Rao, R. P. N., and Ballard, D. H. 1996. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation 9:721--763.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Some types of eigen features can be learned and updated incrementally [130] Hidden nodes in a neural network may be seen as computing features from an infinite set. In particular, neural networks can implement several projection pursuit methods as well as PCA in biologically plausible ways [47, 48, 91]. Projection pursuit iteratively seeks low dimensional projections of high dimensional data that maximize a given projection index. The projection index encodes some measure of interestingness of the data, typically based on the deviation 11 from Gaussian normality [59, 36, 99] The projections ....

....using a sparseness or minimum description length objective that favors representations with many vanishing coe#cients, then basis functions emerge that resemble oriented bandpass filters. Notably, these are strongly localized even without an explicit constraint or bias toward locality [80, 91]. This result has been well established in the literature, and serves as a natural explanation for the 19 shape of receptive fields in the mammalian early visual pathway. The receptive fields of visual neurons in the primary visual cortex have often been modeled by oriented derivatives of ....

Rao, R. P. N., and Ballard, D. H. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation 9, 4 (May 1997), 721--763.

....to the input query and de activated if they do not match. Also similar in spirit to our approach is the bidirectional model of Kosko[10] for more recent work see, e.g. Sommer and Palm[20] Other models iteratively combine top down and bottom up information (e.g. Hinton et al. 5] Rao and Ballard[14]) although these are not used as part of a memory system with complete items stored in memory. Our model differs from all of these in using a Markov model as an intermediate layer between the input and the dictionary. This allows the model to answer superghost queries, and leads to different ....

R. Rao and D. Ballard. "Dynamic Model of Visual Recognition Predicts Neural Response Properties in the Visual Cortex," Neural Computation, 9(4):721-763, 1997.

.... 331, 241, 249, 42] multisensor fusion for hydrology applications [84, 198, 139] process control [306, 196, 327, 18] synthetic aperture radar image analysis and fusion [309, 77, 160, 119, 185] geographic systems [93, 189] medical image analysis [290] models of neural responses in human vision [274]; and mathematical physics [136, 15, 94] In this section we introduce several of these applications which serve to provide context, motivation, and illustrations for the development that follows, as well as to indicate the breadth of problems to which these methods can be applied. 2.1 Ocean ....

....in so called multirate Kalman filtering and estimation theory [150, 151, 51, 96, 79] or, as in the methods discussed in Section 7.1, in which time is treated as a sequential variable but space is treated in a MR graphical manner. The results we have presented (and others in the literature such as [274]) represent a start to this very important area which extends well beyond MR modeling to the investigation of Dynamic Bayesian Networks. As this discussion and the results summarized in the preceding sections illustrate, multiresolution statistical modeling and inference remains a fertile, ....

R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Comput., 9(4):721--763, May 1997.

....rewards may be delayed. To fulfil these constraints, different approaches are viable. A useful way, which handles uncertainty by allowing probabilistic transitions between states , is provided by hidden Markov models [45] or, analogously, in the optimal control formulation, by Kalman filtering [23], 58] Unfortunately, Markov models cannot cope with agent s actions that change the world. This task requires an extension to Markov decision processes (MDP) that can incorporate learn the different actions available to the agent. One such tool is reinforcement learning (RL) 5.1 ....

R. P. N. Rao and D. H. Ballard: "Dynamic model of visual recognition predicts neural response properties in the visual cortex": Neut. Comp.: vol 9 (1997),pp. 721 763.

....some advantages of an iterative projection algorithm that can work with a range of possible feature sets. These approaches can be combined in the future by applying our algorithm to different sorts of features, such as the output of multi scale filters or some steerable filter. Rao and Ballard[99] presents a different way of doing this. 154 Thus, to tie up, we can say the following. Referring back to the skeletal iteration scheme in section 5.4, we see that combining the two steps 5.7 and 5.4; as well as the steps 5.5 and 5.6; result in an iteration scheme that stays entirely in the ....

....Our work differs from feed forward methods in many ways, especially in that our method is iterative, and uses features symmetrically to relate the memory to input in both directions. Many other models iteratively combine top down and bottom up information (e.g. Hinton et a1154] Rao and Ballard[99]) The structure of our algorithm is particularly related to methods like the Wake Sleep algorithm of Hinton et al., although we differ from these in many ways, especially our use of this for associative memory with complete memory of stored items. In spirit our approach is also similar to that of ....

