Fig. 4.

Simplification of 3D volumetric template matching to a 2D integral with a 1D template. (a) The entire template is shown, with the coordinates $\left(u_x,u_y,u_z\right)$ given in a consistent template space. Cross-sections of the template are shown along the y(b) and x(c) axes. Note that the template at $u_x=0\text{and}{u}_y=0$ are identical (d), while the template function itself can be expressed as a 1D function of distance from $\left(u_x,u_y\right)=(0,0).$