). The latter can be a set of connected or disjoint black blocks. The basic idea behind the algorithm is to allow the region to grow “inwards” while restraining its growth “outwards” by the use of the block-bits technique introduced by the authors in a previous paper. The new features introduced by this paper are: (i) the low worst-case time complexity, as compared with previous algorithms, (ii) the fact that the basic space requirements consist of the input, output and 4n or 8n pointers, and (iii) its 3D implementation. The last capability has been developed for medical imaging purposes and 3D modelling.

[1]  Irene Gargantini,et al.  An effective way to represent quadtrees , 1982, CACM.

[2]  Irene Gargantini,et al.  Counting regions, holes, and their nesting level in time proportional to the border , 1984, Comput. Vis. Graph. Image Process..

[3]  David M. Mark,et al.  Linear Quadtrees from Vector Representations of Polygons , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Martti Mäntylä,et al.  Ray-casting and block model conversion using a spatial index , 1984 .

[5]  T. Pavlidis.  Algorithms for Graphics and Image Processing , 1981, Springer Berlin Heidelberg.

[6]  Michael Laurence Rhodes.  Interactive object isolation from parallel image planes. , 1978 .

[7]  Hanan Samet,et al.  On Encoding Boundaries with Quadtrees , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Theodosios Pavlidis.  Contour filling in raster graphics , 1981, SIGGRAPH '81.

[9]  Irene Gargantini,et al.  Linear quadtrees: A blocking technique for contour filling , 1984, Pattern Recognit..

[10]  Irene Gargantini,et al.  Linear octtrees for fast processing of three-dimensional objects , 1982, Comput. Graph. Image Process..

[11]  Hanan Samet,et al.  Region representation: quadtrees from boundary codes , 1980, CACM.

[12]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.

[13]  Theo Pavlidis,et al.  Filling algorithms for raster graphics , 1979 .

[14]  M. V. S. Ramanath,et al.  Improvements to a recent 3d-border algorithm , 1985, Pattern Recognit..

[15]  T. Walsh.  On the size of quadtrees generalized to d-dimensional binary pictures , 1985 .