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System Identification, Approximation and Complexity
 International Journal of General Systems
, 1977
"... This paper is concerned with establishing broadlybased systemtheoretic foundations and practical techniques for the problem of system identification that are rigorous, intuitively clear and conceptually powerful. A general formulation is first given in which two order relations are postulated on a ..."
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Cited by 34 (22 self)
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This paper is concerned with establishing broadlybased systemtheoretic foundations and practical techniques for the problem of system identification that are rigorous, intuitively clear and conceptually powerful. A general formulation is first given in which two order relations are postulated on a class of models: a constant one of complexity; and a variable one of approximation induced by an observed behaviour. An admissible model is such that any less complex model is a worse approximation. The general problem of identification is that of finding the admissible subspace of models induced by a given behaviour. It is proved under very general assumptions that, if deterministic models are required then nearly all behaviours require models of nearly maximum complexity. A general theory of approximation between models and behaviour is then developed based on subjective probability concepts and semantic information theory The role of structural constraints such as causality, locality, finite memory, etc., are then discussed as rules of the game. These concepts and results are applied to the specific problem or stochastic automaton, or grammar, inference. Computational results are given to demonstrate that the theory is complete and fully operational. Finally the formulation of identification proposed in this paper is analysed in terms of Klir’s epistemological hierarchy and both are discussed in terms of the rich philosophical literature on the acquisition of knowledge. 1
Recognition by Symmetry Derivatives and the Generalized Structure Tensor
 IEEEPAMI
, 2004
"... We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show t ..."
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Cited by 24 (15 self)
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We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show that, in contrast to ordinary derivatives, all orders of symmetry derivatives of Gaussians yield a remarkable invariance: They are obtained by replacing the original differential polynomial with the same polynomial, but using ordinary coordinates x and y corresponding to partial derivatives. Moreover, the symmetry derivatives of Gaussians are closed under the convolution operator and they are invariant to the Fourier transform. The equivalent of the structure tensor, representing and extracting orientations of curve patterns, had previously been shown to hold in harmonic coordinates in a nearly identical manner. As a result, positions, orientations, and certainties of intricate patterns, e.g., spirals, crosses, parabolic shapes, can be modeled by use of symmetry derivatives of Gaussians with greater analytical precision as well as computational efficiency. Since Gaussians and their derivatives are utilized extensively in image processing, the revealed properties have practical consequences for local orientation based feature extraction. The usefulness of these results is demonstrated by two applications: 1) tracking cross markers in long image sequences from vehicle crash tests and 2) alignment of noisy fingerprints.
Size Invariant Circle Detection
, 1999
"... The Circle Hough Transform (CHT) has become a common method for circle detection in numerous image processing applications. Various modifications to the basic CHT operation have been suggested which include: the inclusion of edge orientation, simultaneous consideration of a range of circle radii, us ..."
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Cited by 14 (0 self)
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The Circle Hough Transform (CHT) has become a common method for circle detection in numerous image processing applications. Various modifications to the basic CHT operation have been suggested which include: the inclusion of edge orientation, simultaneous consideration of a range of circle radii, use of a complex accumulator array with the phase proportional to the log of radius, and the implementation of the CHT as filter operations. However, there has also been much work recently on the definition and use of invariance filters for object detection including circles. The contribution of the work presented here is to show that a specific combination of modifications to the CHT is formally equivalent to applying a scale invariant kernel operator. This work brings together these two themes in image processing which have herewith been quite separate. Performance results for applying various forms of CHT filters incorporating some or all of the available modifications, along with results from the invariance kernel, are included. These are in terms of an analysis of the peak width in the output detection array (with and without the presence of noise), and also an analysis of the peak position in terms of increasing noise levels. The results support the equivalence between the specific form of the CHT developed in this work and the invariance kernel. # 1999 Elsevier Science B.V. All rights reserved.
Visual Space Distortion
 Biological Cybernetics
, 1997
"... We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metr ..."
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Cited by 12 (11 self)
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We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can be computed. This paper develops a computational geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence, the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters c...
A critical review of Luneburg's model with regard to global structure of visual space
 Psychol Rev
, 1991
"... Visual space (VS) is a coherent selforganized dynamic complex that is structured into objects, backgrounds, and the self. As a concrete example of geometrical properties in VS, experimental results on parallel and (equi) distance alleys in a frameless VS were reviewed, and Luneburg's interpretation ..."
