Seite - 50 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

minqj∈S2 |pi−qj|. Distancemetricdorthodenotes theEuclideandistancebetweenpi and thepointob- tainedby intersectingS2 with the surfacenormalatpi: dortho(pi,S2) = |pi−surfn(pi)∩S2|. Let |V |denote the volume of a 3-D binary imageV . Volume conformity is measured by calculating thedifferenceofvolumes(DOV):simDOV = 1−abs(|Vorig|−|Vrec|)/|Vorig|. Toassessshapeconfor- mity, the volume of differences (VOD) metric is used: simVOD = 1−|xor(Vorig,Vrec)|/|Vorig|. An alternative metric for shape conformity, derived from kappa statistic, quantifies the overlap between twobinarymasks: simκ= 2|V1∪V2|/(|V1|+ |V2|). 4.2. EvaluationbasedonSimulatedData Evaluation with simulated data is performed based on leave-one-out experiments. From the 20 seg- mentedCTdatasets, allbutoneareused to learnaSSM.SimulatedangiogramsfromRAOandLAO viewarecalculated for the left-outdatasetasdescribed inSec.3.4, andfromtheseangiogramsshape is recovered by fitting the learned SSM. The recovered shape is compared with the segmented shape of the left-out data set using the defined similarity metrics. This procedure is repeated for each data set. TheDOVmetric inTab.1shows that theoriginalvolume isapproximatedathighaccuracy. This is essential for assessingvolume-based diagnostic parameters, like EF. Concerningshape conformity we can see that a high overlap between the two shapes is achieved, although theVOD is still im- provable. The distance metrics dmin and dortho are near the mean reconstruction error of 2.3 mm [11]. Sim. Metric Mean Std. Min. Max. dmin (mm) 2.61 0.65 1.65 3.53 dortho (mm) 2.49 0.77 1.38 3.72 DOV (%) 94.56 3.55 87.35 98.73 VOD(%) 78.17 5.30 68.88 84.91 κ (%) 87.12 2.53 82.54 90.18 Table1. EvaluationofLVshaperecovery fromsimulatedangiograms. 4.3. EvaluationbasedonRealPatientData For three patients, a corresponding CT image is available for the RAO/LAO in-vivo angiograms. Note that this allows an accurate evaluation of our approach since the true 3-D LV shape is exactly knownfromCT.Evaluationbasedonthe three in-vivoangiogramsisperformedasfollows: 1)aSSM is learned from 19 of the 20 data sets, with the CT data set corresponding to the angiograms being excluded, 2) the model is fit to interpolated angiographic RAO/LAO frames of a single cardiac cycle showing the LV at 65% of the heart phase, and 3) the recovered shape is compared with the true 3-D shape of the excluded CT data set using the defined similarity metrics. The angiograms are acquired using a Siemens Bicor and a Siemens AXIOM Artis dBC system, capturing images of 512×512 pixels and 8-bit gray level depth at a frame-rate of 25 fps. For temporal registration with CT data in step 2, the ECG information accompanying the angiograms is utilized. The results for three in-vivo angiograms are given in Tab. 2. Our experiments indicate that values similar to the evaluation with simulated data are achieved, although the number of data sets is relatively small. The best shape conformity is achieved forexample#2. Forexample#3, the reconstructionyields suboptimal results. 50