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20 nips-2010-A unified model of short-range and long-range motion perception

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Author: Shuang Wu, Xuming He, Hongjing Lu, Alan L. Yuille

Abstract: The human vision system is able to effortlessly perceive both short-range and long-range motion patterns in complex dynamic scenes. Previous work has assumed that two different mechanisms are involved in processing these two types of motion. In this paper, we propose a hierarchical model as a uniﬁed framework for modeling both short-range and long-range motion perception. Our model consists of two key components: a data likelihood that proposes multiple motion hypotheses using nonlinear matching, and a hierarchical prior that imposes slowness and spatial smoothness constraints on the motion ﬁeld at multiple scales. We tested our model on two types of stimuli, random dot kinematograms and multiple-aperture stimuli, both commonly used in human vision research. We demonstrate that the hierarchical model adequately accounts for human performance in psychophysical experiments.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 A uniﬁed model of short-range and long-range motion perception Shuang Wu Department of Statistics UCLA Los Angeles , CA 90095 shuangw@stat. [sent-1, score-0.765]

2 edu Abstract The human vision system is able to effortlessly perceive both short-range and long-range motion patterns in complex dynamic scenes. [sent-8, score-0.847]

3 In this paper, we propose a hierarchical model as a uniﬁed framework for modeling both short-range and long-range motion perception. [sent-10, score-0.755]

4 Our model consists of two key components: a data likelihood that proposes multiple motion hypotheses using nonlinear matching, and a hierarchical prior that imposes slowness and spatial smoothness constraints on the motion ﬁeld at multiple scales. [sent-11, score-1.719]

5 We tested our model on two types of stimuli, random dot kinematograms and multiple-aperture stimuli, both commonly used in human vision research. [sent-12, score-0.308]

6 As illustrated by the motion sequence depicted in Figure 1, humans readily perceive the baseball player’s body movements and the fastermoving baseball simultaneously. [sent-15, score-0.928]

7 Separate motion systems have been proposed to explain human perception in scenarios like this example. [sent-19, score-0.83]

8 In particular, Braddick [1] proposed that there is a short-range motion system which is responsible for perceiving movements with relatively small displacements (e. [sent-20, score-0.829]

9 , the player’s movement), and a long-range motion system which perceives motion with large displacements (e. [sent-22, score-1.406]

10 Lu and Sperling [2] have further argued for the existence of three motion systems in human vision. [sent-25, score-0.734]

11 The ﬁrst and secondorder systems conduct motion analysis on luminance and texture information respectively, while the third-order system uses a feature-tracking strategy. [sent-26, score-0.694]

12 In the baseball example, the ﬁrst-order motion system would be used to perceive the player’s movements, but the third-order system would be required for perceiving the faster motion of the baseball. [sent-27, score-1.595]

13 Short-range motion and ﬁrst-order motion appear to apply to the same class of phenomena, and can be modeled using computational theories that are based on motion energy or related techniques. [sent-28, score-2.113]

14 However, long-range motion and third-order 1 Figure 1: Left panel: Short-range and long-range motion: two frames from a baseball sequence where the ball moves with much faster speed than the other objects. [sent-29, score-0.788]

15 Each node represents motion at different location and scales. [sent-31, score-0.716]

16 A child node can have multiple parents, and the prior constraints on motion are expressed by parent-child interactions. [sent-32, score-0.81]

17 motion employ qualitatively different computational strategies involving tracking features over time, which may require attention-driven processes. [sent-33, score-0.669]

18 In contrast to these previous multi-system theories [2, 3], we develop a uniﬁed single-system framework to account for these phenomena of human motion perception. [sent-34, score-0.756]

19 We model motion estimation as an inference problem which uses ﬂexible prior assumptions about motion ﬂows and statistical models for quantifying the uncertainty in motion measurement. [sent-35, score-2.063]

20 First, the prior model is deﬁned over a hierarchical graph, see Figure 1, where the nodes of the graph represent the motion at different scales. [sent-37, score-0.912]

21 Such a representation makes it possible to deﬁne motion priors and contextual effects at a range of different scales, and so differs from other models of motion perception based on motion priors [5, 6]. [sent-39, score-2.126]

