nips nips2012 nips2012-83 knowledge-graph by maker-knowledge-mining

83 nips-2012-Controlled Recognition Bounds for Visual Learning and Exploration


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Author: Vasiliy Karasev, Alessandro Chiuso, Stefano Soatto

Abstract: We describe the tradeoff between the performance in a visual recognition problem and the control authority that the agent can exercise on the sensing process. We focus on the problem of “visual search” of an object in an otherwise known and static scene, propose a measure of control authority, and relate it to the expected risk and its proxy (conditional entropy of the posterior density). We show this analytically, as well as empirically by simulation using the simplest known model that captures the phenomenology of image formation, including scaling and occlusions. We show that a “passive” agent given a training set can provide no guarantees on performance beyond what is afforded by the priors, and that an “omnipotent” agent, capable of infinite control authority, can achieve arbitrarily good performance (asymptotically). In between these limiting cases, the tradeoff can be characterized empirically. 1

Reference: text


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 We focus on the problem of “visual search” of an object in an otherwise known and static scene, propose a measure of control authority, and relate it to the expected risk and its proxy (conditional entropy of the posterior density). [sent-2, score-0.683]

2 We show that a “passive” agent given a training set can provide no guarantees on performance beyond what is afforded by the priors, and that an “omnipotent” agent, capable of infinite control authority, can achieve arbitrarily good performance (asymptotically). [sent-4, score-0.376]

3 1 Introduction We are interested in visual learning for recognition of objects and scenes embedded in physical space. [sent-6, score-0.235]

4 Rather than using datasets consisting of collections of isolated snapshots, however, we wish to actively control the sensing process during learning. [sent-7, score-0.296]

5 Visual learning is thus a process of discovery, literally uncovering occluded portions of an object or scene, and viewing it from close enough that all structural details are revealed. [sent-9, score-0.306]

6 1 We call this phase of learning exploration or mapping, accomplished by actively controlling the sensor motion within a scene, or by manipulating an object so as to discover all aspects. [sent-10, score-0.445]

7 2 Once exploration has been performed, one has a model (or “map” or “representation”) of the scene or object of interest. [sent-11, score-0.505]

8 One can then attempt to detect, localize or recognize a particular object or scene, or a class of them, provided intra-class variability has been exposed during exploration. [sent-12, score-0.27]

9 This phase can yield localization – where one wishes to recognize a portion of a mapped scene and, as a byproduct, infer the pose relative to the map – or search where a particular object mapped during the exploration phase is detected and localized within an otherwise known scene. [sent-13, score-0.684]

10 2 Note that we are not suggesting that one should construct a three-dimensional (3-D) model of an object or a scene for recognition, as opposed to using collections of 2-D images. [sent-16, score-0.418]

11 The multiple images must portray the same scene or object, lest one cannot attribute the variability in the data to nuisance factors as opposed to intrinsic variability of the object of interest. [sent-19, score-0.493]

12 1 where a known object is sought in an unknown map, exploration and search have to be conducted simultaneously. [sent-22, score-0.459]

13 Within this scenario, exploration and search can be framed as optimal control and optimal stopping time problems. [sent-23, score-0.358]

14 In this manuscript we consider the problem of detecting and estimating discrete parameters of an unknown object in a known environment. [sent-26, score-0.285]

15 Discuss the tradeoff between performance in a visual decision task and the control authority that the explorer possesses. [sent-31, score-0.85]

16 This tradeoff is akin the tradeoff between rate and distortion in a communication system, but it pertains to decision and control tasks, as opposed to the transmission of data. [sent-32, score-0.349]

17 We characterize this tradeoff for the simple case of a static environment, where control authority relates to reachability and energy. [sent-33, score-0.62]

18 Discuss and test algorithms for visual search based on the maximization of the conditional entropy of future measurements and the proxies of this quantity. [sent-35, score-0.452]

19 These algorithms can be used to locate an unknown object in unknown position of a known environment, or to perform change detection in an otherwise known map, for the purpose of updating it. [sent-36, score-0.331]

20 1 Related prior work Active search and recognition of objects in the scene has been one of the mainstays of Active Perception in the eighties [2, 3], and has recently resurged (see [4] and references therein). [sent-40, score-0.39]

