Incremental Bit-Quads Count in Tree of Shapes

Bit-quads are \(2\times 2\) binary patterns which are counted within a binary image and can be used to compute attributes. Based on previous works which proposed an efficient algorithm to count bit-quads in component trees, in this paper, we discuss how we can count these patterns in tree of shapes by presenting two approaches. In the first one, we show how counting quads in component trees can be used to count them in tree of shapes by using the depth of the node as the value of pixels in a larger and interpolated image representation (used in an algorithm for constructing tree of shapes). In the second approach, we propose a novel algorithm which uses this larger image representation, but, the resulting quad counts are for the input image. In this way, our approach gives exactly the counts for the original image. We also provide experimental results showing that our algorithm is much faster than the non-incremental naive approach.