Page - 49 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

3.3.2. ExtractionofContourandDensitometric Information Inthecaseof in-vivoangiograms, theendocardialcontour issegmentedbyexperts incardiologyprior to reconstruction. Densitometric information is derived by means of digital subtraction angiography. From the initial frames of an angiographic sequence showing no contrast agent, a mask is deduced. Logarithmicsubtractionofmaskandcurrent frameisperformeddue to theexponentialattenuationof x-rays. To reduce noise and the inhomogeneous saturation of contrast agent within the ventricle, two frames before and after a frame are used for averaging. In the case of simulated angiograms, contour information isextractedbyborderdetection,whereasdensitometric information ismeasureddirectly. 3.4. SimulationofAngiographicProjections Both the presented reconstruction approach and the following evaluation strategy require the simula- tion of projections. Our model of the bi-planar angiographic device calculates the exact position of the x-ray sources and the image intensifier planes for the projections. For a given viewing direction, shape and pose parameter vector, a simulated projection of the SSM in image space is obtained in two steps. First, the polygonal model is converted into a 3-D binary image,V , whose values denote the presence/absence of contrast agent. Then, a projection is derived using ray-casting. Since densit- ometric information is expected to be linear for reconstruction, an exponential attenuation of x-rays hasnotbeen incorporated into the simulation process. 4. Results Thepresentedmethodsare implementedandevaluatedusingMatlabandtheImageSegmentationand Registration Toolkit (ITK) C++ library. To quantify the difference between original and recovered shape, twogeometricandthreevolumetricsimilaritymetricsaredefinedforcomparing thepolygonal models and the binary image representations, respectively. Anexemplary reconstruction result of the performed leave-one-out experiments is illustrated inFig.3. Figure3.Reconstructionexample showingoriginal shape (bright)andrecoveredshape (dark). 4.1. SimilarityMetrics Similarity of two polygonal models S1 and S2 is measured based on a given distance metric d: simd(S1,S2) = 1 2 (1 n ∑n i=1d(pi,S2)+ 1 m ∑m j=1d(qj,S1)),pi=1,...,n∈S1,qj=1,...,m∈S2. Distancemet- ricdmin isdefinedastheEuclideandistancebetweenpointpianditsclosestpointonS2:dmin(pi,S2) = 49