R. Rao and D. Ballard, "Dynamic Model of Visual Recognition Predicts Neural Response Properties in the Visual Cortex", Neural Computation, vol. 9, no. 4, pp. 721 763, 1997.

....(see also Baum, et al. 2] Our work differs from feedforward methods in that our method is iterative, and uses features symmetrically to relate the memory to input in both directions. Other models iteratively combine top down and bottom up information (e.g. Hinton et al. 3] Rao and Ballard[11]) The structure of our algorithm is related to methods like the Wake Sleep algorithm of Hinton et al. although we differ in our use of this for associative memory with complete memory of stored items. Our model is designed to handle more complex tasks than standard associative memory, in which ....

R. Rao and D. Ballard. "Dynamic Model of Visual Recognition Predicts Neural Response Properties in the Visual Cortex," Neural Computation, 9(4):721-763, 1997.

....the system makes a guess about the object that may be in the image, synthesizes a neural representation of it relying on stored memories, measures the difference between the hallucination and the actual visual input and proceeds to correct the initial hypothesis. The models of Rao Ballard [35], or of Mumford [30] and in part Ullman s [49] belong to this category. Other models use feedback control to renormalize the input image in position and scale before attempting to match it to a database of stored objects (as in the shifter circuit [2, 31] or to conversely tune the ....

Rao, R. and Ballard, D. (1997). Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Comp. 9, 721--763.

....tool that was used in [Welsh 1996] to smooth incomplete motion tracking data, and this could also be implemented to counteract the spatial and temporal inaccuracies of the eye tracker, and the physiological noise described above. A Kalman filter model of the human cortex is presented in [Rao and Ballard 1997], and is used to explain the fixation behaviour of monkeys freely viewing a natural scene. 3.3 Physiology and Neurophysiology We now provide an overview of the anatomy and physiology of the eye and the neurophysiology of the visual cortex. More detailed explanations may be found in [De Valois ....

Rao, R.P.N. Ballard, D.H. Dynamic Model of Visual Recognition Predicts Neural Response Properties in the Visual Cortex. Neural Computation, 9(4) 721-763

....here is relatively sparse. Most of the work which exploits neural network architectures adopts the working model that the recognition process should be trained from a few examples and that the generalisation properties of the network should be exploited to accommodate variable object appearance (Rao and Ballard, 1997). An example of a more principled approach is Bregler and Maliks (Bregler and Malik, 1996) use of the expectation maximisation (Dempster et al. 1977) algorithm to learn the channel mixing proportions. This procedure has been demonstrated to work effectively on relatively noise free and ....

Rao, R. P. N. and Ballard, D. H. (1997). Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9:721--763.

....activations the data are under estimated during reconstruction. The weights will compensate by learning larger values in order to increase the activations. To preserve sparse coding a weight constraint must be introduced. The hidden representation can span more than just one hierarchical level [14][11] Then a given neuron not only adjusts its activation to minimize the reconstruction error on the lower level but also to match the feedback ( prediction ) from a higher level representation. Concatenation of levels In a model for the evolution of a two level hierarchy all hidden neurons have ....

R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties of the visual cortex. Neur. Comp., 9(4):721--763, 1997.

....1996; Lu et al. 1996) Some of these were trained on natural images, but with the exception of Press and Lee (1996) and Lu et al. 1996) they did not show a full family of receptive fields for forming a complete image code. Finally, in the realm of generative models, Dayan et al. 1995) and Rao and Ballard (1996) have described methods for learning the causal structure in data in a hierarchical fashion. Rao and Ballard s network, when reduced to a single layer system such as ours, is very similar but uses a quadratic penalty term (corresponding to a Gaussian prior) When trained on natural images, it does ....

Rao RPN, Ballard DH (1996) "Dynamic model of visual recognition predicts neural response properties in the visual cortex," Neural Computation, in review.

....cells in this region show an enhanced response, to background, in anticipation of rewarding events, which in turn can be suppressed below background in case the anticipated reward does not occur. In addition an equivalent method has been successfully applied to the study of cortical dynamics [Rao and Ballard, 1997]. In current work we are exploring the option to allow the recurrent inhibition of the CS population to change the level of activity given a particular level of background activity. This implies, however, that the dynamics of the weights needs to be extended with a variable threshold as proposed ....

Rao, R. and Ballard, D. (1997). Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9:712--763.

