Circle detection of edge images can involve significant time and memory requirements, particularly if the circles have unknown radii over a large range. We describe an algorithm that processes an edge image in a single linear pass, compiling statistics of connected components that can be used by two distinct least square methods. Because the compiled statistics are all sums, these components can then be quickly merged without any further examination of image pixels. Fusing multiple circle detectors allows more powerful circle detection. The resulting algorithm is of linear complexity in the number of image pixels, and quadratic complexity in a much smaller number of cluster statistics.