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5 nips-2005-A Computational Model of Eye Movements during Object Class Detection

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Author: Wei Zhang, Hyejin Yang, Dimitris Samaras, Gregory J. Zelinsky

Abstract: We present a computational model of human eye movements in an object class detection task. The model combines state-of-the-art computer vision object class detection methods (SIFT features trained using AdaBoost) with a biologically plausible model of human eye movement to produce a sequence of simulated ﬁxations, culminating with the acquisition of a target. We validated the model by comparing its behavior to the behavior of human observers performing the identical object class detection task (looking for a teddy bear among visually complex nontarget objects). We found considerable agreement between the model and human data in multiple eye movement measures, including number of ﬁxations, cumulative probability of ﬁxating the target, and scanpath distance.

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu‡ Abstract We present a computational model of human eye movements in an object class detection task. [sent-10, score-1.371]

2 The model combines state-of-the-art computer vision object class detection methods (SIFT features trained using AdaBoost) with a biologically plausible model of human eye movement to produce a sequence of simulated ﬁxations, culminating with the acquisition of a target. [sent-11, score-1.665]

3 We validated the model by comparing its behavior to the behavior of human observers performing the identical object class detection task (looking for a teddy bear among visually complex nontarget objects). [sent-12, score-1.518]

4 We found considerable agreement between the model and human data in multiple eye movement measures, including number of ﬁxations, cumulative probability of ﬁxating the target, and scanpath distance. [sent-13, score-1.046]

5 Introduction Object detection is one of our most common visual operations. [sent-15, score-0.335]

6 Whether we are driving [1], making a cup of tea [2], or looking for a tool on a workbench [3], hundreds of times each day our visual system is being asked to detect, localize, or acquire through movements of gaze objects and patterns in the world. [sent-16, score-0.572]

7 In the human behavioral literature, this topic has been extensively studied in the context of visual search. [sent-17, score-0.496]

8 In a typical search task, observers are asked to indicate, usually by button press, whether a speciﬁc target is present or absent in a visual display (see [4] for a review). [sent-18, score-0.527]

9 A bedrock ﬁnding in this literature is that, for targets that cannot be deﬁned by a single visual feature, target detection times increase linearly with the number of nontargets, a form of clutter or ”set size” effect. [sent-20, score-0.609]

10 Moreover, the slope of the function relating detection speed to set size is steeper (by roughly a factor of two) when the target is absent from the scene compared to when it is present. [sent-21, score-0.499]

11 Search theorists have interpreted these ﬁndings as evidence for visual attention moving serially from one object to the next, with the human detection operation typically limited to those objects ﬁxated by this ”spotlight” of attention [5]. [sent-22, score-1.225]

12 Object class detection has also been extensively studied in the computer vision community, with faces and cars being the two most well researched object classes [6, 7, 8, 9]. [sent-23, score-0.664]

13 The related but simpler task of object class recognition (target recognition without localization) has also been the focus of exciting recent work [10, 11, 12]. [sent-24, score-0.471]

14 Scenes are typically realistic and highly cluttered, with object appearance varying greatly due to illumination, view, and scale changes. [sent-26, score-0.298]

15 The task addressed in this paper falls between the class detection and recognition problems. [sent-27, score-0.348]

16 Like object class detection, we will be detecting and localizing class-deﬁned targets; unlike object class detection the test images will be composed of at most 20 objects appearing on a simple background. [sent-28, score-1.218]

17 Both the behavioral and computer vision literatures have strengths and weaknesses when it comes to understanding human object class detection. [sent-29, score-0.864]

18 Moreover, this literature has focused almost entirely on object-speciﬁc detection, cases in which the observer knows precisely how the target will appear in the test display (see [15] for a discussion of target non-speciﬁc search using featurally complex objects). [sent-31, score-0.504]

19 The current study draws upon the strengths of both of these literatures to produce the ﬁrst joint behavioral-computational study of human object class detection. [sent-33, score-0.718]

20 First, we use an eyetracker to quantify human behavior in terms of the number of ﬁxations made during an object class detection task. [sent-34, score-0.985]