....problem. They made a connection between this method and the Baum Welch estimation algorithm for hidden Markov models (HMMs) North and Blake (North and Blake 1998) have implemented the method to learn linear dynamic state space models used for tracking contours in images. Rao and Ballard (Rao and Ballard 1997) have also explored the relevance of the EM algorithm together with state space estimation in the field of vision. They have developed an hierarchical network model of visual recognition that encapsulates these concepts. Ghahramani (Ghahramani 1997) has embedded the EM method for learning dynamic ....

Rao, R. P. N. and Ballard, D. H. (1997). Dynamic model of visual recognition predicts neural response properties in the visual cortex, Neural Computation 9(4): 721--763.

.... These loops can serve to amplify the feedforward signals as an effective conductance [3] or send down foci of attention or expectations [4, 5] Feedforward and feedback pathways respectively can carry information residuals and input predictions in a kind of hierarchical Kalman Filter [6, 7]. ART was among the first theories that interpreted this recursive flow of information in terms of functional relevance (see [8] for a recent review with an emphasis on biological topics) The fact that ART was inspired by recurrent brain structures should not be confused with issues of ....

P.N. Rajesh Rao and D.H. Ballard, "Dynamic Model of Visual Recognition Predicts Neural Response Properties in the Visual Cortex", (to appear in Neural Computation) Technical report Rochester Univ., 96.2 (revision of TR 95.4), 1996.

....problem. They made a connection between this method and the Baum Welch estimation algorithm for hidden Markov models (HMMs) North and Blake (North and Blake 1998) have implemented the method to learn linear dynamic state space models used for tracking contours in images. Rao and Ballard (Rao and Ballard 1997) have also explored the relevance of the EM algorithm together with state space estimation in the field of vision. They have developed a hierarchical network model of visual recognition that encapsulates those concepts. Ghahramani (Ghahramani 1997) has embedded the EM method for learning dynamic ....

Rao, R. P. and Ballard, D. H. (1997). Dynamic model of visual recognition predicts neural response properties in the visual cortex, Neural Computation 9: 721--763.

....to receive. Comparing the expected stimulus to the received stimulus allows the unit to perform a number of functions including filtering of expected redundant inputs, contrast enhancement for image recognition when compared to a stored prototype, and novelty detection. Recently Rao and Ballard ([5]) have proposed a similar neural architecture using feedback connections for carrying an expectation signal. They demonstrate that units of their network develop receptive fields qualitatively similar to those found in visual areas V1 and V2 of the brain, lending further support to the notion that ....

Rajesh P. N. Rao and Dana H. Ballard, "Dynamic model of visual recognition predicts neural response properties in the visual cortex", Tech. Rep. 96.2, Department of Computer Science, University of Rochester, 1996.

....inaccurate[7, 8] 2. Up propagation has an explicit generative model, and recognition is done by inverting the generative model. The accuracy of this implicit recognition model has not yet been tested empirically. Iterative inversion of generative models has also been proposed for linear networks[2, 9] and probabilistic belief networks[10] 3. In the autoencoder[11] and the Helmholtz machine[12] there are separate models of recognition and generation, both explicit. Recognition uses only bottom up connections, and generation uses only top down connections. Neither process is iterative. Both ....

R. P. N. Rao and D. H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Comput., 9:721--63, 1997.

....to the speech recognition problem. They made a connection between this method and the Baum Welch estimation algorithm for hidden Markov models (HMMs) North and Blake [28] have implemented the method to learn linear dynamic state space models used for tracking contours in images. Rao and Ballard [30] have also explored the relevance of the EM algorithm together with state space estimation in the field of vision. They have developed a hierarchical network model of visual recognition that encapsulates those concepts. Ghahramani [11] has embedded the EM method for learning dynamic linear systems ....

R P Rao and D H Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9:721-- 763, 1997.

....closer to the primary area to those further away follow the FF pattern, while those in the opposite direction follow the FB pattern (fig. 1, left) Presumably these patterns reflect a computational need to treat stimulus driven activity differently from internal state driven activity in each area [10], however it is difficult to make this more precise simply based on the anatomy, because most cortical celltypes possess dendritic and axonal arborizations extending over multiple layers [6] fig. 1, right) On the other hand, technical constraints Preprint submitted to Elsevier Preprint 10 ....

