nips nips2001 nips2001-193 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Yang Song, Luis Goncalves, Pietro Perona
Abstract: This paper presents an unsupervised learning algorithm that can derive the probabilistic dependence structure of parts of an object (a moving human body in our examples) automatically from unlabeled data. The distinguished part of this work is that it is based on unlabeled data, i.e., the training features include both useful foreground parts and background clutter and the correspondence between the parts and detected features are unknown. We use decomposable triangulated graphs to depict the probabilistic independence of parts, but the unsupervised technique is not limited to this type of graph. In the new approach, labeling of the data (part assignments) is taken as hidden variables and the EM algorithm is applied. A greedy algorithm is developed to select parts and to search for the optimal structure based on the differential entropy of these variables. The success of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled real image sequences.
Reference: text
sentIndex sentText sentNum sentScore
1 edu ¡ Abstract This paper presents an unsupervised learning algorithm that can derive the probabilistic dependence structure of parts of an object (a moving human body in our examples) automatically from unlabeled data. [sent-3, score-0.898]
2 The distinguished part of this work is that it is based on unlabeled data, i. [sent-4, score-0.184]
3 , the training features include both useful foreground parts and background clutter and the correspondence between the parts and detected features are unknown. [sent-6, score-1.13]
4 We use decomposable triangulated graphs to depict the probabilistic independence of parts, but the unsupervised technique is not limited to this type of graph. [sent-7, score-1.141]
5 In the new approach, labeling of the data (part assignments) is taken as hidden variables and the EM algorithm is applied. [sent-8, score-0.304]
6 A greedy algorithm is developed to select parts and to search for the optimal structure based on the differential entropy of these variables. [sent-9, score-0.641]
7 The success of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled real image sequences. [sent-10, score-0.558]
8 1 Introduction Human motion detection and labeling is a very important but difficult problem in computer vision. [sent-11, score-0.426]
9 Given a video sequence, we need to assign appropriate labels to the different regions of the image (labeling) and decide whether a person is in the image (detection). [sent-12, score-0.161]
10 To detect and label a moving human body, a feature detector/tracker (such as corner detector) is first run to obtain the candidate features from a pair of frames. [sent-14, score-0.355]
11 The combination of features is then selected based on maximum likelihood by using the joint probability density function formed by the position and motion of the body. [sent-15, score-0.391]
12 One key factor in the method is the probabilistic model of human motion. [sent-18, score-0.117]
13 In order to avoid exponential combinatorial search, we use conditional independence property of body parts. [sent-19, score-0.249]
14 target objects and background clutter with no identity attached to each feature. [sent-25, score-0.276]
15 This case is interesting because the candidate features can be acquired automatically. [sent-26, score-0.185]
16 Our algorithm leads to systems able to learn models of human motion completely automatically from real image sequences - unlabeled training features with clutter and occlusion. [sent-27, score-0.941]
17 We restrict our attention to triangulated models, since they both account for much correlation between the random variables that represent the position and motion of each body part, and they yield efficient algorithms. [sent-28, score-0.909]
18 Our goal is to learn the best triangulated model, i. [sent-29, score-0.633]
19 The distinguished part of this paper is that it is an unsupervised learning method based on unlabeled data, i. [sent-33, score-0.263]
20 , the training features include both useful foreground parts and background clutter and the correspondence between the parts and detected features are unknown. [sent-35, score-1.13]
21 Although we work on triangulated models here, the unsupervised technique is not limited to this type of graph. [sent-36, score-0.631]
