Page - 48 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

mode #1 mode #2 mode #3 +2 √ λi mean −2 √ λi Figure2. First threemodesofvariationof theLVSSM. model space to image space the following equation is used: y =R((x¯+Φb)s+T). Both shape parameter vector b and the parameters for pose p= {R,s,T}, i.e. rotation matrixR, scale factor s and translation vectorT, have to be found so that the registration error is minimized. Unlike [4] and [1],wederiveR fromEulerangles to reduce thedimensionalityof the registrationproblem. Orienta- tion in 3-D space is thus described using 3 angles, i.e.Rα,β,γ, instead of a 3×3 matrix. To generate statistically plausible shapes [2], b is constrained by±2√λi. In contrast to [4] and [1], we exploit the training data to derive constraints for p. The training instances in model space are transformed to image space and the range of the pose vector components is analyzed. Note that this can be re- gardedasadditional a-priori information. Tominimizeourcost function, theNelder-Meadalgorithm is applied. Experiments showed that optimizing pose and shape sequentially is more efficient than optimizingboth simultaneously. 3.3.1. CostFunction Our cost function depends on the shape and the pose parameter vector and incorporates both contour and densitometric information derived from the given projectionsPi and the simulated projections P ′i(b,p): (b,p) = ∑nP i=1(ωC C(Pi,P ′ i(b,p))+ωD D(Pi,P ′ i(b,p))). Contour-related error C is ob- tainedbyequiangularsamplingof thegivenandthesimulatedcontourandbycalculating theSSDfor the sampled points. As density-related error D, the sum of squared difference metric is used. Total error is definedas theweightedsum of C and D over allnP = 2projections. 48