Abstract

Every object has a unique centroid. However, a given entity might be considered an object by itself or part of a larger object depending entirely on the scale at which it is viewed. We demonstrate that by tracking centroids of an image through a complete range of scales, a representation results that reveals some of the underlying structure of the image. We call this representation a centroid scale-space map. We show that this has a particularly simple form compared with other scale-space representations. The centroid scale-space map is formed by cross-correlating an input image f(x, y) with the windowed centroid kernel $(x+iy)\cdot \mathrm{circ}\left(\sqrt{x^2+y^2}/r\right)$. The zero-crossings of the cross-correlation outputs correspond to centroid locations. These zero-crossings are mapped against both the scale coordinate rand the space coordinates (x, y) to form a centroid scale-space map. A real-time optical correlator based on degenerate-four-wave mixing is suggested to perform the correlations.

© 1988 Optical Society of America