. Author manuscript; available in PMC: 2016 Dec 1.

Published in final edited form as: Comput Med Imaging Graph. 2015 Sep 25;46(0 3):277–290. doi: 10.1016/j.compmedimag.2015.09.002

Algorithm 1.

Multi-resolution regression-guided landmark detection

Input: An unseen MR brain image I

A set of learned regression forests {F_i} at different resolutions

Notations: ρ_p denotes a local patch centered at image point p

F(ρ_p) returns a predicted 3D displacement by forest F based on the local patch ρ_p

Output: Detected landmark location l

Init: l = the image center of I

for i from the coarsest scale index to the finest scale index do

Uniformly and sparsely sample a set of testing points P_Test = {p_j} within the bounding box indexed by l − b_i/2 and l + b_i/2, as shown in Fig. 5. (Here, b_i is the side-length vector of the bounding box B_i at resolution i, which gradually decreases as the resolution goes from coarse to fine.)

for each point p_j in P_Test do

count = 0, p = p_j; L = +Inf

while count ≤ MAX_JUMP do

if ||F_i(ρ_p)|| ≤ T_Len then break; endif

if L − ||F_i(ρ_p)|| ≤ ε then break; endif

if p + F_i(ρ_p) outside of image domain then break; endif

L = ||F_i(ρ_p)||; p = p + F_i(ρ_p); count = count + 1

end while

p_j = p

end for

l = argmin_{p∈P_Test}||F_i(ρ_p)||

end for

Output: l

In the above, T_Len is the threshold for controlling the minimum length for landmark jumping; ε enforces the length of point jumping to be decreasing with some toleration, and ε is usually set to a negative value close to 0.