1 Review of RJMCMC. α(o, o ) = min(1, π(o ) Q(o ; o ) ), (1)

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1 Review of RJMCMC Starting with an initial state, RJMCMC proposes a new state o from a proposal distribution Q(o ; o) that depends on the current state o. The proposed state is probabilistically accepted as the next state in the Markov Chain according to the acceptance ratio α(o, o ) = min(, π(o ) Q(o ; o ) π(o) Q(o ; o) J F o o ), () where the target distribution π is the posterior distribution P (o Z) (Eqn. 8) and J is the Jacobian determinant of a dimension matching function F [], which for all of our move proposals simplifies to a constant value of one. Notice that we no longer need to worry about the intractable normalizing constant as it cancels out in the acceptance ratio. The algorithm is outlined in the table below. Algorithm. RJMCMC Input: Z, W, ITERMAX Output: o Initialization: o o for t = to ITERMAX choose a move c according to the distribution p c (o t ) propose o from the move-specific proposal Q c (o t ; ) sample u Uniform(, ) if log(u) < log(α(o t, o )) o t o else o t o t if P (o t Z) > P (o Z) o o t

2 2 Additional Results for S2L Ground-truth Annotation We compute the ground truth annotations by hand from four camera views, beginning by manually clicking on the head of each person in each view. For the people visible in more than one view, 3D head location is computed by triangulation of head viewing rays. For people visible in only one view, 3D head location is computed by intersecting the head viewing ray with a horizontal plane of average person height. For each computed (X,Y,Z) head location, we form a vertical 3D cylinder spanning from head position (X,Y,Z) to foot position (X,Y,). The projection of this 3D cylinder into each 2D view gives us an initial set of 2D annotated bounding boxes. Small manual adjustments to the position of these 2D rectangular boxes are made as needed to better align the boxes to the people in each view. Performance Metrics We evaluated each algorithm based on the MODA (Multiple Object Detection Accuracy) and MODP (Multiple Object Detection Precision) metrics from the CLEAR evaluation framework [2]. For a frame t, let G t i denote the annotated box and D t i the detection box. A detection is counted as correct if the overlap ratio, OL t i = Gt i D t i G t i Dt i, is greater than some threshold τ. Letting N t G be the total number of annotated objects, N t m the number of correct detections, m t the number of false negatives, and f t the number of false positives, MODP measures the localization quality of the correct detections, MODP t = N t m i= OLt i, Nm t while MODA is a detection accuracy measure taking into account both false negatives and false positives, For both metrics, larger values are better. MODA t = m t + f t. NG t 2

3 View View 5 MODP ASEF MODP Cascade MODP Parts MODA ASEF MODA Cascade MODA Parts View 6 View Figure : Evaluation results on S2L (MODP&MODA). 3

4 Table : Evaluation results on S2L (MODP&MODA). Overlap Method View View 5 View 6 View 8 Multiview Baseline Singleview POM+LP ASEF Cascade Parts Multiview Baseline Singleview POM+LP ASEF Cascade Parts Multiview Baseline Singleview POM+LP ASEF Cascade Parts Multiview Baseline Singleview POM+LP ASEF Cascade Parts Multiview Baseline Singleview POM+LP ASEF Cascade Parts

5 View View Recall ASEF Recall Cascade.5 Recall Parts.3.3. Precision ASEF Precision Cascade. Precision Parts View 6 View Figure 2: Evaluation results on S2L (Recall&Precision). 5

6 Table 2: Evaluation results on SL (Recall&Precision). Overlap Method View View 5 View 6 View 8 Multiview Baseline Singleview POM+LP ASEF Cascade Parts Multiview Baseline Singleview POM+LP ASEF Cascade Parts Multiview Baseline Singleview POM+LP ASEF Cascade Parts Multiview Baseline Singleview POM+LP ASEF Cascade Parts Multiview Baseline Singleview POM+LP ASEF Cascade Parts

7 References [] Green, P.: Reversible jump Markov chain Monte-Carlo computation and Bayesian model determination. Biometrika 82 (995) [2] Kasturi, R., Goldgof, D., Soundararajan, P., Manohar, V., Garofolo, J., Boonstra, M., Korzhova, V.,, Zhang, J.: Framework for performance evaluation of face, text, and vehicle detection and tracking in video: Data, metrics, and protocol. IEEE Transactions on Pattern Analysis and Machine Intelligence 3 (29)