21 Then we introduce a computational model that not only performs the detection task at a level comparable to that of the human observers, but also generates a sequence of simulated eye movements similar in pattern to those made by humans performing the identical detection task. [sent-35, score-1.343]

22 Experimental methods An effort was made to keep the human and model experiments methodologically similar. [sent-37, score-0.376]

23 Both experiments used training, validation (practice trials in the human experiment), and testing phases, and identical images were presented to the model and human subjects in all three of these phases. [sent-38, score-0.867]

24 The target class consisted of 378 teddy bears scanned from [16]. [sent-39, score-0.493]

25 Nontargets consisted of 2,975 objects selected from the Hemera Photo Objects Collection. [sent-40, score-0.224]

26 Samples of the bear and nontarget objects are shown in Figure 1. [sent-41, score-0.387]

27 Figure 1: Representative teddy bears (left) and nontarget objects (right). [sent-43, score-0.51]

28 In the case of the human experiment, each of these objects was shown centered on a white background and displayed for 1 second. [sent-45, score-0.482]

29 No objects were repeated between training and testing, and no objects were repeated within either of the training or testing phases. [sent-47, score-0.442]

30 Test images depicted 6, 13, or 20 color objects randomly positioned on a white background. [sent-48, score-0.327]

31 Human subjects were instructed to indicate, by pressing a button, whether a teddy bear appeared among the displayed objects. [sent-50, score-0.297]

32 Each test trial in the human experiment began with the subject ﬁxating gaze at the center of the display, and eye position was monitored throughout each trial using an eyetracker. [sent-52, score-0.816]

33 Model of eye movements during object class detection Figure 2: The ﬂow of processing through our model. [sent-55, score-1.028]

34 Retina transform With each change in gaze position (set initially to the center of the image), our model transforms the input image so as to reﬂect the acuity limitations imposed by the human retina. [sent-60, score-0.61]

35 We used the method described in [19, 20], which was shown to provide a close approximation to human acuity limitations, to implement this dynamic retina transform. [sent-61, score-0.338]

36 Create target map Each point on the target map ranges in value between 0 and 1 and indicates the likelihood that a target is located at that point. [sent-64, score-0.623]

37 2), then compare the features surrounding these points to features of the target object class extracted during training. [sent-67, score-0.756]

38 Two types of discriminative features were used in this study: color features and texture features. [sent-68, score-0.395]

39 Color features Color has long been used as a feature for instance object recognition [21]. [sent-72, score-0.486]

40 In our study we explore the potential use of color as a discriminative feature for an object class. [sent-73, score-0.449]

41 Given a test image, It , and its color feature, Ht , we compute the distances between Ht and the color features of the training set {Hi , i = 1, . [sent-79, score-0.376]

42 Texture features Local texture features were extracted on the gray level images during both training and testing. [sent-87, score-0.353]

43 Following the method described in [11, 12], we used AdaBoost during training to select a small set of SIFT features from among all the SIFT features computed for each sample in the training set. [sent-91, score-0.292]

44 Eventually, T features were chosen having the best ability to discriminate the target object class from the nontargets. [sent-99, score-0.651]

45 Each of these selected features forms a weak classiﬁer, hk , consisting of three components: a feature vector, (fk ), a distance threshold, (θk ), and an output label, (uk ). [sent-100, score-0.237]

46 Validation A validation set, consisting of the practice trials viewed by the human observers, was used to set parameters in the model. [sent-108, score-0.396]

47 (4) c Wtexture = c + t The ﬁnal combined output was used to generate the values in the target map and, ultimately, to guide the model’s simulated eye movements. [sent-114, score-0.607]

48 Recognition We deﬁne the highest-valued point on the target map as the hotspot. [sent-117, score-0.227]

49 If the hotspot value exceeds the high target-present threshold, then the object will be recognized as an instance of the target class. [sent-119, score-0.639]

50 If the hotspot value falls below the target-absent threshold, then the object will be classiﬁed as not belonging to the target class. [sent-120, score-0.639]