22 This model connects lower level nodes to multiple coarser-level nodes, resulting in a loopy graph structure, which imposes a more ﬂexible prior than tree-structured models (eg. [sent-40, score-0.245]

23 We deﬁne a probability distribution on this graph using potentials deﬁned over the graph cliques to capture spatial smoothness constraints [10] at different scales and slowness constraints [5, 11, 12, 13]. [sent-42, score-0.3]

24 , the likelihood term allows many possible motions) which is resolved in our model by imposing the hierarchical motion prior. [sent-46, score-0.779]

25 Instead we use a bottom-up compositional/hierarchical approach where local hypotheses about the motion are combined to form hypotheses for larger regions of the image. [sent-48, score-0.727]

26 We tested our model using two types of stimuli commonly used in human vision research. [sent-50, score-0.28]

27 The ﬁrst stimulus type are random dot kinematograms (RDKs), where some of the dots (the signal) move coherently with large displacements, whereas other dots (the noise) move randomly. [sent-51, score-0.594]

28 RDKs are one of the most important stimuli used in both physiological and psychophysical studies of motion perception. [sent-52, score-0.88]

29 For example, electrophysiological studies have used RDKs to analyze the neuronal basis of motion perception, identifying a functional link between the activity of motion-selective neurons and behavioral judgments of motion perception [15]. [sent-53, score-1.434]

30 Psychophysical studies have used RDKs to measure the sensitivity of the human visual system for perceiving coherent motion, and also to infer how motion information is integrated to perceive global motion under different viewing conditions [16]. [sent-54, score-1.698]

31 We used two-frame RDKs as an example of a long-range motion stimulus. [sent-55, score-0.669]

32 The second stimulus type are moving gratings or plaids. [sent-56, score-0.282]

33 For example, when randomly orientated lines or grating elements drift behind apertures, the perceived direction of motion is heavily biased by the orientation of the lines/gratings, as well as by the shape and contrast of the apertures [17, 18, 19]. [sent-58, score-0.873]

34 Multiple-aperture stimuli have also recently been used to study coherent motion perception with short-range motion stimulus [20, 21]. [sent-59, score-1.768]

35 For both types of stimuli we compared the model predictions with human performance across various experimental conditions. [sent-60, score-0.25]

36 2 2 Hierarchical Model for Motion Estimation Our hierarchical model represents a motion ﬁeld using a graph G = (V, E), which has L + 1 hierarchical levels, i. [sent-61, score-0.891]

37 The edges E of the graph connect nodes at each level of the hierarchy to nodes in the neighboring levels. [sent-84, score-0.35]

38 Speciﬁcally, edges connect node ν l (i, j) at level l to a set of child nodes Chl (i, j) = {ν l−1 (i , j )} at level l − 1 satisfying 2i − d ≤ i ≤ 2i + d, 2j − d ≤ j ≤ 2j + d. [sent-85, score-0.317]

39 To apply the model to motion estimation, we deﬁne state variable ul (i, j) at each node to represent the motion, and connect the 0th level nodes to two consecutive image frames, D = (It (x), It+1 (x)). [sent-89, score-1.284]

40 The problem of motion estimation is to estimate the 2D motion ﬁeld u(x) at time t for every pixel site x from input D. [sent-90, score-1.369]

41 For simplicity, we use ul to denote the motion instead of ul (i, j) in the i following sections. [sent-91, score-1.453]

42 This robust norm helps deal with the measurement noise that often occur at motion boundary and to prevent over-smoothing at the higher levels. [sent-95, score-0.693]

43 The second i term imposes a slowness prior on the motion which is weighted by the coefﬁcient α. [sent-100, score-0.821]

44 These similarity scores at x gives conﬁdence for different local motion hypotheses: higher similarity means the motion is more likely while lower means it is less likely. [sent-102, score-1.338]

45 l 2) The Hierarchical Prior {Eu } We deﬁne a hierarchical prior on the slowness and spatial smoothness of motion ﬁelds. [sent-103, score-0.984]