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Cited by 10 (0 self)
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Visual space (VS) is a coherent selforganized dynamic complex that is structured into objects, backgrounds, and the self. As a concrete example of geometrical properties in VS, experimental results on parallel and (equi) distance alleys in a frameless VS were reviewed, and Luneburg's interpretation on the discrepancy between these 2 alleys was sketched with emphasis on the 2 hypotheses involved: VS is a Riemannian space of constant curvature (RCC) and the a priori assumed correspondence between VS and the physical space in which stimulus points are presented. Dissociating these 2 assumptions, the author tried to see to what extent the global structure of VS under natural conditions is in accordance with the hypothesis of RCC and to make explicit the logic underlying RCC. Several open questions about the geometry of VS per se have been enumerated. Visual space (VS) is the final product of the long series of processes from retina to brain, and phenomenologically it is articulated into individual objects, backgrounds, and the self (Figure 1). The self is a percept consisting of visual and proprioceptive experiences. Other visual percepts are due to stimuli
Signal Representation and Processing using Operator Groups
 Linköping University, Sweden
, 1995
"... This thesis presents a signal representation in terms of operators. The signal is assumed to be an element of a vector space and subject to transformations of operators. The operators form continuous groups, socalled Lie groups. The representation can be used for signals in general, in particular i ..."
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Cited by 9 (3 self)
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This thesis presents a signal representation in terms of operators. The signal is assumed to be an element of a vector space and subject to transformations of operators. The operators form continuous groups, socalled Lie groups. The representation can be used for signals in general, in particular if spatial relations are undefined, and it does not require a basis of the signal space to be useful. Special attention is given to orthogonal operator groups which are generated by antiHermitian operators by means of the exponential mapping. It is shown that the eigensystem of the group generator is strongly related to properties of the corresponding operator group. For oneparameter orthogonal operator groups, a phase concept is introduced. This phase can for instance be used to distinguish between spatially even and odd signals and, therefore, corresponds to the usual phase for multidimensional signals. Given one operator group that represents the variation of the signal and one operator ...
Invariance Signatures: Characterizing contours by their departures from invariance
, 1999
"... this paper, a new invariant feature of twodimensional contours is reported: ..."
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Cited by 8 (0 self)
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this paper, a new invariant feature of twodimensional contours is reported:
The computational magic of the ventral stream: sketch of a theory (and why some deep architectures work).
, 2012
"... ..."
Neural Mechanisms Underlying Processing in the Visual Areas of the Occipital and Temporal Lobes
 Oxford University
, 1994
"... There is evidence that over a series of cortical processing stages, the visual system of primates produces a representation of objects which shows invariance with respect to, for example, translation, size, and view, as shown by recordings from single neurons in the temporal lobe (Rolls, 1992; Desim ..."
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Cited by 4 (2 self)
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There is evidence that over a series of cortical processing stages, the visual system of primates produces a representation of objects which shows invariance with respect to, for example, translation, size, and view, as shown by recordings from single neurons in the temporal lobe (Rolls, 1992; Desimone, 1991; Tanaka et al., 1991). To clarify how such a system might learn to recognise `naturally' transformed objects, I investigate a model of cortical visual processing which incorporates a number of features of the primate visual system. The model consists of a series of layers with convergence from a limited region of the preceding layer, and mutual inhibition over a short range within a layer. The feedforward connections provide the inputs to competitive networks, each utilising a modified Hebblike learning rule which incorporates a temporal trace of the preceding neuronal activity. The modified Hebbrule, called simply the trace learning rule, is aimed at enabling neurons to learn t...
Representing Stimulus Similarity
, 2002
"... v Declaration .................................... ix Acknowledgements................................ xi 1Prelude 1 TheVeryIdeaofRepresentation......................... 2 TypesofSimilarity ................................ 8 IsSimilarityIndeterminate? ........................... 11 TheRoleofS ..."
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Cited by 2 (2 self)
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v Declaration .................................... ix Acknowledgements................................ xi 1Prelude 1 TheVeryIdeaofRepresentation......................... 2 TypesofSimilarity ................................ 8 IsSimilarityIndeterminate? ........................... 11 TheRoleofSimilarityinCognition....................... 11 Summary&GeneralDiscussion......................... 14 2 Theories of Similarity 17 SimilarityDataSets................................ 17 SpatialRepresentation .............................. 21 FeaturalRepresentation.............................. 31 TreeRepresentation................................ 40 NetworkRepresentation ............................. 47 AlignmentBasedSimilarityModels....................... 48 TransformationalSimilarityModels ....................... 50 Summary&GeneralDiscussion......................... 54 i 3 On Representational Complexity 55 ApproachestoModelSelection ......................... 57 ChoosinganAdditiveClusteringRepresentation ................ 67 ChoosinganAdditiveTreeRepresentation ................... 82 ChoosingaSpatialRepresentation........................ 94 Summary&GeneralDiscussion......................... 95 4 Featural Representation 97 AMenagerieofFeaturalModels......................... 98 ClusteringModels.................................104 GeometricComplexityCriteria..........................106 AlgorithmsforFittingFeaturalModels .....................107 MonteCarloStudyI:DotheAlgorithmsWork? ................109 RepresentationsofKinshipTerms ........................117 MonteCarloStudyII:Complexity........................122 ExperimentI:Faces................................125 ExperimentII:Countries .............................1...