51 This constraint was introduced so as to avoid extremely high false positive rates stemming from the creation of false targets in the blurred periphery of the retina-transformed image. [sent-123, score-0.242]

52 Eye movement If neither the target-present nor the target-absent thresholds are satisﬁed, processing passes to the eye movement stage of our model. [sent-126, score-0.639]

53 If the simulated fovea is not on the hotspot, the model will make an eye movement to move gaze steadily toward the hotspot location. [sent-127, score-0.946]

54 Fixation in our model is deﬁned as the centroid of activity on the target map, a computation consistent with a neuronal population code. [sent-128, score-0.262]

55 Eventually, this thresholding operation will cause the centroid of the target map to pass an eye movement threshold, resulting in a gaze shift to the new centroid location. [sent-130, score-0.977]

56 See [18] for details regarding the eye movement generation process. [sent-131, score-0.464]

57 If the simulated fovea does acquire the hotspot and the target-present threshold is still not met, the model will assume that a nontarget was ﬁxated and this object will be ”zapped”. [sent-132, score-0.768]

58 Zapping consists of applying a negative Gaussian ﬁlter to the hotspot location, thereby preventing attention and gaze from returning to this object (see [24] for a previous computational implementation of a conceptually related operation). [sent-133, score-0.707]

59 Experimental results Model and human behavior were compared on a variety of measures, including error rates, number of ﬁxations, cumulative probability of ﬁxating the target, and scanpath ratio (a measure of how directly gaze moved to the target). [sent-135, score-0.733]

60 For each measure, the model and human data were in reasonable agreement. [sent-136, score-0.343]

61 Table 1: Error rates for model and human subjects. [sent-137, score-0.379]

62 2% Table 1 shows the error rates for the human subjects and the model, grouped by misses and false positives. [sent-142, score-0.549]

63 Note that the data from all eight of the human subjects are shown, resulting in the greater number of total trials. [sent-143, score-0.398]

64 First, despite the very high level of accuracy exhibited by the human subjects in this task, our model was able to Table 2: Average number of ﬁxations by model and human. [sent-145, score-0.48]

65 Second, and consistent with the behavioral search literature, miss rates were larger than false positive rates for both the humans and model. [sent-163, score-0.352]

66 To the extent that our model offers an accurate account of human object detection behavior, it should be able to predict the average number of ﬁxations made by human subjects in the detection task. [sent-164, score-1.516]

67 Data are grouped by targetpresent (p), target-absent (a), and the number of objects in the scene (6, 13, 20). [sent-166, score-0.221]

68 In all conditions, the model and human subjects made comparable numbers of ﬁxations. [sent-167, score-0.472]

69 Also consistent with the behavioral literature, the average number of ﬁxations made by human subjects in our task increased with the number of objects in the scenes, and the rate of this increase was greater in the target-absent data compared to the target-present data. [sent-168, score-0.692]

70 The fact that our model is able to capture an interaction between set size and target presence in terms of the number of ﬁxations needed for detection lends support for our method. [sent-170, score-0.466]

71 Plotted are the cumulative probabilities of ﬁxating the target as a function of the number of objects ﬁxated during the search task. [sent-173, score-0.473]

72 When the scene contained only 6 or 13 objects, the model and the humans ﬁxated roughly the same number of nontargets before ﬁnally shifting gaze to the target. [sent-174, score-0.417]

73 When the scene was more cluttered (20 objects), the model ﬁxated an average of 1 additional nontarget relative to the human subjects, a difference likely indicating a liberal bias in our human subjects under these search conditions. [sent-175, score-1.034]

74 Overall, these analyses suggest that our model was not only making the same number of ﬁxations as humans, but it was also ﬁxating the same number of nontargets during search as our human subjects. [sent-176, score-0.524]

75 Table 3: Comparison of model and human scanpath distance #Objects Human Model MODEL 6 1. [sent-177, score-0.54]

76 43 Human gaze does not jump randomly from one item to another during search, but instead moves in a more orderly way toward the target. [sent-186, score-0.231]