46 The ﬁrst term of this prior is expressed by energy terms between nodes at different levels of the hierarchy and enforces a smoothness preference for their states u – that the motion of a child node is similar to the motion of its parent. [sent-104, score-1.828]

47 This imposes weak smoothness on the motion ﬁeld and allows abrupt change on motion boundaries. [sent-106, score-1.464]

48 The second term is a L1 norm of motion velocities that encourages the slowness. [sent-107, score-0.669]

49 Note that our hierarchical smoothness prior differs from conventional smoothness constraints, e. [sent-116, score-0.316]

50 , [10], because they impose smoothness ’sideways’ between neighboring pixels at the same resolution level, which requires that the motion is similar between neighboring sites at the pixel level only. [sent-118, score-0.939]

51 By contrast, we impose smoothness by requiring that child nodes have similar motions to their parent nodes. [sent-121, score-0.321]

52 2 Motion Estimation ˆ We estimate the motion ﬁeld by computing the most probable motion U = arg maxU P (U |D), where P (U |D) was deﬁned as a Gibbs distribution in equation (1). [sent-124, score-1.338]

53 Performing inference on this model is challenging since the energy is deﬁned over a hierarchical graph structure with many closed loops, the state variables U are continuous-valued, and the energy function is non-convex. [sent-125, score-0.331]

54 Our strategy is to convert this into a discrete optimization problem by quantizing the motion state space. [sent-126, score-0.669]

55 For example, we estimate the motion at an integer-valued resolution if the accuracy is sufﬁcient for certain experimental settings. [sent-127, score-0.669]

56 We ﬁrst approximate the hierarchial graph with a tree-structured model by making multiple copies of child nodes such that each child node has a single parent (see [23]). [sent-133, score-0.347]

57 More ˜ speciﬁcally, we compute an approximate energy function E(U ) recursively by exploiting the tree 4 structure: ˜ E(ul+1 ) = i l ˜ j min[Eu (ul+1 , ul ) + E(ul )] j i j∈Chl+1 (i) ul j ˜ where E(u0 ) at the bottom level is the data energy Ed (u0 ; D). [sent-135, score-1.027]

58 Given the top-level motion (ˆL ), we then compute the optimal motion conui ﬁguration for other levels using the following top-down procedure. [sent-138, score-1.376]

59 We minimize the following energy function recursively for each node: ˆj ul = arg min[ ul j l ˜ j Eu (ˆ l+1 ; ul ) + E(ul )] ui j i∈P al (j) where P al (j) is the set of parents of level-l node j. [sent-140, score-1.352]

60 In the top-down pass, the spatial smoothness is imposed to the motion estimates at higher levels which provide context information to disambiguate the motion estimated at lower levels. [sent-141, score-1.533]

61 1 The stimuli and simulation procedures Random dot kinematogram (RDK) stimuli consist of two image frames with N dots in each frame [1, 16, 6]. [sent-146, score-0.67]

62 The difﬁculty of perceiving coherent motion in RDK stimuli is due to the large correspondence uncertainty introduced by the noise dots as shown in rightmost panel in ﬁgure (3). [sent-152, score-1.279]

63 Figure 3: The left three panels show coherent stimuli with N = 20, C = 0. [sent-153, score-0.264]

64 The arrows show the motion of those dots which are moving coherently. [sent-158, score-0.83]

65 Correspondence noise is illustrated by the rightmost panel showing that a dot in the ﬁrst frame has many candidate matches in the second frame. [sent-159, score-0.317]

66 Barlow and Tripathy [16] used RDK stimuli to investigate how dot density can affect human performance in a global motion discrimination task. [sent-160, score-1.037]

67 They found that human performance (measured by the coherence threshold) vary little with dot density. [sent-161, score-0.33]

68 We tested our model on the same task to judge 5 Figure 4: Estimated motion ﬁelds for random dot kinematograms. [sent-162, score-0.797]

69 First row: 50 dots in the RDK stimulus; Second row: 100 dots in the RDK stimulus; Column-wise, coherence ratio C = 0. [sent-163, score-0.454]

70 The arrows indicate the motion estimated for each dot. [sent-168, score-0.691]

71 the global motion direction using RDK motion stimulus as the input image. [sent-169, score-1.495]