22 In section 2 we summarize the main facts about the triangulated probability model. [sent-38, score-0.552]
23 In section 3 we address the learning problem when the training features are labeled, i. [sent-39, score-0.11]
24 , the parts of the model and the correspondence between the parts and observed features are known. [sent-41, score-0.566]
25 In section 4 we address the learning problem when the training features are unlabeled. [sent-42, score-0.11]
26 2 Decomposable triangulated graphs Discovering the probability structure (conditional independence) among variables is important since it makes efficient learning and testing possible, hence some computationally intractable problems become tractable. [sent-44, score-0.665]
27 The decomposable triangulated graph is another type of graph which has been demonstrated to be useful for biological motion detection and labeling [8, 1]. [sent-46, score-1.685]
28 A decomposable triangulated graph [1] is a collection of cliques of size three, where there is an elimination order of vertices such that when a vertex is deleted, it is only contained in one triangle and the remaining subgraph is again a collection of triangles until only one triangle left. [sent-47, score-1.325]
29 Decomposable triangulated graphs are more powerful than trees since each node can be thought of as having two parents. [sent-48, score-0.632]
30 Conditional independence among random variables (parts) can be described by a decombe the set of parts, and posable triangulated graph. [sent-50, score-0.64]
31 If the joint probability density function can be decomposed as a decomposable triangulated graph, it can ) 0 ) 1#! [sent-52, score-0.962]
32 We want to find the decomposable triangulated graph , such that is maximized. [sent-61, score-1.075]
33 is the probability of graph being the ’correct’ one given the observed data . [sent-62, score-0.146]
34 Here we use to denote both the decomposable graph and the conditional (in)dependence depicted by the graph. [sent-63, score-0.566]
35 From the previous section, a decomposable triangulated graph is represented by , then can be computed as follows, 8 D 7 ) S E U S C Q ) E ! [sent-65, score-1.075]
36 DC %¤9 3 Q @ @ I@ (2) w 1) I R UE where is differential entropy or conditional differential entropy [3] (we consider continuous random variables here). [sent-66, score-0.449]
37 Equation (2) is an approximation which converges to equality for due to the weak Law of Large numbers and definitions and properties of differential entropy [3, 2, 4, 5, 6]. [sent-67, score-0.189]
38 1 Greedy search Though for tree cases, the optimal structure can be obtained efficiently by the maximum spanning tree algorithm [2, 6], for decomposable triangulated graphs, there is no existing algorithm which runs in polynomial time and guarantees to the optimal solution [9]. [sent-70, score-1.108]
39 We develop a greedy algorithm to grow the graph by the property of decomposable graphs. [sent-71, score-0.677]
40 For each possible choice of (the last vertex of the last triangle), find the best which , then get the best child of edge as , i. [sent-72, score-0.15]
41 The next vertex is added one by one to the existing graph by choosing the best child of all the edges (legal parents) of the existing graph until all the vertices are added to the graph. [sent-75, score-0.426]
42 For each choice of , one such graph can be grown, so there are candidate graphs. [sent-76, score-0.221]
43 The final result is the graph with the highest among the graphs. [sent-77, score-0.146]
44 The algorithm is a greedy algorithm, with no guarantee that the global optimal solution could be found. [sent-80, score-0.154]
45 2 Computation of differential entropy - translation invariance R @ f 2 @ d G2E R @ f 2 @ d 2 @ ` E2 g In the greedy search algorithm, we need to compute and , . [sent-83, score-0.374]
46 If we assume that they are jointly Gaussian, then the differential entropy can be computed by , where is the dimension and is the covariance matrix. [sent-84, score-0.223]
47 } s R E" HI x x} q k i yxh { z |$ 7 F 7 a r v In our applications, position and velocity are used as measurements for each body part, but humans can be present at different locations of the scene. [sent-85, score-0.22]
48 , we can take one body part (for example ) as system for each triangle the origin, and use relative positions for other body parts. [sent-89, score-0.443]
49 £ V 1 s ¨ © In the greedy search algorithm, the differential entropy of all the possible triplets are needed and different triplets are with different origins. [sent-93, score-0.442]
