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Recognition by directed attention to recursively partitioned images
A learning/recognition model (and instantiating program) is described which recursively combines the learning paradigms of conceptual clustering (Michalski, 1980) and learning-from-examples to resolve the ambiguities of real-world recognition. The model is based on neuropsychological and psychological evidence that the visual system is analytic, hierarchical, and composed of a parallel/serial dichotomy (many, see conclusions by Crick, 1984). Emulating the experimental evidence, parallel processes in the model decompose the image into components and cluster the constituents in much the same way as the image processing technique known as moment analysis (Alt, 1962). Serial, attentive mechanisms then reassemble the decompositions by investigating spatial relationships between components. The use of attentive mechanisms extends the moment analysis technique to handle alterations in structure and solves the contention problem created by combining the two learning paradigms. The contention results from a disagreement between the teacher and the model on what constitutes the salient features at the highest level of the symbol. There are four cases ZBT must handle, two of which result from the disagreement with the teacher. The parallel/serial dichotomy represents a vertical/horizontal tradeoff between the invariant and variant features of a domain. The resultant learned hierarchy allows ZBT to recognize structural differences while avoiding problems of exponential growth
Vortex Counting and Lagrangian 3-manifolds
To every 3-manifold M one can associate a two-dimensional N=(2,2)
supersymmetric field theory by compactifying five-dimensional N=2
super-Yang-Mills theory on M. This system naturally appears in the study of
half-BPS surface operators in four-dimensional N=2 gauge theories on one hand,
and in the geometric approach to knot homologies, on the other. We study the
relation between vortex counting in such two-dimensional N=(2,2) supersymmetric
field theories and the refined BPS invariants of the dual geometries. In
certain cases, this counting can be also mapped to the computation of
degenerate conformal blocks in two-dimensional CFT's. Degenerate limits of
vertex operators in CFT receive a simple interpretation via geometric
transitions in BPS counting.Comment: 70 pages, 29 figure
Knot Invariants from Four-Dimensional Gauge Theory
It has been argued based on electric-magnetic duality and other ingredients
that the Jones polynomial of a knot in three dimensions can be computed by
counting the solutions of certain gauge theory equations in four dimensions.
Here, we attempt to verify this directly by analyzing the equations and
counting their solutions, without reference to any quantum dualities. After
suitably perturbing the equations to make their behavior more generic, we are
able to get a fairly clear understanding of how the Jones polynomial emerges.
The main ingredient in the argument is a link between the four-dimensional
gauge theory equations in question and conformal blocks for degenerate
representations of the Virasoro algebra in two dimensions. Along the way we get
a better understanding of how our subject is related to a variety of new and
old topics in mathematical physics, ranging from the Bethe ansatz for the
Gaudin spin chain to the -theory description of BPS monopoles and the
relation between Chern-Simons gauge theory and Virasoro conformal blocks.Comment: 117 page
Time-causal and time-recursive spatio-temporal receptive fields
We present an improved model and theory for time-causal and time-recursive
spatio-temporal receptive fields, based on a combination of Gaussian receptive
fields over the spatial domain and first-order integrators or equivalently
truncated exponential filters coupled in cascade over the temporal domain.
Compared to previous spatio-temporal scale-space formulations in terms of
non-enhancement of local extrema or scale invariance, these receptive fields
are based on different scale-space axiomatics over time by ensuring
non-creation of new local extrema or zero-crossings with increasing temporal
scale. Specifically, extensions are presented about (i) parameterizing the
intermediate temporal scale levels, (ii) analysing the resulting temporal
dynamics, (iii) transferring the theory to a discrete implementation, (iv)
computing scale-normalized spatio-temporal derivative expressions for
spatio-temporal feature detection and (v) computational modelling of receptive
fields in the lateral geniculate nucleus (LGN) and the primary visual cortex
(V1) in biological vision.
We show that by distributing the intermediate temporal scale levels according
to a logarithmic distribution, we obtain much faster temporal response
properties (shorter temporal delays) compared to a uniform distribution.
Specifically, these kernels converge very rapidly to a limit kernel possessing
true self-similar scale-invariant properties over temporal scales, thereby
allowing for true scale invariance over variations in the temporal scale,
although the underlying temporal scale-space representation is based on a
discretized temporal scale parameter.
We show how scale-normalized temporal derivatives can be defined for these
time-causal scale-space kernels and how the composed theory can be used for
computing basic types of scale-normalized spatio-temporal derivative
expressions in a computationally efficient manner.Comment: 39 pages, 12 figures, 5 tables in Journal of Mathematical Imaging and
Vision, published online Dec 201
D-branes, orbifolds, and Ext groups
In this note we extend previous work on massless Ramond spectra of open
strings connecting D-branes wrapped on complex manifolds, to consider D-branes
wrapped on smooth complex orbifolds. Using standard methods, we calculate the
massless boundary Ramond sector spectra directly in BCFT, and find that the
states in the spectrum are counted by Ext groups on quotient stacks (which
provide a notion of homological algebra relevant for orbifolds). Subtleties
that cropped up in our previous work also appear here. We also use the McKay
correspondence to relate Ext groups on quotient stacks to Ext groups on (large
radius) resolutions of the quotients. As stacks are not commonly used in the
physics community, we include pedagogical discussions of some basic relevant
properties of stacks.Comment: 51 pages, 3 figures; v2: material on Freed-Witten added; v3: more
typos fixe
Robust and efficient Fourier-Mellin transform approximations for invariant grey-level image description and reconstruction
International audienceThis paper addresses the gray-level image representation ability of the Fourier-Mellin Transform (FMT) for pattern recognition, reconstruction and image database retrieval. The main practical di±culty of the FMT lies in the accuracy and e±ciency of its numerical approximation and we propose three estimations of its analytical extension. Comparison of these approximations is performed from discrete and ¯nite-extent sets of Fourier- Mellin harmonics by means of experiments in: (i) image reconstruction via both visual inspection and the computation of a reconstruction error; and (ii) pattern recognition and discrimination by using a complete and convergent set of features invariant under planar similarities. Experimental results on real gray-level images show that it is possible to recover an image to within a speci¯ed degree of accuracy and to classify objects reliably even when a large set of descriptors is used. Finally, an example will be given, illustrating both theoretical and numerical results in the context of content-based image retrieval
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