21 Active recognition using next-best-view generation and object appearance is discussed in [6] where authors use PCA to embed object images in a linear, low dimensional space. [sent-42, score-0.558]

22 More recently, information driven sensor control for object recognition was used in [7, 8, 9], who deal with visual and sonar sensors, but take features (e. [sent-44, score-0.639]

23 A utility function that accounts for occlusions, viewing angle, and distance to the object is proposed in [10] who aim to actively learn object classifiers during the training stage. [sent-47, score-0.548]

24 Exploration and learning of 3D object surface models by robotic manipulation is discussed in [11]. [sent-48, score-0.282]

25 The case of object localization (and tracking if object is moving) is discussed in [12]; information-theoretic approach for solving this problem using a sensor network is described in [13]. [sent-49, score-0.564]

26 With regards to models, our work is different in several aspects: instead of choosing the next best view on a sphere centered at the object, we model a cluttered environment where the object of interest occupies a negligible volume and is therefore fully occluded when viewed from most locations. [sent-52, score-0.419]

27 Third, given the significance of quantization-scale and occlusions in a visual recognition task, we model the sensing process such that it accounts for both. [sent-54, score-0.246]

28 We use the problem of visual search (finding a not previously seen object in a scene) as a motivation. [sent-64, score-0.407]

29 Constraints on the controller enter through f ; photometric nuisances, quantization and occlusions enter through the measurement map h. [sent-67, score-0.297]

30 1 Signal models The simplest model that includes both scaling and occlusion nuisances is the “cartoon flatland”, where a bounded subset of R2 is populated by self-luminous line segments, corresponding to clutter objects. [sent-70, score-0.401]

31 The number of objects in the scene C is the clutter density parameter that can possibly grow to be infinite in the limit. [sent-75, score-0.499]

32 Each object is described by its center (ck ), length (lk ), binary orientation (ok ), and radiance function supported on the segment ⇢k . [sent-76, score-0.358]

33 R+ ] (3) An agent can move continuously throughout the search domain. [sent-78, score-0.249]

34 We take the state gt 2 R2 to be its current position, ut 2 R2 the currently exerted move, and assume trivial dynamics: gt+1 = gt + ut . [sent-79, score-0.942]

35 More complex agents where gt 2 SE(3) can be incorporated without conceptual difficulties. [sent-80, score-0.234]

36 The measurement model is that of an omnidirectional m-pixel camera, with each entry of yt 2 Rm in (2) given by: Z (i+ 1 ) 2⇡ Z 1 2 m yt (i) = ⇢`(✓,gt ) (z)d✓d⌧ + nt (i), with z = (⌧ cos(✓), ⌧ sin(✓)) (4) (i 1 2⇡ 2) m 0 where is the angle subtended by each pixel. [sent-81, score-0.666]

37 The index of the object (clutter or object of interest) that contributes to the image is denoted by `(✓, gt ) and is defined as: ✓ ◆ n o l k lk ok `(✓, gt ) = arg min k 9(sk , k ) 2 [ , ] ⇥ R+ s. [sent-84, score-1.128]

38 ck , lk , and ok ˆ are k-th segment center, length, and orientation. [sent-87, score-0.251]

39 In order to design control sequences to minimize risk, we need to evaluate the uncertainty of future measurements, those we have not yet measured, which are a function of the control action to be taken. [sent-95, score-0.4]

40 3 We first describe the general case of visual exploration where the environment is unknown. [sent-97, score-0.287]

41 The density can be decomposed as a product of likelihoods since knowledge of environment (⇠) and location (gt ) is sufficient to predict measurement yt up to Gaussian noise. [sent-107, score-0.554]

42 In this paper we focus on visual search of a particular object in an otherwise known environment, so marginalization is only performed with respect to a single object in the environment, x, whose parameters are discrete, but otherwise analogous to (6): p(x) = U {0, . [sent-109, score-0.677]

43 , |X | object with parameters (ci , li , oi , ⇢i ) and write ⇠i = (xi , 1 , . [sent-118, score-0.239]

44 , C ) to denote the scene with known clutter objects 1 , . [sent-121, score-0.448]

45 This depends upon whether ut is sufficiently exciting, a “richness” condition that has been extensively used in the identification and adaptive control literature [17, 18], which guarantees that the state trajectory g t explores the space of interest. [sent-130, score-0.421]