77 The ultimate test of our model would be to reproduce this orderly movement of gaze. [sent-187, score-0.222]

78 , the summed distance traveled by the eye) and the distance between the target and the center of the image (i. [sent-191, score-0.316]

79 , the minimum distance that the eye would need to travel to ﬁxate the target). [sent-193, score-0.381]

80 As indicated in Table 3, the model and human data are in close agreement in the 6 and 13-object scenes, but not in the 20-object scenes. [sent-194, score-0.384]

81 Upon closer inspection of the data, we found several cases in which the model made multiple ﬁxations between two nontarget objects, a very unnatural behavior arising from too small of a setting for our Gaussian ”zap” window. [sent-195, score-0.254]

82 When these 6 trials were removed, the model data (MODEL) and the human data were in closer agreement. [sent-196, score-0.374]

83 Model data are shown in thick red lines, human data are shown in thin green lines. [sent-198, score-0.302]

84 Figure 4 shows representative scanpaths from the model and one human subject for two search scenes. [sent-199, score-0.487]

85 Although the scanpaths do not align perfectly, there is a qualitative agreement between the human and model in the path followed by gaze to the target. [sent-200, score-0.605]

86 Very often, we need to search for dogs, or chairs, or pens, without any clear idea of the visual features comprising these objects. [sent-203, score-0.292]

87 Despite the prevalence of these tasks, the problem of object class detection has attracted surprisingly little research within the behavioral community [15], and has been applied to a relatively narrow range of objects within the computer vision literature [6, 7, 8, 9]. [sent-204, score-0.982]

88 First, we provide a detailed eye movement analysis of human behavior in an object class detection task. [sent-206, score-1.416]

89 Second, we incorporate state-of-the-art computer vision object detection methods into a biologically plausible model of eye movement control, then validate this model by comparing its behavior to the behavior of our human observers. [sent-207, score-1.535]

90 Computational models capable of describing human eye movement behavior are extremely rare [25]; the fact that the current model was able to do so for multiple eye movement measures lends strength to our approach. [sent-208, score-1.356]

91 Moreover, our model was able to detect targets nearly as well as the human observers while maintaining a low false positive rate, a difﬁcult standard to achieve in a generic detection model. [sent-209, score-0.762]

92 Such agreement between human and model suggests that simple color and texture features may be used to guide human attention and eye movement in an object class detection task. [sent-210, score-2.094]

93 Future computational work will explore the generality of our object class detection method to tasks with visually complex backgrounds, and future human work will attempt to use neuroimaging techniques to localize object class representations in the brain. [sent-211, score-1.352]

94 In what ways do eye movements contribute to everyday activities. [sent-226, score-0.429]

95 A statistical method for 3d object detection applied to faces and cars. [sent-250, score-0.52]

96 Rapid object detection using a boosted cascade of simple features. [sent-256, score-0.52]

97 Weak hypotheses and boosting for generic object detection and recognition. [sent-279, score-0.555]

98 Efﬁcient visual search by category: Specifying the features that mark the difference between artifacts and animal in preattentive vision. [sent-307, score-0.292]

99 ), Neurobiology of attention, chapter Specifying the components of attention in a visual search task, pages 395–400. [sent-327, score-0.275]

