Optimal geometric algorithms for digitized images on arrays with reconfigurable optical buses

Geometric algorithms play an important role in computer graphics and digital image analysis. This paper makes an improvement of computing geometric properties of labelled images using arrays with reconfigurable optical buses (AROB). For an N × N image, we first design two constant time algorithms for computing the leftmost one problem and for the component reallocation problem. Then, several geometric algorithms for the labelled images are derived. These include finding the border pixels, computing the perimeter and area, computing the convex hull, determining whether two figures are linearly separable, computing the smallest enclosing box, solving the nearest neighbor problems, and computing the width and diameter. The major contribution of this work is to design both time and cost optimal algorithms for these problems. To the best of our knowledge, the proposed algorithms are the first constant time algorithms for these problems on the labelled images.