....propagates further, faster, and with greater amplitude. The middle layer was intermediate. waves in our anatomically based models suggests that they should be included as well; theoretical analyses [4] emphasize that lateral length constants are important. Comparatively few cortical models [10] have incorporated laminar structure, largely because the relevant architectural details are not clear from the biology. The present work suggests based on convergent evidence that processing with different compartments is partially independent, and it lays foundations for investigating this ....

R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation 9 (1997) 805--47.

....utilizes relaxation dynamics (Fomin T, Kormendy R acz J, and Lorincz A 1997; Lorincz A 1997b) DCR architecture is closely related to the relaxation equations of Olshausen and Field (Olshausen BA and Field DJ 1996) that optimize information transfer. The Kalman filter approach of Rao and Ballard (Rao RPN and Ballard DH 1997) can be seen as a DCR architecture extended by predictive connections. At first sight, reconstruction dynamics is disadvantageous since it gives rise to delays. Realistic models of reconstruction dynamics should also take losses, i.e. the leaky nature of neural processing, into account and this ....

Rao RPN and Ballard DH (1997). Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation 9, 721--763.

....1996; Lu et al. 1996) Some of these were trained on natural images, but with the exception of Press and Lee (1996) and Lu et al. 1996) they did not show a full family of receptive fields for forming a complete image code. Finally, in the realm of generative models, Dayan et al. 1995) and Rao and Ballard (1997) have described methods for learning the causal structure in data in a hierarchical fashion. Rao and Ballard s network, when reduced to a single layer system such as ours, is very similar but uses a quadratic penalty term (corresponding to a Gaussian prior) When trained on natural images, it does ....

Rao RPN, Ballard DH (1997) "Dynamic model of visual recognition predicts neural response properties in the visual cortex," Neural Computation, 9: 721-763.

No context found.

Rajesh P. N. Rao and Dana H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9:721-763, 1997.

.... Van Essen, 1994, Zemel et al. 1998, Deneve et al. 1999, Pouget et al. 2000] Other models have relied on mean field approximations or various forms of Gibbs sampling for perceptual inference [Hinton and Sejnowski, 1986, Dayan et al. 1995, Dayan and Hinton, 1996, Hinton and Ghahramani, 1997, Rao and Ballard, 1997, Rao, 1999, Rao and Ballard, 1999, Hinton and Brown, 2002] We describe a new approach to Bayesian computation in a cortical network model. We specify how the feedforward and recurrent connections in the network may be selected to perform Bayesian inference for an arbitrary hidden Markov model. ....

....could be extended to allow hierarchical Bayesian inference in multi layer cortical networks. Previous models of hierarchical inference and learning in cortical circuits should prove useful in addressing this question [Dayan et al. 1995, Dayan and Hinton, 1996, Hinton and Ghahramani, 1997, Rao and Ballard, 1997, Rao and Ballard, 1999] A fi nal question of interest is how the rewards associated with various choices available in a task influence the decision neurons in the model. We expect ideas from reinforcement learning and Bayesian decision theory as well as recent neurophysiological results in the ....

Rao, R. P. N. and Ballard, D. H. (1997). Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9(4):721--763.

....network develop localized oriented receptive fields tuned towards various transformations, thus suggesting an alternate functional interpretation of cortical neurons with such receptive fields. The model described herein extends the previously proposed Kalman filter model of the visual cortex [15] by including a first order component that represents transformations of input features, in addition to the zeroth order component that represents object centered features. The functional dichotomy between object recognition and transformation estimation utilized by this extended model parallels ....

.... r r r r (10) where ) It is easy to show that minimizing is equivalent to maximizing the log likelihood of generating the observed data with respect to the model parameters , r, and x (see, for example, [15]) We can additionally add to the terms relating to prior distributions for the parameters. Here, we use zero mean Gaussian distributions for the model priors (see [12] for other alternatives) yielding the optimization function: 287 r x ....

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R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9(4):721--763, 1997.

....rotations, and expansions contractions [2] Thus, the neurobiological data strongly suggest that the visual system factors retinal stimuli into object centered features and their relative transformations. We have previously introduced a dynamic Kalman filter based model of visual recognition [10]. The central idea behind this model is that the visual cortex can be regarded as a network that gains enormous efficacies by hierarchically encoding image features and dynamically predicting input stimuli. This model was however susceptible to image plane transformations of previously encoded ....

