nips nips2005 nips2005-109 knowledge-graph by maker-knowledge-mining

109 nips-2005-Learning Cue-Invariant Visual Responses

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Author: Jarmo Hurri

Abstract: Multiple visual cues are used by the visual system to analyze a scene; achromatic cues include luminance, texture, contrast and motion. Singlecell recordings have shown that the mammalian visual cortex contains neurons that respond similarly to scene structure (e.g., orientation of a boundary), regardless of the cue type conveying this information. This paper shows that cue-invariant response properties of simple- and complex-type cells can be learned from natural image data in an unsupervised manner. In order to do this, we also extend a previous conceptual model of cue invariance so that it can be applied to model simple- and complex-cell responses. Our results relate cue-invariant response properties to natural image statistics, thereby showing how the statistical modeling approach can be used to model processing beyond the elemental response properties visual neurons. This work also demonstrates how to learn, from natural image data, more sophisticated feature detectors than those based on changes in mean luminance, thereby paving the way for new data-driven approaches to image processing and computer vision. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Box 68, FIN-00014 University of Helsinki, Finland Abstract Multiple visual cues are used by the visual system to analyze a scene; achromatic cues include luminance, texture, contrast and motion. [sent-3, score-0.479]

2 Singlecell recordings have shown that the mammalian visual cortex contains neurons that respond similarly to scene structure (e. [sent-4, score-0.264]

3 , orientation of a boundary), regardless of the cue type conveying this information. [sent-6, score-0.392]

4 This paper shows that cue-invariant response properties of simple- and complex-type cells can be learned from natural image data in an unsupervised manner. [sent-7, score-0.787]

5 In order to do this, we also extend a previous conceptual model of cue invariance so that it can be applied to model simple- and complex-cell responses. [sent-8, score-0.293]

6 Our results relate cue-invariant response properties to natural image statistics, thereby showing how the statistical modeling approach can be used to model processing beyond the elemental response properties visual neurons. [sent-9, score-0.871]

7 This work also demonstrates how to learn, from natural image data, more sophisticated feature detectors than those based on changes in mean luminance, thereby paving the way for new data-driven approaches to image processing and computer vision. [sent-10, score-0.411]

8 Spatiotemporal variations in the mean luminance level – which are also called ﬁrst-order cues – are computationally the simplest of these; the name ’ﬁrst-order’ comes from the idea that a single linear ﬁltering operation can detect these cues. [sent-12, score-0.324]

9 Other types of visual cues include contrast, texture and motion; in general, cues related to variations in other characteristics than mean luminance are called higher-order (also called non-Fourier) cues; the analysis of these is thought to involve more than one level of processing/ﬁltering. [sent-13, score-0.612]

10 Single-cell recordings have shown that the mammalian visual cortex contains neurons that are selective to both ﬁrst- and higher-order cues. [sent-14, score-0.271]

11 For example, a neuron may exhibit similar selectivity to the orientation of a boundary, regardless of whether the boundary is a result of spatial changes in mean luminance or contrast [1]. [sent-15, score-0.518]

12 Monkey cortical areas V1 and V2, and cat cortical areas 17 and 18, contain both simple- (orientation-, frequency- and phase-selective) and complex-type (orientation- and frequency-selective, phase-invariant) cells that exhibit such cue-invariant response properties [2, 1, 3, 4, 5]. [sent-16, score-0.532]

13 Recent computational modeling of the visual system has produced fundamental results relating stimulus statistics to ﬁrst-order response properties of simple and complex cells (see, e. [sent-18, score-0.689]

14 The linear stream responds to ﬁrst-order cues, while the nonlinear stream responds to higher-order cues. [sent-22, score-0.262]

15 The model consists of simple cells, complex cells and a feedback path leading from a population of high-frequency ﬁrst-order complex cells to low-frequency cue-invariant simple cells. [sent-26, score-1.114]

16 In a cue-invariant simple cell, the feedback is ﬁltered with a ﬁlter that has similar spatial characteristics as the feedforward ﬁlter of the cell. [sent-27, score-0.88]

17 Note that while our model results in cue-invariant response properties, it is not a model of cue integration, because in the sum the two paths can cancel out. [sent-29, score-0.49]

18 In this instance of the model, the high-frequency cells prefer horizontal stimuli, while the low-frequency cue-invariant cells prefer vertical stimuli; in other instances, this relationship can be different. [sent-31, score-0.427]

19 statistics -based framework for cue-invariant responses of both simple and complex cells. [sent-34, score-0.284]

20 In order to achieve this, we also extend the two-stream model of cue-invariant responses (Figure 1A) to account for cue-invariant responses at both simple- and complex-cell levels. [sent-35, score-0.398]

21 In Section 2 we describe our version of the two-stream model of cue-invariant responses, which is based on feedback from complex cells to simple cells. [sent-37, score-0.792]