100 Algorithms for deﬁning visual regions-of-interest: comparison with eye ﬁxations. [sent-371, score-0.445]

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Informal correlates of surprise exist at nearly all stages of neural processing. In sensory neuroscience, it has been suggested that only the unexpected at one stage is transmitted to the next stage [2]. Hence, sensory cortex may have evolved to adapt to, to predict, and to quiet down the expected statistical regularities of the world [3, 4, 5, 6], focusing instead on events that are unpredictable or surprising. Electrophysiological evidence for this early sensory emphasis onto surprising stimuli exists from studies of adaptation in visual [7, 8, 4, 9], olfactory [10, 11], and auditory cortices [12], subcortical structures like the LGN [13], and even retinal ganglion cells [14, 15] and cochlear hair cells [16]: neural response greatly attenuates with repeated or prolonged exposure to an initially novel stimulus. Surprise and novelty are also central to learning and memory formation [1], to the point that surprise is believed to be a necessary trigger for associative learning [17, 18], as supported by mounting evidence for a role of the hippocampus as a novelty detector [19, 20, 21]. Finally, seeking novelty is a well-identiﬁed human character trait, with possible association with the dopamine D4 receptor gene [22, 23, 24]. In the Bayesian framework, we develop the only consistent theory of surprise, in terms of the difference between the posterior and prior distributions of beliefs of an observer over the available class of models or hypotheses about the world. We show that this deﬁnition derived from ﬁrst principles presents key advantages over more ad-hoc formulations, typically relying on detecting outlier stimuli. Armed with this new framework, we provide direct experimental evidence that surprise best characterizes what attracts human gaze in large amounts of natural video stimuli. We here extend a recent pilot study [25], adding more comprehensive theory, large-scale human data collection, and additional analysis. 1 Theory Bayesian Deﬁnition of Surprise. We propose that surprise is a general concept, which can be derived from ﬁrst principles and formalized across spatio-temporal scales, sensory modalities, and, more generally, data types and data sources. Two elements are essential for a principled deﬁnition of surprise. First, surprise can exist only in the presence of uncertainty, which can arise from intrinsic stochasticity, missing information, or limited computing resources. A world that is purely deterministic and predictable in real-time for a given observer contains no surprises. Second, surprise can only be deﬁned in a relative, subjective, manner and is related to the expectations of the observer, be it a single synapse, neuronal circuit, organism, or computer device. The same data may carry different amount of surprise for different observers, or even for the same observer taken at different times. In probability and decision theory it can be shown that the only consistent and optimal way for modeling and reasoning about uncertainty is provided by the Bayesian theory of probability [26, 27, 28]. Furthermore, in the Bayesian framework, probabilities correspond to subjective degrees of beliefs in hypotheses or models which are updated, as data is acquired, using Bayes’ theorem as the fundamental tool for transforming prior belief distributions into posterior belief distributions. Therefore, within the same optimal framework, the only consistent deﬁnition of surprise must involve: (1) probabilistic concepts to cope with uncertainty; and (2) prior and posterior distributions to capture subjective expectations. Consistently with this Bayesian approach, the background information of an observer is captured by his/her/its prior probability distribution {P (M )}M ∈M over the hypotheses or models M in a model space M. Given this prior distribution of beliefs, the fundamental effect of a new data observation D on the observer is to change the prior distribution {P (M )}M ∈M into the posterior distribution {P (M |D)}M ∈M via Bayes theorem, whereby P (D|M ) ∀M ∈ M, P (M |D) = P (M ). (1) P (D) In this framework, the new data observation D carries no surprise if it leaves the observer beliefs unaffected, that is, if the posterior is identical to the prior; conversely, D is surprising if the posterior distribution resulting from observing D signiﬁcantly differs from the prior distribution. Therefore we formally measure surprise elicited by data as some distance measure between the posterior and prior distributions. This is best done using the relative entropy or Kullback-Leibler (KL) divergence [29]. Thus, surprise is deﬁned by the average of the log-odd ratio: P (M |D) S(D, M) = KL(P (M |D), P (M )) = P (M |D) log dM (2) P (M ) M taken with respect to the posterior distribution over the model class M. Note that KL is not symmetric but has well-known theoretical advantages, including invariance with respect to Figure 1: Computing surprise in early sensory neurons. (a) Prior data observations, tuning preferences, and top-down inﬂuences contribute