....image Jacobian with the 1 vector 0 , which describes the relative transformation that the image has undergone. We assume, for simplicity, that 0 and use D to denote the difference e 36228 . We can then model the above equation using the following stochastic model (cf. [10]) D # ) 2) where is a set of generative weights approximating the Jacobian and ( is a zero mean Gaussian noise process with covariance S ( For deriving the learning rules, it is convenient to view the matrix as an , 1 vector .0 1 ....

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R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation (in press). Copy available at ftp://ftp.cs.rochester.edu/pub/u/rao/papers/dynrec.ps.Z, 1996.

.... network that includes the additional constraint of maximizing the sparseness of the distribution of output activities develops, when trained on static natural images, synaptic weights with localized, oriented spatial receptive fields [Olshausen and Field, 1996 ] see also [Harpur and Prager, 1996; Rao and Ballard, 1997a ] and related work on projection pursuit [Huber, 1985] based learning methods [Intrator, 1992; Law and Cooper, 1994; Shouval, 1995 ] Similar results have also been obtained using an algorithm that extracts the independent components of a set of static natural images [Bell and Sejnowski, 1997 ] ....

....by the redundancy reduction principle. Our approach utilizes a spatiotemporal generative model that can be viewed as a simple extension of the spatial generative model used by Harpur and Prager[Harpur and Prager, 1996 ] Olshausen and Field [Olshausen and 2 Field, 1996] Rao and Ballard [Rao and Ballard, 1997a ] and others. The spatiotemporal generative model allows neurons in the network to perform not just a spatial summation of the current input, but a spatiotemporal summation of both current and past inputs over a finite spatiotemporal extent. The network learns efficient sparse distributed ....

[Article contains additional citation context not shown here]

R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9(4):721--763, 1997.

....[Cipra, 1993] Even today, Kalman filters form the heart of inertial navigation systems that safely guide commercial airplanes to their respective destinations. In this paper, we describe a hierarchical Kalman filter based model of dynamic recognition and visual learning. As described elsewhere [Rao and Ballard, 1996a] the Kalman filter model of recognition can be regarded as a natural generalization of some previous schemes for appearancebased recognition such as principal component analysis (PCA) cf. the Eigenface method of [Turk and Pentland, 1991] and the Eigenspace method of [Murase and Nayar, 1995] ....

....Faugeras, 1986; Blake and Yuille, 1992; Broida and Chellappa, 1986; Dickmanns and Mysliwetz, 1992; Hallam, 1983; Matthies et al. 1989; Pentland, 1992] However, in complex dynamic environments, the formulation of such hand coded models becomes increasingly difficult. An interesting alternative [Rao and Ballard, 1996a] is to initialize the matrices U and V to small random values, and then adapt these values in response to input data, thereby learning an internal model of the input environment. We explore this alternative in this section. 6.1 Learning the Measurement Matrix The starting point for deriving ....

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R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9(4):805-847, 1997. Also, Technical Report 96.2, National Resource Laboratory for the Study of Brain and Behavior, Department of Computer Science, University of Rochester, 1996.

....than n, the response vector r is an efficient compressed representation of the inputimage. A reconstruction of the input image b I can be generated from r by using the following relation which simply inverts the transformation in Equation 1: b I = Ur (2) It is well known (see, for example, [14]) that the eigenvector matrix U minimizes the pixel wise expected reconstruction error function: J(U ) n X i=1 (I i Gamma U i r) 2 = I Gamma Ur) T (I Gamma Ur) 3) where I i denotes the ith pixel of I and U i denotes the ith row of U ) over all inputs subject to the constraint that ....

....first two terms in the sum above arise from the prior Gaussian densities for r and u as given by G(r; M ) and G(u; S) while the latter two terms are non linear functions of r and u associated with w. For example, one could use f(x) g(x) ffx 2 to allow regularization and avoid overfitting [14]. Using a function such as f(x) ff log(1 x 2 ) causes higher order correlations to be sought [12] These functions are applied to all components x of a given vector x and the results are summed in the optimization function. 2.2. MDL Based Kalman Filters In this section, we use the ....

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R. Rao and D. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9:805--847, 1997.

....whose primary goal is visual recognition This research was supported by NIH PHS research grant 1 P41 RR09283. I am greatly indebted to Dana Ballard for many useful discussions and suggestions. In this paper, we extend a previously proposed Kalman filter based model of visual recognition [13, 12] to handle the case of multiple objects, occlusions, and clutter in the visual field. We provide simulation results suggesting that certain forms of attention can be viewed as an emergent property of the interaction between bottom up signals and top down expectations during visual recognition. The ....