46 Under this scenario it is easy to prove that, averaging over the possible scenes and initial agent locations, the probability of error approaches chance (i. [sent-134, score-0.225]

47 that given by the prior distribution) as clutter density and/or the environment volume increase. [sent-136, score-0.395]

48 Full control on g t : if the control action can take the “omnipotent agent” anywhere, and infinite time is available to collect measurements, then the conditional entropy H(x|y t ) decreases asymptotically to zero thus providing arbitrarily good recognition rate in the limit. [sent-138, score-0.659]

49 yt+T ) 4 In general, there is a tradeoff between the ability to gather new information through suitable control actions, which we name “control authority”, and the recognition rate. [sent-151, score-0.294]

50 In the sequel we shall propose a measure for the “control authority” over the sensing process; later in the paper we will consider conditional entropy as a proxy (upper bound) on probability of error and evaluate empirically how control authority affects the conditional entropy decrease. [sent-152, score-1.092]

51 1 Control authority Unlike the passive case, in the controlled scenario time plays an important role. [sent-154, score-0.446]

52 If objects in the scene move, this can be done only at an expense in energy, and achieving asymptotic performance may not be possible under control limitations. [sent-157, score-0.438]

53 Control authority depends on (i) the controller u, as measured for instance by a norm5 kuk : U [0, T ] ! [sent-160, score-0.501]

54 We propose to measure control authority in the following manner: associate to each pair of locations in the state space (go , gf ) and a given time horizon T the cost kuk required to move from go at time t = 0 to gf at time t = T along a minimum cost path i. [sent-162, score-1.218]

55 J⇠ (go , gf , T ) = inf kuk (13) u : gu (0)=go ,gu (T )=gf ⇠ where gu (t) is the state vector at time t under control u. [sent-165, score-0.503]

56 If gf is not reachable from go in time T we set J⇠ (go , gf , T ) = 1. [sent-166, score-0.662]

57 This will depend on the dynamical properties of the agent g = f (g, u) (or ˙ gt+1 = f (gt , ut ) for discrete time) as well as on the scene ⇠ where the agent has to navigate through while avoiding obstacles. [sent-167, score-0.74]

58 The control authority (CA) can be measured via the volume of the reachable space for fixed control cost, and will be a function of the initial configuration g0 and of the scene ⇠, i. [sent-168, score-1.095]

59 CA(k, go , ⇠) = V ol{gf : J⇠ (g0 , gf , k)  1} (14) If instead one is interested in average performance (e. [sent-171, score-0.319]

60 the possible scene distributions with fixed clutter density), a reasonable measure is the average of smallest volume (as g0 varies) of the reachable space with a unit cost input ⇥ ⇤ . [sent-176, score-0.546]

61 CA(k) = E⇠ inf CA(k, go , ⇠) (15) go If planning on an indefinitely long time horizon is allowed, then one would minimize J(go , gf , T ) over time T : . [sent-177, score-0.515]

62 J(go , gf ) = inf J(go , gf , T ) (16) T with 0 . [sent-178, score-0.435]

63 CA1 = inf (V ol{gf : J(go , gf )  1}) go (17) The figures CA(k, go , ⇠) in (14), CA(k) and CA1 in (17) are proxies of the exploration ability which, in turn, is related to the ability to gather new information on the task at hand. [sent-179, score-0.588]

64 The data acquisition process can be regarded as an experiment design problem [16] where the choice of the control signal guides the experiment. [sent-180, score-0.216]

65 More control authority corresponds to more freedom in the choice of which samples one is taking (from which location and at which scale). [sent-183, score-0.603]

66 Therefore the risk, considered against CA(k) in (15), CA(k, go , ⇠) in (14) or CA1 in (17) will follow a surface that depends on the clutter: For any given clutter (or clutter density), the risk will be a monotonically non-increasing function of control authority CA(k). [sent-184, score-1.117]

67 As is standard, we can settle for the greedy k = 1 case: Z u⇤ = arg min p(yt+1 |y t , ut ) 1 max p(xi |y t , yt+1 , ut ) dyt+1 t ut i (19) but it is still often impractical. [sent-189, score-0.747]

68 H(yt+1 |y t , ut ) is the entropy of a Gaussian mixture distribution which can be easily approximated by Monte Carlo, and for which both lower [20] and upper bounds [21] are known. [sent-191, score-0.449]