72 We applied our model to estimate motion ﬁelds and used the average velocity to indicate the global motion direction (to the left or to the right). [sent-170, score-1.392]

73 The dot number varies with N = 40, 80, 100, 200, 400, 800 respectively, corresponding to a wide range of dot densities. [sent-172, score-0.256]

74 The model performance was computed for each coherence ratio to ﬁt psychometric functions and to ﬁnd the coherence threshold at which model performance can reach 75% accuracy. [sent-173, score-0.354]

75 2 The Results Figure (4) shows examples of the estimated motion ﬁeld for various values of dot number N and coherence ratio C. [sent-175, score-0.993]

76 The model outputs provide visually coherent motion estimates when the coherence ratio was greater than 0. [sent-176, score-0.941]

77 With the increase of coherence ratio, the estimated motion ﬂow appears to be more coherent. [sent-178, score-0.828]

78 The coherence threshold, using the criterion of 75% accuracy, showed that model performance varied little with the increase of dot density, which is consistent with human performance reported in psychophysical experiments [16, 6]. [sent-181, score-0.387]

79 Two types of elements were used in our simulations: (i) drifting sine-wave gratings with random orientation, and (ii) plaids which includes two gratings with orthogonal orientations. [sent-184, score-0.501]

80 For the CN signal gratings, the motion vi was set to a ﬁxed value v. [sent-190, score-0.692]

81 005 0 40 80 100 200 N 400 800 Figure 5: Left panel: Figure 2 in [16] showing that the coherence ratio threshold varies very little with dot density. [sent-201, score-0.302]

82 The plaid elements combine two gratings with orthogonal orientations (each grating has the same speed but can have a different motion direction). [sent-208, score-0.986]

83 1 Figure 7: Left two panels: Estimated motion ﬁelds of grating and plaids stimuli. [sent-227, score-0.904]

84 Rightmost panel: Psychometric functions of gratings and plaids stimuli. [sent-228, score-0.288]

85 2 Simulation procedures and results The left two panels in Figure (7) show the estimated motion ﬁelds for the two types of stimulus we studied with the same coherence ratios 0. [sent-230, score-0.995]

86 Plaids stimuli produce more coherent estimated motion ﬁeld than grating stimuli, which is understandable. [sent-232, score-1.027]

87 We tested our model in an 8-direction discrimination task for estimating global motion direction [20]. [sent-234, score-0.723]

88 We ran 300 trials for each stimulus type, and used the direction of the average motion to predict the global motion direction. [sent-236, score-1.495]

89 the number of times our model predicted the correct motion direction from 8 alternatives – was calculated at different coherence ratio levels. [sent-239, score-0.876]

90 This difference between gratings and plaids is shown in the rightmost panel of Figure (7), where the psychometric function of plaids stimuli is always above that of grating stimuli, indicating better performance. [sent-240, score-0.846]

91 It differs from traditional motion energy models because it does not use spatiotemporal ﬁltering. [sent-243, score-0.776]

92 Note that it was shown in [6] that motion energy models are not well suited to the long-range motion stimuli studied in this paper. [sent-244, score-1.576]

93 The local ambiguities of motion are resolved by a novel hierarchical prior which combines slowness and smoothness at a range of different scales. [sent-245, score-1.014]

94 Our model accounts well for human perception of both short-range and long-range motion using the two standard stimulus types (RDKs and gratings). [sent-246, score-0.964]

95 It also has the computational motivation of being able to represent prior knowledge about motion at different scales and to allow efﬁcient computation. [sent-248, score-0.698]

96 Three-systems theory of human visual motion perception: review and update. [sent-260, score-0.785]

97 Cortical dynamics of visual motion perception: short-range and long-range apparent motion. [sent-319, score-0.744]

98 The inﬂuence of terminators on motion integration across space. [sent-395, score-0.669]

99 Adaptive pooling of visual motion signals by the human visual system revealed with a novel multi-element stimulus. [sent-409, score-0.861]

100 A comparison of global motion perception using a multiple-aperture stimulus. [sent-415, score-0.786]

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