.... 2 A KALMAN FILTER MODEL OF VISUAL RECOGNITION We have previously introduced a Kalman filter based model of visual recognition and have shown how this model can be used to explain neurophysiological effects such as endstopping and neural response suppression during free viewing of natural images [12, 13]. The Kalman filter [7] is essentially a linear dynamical system that attempts to mimic the behavior of an observed natural process. At any time instant t, the filter assumes that the internal state of the given natural process can be represented as a k Theta 1 vector r(t) Although not directly ....

[Article contains additional citation context not shown here]

R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9(4):721--763, 1997.

....network develop localized oriented receptive fields tuned towards various transformations, thus suggesting an alternate functional interpretation of cortical neurons with such receptive fields. The model described herein extends the previously proposed Kalman filter model of the visual cortex [15] by including a first order component that represents transformations of input features, in addition to the zeroth order component that represents object centered features. The functional dichotomy between object recognition and transformation estimation utilized by this extended model parallels ....

....(9) I(x) Gamma Ur Gamma XUr) T (I(x) Gamma Ur Gamma XUr) 10) where X = P m i=1 x i D i . It is easy to show that minimizing E 1 is equivalent to maximizing the log likelihood of generating the observed data I(x) with respect to the model parameters U , D, r, and x (see, for example, [15]) We can additionally add to E 1 the terms relating to prior distributions for the parameters. Here, we use zero mean Gaussian distributions for the model priors (see [12] for other alternatives) yielding the optimization function: E = E 1 ffjjrjj 2 fijjxjj 2 fljjU jj 2 jjDjj 2 ....

[Article contains additional citation context not shown here]

R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9(4):721--763, 1997.

.... network that includes the additional constraint of maximizing the sparseness of the distribution of output activities develops, when trained on static natural images, synaptic weights with localized, oriented spatial receptive fields [Olshausen and Field, 1996] see also [Harpur and Prager, 1996; Rao and Ballard, 1997a] and related work on projection pursuit [Huber, 1985] based learning methods [Intrator, 1992; Law and Cooper, 1994; Shouval, 1995] Similar results have also been obtained using an algorithm that extracts the independent components of a set of static natural images [Bell and Sejnowski, 1997] ....

....by the redundancy reduction principle. Our approach utilizes a spatiotemporal generative model that can be viewed as a simple extension of the spatial generative model used by Harpur and Prager [Harpur and Prager, 1996] Olshausen and Field [Olshausen and Field, 1996] Rao and Ballard [Rao and Ballard, 1997a] and others. The spatiotemporal generative model allows neurons in the network to perform not just a spatial summation of the current input, but a spatiotemporal summation of both current and past inputs over a finite spatiotemporal extent. The network learns efficient sparse distributed ....

[Article contains additional citation context not shown here]

R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9(4):721--763, 1997.

....in input data I from influencing the robust Kalman filter estimate br. Note that the entire filter can be implemented in a recurrent neural network, each matrix in the filter corresponding to the synaptic weights of a set of neurons, each with a linear activation function [Rao and Ballard, 1996b; Rao and Ballard, 1996a] where c is a threshold parameter that can be modulated according to the application at hand. To understand the behavior of this function, note that S effectively clips the ith summand in J 0 to a constant value c whenever the ith squared residual (I i Gamma U i r) 2 exceeds the ....

....accurate dynamic physical models of the object properties being estimated. In complex dynamic environments, the formulation of such hand coded models becomes increasingly difficult. An alternate approach is to learn an internal model of the input dynamics from observed data, as suggested in [Rao and Ballard, 1996a] Let u and v denote the vectorized forms of the matrices U and V respectively. For example, the n Theta k generative matrix U can be collapsed into an nk Theta 1 vector u = U 1 U 2 : U n ] T where U i denotes the ith row of U . Note that (I Gamma Ur) I Gamma Ru) where R is ....

[Article contains additional citation context not shown here]

R.P.N. Rao and D.H. Ballard, "Dynamic Model of Visual Recognition Predicts Neural Response Properties in the Visual Cortex," Neural Computation (in press). Also, Technical Report 96.2, National Resource Laboratory for the Study of Brain and Behavior, Department of Computer Science, University of Rochester, 1996.