69 is unable to traverse the environment in one step, optimization is taken over a small ball in R2 centered at current location gt . [sent-194, score-0.426]

70 Since this location is typically not reachable in a single step, one can adopt a “stubborn” strategy that follows the planned path to the target location before choosing next action, and an “indecisive” – that replans as soon as additional information becomes available as a consequence of motion. [sent-197, score-0.336]

71 We demonstrate the characteristics of conditional entropy as a criterion for planning in Fig. [sent-198, score-0.255]

72 To test average performance of these strategies, we consider search in 100 environment instances, each containing 40 known clutter objects and one unknown object. [sent-204, score-0.521]

73 Clutter objects are sampled from the continuous prior distribution (6) and unknown object is chosen from the prior (10) discretized to |X | ⇡ 9000. [sent-205, score-0.394]

74 Agent’s sensor has m = 30 pixels, with additive noise set to half of the difference between object colors. [sent-206, score-0.325]

75 Search is terminated once residual entropy falls below a threshold value: H(x|y t ) < 0. [sent-208, score-0.225]

76 In all cases, the agent is at the bottom of the environment, and a small unknown object is at the top. [sent-212, score-0.447]

77 The agent has made one measurement (y1 ) and must now determine the best location to visit. [sent-213, score-0.279]

78 The left three panels demonstrate a case of scaling: object is seen, but due to noise and quantization its parameters are uncertain. [sent-214, score-0.269]

79 Agent gains information if putative object location (top) is approached. [sent-215, score-0.283]

80 Middle three panels demonstrate partial occlusion: a part of the object has been seen, and there is now a region (bottom right corner) that is uninformative – measurements taken there are predictable. [sent-216, score-0.282]

81 The object has not been seen (due to occluder in the middle of the environment) and the best action is to visit new area. [sent-218, score-0.271]

82 Objects are colored according to their radiance and the unknown object is shown as a thick line. [sent-223, score-0.354]

83 we define as the excess fraction of the minimum energy path to the center of the unknown object (c0 ) . [sent-230, score-0.38]

84 Because it is not always necessary to reach the object to recognize it (viewing it closely from multiple viewpoints may be sufficient), this quantity is an approximation to minimum search effort. [sent-232, score-0.357]

85 “Random-walk” strategy was unable to find the object unless it was visible initially or became visible by chance. [sent-241, score-0.268]

86 We next indecisive stubborn Average search duration max-ent max-var max-p(x|y t ) 28. [sent-242, score-0.407]

87 prior entropy environment volume reachable volume without clutter Figure 4: Left: Control authority. [sent-258, score-0.691]

88 Right: Residual entropy H(x|y t ), as a function of control authority and clutter density. [sent-261, score-0.927]

89 Lines correspond to residual entropy for a given control authority averaged over the test suite; markers – to residual entropy on a specific problem instance. [sent-263, score-1.009]

90 For certain scenes, agent is unable to significantly reduce entropy because the object never becomes unoccluded (once object is seen, there is a sharp drop in residual entropy, as shown in Fig. [sent-264, score-0.894]

91 empirically evaluated explorer’s exploration ability under finite control authority. [sent-266, score-0.301]

92 Reachable volume was computed by Monte Carlo sampling, following (14)-(15) for several clutter density values. [sent-267, score-0.276]

93 For each clutter density, we generated 40 scene instances and tested ”indecisive” max-entropy strategy with respect to control authority. [sent-268, score-0.557]

94 We have then related the amount of “control authority” the agent can exercise during the data acquisition process with the performance in the visual search task. [sent-273, score-0.393]

95 In the limit of infinite control authority, arbitrarily good decision performance can be attained. [sent-275, score-0.227]

96 In between, we have empirically characterized the tradeoff between decision performance and control authority. [sent-276, score-0.318]

97 Active perception and scene modeling by planning with probabilistic 6d object poses. [sent-315, score-0.463]

98 Robotic object detection: Learning to improve the classifiers using sparse graphs for path planning. [sent-335, score-0.293]

99 Autonomous generation of complete 3d object models using next best view manipulation planning. [sent-341, score-0.239]

100 Mobile sensor network control using mutual information methods and particle filters. [sent-356, score-0.27]


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