Fig. 4.

Ellipsoids of the confidence regions for the parameters of 2D similarity transformation (left and middle) and the coordinates (0,0) (right). The confidence regions were estimated using identical copies 2D reference image (top-right image in Fig. 1). For transformation parameters, we first computed confidence region in the four-dimensional space of the parameters, and then projected the region on the 2D parameter spaces of the X-translation and Y-translation (left), and the scale and theta (middle). Blue: region of 68.5% confidence; green: region of 95% confidence; and orange: region of 99% confidence. Because we used identical copies of the reference image, the confidence regions are less than a pixel wide. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)