.... of the basis vectors and the input image as it is in the case of PCA (Equation 2) This is especially true in cases where the basis vectors are not mutually orthogonal or when there is top down information from a higher hierarchical level that can influence the state at a lower level (cf. Rao and Ballard, 1997a ] 3) PCA based methods have typically been applied to the analysis of static images and it is not clear how these methods can be extended to the spatiotemporal case for prediction and learning of image dynamics directly from the input stream. 4) Principal component methods are suitable only ....

....(d) A completely novel object results in a prediction resembling a mixture of the training images, with large residual errors. These residuals can be used to learn the new object (using Equation 18) in case the object is deemed relevant to the recognition system. scheme see, for example, Rao and Ballard, 1997a ] The matrix U was of size 1024 Theta 50. As shown in Figure 8, after training, the model produced accurate predictions (reconstructions) of the training images with low residuals (top two rows) An intermediate view that was 5 ffi from the nearest training view generated Input Residual ....

[Article contains additional citation context not shown here]

R. P. N. Rao and D. H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9(4):721--763, 1997.

....0.5000 0.2500 0.2500 0.5000 0.3333 0.3333 0.0000 0.5000 R G B R G B Y Figure 1: Spatiochromatic Basis Functions. Motivation for these basis functions comes from statistical characterizations of natural image stimuli [Derrico and Buchsbaum, 1991; Hancock et al. 1992; Olshausen and Field, 1996; Rao and Ballard, 1997b; Bell and Sejnowski, 1996] a) shows the weights assigned to the three input color channels, generating a single achromatic channel (R G B) and two color opponent channels (R G and B Y) b) shows the nine oriented spatial filters at three octave separated scales for each of the three channels ....

....general provides an almost unique representation of the local image region surrounding that location. The basis functions described above were picked a priori, but very similar functions can be learned from samples of natural images [Barrow, 1987; Hancock et al. 1992; Olshausen and Field, 1996; Rao and Ballard, 1997b; Bell and Sejnowski, 1996] For example, a set of basis functions can be learned by using a soft form of the competitive learning rule [Yair et al. 1992; Nowlan, 1990] For a given input, each weight vector (basis function) encoding the synaptic strength from the inputs to an output unit in ....

[Article contains additional citation context not shown here]

R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9:805--847, 1997.

....rotations, and expansions contractions [2] Thus, the neurobiological data strongly suggest that the visual system factors retinal stimuli into object centered features and their relative transformations. We have previously introduced a dynamic Kalman filter based model of visual recognition [10]. The central idea behind this model is that the visual cortex can be regarded as a network that gains enormous efficacies by hierarchically encoding image features and dynamically predicting input stimuli. This model was however susceptible to image plane transformations of previously encoded ....

....with the k Theta 1 vector (x Gamma x 0 ) which describes the relative transformation that the image has undergone. We assume, for simplicity, that x 0 = 0 and use DI to denote the difference I(x) Gamma I(0) We can then model the above equation using the following stochastic model (cf. [10]) DI(t) U (t)x(t) n d (t) 2) where U is a set of generative weights approximating the Jacobian and n d is a zero mean Gaussian noise process with covariance S d (t) For deriving the learning rules, it is convenient to view the n Theta k matrix U as an nk Theta 1 vector u = U 1 U 2 : ....

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R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation (in press). Copy available at ftp://ftp.cs.rochester.edu/pub/u/rao/papers/dynrec.ps.Z, 1996.

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Rao, R. P. N., and Ballard, D. H. 1996. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation 9:721--763.

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Rao, RPN, & Ballard, DH (1997) Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation 9, 721-763.

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R. Rao and D. Ballard, "Dynamic model of visual recognition predicts neural response properties in the visual cortex, " Neural Comput. 9, 721--763 (1997).

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R. P. N. Rao and D. H. Ballard, "Dynamic model of visual recognition predicts neural response properties in the visual cortex," Neur. Comp., vol 9, 1997, pp. 721--763.

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R. Rao, D. Ballard, "Dynamic model of visual recognition predicts neural response properties in the visual cortex," Neural Computation, 9 721-763 (1997).

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R. Rao, D. Ballard, "Dynamic model of visual recognition predicts neural response properties in the visual cortex," Neural Computation 9, 721-763 (1997).

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Rao, RPN & Ballard, DH (1997) Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation 9:721-763.

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R. P. N. Rao and D. H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9:721--763, 1997.

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Rao, R. P. N. and Ballard, D. H. (1997). Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9:805--47.

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R.P.N. Rao and D.H. Ballard. Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Computation, 9:805--47, 1997.

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