Human Detection in Video over Large Viewpoint Changes

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1252 G. Duan, H. Ai, and S. Lao memory requirements impractical. With the distance of two granules defined in Sec. 3.1, two effective constraints are introduced into I 2 CF : 1)Motivated by [5], the first pair of granules in I 2 CF is constrained as d(g i 1, g j 1 ) ≤ T 1. 2) Considering of the consistency in one frame or two near video frames, we constrain that the second pair of granules in I 2 CF is in the neighborhood of the first pair as shown in Fig. 2 (d): d(g i 1, g i 2) ≤ T 2 , d(g j 1 , gj 2 ) ≤ T 2. (7) We set T 1 = 8, T 2 = 4 in our experiments. Table 1: Learning algorithm of I 2 CF . Input: Sample set S = {(x i , y i )|1 ≤ i ≤ m} where y i = ±1. Initialize: Cell space (CS) with all possible cells and empty I 2 CF . Output: The learned I 2 CF . Loop: – Learn the first pair of granules as [5]. Denote the best f pairs as a set F . – Construct a new set CS’: In each cell of CS’, the first pair of granules is from F , the second pair of granules is generated by Eq. 7 and its mode is A-mode, D-mode or C-mode. Calculate Z value of I 2 CF by adding each cell in CS’. – Select the cell with the lowest Z value, denoted as c ∗ . Add c ∗ to I 2 CF . – Refine I 2 CF by replacing one or two granules in it without changing the mode. Heuristically learning I 2 CF starts with an empty I 2 CF . Each time select the most discriminative cell and add it to I 2 CF . The discriminability of a weak feature is measured by Z value, which reflects the classification power of the weak classifier as [17]: Z = 2 ∑ √ W+W j −, j (8) j where W j + is the weight of positive samples that fall into the j th bin while W j − is that of negatives. The less Z value is, the more discriminative a weak feature is. The learning algorithm of I 2 CF is summarized in Table 1. (See more details in [5] [16].) 4 EMC-Boost We propose the EMC-Boost to co-cluster the sample space and discriminative features automatically. A perceptual clustering problem is shown in Fig. 3 (a)- (c). EMC-Boost consists of three components, Cascade Component (CC), Mixed Component (MC) and Separated Component (SC). The three components are combined to become EMC-Boost. In fact, SC is similar to MC-Boost [13], which is the reason that our boosting algorithm is named as EMC-Boost. In the following descriptions, we formulate the three components explicitly first, and then demonstrate the learning algorithms, and summarize EMC-Boost at the end of this section.
Human Detection in Video over Large Viewpoint Changes 1253 CC MC Cluster (b) SC Classifier (a) (c) (d) Fig. 3: A perceptual clustering problem in (a)-(c) and a general EMC-Boost in (d) where CC, MC and SC are three components of EMC-Boost. 4.1 Three components CC/MC/SC CC deals with a standard 2-class classification problem that can be solved by any boosting algorithm. MC and SC deal with K clusters. We formulate the detectors of MC or SC as K strong classifiers, each of which is a linear combination of weak learners H k (x) = ∑ t α kth kt (x), k = 1, · · · , K with a threshold θ k (default is 0). Note that the K classifiers H k (x), k = 1, · · · , K are same in MC with K different thresholds θ k , which means H 1 (x) = H 2 (x) = · · · = H k (x), but they are totally different in SC. We present MC and SC uniformly below. The score y ik of the i th sample belonging to the k th clusters can be computed as y ik = H k (x i )−θ k . Therefore, the probability of x i belonging to the k th cluster 1 is P ik (x) = . For aggregating all scores of one sample on K classifiers, 1+e −y ik we formulate Noisy-OR like [18] [13] as P i (x) = 1 − K∏ (1 − P ik (x i )). (9) k=1 The cost function is defined as J = ∏ i P ti i (1 − P i) 1−ti where t i ∈ {0, 1} is the label of i th sample, which is equivalent to maximize the log-likelihood log J = ∑ i t i log P i + (1 − t i ) log(1 − P i ). (10) 4.2 Learning algorithms of CC/MC/SC The learning algorithm of CC is directly Real Adaboost [17]. The learning algorithm of MC or SC is different from that of CC. MC and SC learn weak classifiers to maximize ∑ K ∑ k i w kih kt (x i ) and ∑ i w kih kt (x i ) respectively at t th round of boosting. Initially, the sample weights are: 1) For positives, w ki = 1 if x i ∈ k and w ki = 0 otherwise, where i denotes the i th sample and k denotes the k th cluster or classifier; 2) For all negatives we set w ki = 1/K. Following the AnyBoost method [19], we set the sample weights as the derivative of the cost function
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