to shaping a set of “prior beliefs” a neuron may have over a class of internal models or hypotheses about the world. For instance, M may be a set of Poisson processes parameterized by the rate λ, with {P (M )}M ∈M = {P (λ)}λ∈I +∗ the prior distribution R of beliefs about which Poisson models well describe the world as sensed by the neuron. New data D updates the prior into the posterior using Bayes’ theorem. Surprise quantiﬁes the difference between the posterior and prior distributions over the model class M. The remaining panels detail how surprise differs from conventional model ﬁtting and outlier-based novelty. (b) In standard iterative Bayesian model ﬁtting, at every iteration N , incoming data DN is used to update the prior {P (M |D1 , D2 , ..., DN −1 )}M ∈M into the posterior {P (M |D1 , D2 , ..., DN )}M ∈M . Freezing this learning at a given iteration, one then picks the currently best model, usually using either a maximum likelihood criterion, or a maximum a posteriori one (yielding MM AP shown). (c) This best model is used for a number of tasks at the current iteration, including outlier-based novelty detection. New data is then considered novel at that instant if it has low likelihood for the best model b a (e.g., DN is more novel than DN ). This focus onto the single best model presents obvious limitations, especially in situations where other models are nearly as good (e.g., M∗ in panel (b) is entirely ignored during standard novelty computation). One palliative solution is to consider mixture models, or simply P (D), but this just amounts to shifting the problem into a different model class. (d) Surprise directly addresses this problem by simultaneously considering all models and by measuring how data changes the observer’s distribution of beliefs from {P (M |D1 , D2 , ..., DN −1 )}M ∈M to {P (M |D1 , D2 , ..., DN )}M ∈M over the entire model class M (orange shaded area). reparameterizations. A unit of surprise — a “wow” — may then be deﬁned for a single model M as the amount of surprise corresponding to a two-fold variation between P (M |D) and P (M ), i.e., as log P (M |D)/P (M ) (with log taken in base 2), with the total number of wows experienced for all models obtained through the integration in eq. 2. Surprise and outlier detection. Outlier detection based on the likelihood P (D|M best ) of D given a single best model Mbest is at best an approximation to surprise and, in some cases, is misleading. Consider, for instance, a case where D has very small probability both for a model or hypothesis M and for a single alternative hypothesis M. Although D is a strong outlier, it carries very little information regarding whether M or M is the better model, and therefore very little surprise. Thus an outlier detection method would strongly focus attentional resources onto D, although D is a false positive, in the sense that it carries no useful information for discriminating between the two alternative hypotheses M and M. Figure 1 further illustrates this disconnect between outlier detection and surprise. 2 Human experiments To test the surprise hypothesis — that surprise attracts human attention and gaze in natural scenes — we recorded eye movements from eight na¨ve observers (three females and ı ﬁve males, ages 23-32, normal or corrected-to-normal vision). Each watched a subset from 50 videoclips totaling over 25 minutes of playtime (46,489 video frames, 640 × 480, 60.27 Hz, mean screen luminance 30 cd/m2 , room 4 cd/m2 , viewing distance 80cm, ﬁeld of view 28◦ × 21◦ ). Clips comprised outdoors daytime and nighttime scenes of crowded environments, video games, and television broadcast including news, sports, and commercials. Right-eye position was tracked with a 240 Hz video-based device (ISCAN RK-464), with methods as previously [30]. Two hundred calibrated eye movement traces (10,192 saccades) were analyzed, corresponding to four distinct observers for each of the 50 clips. Figure 2 shows sample scanpaths for one videoclip. To characterize image regions selected by participants, we process videoclips through computational metrics that output a topographic dynamic master response map, assigning in real-time a response value to every input location. A good master map would highlight, more than expected by chance, locations gazed to by observers. To score each metric we hence sample, at onset of every human saccade, master map activity around the saccade’s future endpoint, and around a uniformly random endpoint (random sampling was repeated 100 times to evaluate variability). We quantify differences between histograms of master Figure 2: (a) Sample eye movement traces from four observers (squares denote saccade endpoints). (b) Our data exhibits high inter-individual overlap, shown here with the locations where one human saccade endpoint was nearby (≈ 5◦ ) one (white squares), two (cyan squares), or all three (black squares) other humans. (c) A metric where the master map was created from the three eye movement traces other than that being tested yields an upper-bound KL score, computed by comparing the histograms of metric values at human (narrow blue bars) and random (wider green bars) saccade