22 In Section 3 we formulate an unsupervised learning rule for learning these feedback connections. [sent-38, score-0.568]

23 We apply our learning rule to natural image data, and show that this results in the emergence of connections that give rise to cue-invariant responses at both simple- and complex-cell levels. [sent-39, score-0.482]

24 2 A model of cue-invariant responses The most prominent model of cue-invariant responses introduced in previous research is the two-stream model (see, e. [sent-41, score-0.45]

25 In this research we have extended this model so that it can be applied directly to model the cue-invariant responses of simple and complex cells. [sent-44, score-0.336]

26 (a) The feedforward ﬁlter (Gabor function [10]) of a high-frequency ﬁrst-order simple cell; the ﬁlter has size 19 × 19 pixels, which is the size of the image data in our experiments. [sent-47, score-0.482]

27 (b) The feedforward ﬁlter of another ﬁrst-order simple cell. [sent-48, score-0.348]

28 This feedforward ﬁlter is otherwise similar to the one in (a), except that there is a phase difference of π/2 between the two; together, the feedforward ﬁlters in (a) and (b) are used to implement an energy model of a complex cell. [sent-49, score-0.834]

29 (c) A lattice of size 7 × 7 of high-frequency ﬁlters of the type shown in (a); these ﬁlters are otherwise identical, except that their spatial locations vary. [sent-50, score-0.209]

30 Together, the lattices shown in (c) and (d) are used to implement a 7 × 7 lattice of energy-model complex cells with different spatial positions; the output of this lattice is the feedback relayed to the low-frequency cueinvariant cells. [sent-52, score-1.176]

31 (g) A feedback ﬁlter of size 7 × 7 for the simple cell whose feedforward ﬁlter is shown in (e); in order to avoid confusion between feedforward ﬁlters and feedback ﬁlters, the latter are visualized as lattices of slightly rounded rectangles. [sent-54, score-1.847]

32 (h) A feedback ﬁlter for the simple cell whose feedforward ﬁlter is shown in (f). [sent-55, score-0.948]

33 The feedback ﬁlters in (g) and (h) have been obtained by applying the learning algorithm introduced in this paper (see Section 3 for details). [sent-56, score-0.492]

34 models of simple cells and energy models of complex cells [10], and a feedback path from the complex-cell level to the simple-cell level. [sent-57, score-1.04]

35 This feedback path introduces a second, nonlinear input stream to cue-invariant cells, and gives rise to cue-invariant responses in these cells. [sent-58, score-0.87]

36 To avoid confusion between the two types of ﬁlters – one type operating on the input image and the other on the feedback – we will use the term ’feedforward ﬁlter’ for the former and the term ’feedback ﬁlter’ for the latter. [sent-59, score-0.681]

37 Figure 2 shows the feedforward and feedback ﬁlters of a concrete instance (implementation) of our model. [sent-60, score-0.811]

38 Gabor functions [10] are used to model simple-cell feedforward ﬁlters. [sent-61, score-0.345]

39 Figure 3 illustrates the design of higher-order gratings, and shows how the complex-cell lattice of the model transforms higher-order cues into feedback activity patterns that resemble corresponding ﬁrst-order cues. [sent-62, score-0.895]

40 These measurements show that our model possesses the fundamental cueinvariant response properties: in our model, a cue-invariant neuron has similar selectivity to the orientation, frequency and phase of a grating stimulus, regardless of cue type (see ﬁgure caption for details). [sent-64, score-0.923]

41 We now proceed to show how the feedback ﬁlters of our model (Figures 2g and h) can be learned from natural image data. [sent-65, score-0.799]

42 1 Learning feedback connections in an unsupervised manner The objective function and the learning algorithm In this section we introduce an unsupervised algorithm for learning feedback connection weights from complex cells to simple cells. [sent-67, score-1.457]

43 Design of grating stimuli: Each row illustrates how, for a particular cue, a grating stimulus is composed of sinusoidal constituents; the equation of each stimulus (B, G, K) as a function of the constituents is shown under the stimulus. [sent-69, score-0.48]

44 Note that the orientation, frequency and phase of each grating is determined by the ﬁrst sinusoidal constituent (A, D, I); here these parameters are the same for all stimuli. [sent-70, score-0.31]

45 Feedback activity: The rightmost column shows the feedback activity – that is, response of the complex-cell lattice (see Figures 2c and d) – for the three types of stimuli. [sent-72, score-0.927]

46 (C) There is no response to the luminance stimuli, since the orientation and frequency of the stimulus are different from those of the high-frequency feedforward ﬁlters. [sent-73, score-0.953]

