Modal Matching for Correspondence and Recognition

Modal matching is a new method for establishing correspondences and computing canonical descriptions. The method is based on the idea of describing objects in terms of generalized symmetries, as defined by each object's eigenmodes. The resulting modal description is used for object recognition and categorization, where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects. In general, modes provide a global-to-local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison. In contrast to previous techniques, which required correspondence to be computed with an initial or prototype shape, modal matching utilizes a new type of finite element formulation that allows for an object's eigenmodes to be computed directly from available image information. This improved formulation provides greater generality and accuracy, and is applicable to data of any dimensionality. Correspondence results with 2-D contour and point feature data are shown, and recognition experiments with 2-D images of hand tools and airplanes are described.

An Invariant Representation for Matching Trajectories across Uncalibrated Video Streams

We introduce a view-point invariant representation of moving object trajectories that can be used in video database applications. It is assumed that trajectories lie on a surface that can be locally approximated with a plane. Raw trajectory data is first locally approximated with a cubic spline via least squares fitting. For each sampled point of the obtained curve, a projective invariant feature is computed using a small number of points in its neighborhood. The resulting sequence of invariant features computed along the entire trajectory forms the view invariant descriptor of the trajectory itself. Time parametrization has been exploited to compute cross ratios without ambiguity due to point ordering. Similarity between descriptors of different trajectories is measured with a distance that takes into account the statistical properties of the cross ratio, and its symmetry with respect to the point at infinity. In experiments, an overall correct classification rate of about 95% has been obtained on a dataset of 58 trajectories of players in soccer video, and an overall correct classification rate of about 80% has been obtained on matching partial segments of trajectories collected from two overlapping views of outdoor scenes with moving people and cars.

Fixed Point vs. First-Order Logic on Finite Ordered Structures with Unary Relations

We prove that first order logic is strictly weaker than fixed point logic over every infinite classes of finite ordered structures with unary relations: Over these classes there is always an inductive unary relation which cannot be defined by a first-order formula, even when every inductive sentence (i.e., closed formula) can be expressed in first-order over this particular class. Our proof first establishes a property valid for every unary relation definable by first-order logic over these classes which is peculiar to classes of ordered structures with unary relations. In a second step we show that this property itself can be expressed in fixed point logic and can be used to construct a non-elementary unary relation.

Object Matching in Distributed Video Surveillance Systems by LDA-Based Appearance Descriptors

Establishing correspondences among object instances is still challenging in multi-camera surveillance systems, especially when the cameras’ fields of view are non-overlapping. Spatiotemporal constraints can help in solving the correspondence problem but still leave a wide margin of uncertainty. One way to reduce this uncertainty is to use appearance information about the moving objects in the site. In this paper we present the preliminary results of a new method that can capture salient appearance characteristics at each camera node in the network. A Latent Dirichlet Allocation (LDA) model is created and maintained at each node in the camera network. Each object is encoded in terms of the LDA bag-of-words model for appearance. The encoded appearance is then used to establish probable matching across cameras. Preliminary experiments are conducted on a dataset of 20 individuals and comparison against Madden’s I-MCHR is reported.

AIRSTREAM: A Neural Network Model of Auditory Scene Analysis and Source Segregation

Multiple sound sources often contain harmonics that overlap and may be degraded by environmental noise. The auditory system is capable of teasing apart these sources into distinct mental objects, or streams. Such an "auditory scene analysis" enables the brain to solve the cocktail party problem. A neural network model of auditory scene analysis, called the AIRSTREAM model, is presented to propose how the brain accomplishes this feat. The model clarifies how the frequency components that correspond to a give acoustic source may be coherently grouped together into distinct streams based on pitch and spatial cues. The model also clarifies how multiple streams may be distinguishes and seperated by the brain. Streams are formed as spectral-pitch resonances that emerge through feedback interactions between frequency-specific spectral representaion of a sound source and its pitch. First, the model transforms a sound into a spatial pattern of frequency-specific activation across a spectral stream layer. The sound has multiple parallel representations at this layer. A sound's spectral representation activates a bottom-up filter that is sensitive to harmonics of the sound's pitch. The filter activates a pitch category which, in turn, activate a top-down expectation that allows one voice or instrument to be tracked through a noisy multiple source environment. Spectral components are suppressed if they do not match harmonics of the top-down expectation that is read-out by the selected pitch, thereby allowing another stream to capture these components, as in the "old-plus-new-heuristic" of Bregman. Multiple simultaneously occuring spectral-pitch resonances can hereby emerge. These resonance and matching mechanisms are specialized versions of Adaptive Resonance Theory, or ART, which clarifies how pitch representations can self-organize durin learning of harmonic bottom-up filters and top-down expectations. The model also clarifies how spatial location cues can help to disambiguate two sources with similar spectral cures. Data are simulated from psychophysical grouping experiments, such as how a tone sweeping upwards in frequency creates a bounce percept by grouping with a downward sweeping tone due to proximity in frequency, even if noise replaces the tones at their interection point. Illusory auditory percepts are also simulated, such as the auditory continuity illusion of a tone continuing through a noise burst even if the tone is not present during the noise, and the scale illusion of Deutsch whereby downward and upward scales presented alternately to the two ears are regrouped based on frequency proximity, leading to a bounce percept. Since related sorts of resonances have been used to quantitatively simulate psychophysical data about speech perception, the model strengthens the hypothesis the ART-like mechanisms are used at multiple levels of the auditory system. Proposals for developing the model to explain more complex streaming data are also provided.