50 " 1 and (4) ( From the above equations, we can first estimate the mean and covariance of (including all the body parts and without removing translation), then take the dimensions corresponding to the triangle and use equations (4) and (5) to get the mean and covariance for . [sent-97, score-0.483]
51 } ) R @ f 2 @ d 2 @ e E2 g s W s X s W 4 Unsupervised learning of the decomposable graph i 0 r2 ''%&%'% I 2 H 2 1 In this section, we consider the case when only unlabeled data are available. [sent-99, score-0.642]
52 Each sample , , is a group of detected features which contains the target object, but is unlabeled, which means the correspondence between the candidate features and the parts of the object is unknown. [sent-101, score-0.712]
53 For example when we run a feature detector (such as Lucas-Tomasi-Kanade detector [10]) on real image sequences, the detected features can be from target objects and background clutter with no identity attached to each feature. [sent-102, score-0.789]
54 We want to select the useful composite parts of the object and learn the probability structure from . [sent-103, score-0.358]
55 1 All foreground parts observed Here we first assume that all the foreground parts are observed for each sample. [sent-105, score-0.63]
56 If the labeling for each is taken as a hidden variable, then the EM algorithm can be used to learn the probability structure and parameters. [sent-106, score-0.363]
57 Our method was developed from [11], but here we learn the probabilistic independence structure and all the candidate features are with the same type. [sent-107, score-0.371]
58 If contains features, then is an -dimensional vector with each element taken a value from ( is the background clutter label). [sent-109, score-0.272]
59 The observations for the EM algorithm are , the hidden variables are , and the parameters to optimize are the probability (in)dependence structure (i. [sent-110, score-0.152]
60 the decomposable triangulated graph) and parameters for its associated probability density function. [sent-112, score-0.929]
61 Under the labeling hypoth, is divided into the foreground features , which are parts of the esis object, and background (clutter) . [sent-119, score-0.667]
62 If the foreground features are independent of , then, clutter 2 (9) 5q ) P) I G H% 2 2 xw q GB% G H% P) I #%" P) I ! [sent-120, score-0.397]
63 % G H% G B% ) P) I % 1 5q Q %$q R H g E R w 5 R 5 FD E ) 1 2 5q q % G H% q q 2 For simplicity, we will assume the priors are the same for different , and are the same for different graph structures. [sent-121, score-0.146]
64 If we assume uniform background densities [11, 8], then , where is the volume of the space a background feature lies in, is the same for different . [sent-122, score-0.161]
65 However, if there is one hypothesis labeling that is much better than other hypotheses,, i. [sent-126, score-0.221]
66 4¤% C I 3¤% 9 3 £ # % 5' @ q f 2 ' @5 5 q d 2 ' @5 q g 2 ) 7 I 7 ¡ 1 5 q 5 ) 'q where and are measurements corresponding to the best labeling . [sent-131, score-0.294]
67 Comparing with equation (2) and also by the weak law of large numbers, we know for iteration , if the best hypothesis is used as the ’true’ labeling, then the decomposable triangulated graph structure can be obtained through the algorithm described in section 3. [sent-132, score-1.322]
68 One approximation we make here is that the best hypothesis labeling for each is really dominant among all the possible labelings so that hard assignment for labelings can be used. [sent-133, score-0.384]
69 2 Dealing with missing parts (occlusion) So far we assume that all the parts are observed. [sent-140, score-0.458]
70 In the case of some parts missing, the measurements for the missing parts can be taken as additional hidden variables [11], and the EM algorithm can be modified to handle the missing parts. [sent-141, score-0.709]
71 2 q£ 2 q¢ For each hypothesis , let denote the measurements of the observed parts, be the measurements for the missing parts, and be the measurements of the whole object (to reduce clutter in the notation, we assume that the dimensions can be and to obtain sorted in this way). [sent-142, score-0.559]
72 For each EM iteration, we need to compute the differential entropies and then with its parameters. [sent-143, score-0.184]
73 % ¢ % ( Where (12) All the expectations are conditional expectations with respect to and decomposable graph structure . [sent-149, score-0.617]