47 (H, L) For other cue types, the lattice detects the locations of energy of the vertical high-frequency constituent (E, J), thereby resulting in feedback activity that has a spatial pattern similar to a corresponding luminance pattern (A). [sent-74, score-1.27]

48 Thus, the complex-cell lattice transforms higherorder cues into activity patterns that resemble ﬁrst-order cues, and these can subsequently produce a strong response in a feedback ﬁlter (compare (H) and (L) with the feedback ﬁlter in Figure 2g). [sent-75, score-1.649]

49 was shown in Figure 4, these feedback ﬁlters give rise to cue-invariant response properties. [sent-77, score-0.734]

50 The intuitive idea behind the learning algorithm is the following: in natural images, higherorder cues tend to coincide with ﬁrst-order cues. [sent-78, score-0.345]

51 For example, when two different textures are adjacent, there is often also a luminance border between them; two examples of this phenomenon are shown in Figure 5. [sent-79, score-0.214]

52 Therefore, cue-invariant response properties could be a result of learning in which large responses in the feedforward channel (ﬁrst-order responses) have become associated with large responses in the feedback channel (higherorder responses). [sent-80, score-1.437]

53 Let vector c(n) = T [c1 (n) c2 (n) · · · cK (n)] denote the responses of a set of K ﬁrst-order high-frequency complex cells for the input image with index n. [sent-85, score-0.565]

54 In our case the number of these complex cells is K = 7 × 7 = 49 (see Figures 2c and d), so the dimension of this vector is 49. [sent-86, score-0.245]

55 This vectorization can be done in a standard manner [15] by scanning values from the 2D lattice column-wise into a vector; when the learned feedback ﬁlter is visualized, the ﬁlter is “unvectorized” with a reverse procedure. [sent-87, score-0.71]

56 Let s(n) denote the response of a single low- π/2 cue orientation response 0 0 0. [sent-88, score-0.721]

57 3 cue frequency π 0 cue phase 2π π/2 cue orientation standard simple cell (without feedback) 1 0 0 1 0 0 0. [sent-91, score-1.009]

58 3 cue frequency π/2 π cue orientation F 1 0 0 0. [sent-94, score-0.606]

59 3 cue frequency I 1 0 π 0 2π cue phase J response 0 π H 1 0 −1 response response G 1 0 −1 π 0 cue phase 2π K 0. [sent-97, score-1.412]

60 3 carrier frequency response L response 0 E 1 response 0 π C 1 response response 0 D response B 1 response response A cue-invariant complex cell (with feedback) response cue-invariant simple cell (with feedback) 0. [sent-102, score-2.303]

61 3 carrier frequency Figure 4: Our model fulﬁlls the fundamental properties of cue-invariant responses. [sent-107, score-0.279]

62 The plots show tuning curves for a cue-invariant simple cell – corresponding to the ﬁlters of Figures 2e and g – and complex cell of our new model (two leftmost columns), and a standard simple-cell model without feedback processing (rightmost column). [sent-108, score-0.858]

63 Solid lines show responses to luminance-deﬁned gratings (Figure 3B), dotted lines show responses to texture-deﬁned gratings (Figure 3G), and dashed lines show responses to contrast-deﬁned gratings (Figure 3K). [sent-109, score-0.897]

64 (A–I) In our model, a neuron has similar selectivity to the orientation, frequency and phase of a grating stimulus, regardless of cue type; in contrast, a standard simple-cell model, without the feedback path, is only selective to the parameters of a luminance-deﬁned grating. [sent-110, score-1.064]

65 The preferred frequency is lower for higher-order gratings than for ﬁrst-order gratings; similar observations have been made in single-cell recordings [4]. [sent-111, score-0.225]

66 (J–M) In our model, the neurons are also selective to the orientation and frequency of the carrier (Figure 3J) of a contrast-deﬁned grating (Figure 3K), thus conforming with single-cell recordings [1]. [sent-112, score-0.528]

67 Note that these measurements were made with the feedback ﬁlters learned by our unsupervised algorithm (see Section 3); thus, these measurements conﬁrm that learning results in cue-invariant response properties. [sent-113, score-0.909]

68 Image in (A) contains a near-vertical luminance boundary across the image; the boundary in (B) is nearhorizontal. [sent-115, score-0.32]

69 In both (A) and (B), texture is different on different sides of the luminance border. [sent-116, score-0.244]

70 ) B C D E F A G H I J Figure 6: (A-D, F-I) Feedback ﬁlters (top row) learned from natural image data by using our unsupervised learning algorithm; the bottom row shows the corresponding feedforward ﬁlters. [sent-118, score-0.676]

71 For a quantitative evaluation of the cue-invariant response properties resulting from the learned ﬁlters (A) and (B), see Figure 4. [sent-119, score-0.336]

72 (E, J) The result of a control experiment, in which Gaussian white noise was used as input data; (J) shows the feedforward ﬁlter used in this control experiment. [sent-120, score-0.319]