targets. Indeed, this metric’s map was very sparse (many random saccades landing on locations with nearzero response), yet humans preferentially saccaded towards the three active hotspots corresponding to the eye positions of three other humans (many human saccades landing on locations with near-unity responses). map samples collected from human and random saccades using again the Kullback-Leibler (KL) distance: metrics which better predict human scanpaths exhibit higher distances from random as, typically, observers non-uniformly gaze towards a minority of regions with highest metric responses while avoiding a majority of regions with low metric responses. This approach presents several advantages over simpler scoring schemes [31, 32], including agnosticity to putative mechanisms for generating saccades and the fact that applying any continuous nonlinearity to master map values would not affect scoring. Experimental results. We test six computational metrics, encompassing and extending the state-of-the-art found in previous studies. The ﬁrst three quantify static image properties (local intensity variance in 16 × 16 image patches [31]; local oriented edge density as measured with Gabor ﬁlters [33]; and local Shannon entropy in 16 × 16 image patches [34]). The remaining three metrics are more sensitive to dynamic events (local motion [33]; outlier-based saliency [33]; and surprise [25]). For all metrics, we ﬁnd that humans are signiﬁcantly attracted by image regions with higher metric responses. However, the static metrics typically respond vigorously at numerous visual locations (Figure 3), hence they are poorly speciﬁc and yield relatively low KL scores between humans and random. The metrics sensitive to motion, outliers, and surprising events, in comparison, yield sparser maps and higher KL scores. The surprise metric of interest here quantiﬁes low-level surprise in image patches over space and time, and at this point does not account for high-level or cognitive beliefs of our human observers. Rather, it assumes a family of simple models for image patches, each processed through 72 early feature detectors sensitive to color, orientation, motion, etc., and computes surprise from shifts in the distribution of beliefs about which models better describe the patches (see [25] and [35] for details). We ﬁnd that the surprise metric signiﬁcantly outperforms all other computational metrics (p < 10−100 or better on t-tests for equality of KL scores), scoring nearly 20% better than the second-best metric (saliency) and 60% better than the best static metric (entropy). Surprising stimuli often substantially differ from simple feature outliers; for example, a continually blinking light on a static background elicits sustained ﬂicker due to its locally outlier temporal dynamics but is only surprising for a moment. Similarly, a shower of randomly-colored pixels continually excites all low-level feature detectors but rapidly becomes unsurprising. Strongest attractors of human attention. Clearly, in our and previous eye-tracking experiments, in some situations potentially interesting targets were more numerous than in others. With many possible targets, different observers may orient towards different locations, making it more difﬁcult for a single metric to accurately predict all observers. Hence we consider (Figure 4) subsets of human saccades where at least two, three, or all four observers simultaneously agreed on a gaze target. Observers could have agreed based on bottom-up factors (e.g., only one location had interesting visual appearance at that time), top-down factors (e.g., only one object was of current cognitive interest), or both (e.g., a single cognitively interesting object was present which also had distinctive appearance). Irrespectively of the cause for agreement, it indicates consolidated belief that a location was attractive. While the KL scores of all metrics improved when progressively focusing onto only those locations, dynamic metrics improved more steeply, indicating that stimuli which more reliably attracted all observers carried more motion, saliency, and surprise. Surprise remained signiﬁcantly the best metric to characterize these agreed-upon attractors of human gaze (p < 10−100 or better on t-tests for equality of KL scores). Overall, surprise explained the greatest fraction of human saccades, indicating that humans are signiﬁcantly attracted towards surprising locations in video displays. Over 72% of all human saccades were targeted to locations predicted to be more surprising than on average. When only considering saccades where two, three, or four observers agreed on a common gaze target, this ﬁgure rose to 76%, 80%, and 84%, respectively. Figure 3: (a) Sample video frames, with corresponding human saccades and predictions from the entropy, surprise, and human-derived metrics. Entropy maps, like intensity variance and orientation maps, exhibited many locations with high responses, hence had low speciﬁcity and were poorly discriminative. In contrast, motion, saliency, and surprise maps were much sparser and more speciﬁc, with surprise signiﬁcantly more often on target. For three example frames (ﬁrst