74 Therefore, are the measurements of the observed foreground parts under . [sent-150, score-0.389]
75 Since is Gaussian distributed, conditional expectation and can be computed from observed parts and the mean and covariance matrix of . [sent-151, score-0.282]
76 ' q¢ w 2 H s R q £ E2 5 Experiments We tested the greedy algorithm on labeled motion capture data (Johansson displays) as in [8], and the EM-like algorithm on unlabeled detected features from real image sequences. [sent-152, score-0.808]
77 1 Motion capture data Our motion capture data consist of the 3-D positions of 14 markers fixed rigidly on a subject’s body. [sent-154, score-0.233]
78 From the estimated mean and covariance, we can compute differential entropies for all the possible triplets and pairs and further run the greedy search algorithm to find the approximated best triangulated model. [sent-157, score-1.06]
79 Figure 2(a) shows the expected likelihood (differential entropy) of the estimated joint pdf, of the best triangulated model from the greedy algorithm, of the hand-constructed model from [8], and of randomly generated models. [sent-158, score-0.806]
80 The greedy model is clearly superior to the hand-constructed model and the random models. [sent-159, score-0.111]
81 The gap to the original joint pdf is partly due to the strong conditional independence assumptions of the triangulated model, which are an approximation of the true data’s pdf. [sent-160, score-0.731]
82 Since these datasets were generated from 50 triangulated models, the greedy algorithm (solid curve) can match the true model (dashed curve) extremely well. [sent-162, score-0.706]
83 The solid line with error bars are the expected likelihoods of random triangulated models. [sent-163, score-0.552]
84 2 Real image sequences There are three types of sequences used here: (I) a subject walks from left to right (Figure 3(a,b)); (II) a subject walks from right to left; (III) a subject rides a bike from left to right (Figure3(c,d)). [sent-166, score-0.333]
85 Left-to-right walking motion models were learned from type I sequences and tested on all types of sequences to see if the learned model can detect left-to-right walking and label the body parts correctly. [sent-167, score-1.02]
86 The candidate features were obtained from a Lucas-Tomasi-Kanade algorithm [10] on two frames. [sent-168, score-0.228]
87 We used two frames to simulate the difficult situation, where due to extreme body motion or to loose and textured clothing and occlusion, tracking is extremely unreliable and each feature’s lifetime is short. [sent-169, score-0.365]
88 1, one approximation we made is taking the best hypothesis labeling instead of summing over all the possible hypotheses (equation (11)). [sent-172, score-0.266]
89 Figure 4(c) shows the learned decomposable triangulated probabilistic structure. [sent-180, score-0.968]
90 The red dots (with letter labels) are the maximum likelihood configuration from the left-to-right walking model. [sent-183, score-0.31]
91 The horizontal bar at the bottom left of each frame shows the likelihood of the best configuration. [sent-184, score-0.155]
92 The dots (either filled or empty) are the features selected by Tomasi-Kanade algorithm [10] on two frames. [sent-187, score-0.191]
93 The filled dots (with letter labels) are the maximum likelihood configuration from the left-to-right walking model. [sent-188, score-0.31]
94 The horizontal bar at the bottom left of each frame shows the likelihood of the best configuration. [sent-189, score-0.155]
95 the likelihood is greater than the threshold, a left-to-right walking person is detected. [sent-195, score-0.232]
96 The detection rate is 100% for the left-to-right walking vs. [sent-196, score-0.235]
97 right-to-left walking, and 87% for the left-to-right walking vs. [sent-197, score-0.167]
98 6 Conclusions In this paper we have described a method for learning the structure and parameters of a decomposable triangulated graph in an unsupervised fashion from unlabeled data. [sent-199, score-1.324]
99 We have applied this method to learn models of biological motion that can be used to reliably detect and label biological motion. [sent-200, score-0.327]
100 Perona, “Monocular perception of biological motion in johansson displays”, Computer Vision and Image Understanding, 81:303–327, 2001. [sent-238, score-0.266]
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