73 frequency simple cell for the input image with index n. [sent-121, score-0.339]

74 In our learning algorithm all the feedforward ﬁlters are ﬁxed and only a feedback ﬁlter is learned; this means that c(n) and s(n) can be computed for all n (all images) prior to applying the learning algorithm. [sent-122, score-0.811]

75 Let us denote the K-dimensional feedback ﬁlter with w; this ﬁlter is learned by our algorithm. [sent-123, score-0.546]

76 Let b(n) = w T c(n), that is, b(n) is the signal obtained when the feedback activity from the complex-cell lattice is ﬁltered with the feedback ﬁlter; the overall activity of a cueinvariant simple cell is then s(n) + b(n). [sent-124, score-1.48]

77 To keep the output of the feedback ﬁlter b(n) bounded, we enforce a unit energy constraint on b(n), leading into constraint T 2 h(w) = E b2 (n) = wT E c(n)c(n)T w = wT Cw = 1, (2) where C = E c(n)c(n) is also positive-semideﬁnite and can be computed prior to learning. [sent-126, score-0.59]

78 2 Experiments The algorithm described above was applied to natural image data, which was sampled from a set of over 4,000 natural images [8]. [sent-144, score-0.372]

79 Simple-cell feedforward responses s(n) were computed using the ﬁlter shown in Figure 2e, and the set of high-frequency complex-cell lattice activities c(n) was computed using the ﬁlters shown in Figures 2c and d. [sent-147, score-0.645]

80 This preprocessing tends to weaken contrast borders, implying that in our experiments, learning higher-order responses is mostly based on texture boundaries that coincide with luminance boundaries. [sent-149, score-0.548]

81 It should be noted, however, that in spite of this preprocessing step, the resulting feedback ﬁlters produce cue-invariant responses to both texture- and contrast-deﬁned cues (see Figure 4). [sent-150, score-0.866]

82 In order to make the components of c(n) have zero mean, and focus on the structure of feedback activity patterns instead of overall constant activation, the local mean (DC component) was removed from each c(n). [sent-151, score-0.558]

83 The resulting feedback ﬁlter is shown in Figure 6A (see also Figure 2g). [sent-156, score-0.492]

84 Data sampling, preprocessing and the learning algorithm were then repeated, but this time using the feedforward ﬁlter shown in Figure 2f; the feedback ﬁlter obtained from this run is shown in Figure 6B (see also Figure 2h). [sent-157, score-0.857]

85 The measurements in Figure 4 show that these feedback ﬁlters result in cueinvariant response properties at both simple- and complex-cell levels. [sent-158, score-0.877]

86 Thus, our unsupervised algorithm learns cue-invariant response properties from natural image data. [sent-159, score-0.557]

87 This veriﬁes that our original results do reﬂect the statistics of natural image data. [sent-164, score-0.227]

88 4 Conclusions This paper has shown that cue-invariant response properties can be learned from natural image data in an unsupervised manner. [sent-165, score-0.611]

89 The results were based on a model in which there is a feedback path from complex cells to simple cells, and an unsupervised algorithm which maximizes the correlation of the energies of the feedforward and ﬁltered feedback signals. [sent-166, score-1.753]

90 The intuitive idea behind the algorithm is that in natural visual stimuli, higher-order cues tend to coincide with ﬁrst-order cues. [sent-167, score-0.364]

91 Simulations were performed to validate that the learned feedback ﬁlters give rise to in cue-invariant response properties. [sent-168, score-0.788]

92 First, for the ﬁrst time it has been shown that cue-invariant response properties of simple and complex cells emerge from the statistical properties of natural images. [sent-170, score-0.676]

93 Second, our results suggest that cue invariance can result from feedback from complex cells to simple cells; no feedback from higher cortical areas would thus be needed. [sent-171, score-1.531]

94 Third, our research demonstrates how higher-order feature detectors can be learned from natural data in an unsupervised manner; this is an important step towards general-purpose data-driven approaches to image processing and computer vision. [sent-172, score-0.381]

95 A processsing stream in mammalian visual cortex neurons for non-Fourier responses. [sent-184, score-0.294]

96 Temporal and spatial response to second-order stimuli in cat area 18. [sent-198, score-0.348]

97 Physiological responses of New World monkey V1 neurons to stimuli deﬁned by coherent motion. [sent-207, score-0.289]

98 Independent component ﬁlters of natural images compared with simple cells in primary visual cortex. [sent-225, score-0.41]

99 A two-layer sparse coding model learns simple and complex cell receptive ﬁelds and topography from natural images. [sent-231, score-0.358]

100 Temporal and spatiotemporal coherence in simple-cell responses: a generative model of natural image sequences. [sent-253, score-0.305]

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