column), saccades from one subject are shown (arrows) with corresponding apertures over which master map activity at the saccade endpoint was sampled (circles). (b) KL scores for these metrics indicate signiﬁcantly different performance levels, and a strict ranking of variance < orientation < entropy < motion < saliency < surprise < human-derived. KL scores were computed by comparing the number of human saccades landing onto each given range of master map values (narrow blue bars) to the number of random saccades hitting the same range (wider green bars). A score of zero would indicate equality between the human and random histograms, i.e., humans did not tend to hit various master map values any differently from expected by chance, or, the master map could not predict human saccades better than random saccades. Among the six computational metrics tested in total, surprise performed best, in that surprising locations were relatively few yet reliably gazed to by humans. Figure 4: KL scores when considering only saccades where at least one (all 10,192 saccades), two (7,948 saccades), three (5,565 saccades), or all four (2,951 saccades) humans agreed on a common gaze location, for the static (a) and dynamic metrics (b). Static metrics improved substantially when progressively focusing onto saccades with stronger inter-observer agreement (average slope 0.56 ± 0.37 percent KL score units per 1,000 pruned saccades). Hence, when humans agreed on a location, they also tended to be more reliably predicted by the metrics. Furthermore, dynamic metrics improved 4.5 times more steeply (slope 2.44 ± 0.37), suggesting a stronger role of dynamic events in attracting human attention. Surprising events were signiﬁcantly the strongest (t-tests for equality of KL scores between surprise and other metrics, p < 10−100 ). 3 Discussion While previous research has shown with either static scenes or dynamic synthetic stimuli that humans preferentially ﬁxate regions of high entropy [34], contrast [31], saliency [32], ﬂicker [36], or motion [37], our data provides direct experimental evidence that humans ﬁxate surprising locations even more reliably. These conclusions were made possible by developing new tools to quantify what attracts human gaze over space and time in dynamic natural scenes. Surprise explained best where humans look when considering all saccades, and even more so when restricting the analysis to only those saccades for which human observers tended to agree. Surprise hence represents an inexpensive, easily computable approximation to human attentional allocation. In the absence of quantitative tools to measure surprise, most experimental and modeling work to date has adopted the approximation that novel events are surprising, and has focused on experimental scenarios which are simple enough to ensure an overlap between informal notions of novelty and surprise: for example, a stimulus is novel during testing if it has not been seen during training [9]. Our deﬁnition opens new avenues for more sophisticated experiments, where surprise elicited by different stimuli can be precisely compared and calibrated, yielding predictions at the single-unit as well as behavioral levels. The deﬁnition of surprise — as the distance between the posterior and prior distributions of beliefs over models — is entirely general and readily applicable to the analysis of auditory, olfactory, gustatory, or somatosensory data. While here we have focused on behavior rather than detailed biophysical implementation, it is worth noting that detecting surprise in neural spike trains does not require semantic understanding of the data carried by the spike trains, and thus could provide guiding signals during self-organization and development of sensory areas. At higher processing levels, top-down cues and task demands are known to combine with stimulus novelty in capturing attention and triggering learning [1, 38], ideas which may now be formalized and quantiﬁed in terms of priors, posteriors, and surprise. Surprise, indeed, inherently depends on uncertainty and on prior beliefs. Hence surprise theory can further be tested and utilized in experiments where the prior is biased, for ex- ample by top-down instructions or prior exposures to stimuli [38]. In addition, simple surprise-based behavioral measures such as the eye-tracking one used here may prove useful for early diagnostic of human conditions including autism and attention-deﬁcit hyperactive disorder, as well as for quantitative comparison between humans and animals which may have lower or different priors, including monkeys, frogs, and ﬂies. Beyond sensory biology, computable surprise could guide the development of data mining and compression systems (giving more bits to surprising regions of interest), to ﬁnd surprising agents in crowds, surprising sentences in books or speeches, surprising sequences in genomes, surprising medical symptoms, surprising odors in airport luggage racks, surprising documents on the world-wide-web, or to design surprising advertisements. Acknowledgments: Supported by HFSP, NSF and NGA (L.I.), NIH and NSF (P.B.). 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