Circle size by fusion of pyramidal transform data

Bharath (2000) introduced a method of finding circular shapes in digital images by filtering the responses of low-level gradient operators with a rotating kernel function. The approach is related (but not identical to) a Hough transform circle detection procedure. To find circles of a particular size in an image, the size of the kernel function should be matched to the size of the target circle. This is a severe drawback in two circumstances: the size of the target circle is large, or the size of the circle is not exactly known. To address the first of these problems, a series of multi-rate operators was applied to decompose the image into sub-bands, yielding an over complete pyramidal image representation. In each of these sub-bands, the spatially rotating kernel was then applied to generate a series of shape transform spaces which are optimal for circles of various sizes. The decomposition level at which a strong response peak occurred provided a rough indication of the size of a circle in an image. Here, we make more precise predictions about circle size based on the fusion of responses at different levels of pyramidal response space.